Interest Rate Risk Management 978-1-55827-309-2

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INTEREST RATE RISK MANAGEMENT by Leonard M. Matz

Sheshunofffi 2/10

A03

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MEMORANDUM

To: From:

Subject:

Our Valued Customers Sheshunoff Information Services

Interest Rate Risk Management

Thank you for your order of Interest Rate Risk Management. Interest rate risk management has been a hot topic for financial institutions ever since rate volatility mushroomed in the late 19705. And, as financial instruments and markets have spawned additional and more complex products, the need to understand and manage rate risk has continued to grow.

Interest rate risk management is critical to the overall profitability of your bank. Even if managing interest rate risk is not part of your day-to-day responsibilities, if you oversee and manage the process, you need a clear, definitive understanding of the issues so your bank can stay profitable. The goal of this work is to provide understandable explanations of the many relevant issues, measurement tools, and management techniques necessary to today’s IRR managers. We start with the basic concepts and build, step by step, to the most advanced topics.

Begin using the enclosed manual now so that it remains your definitive source on interest rate risk management. Your comments are welcome, and we encourage your response to Interest Rate Risk Management — how it has helped you, how it can be improved, additional topics to include. To submit such comments, to ask questions, or for information about additional

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Dedication

To Emily, Michael, Kevin, and Sarah.

Interest Rate Risk Management

iv

About the Author

Leonard Matz, consultant ”and bank trainer, has been in the banking

industry since he became a federal bank examiner in 1973. He has spent more than 15 years in banking as a senior manager, including serving as senior vice president for investments and funds management at the largest subsidiary of Michigan National Corporation. He was chairman of the Risk Conferences on Liquidity in 1999 and 2002, has lectured at the Graduate School of Banking at Madison, Wisconsin, and has been a

member of the National Asset/Liability Management Association since 1989. Mr. Matz is the author or coauthor of numerous financial

publications. ACKNOWLEDGMENTS

Credit for many of the examples, anecdotes, and insights that liven the otherwise dry discussion of interest rate risk management topics must be given to the invaluable assistance provided by many friends and associates. They all have my sincere and deep gratitude. In particular, I want to gratefully acknowledge all of the current and past members of NALMA (formerly the National Asset and Liability Management Association, now the North American Asset and Liability Management Association). For more than a decade, I have benefited tremendously from their knowledge, and understanding, from their willingness to divulge war stories and, especially, from their generous sharing of best practices. Thanks to Jim Westfall and Gary Lachmund for reviewing earlier versions of these materials and for providing suggestions. Special thanks to J. Kimball Hobbs for his many suggestions over the years. Kim has also graciously permitted me to use some of his charts that so often provide clear illustrations of otherwise complex points. NALMA members, past and present, have helped me with materials, by sharing information at conferences, in conversations, and with telephone calls and e-mails. This book has benefited enormously from their wisdom and their generosity. I also want to thank editors Pat Booker and Maureen Jablinske for their careful and invaluable assistance.

Interest Rate Risk Manaflent

Preparation of this book has involved reading numerous books and articles and valuable discussions with other bankers over many years. Ideas fi'om many of those sources have contributed to this book in ways not always direct enough to be singled out by specific footnotes. In other cases, ideas from conversations and seminar presentations may have become too commingled or blurred to permit appropriate recognition of their creators. Any omitted acknowledgements are unintended.

vi

Foreword

Interest rate risk management has been a hot topic for financial institutions ever since rate volatility mushroomed in the late 19705. And, as financial instruments and markets have spawned additional and more complex products, the need to understand and manage rate risk has continued to grow. Over the ensuing years, the focus has shified from gap analysis to duration of equity, to income simulation to market or economic value simulation, to value at risk (VaR) and now, to stress testing. Each time, we’ve learned that the “new" tool wasn’t a panacea. Repeatedly, we’ve learned that a mathematically elegant tool is, at best, a rough tool to use in the messy conditions of the real world. Furthermore, each of those topics is a measurement tool. But measurement is merely an intermediate step. The real task is not risk measurement, it is risk management. The literature on interest rate risk also tends to be less than completely satisfying. Several books and many articles address popular views on managing rate risk in community banks at particular periods in history. Many more sources, often written by investment bankers or by math jlmkies, provide specialized in-depth information about particular topics, such as using derivative hedges or value at risk.

The fact is that rate risk must be managed by $10 million credit unions, gazillion-dollar multinational financial conglomerates, and everything in between. Obviously, resources and needs vary significantly among those institutions. Even similarly sized institutions face a wide variety of rate risk issues. A retail-oriented bank, thrift, or credit union has different concerns than a wholesale-oriented bank, even if both are the same size. Furthermore, some small institutions have the resources and expertise to use advanced measurement and management techniques while many intermediate-sized institutions do not. Even so, some problems, such as the rate risk in core deposits without contractual maturities, are the same regardless of the size or complexity of the institution.

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Interest Rate Risk Management

In short, there is a need for a comprehensive treatment of this subject that addresses all of the various manifestations and requirements of rate risk management. Hopefully, this book fills that need. However, merely providing a comprehensive review of interest rate risk measurement and management is not our only goal here. It isn’t even our main goal. Another goal is of this work is to attempt to meld some of the practical realities on the ground — the composition of financial institution balance sheets and the restrictions imposed by business conditions and regulations — with some of the ideas, concepts and theories of interest rate risk management. These two sets of ideas cannot be considered independently. Too many rate risk measurement or management tools are messy to apply to real world conditions. 011 the other hand, bankers can be so focused on practical issues that they neglect fimdamental concepts or the lessons leamed by previous generations. This book attempts to bake a cake using knowledge of theoretical recipes, a good many practical methods, as well as some historical spices. Above all else, the goal of this work is to provide understandable explanations of the many relevant issues, measurement tools, and management techniques. We start with the basic concepts and build, step by step, to the most advanced topics.

ORGANIZATION OF THE CONTENTS This manual is divided into six broad topics.

Overview

∙

In the first section (Chapters 1 and 2) we consider the role of interest rate risk management in banks and other financial institutions. Chapter 2 introduces the two major, complementary approaches to evaluating rate risk.

IRR Measurement Basics

∙

The second section, Chapters 3 through 5, discusses alternative methods for measuring interest rate risk. Income simulation in

viii

Foreword

Chapter 3, duration analysis in Chapter 4, and economic value simulation in Chapter 5. Difficult Volumes

In the third section, Chapters 6 through 11 cover specific rate risk measurement issues in bank loan and deposit products. We begin with detailed discussions of the most thorny measurement problems: indeterminate maturity, administrated rate, and putable deposits in Chapter 6 and loans and investments in Chapter 7. Then we provide an in-depth discussion of interest rates scenarios in Chapter 8. Chapters 9 and 10 focus on rate risk models. Finally, Chapter 11 covers noninterest income and expense followed by a rate risk measurement summary.

IRR Management Policies & Structures The fourth section (Chapters 12 and 13) considers issues related to the management of interest rate risk. In Chapter 12, we discuss ALM policies, management structures and risk limits. In Chapter 13, we cover ALM decision making, implementation, and oversight. [RR Management Tactics

The fifth section, Chapters 14 and 15, considers specific rate risk management tactics for managing loans, investments, deposits, and borrowings to avoid, reduce, or hedge rate risk. Chapter 14 presents tactics that don’t involve off-balance sheet derivatives. Chapter 15’s tactics use these instruments.

IRR in Context The sixth section, Chapter 16, considers interest rate risk management in the broader context of other financial institution management tasks.

Interest Rate Risk Management

Summary Table of Contents

OVERVIEW

Chapter 1: An Interest Rate Risk Management Overview Chapter 2: Defining and Quantifying Interest Rate Risk

IRR MEASUREMENT BASICS Chapter 3: Income Simulation

Chapter 4: Duration and Convexity

Chapter 5: Economic Value Simulation DIFHCULT VOLUIMES

Chapter 6: Measuring the Rate Risk of Indeterminate Maturity, Administered Rate, and Putable Deposits Chapter 7: Measuring the Rate Risk of Loans and Investments

Chapter 8: Rate Changes: Deterministic Scenarios and Stochastic Models

Chapter 9: Selecting and Installing AL Models Chapter 10: Using Models and Managing Model Risk

Chapter 11: Interest Rate Risk Measurement Summary [RR MANAGEIVIENT POLICIES &

STRUCTURES

Chapter 12: ALM Policies, Management Structures, and Risk Limits Chapter 13: ALM Decision Making, Implementation, and Oversight

IRR MANAGEMENT TACTICS Chapter 14: Managing Interest Rate Risk Without Using Off-Balance Sheet Derivatives

Chapter 15: Hedging with Off-Balance Sheet Derivative Instruments

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Interest Rate Risk Management

IRR IN CONTEXT Chapter 16: Perspectives Glossary

Contents

Dedication .............................................................................................. iii About the Author ...................................................................................... v Foreword ............................................................................................... vii Summary Table of Contents ................................................................... xi

OVERVIEW

Chapter 1 An Interest Rate Risk Management Overview Risk and Financial Institutions ............................................................. What Is Risk? ................................................................................... Types of Risk .................................................................................... Credit Risk .................................................................................... Liquidity Risk ............................................................................... Interest Rate Risk ......................................................................... Operations Risk ............................................................................ Legal Risk .................................................................................... Reputation Risk ............................................................................ Exhibit 1.1: Risks Inherent in the Business of Banking as Seen by the Federal Reserve ........................................................ Exhibit 1.2: Risks Inherent in the Business of Banking as Seen by the Comptroller of the Currency ..................................... What Is Interest Rate Risk Management? ........................................ The Focus Is on Interest Rate Risk/Market Risk .......................... Interest Rate/Market Risk ls Neither Simple nor Undifferentiated......................................................................... Primary Components of Interest Rate Risk ................ Repricing Risk ..............................................................................

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xiii

1-1 l-l

1-2 1-2 1-3 1-3 1-4 1-4 1-4 l-5

1-5 l-S

1-6 1 -7

1-7

Interest Rate Risk Management

Basis Risk ..................................................................................... 1-8 Yield Curve Risk ........................................................................ 1-11 Option Risk ................................................................................ 1-12 Secondary Components of Interest Rate Risk ................................ 1-12 Exhibit 1.3: Estimated Components of Interest Rate Risk for a Typical Bank When Interest Rate Volatility Is Low.......... 1-13 Exhibit 1.4: Estimated Components of Interest Rate Risk for a Typical Bank When Interest Rate Volatility Is High ......... 1-13 Measurement Risk ...................................................................... 1-13 Reporting Risk............................................................................ 1-15 People Risk ................................................................................. 1-15 Decision Process Risk ................................................................ 1-15 Summary of Interest Rate Risk Components .................................. 1-15 Managing Interest Rate Risk .............................................................. 1-16 Exhibit 1.5: Interest Rate Risk and Its Components ................... 1-17 Unavoidability of Interest Rate Risk .............................................. 1-18 The Relative Importance of Interest Rate Risk ............................... 1-19 Effect on Credit and Liquidity Risks .............................................. 1-20 Effect on Profitability ..................................................................... 1-21 Measuring, Monitoring, and Controlling Interest Rate Risk .......... 1-22 Elements and Structure of Asset and Liability Management ............. 1-23 Information Requirements .............................................................. l-24 Management Committee ................................................................. 1-25 IRR Management Policy ................................................................ 1-25 Role of Bank’s Treasury Department ............................................. 1-26

Chapter 2 Defining and Quantifying Interest Rate Risk The Influence of Rate Volatility on Rate Risk ..................................... Exhibit 2.1: Change in Average Monthly Rates 10-Year CMT and 3-Month T-Bill ............................................... Rate Volatility Is an Occasional Event ............................................. The Impact of Rate Volatility ....................................................... What the Volatility Requires ............................................................ Coping with Rate Volatility ..............................................................

2-1 2-2 2-3 2-3 2-4 2-5

Contents

It's All About Cash Flow ..................................................................... Exhibit 2.2: Known and Unknown Cash Flow Elements ............. Uncertain Cash Flows ....................................................................... Principal Cash Flows .................................................................... Interest Cash Flows ......................................................................

2-5 2-7 2-8 2-8

2-9

Cash Flow Summary ...................................................................... 2-10 Exhibit 2.3: Principal and Interest Cash Flow Matrix ................ 2-1 1 Focus on the Net Cash Flows ..................................................... 2-11 Embedded Options: Most Important Risk Management Challenge 2-12 Some Defmitions ........................ 2-12 Puts, Calls, Caps, and Floors Put and Call Options ................................................................... 2-13 Caps, Floors, and Collars ........................................................... 2-13 Bank Products and Customer Options ............................................ 2-14 Exhibit 2.4: Embedded Options in'Common Retail Bank Products .................................................................. 2-15 Understanding Key Option Characteristics .................................... 2-16 In-the-Money and Out-of-the-Money Options ........................... 2-16 The Option Time Value .............................................................. 2-17 European-Style and American-Style Options ............................ 2-18 Understanding Option Exercise ...................................................... 2-18 Changes in Prevailing Rates Drive Most Option Decisions ....... 2-18 Changes in Prevailing Rates Do Not Drive All Option Decisions .................................................................................... 2-19 Suggestions for Measuring Rate Risk from Embedded Options ....................................................................................... 2-21 Embedded Options: Risk Measurement Challenge ........................ 2-22 Two Ways to Understand Interest Rate Risk...................................... 2-23 Accounting Perspective Defined .................................................... 2-24 Exhibit 2.5: Illustration of How a Change in Rates Impacts Earnings ........................................................................ 2-25 Economic Perspective Defined....................................................... 2-25 Exhibit 2.6: Illustration of How a Change in Rates Impacts Economic Value ......................................................................... 2-26 How Interest Rate Risk Afi'ects Profits A Sample Calculation ...................................................................................... 2-26 Exhibit 2.7: Sample Balance Sheet on January 1 ....................... 2-27 Exhibit 2.8: Sample Income Statement on December 31 ∙∙∙∙∙∙∙∙∙∙∙ 2-27 Exhibit 2.9: Sample Balance Sheet on December 31 ................. 2-28 Effect on Noninterest Income and Expense.................................... 2-29

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Interest Rate Risk Management

How Interest Rate Risk Affects Equity .......................................... Exhibit 2.10: December 31 Balance Sheets from an Accounting Perspective .............................................................. Exhibit 2.11: December 31 Balance Sheets from an Economic Perspective ................................................................ Accounting Perspective vs. Economic Perspective ........................ Accounting Perspective Advantages and Disadvantages ...... Economic Perspective —— Advantages and Disadvantages......... Best Use for Each Perspective.................................................... Different Audiences Different Points of View ...................... Exhibit 2.12: Different Perspectives on Interest Rate Risk ........ Summary ............................................................................................

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2-29 2-30

2-31 2-32 2-32 2-33 2-34 2-34 2-35 2-35

IRR MEASUREMENT BASICS Chapter 3 Income Simulation An Improved IRR Measurement Approach .......................................... 3-1 What Is Income Sensitivity Simulation? .......................................... 3-2 Prerequisites for Superior Income Simulation........................., ........ 3-3 Understanding the Simulation Process Dynamics .......................... 3-10 Understand the Dangers and Benefits of Simulating Future Business and Risk Management Actions ........................................ 3-10 Exhibit 3.1: Illustration of the Simulation Process ..................... 3-1 1 Income Simulation Inputs, Processes, and Outputs ............................ 3-12 Income Simulation Inputs: Data and Assumptions ........................ 3-13 Income Simulation Outputs: Summary Tables and Graphs ........... 3-15 Exhibit 3.2: ABC Bank Projected Earnings Under Nine Different Rate Scenarios ............................................................ 3-16 Exhibit 3.3: ABC Bank Change in Earnings Under Nine Difl‘erent Rate Scenarios ............................................................ 3-17 Exhibit 3.4: ABC Bank Percent Change in Earnings Under Nine Different Rate Scenarios .................................................... 3-17

xvi

Contents

Uneven Outcomes ...................................................................... 3-18 Earnings at Risk vs. the Rate Sensitivity of Risk-Neutral Earnings...................................................................................... 3-19 Summary Reports Depicting Changes Over Time ..................... 3-19 Exhibit 3.5: Cumulative EAR Caused by a 200 bp Rate Change ........................................................................................ 3-21 Exhibit 3.6: Trend in Net Income: Actual Plus Four Projected Scenarios .................................................................... 3-21 Exhibit 3.7: Quarterly Trend in EAR ......................................... 3-22 Using Income Simulation to Evaluate IRR ........................................ 3-23 Evaluating Bankwide Risk — Dollar Dispersion........................... 3-23 Percentage Deviation from Base Case ............................................ 3-24 Evaluating How the Constituent Elements Contribute to the Overall Risk Level.......................................................................... 3-25 Risk by Product .......................................................................... 3-25 Exhibit 3.8: Forecasted Changes in Asset Yields and Liability Costs (for a 200 basis point rate increase) ................... 3-26 Risk by Information Source ....................................................... 3-27 Exhibit 3.9: Components of Expected Cash Flows .................... 3-27 Using Income Simulation to Manage IRR ...................................... 3-28 Advantages of Income Simulation Modeling ..................................... 3-28 Specific Measure of Rate Risk Exposure ....................................... 3-28 More Accurate Reflection of Reality .............................................. 3-29 Focus on Changes That Count ........................................................ 3-30 Focus on Management’s Reactions to Changes ............................. 3-30 Flexibility in Reflecting Rate Shifts for Different Maturities......... 3-30 Flexibility in Reflecting Basis Changes in Difi'erent Instruments ..................................................................................... 3-31 Integration with Other Management Information Processes .......... 3-32 Disadvantages of Income Simulation Modeling ................................ 3-32 Assumptions Require Careful Development, Analysis, Increased Controls, and Testing ..................................................... 3-33 Assumptions Can Intentionally or Inadvertently Understate Risk Exposures ............................................................................... 3-33 More Complex Interest Rate Risk Management ............................ 3-34 Understatement of Long-Term Interest Rate Risk .......................... 3-35 Limited Number of Alternatives May Not Capture the Full Extent of the Bank’s IRR Exposure ............................................... 3-36

xvii

Interest Rate Risk Management

Accuracy May Be Impaired by Limited Incorporation of Interrelations Between Variables .................................................... 3-37 3-38 Summary

Chapter 4

Duration and Convexity What Is Duration Analysis? .................................................................. 4-l Measuring the Dollar Weighted Average ......................................... 4—3 Measuring the Weighted Average of the Present Value ................... 4-3 Exhibit 4.1: Macaulay Duration for a 6 Percent

Five-Year Bond ............................................................................ 4-4 Exhibit 4.2: Macaulay Duration for a 12 Percent Seven-Year Bond ......................................................................... 4-5 Using Duration ..................................................................................... 4-5 Comparing Maturities with Weighted Averages and Durations ....... 4-6 Exhibit 4.3: Cash Flows of Assets with Five-Year Maturities ..... 4-7 Exhibit 4.4: Cash Flows Weighted Averages and Durations ............................................................................... 4-8 Characteristics of Duration............................................................... 4-9 Modified Duration .............................................................................. 4-10 Calculating Modified Duration....................................................... 4-11 Convexity ........................................................................................... 4-12 Exhibit 4.5: Rate Sensitivity of a 6 Percent lO-Year Treasury ...................................................................................... 4-13 Positive Convexity .......................................................................... 4-15 Exhibit 4.6: Price/Yield Relationship 6 Percent lO-Year Noncallable Bond ....................................................................... 4-15 Negative Convexity ........................................................................ 4-l6 Exhibit 4.7: Price/Rate Relationship 5.5 Percent 30-Year FNMA Pool ................................................................................ 4-16 Characteristics of Convexity .......................................................... 4-17 Convexity Describes Duration Errors That Only Become Material for Large Changes in Rates .......................................... 4-17 Convexity Describes Duration Errors in Particular Directions ................................................................................... 4-1 7

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xviii

Contents

Convexity Is More Material for Longer Term Instruments Than for Shorter Term Instruments ............................................ 4-18 Exhibit 4.8: Comparative Convexity .......................................... 4-18 Convexity Is More Material for Amortizing Instruments .......... 4-19 Exhibit 4.9: Volatility Comparison Between a IO-Year Treasury Bond and a 12-Year Mortgage Pass-Through Bond .................................................................... 4-20 Adjusting Duration to Compensate for Convexity ......................... 4-20 Limitations of Macaulay and Modified Duration............................... 4-2] Effective Duration, Option Adjusted Duration, and Partial Duration.............................................................................................. 4-24 Effective Duration and Empirical Duration.................................... 4-25 Effective Duration and Option-Adjusted Duration......................... 4-26 Key Rate Duration.......................................................................... 4-27 Exhibit 4.10: Key Rate Duration Table ...................................... 4-28 Partial Duration .............................................................................. 4-28 Applying Duration to Measure IRR for the Entire Bank .................... 4-29 Calculating Duration of Equity....................................................... 4-30 Understanding Changes in Duration of Equity ........................... 4—31 Key Rate Duration for the Whole Bank ......................................... 4-33 Exhibit 4.11: Key Rate Duration Graph ..................................... 4-33 An Empirical Alternative ................................................................ 4-33 Positive and Negative Durations .................................................... 4-34 Capturing the Duration of All Cash Flows ..................................... 4—35 Advantages of Duration...................................................................... 4-35 Captures Interest Rate Risk from All Time Periods ....................... 4-36 Expresses the Measured Quantity of IRR as a Single Value .......... 4-37 Expresses the Measured Quantity of IR as a Change in a Well-Understood Variable ........................................................... 4-37 Captures IRR Obscured by Accrual Accounting Methods ............. 4-38 Facilitates Segregation of Rate Risk Components .......................... 4-39 Disadvantages of Duration ................................................................. 4-39 Managing Duration Can Increase Earnings Volatility .................... 4-39 Duration Relies on the Unlikely Assumption That All Rates Change at the Same Time ..................................................... 4-40 Duration Ignores Basis Risk ........................................................... 4-40 Duration Is Difficult to Calculate for Products with Administered Interest Rates............................................................ 4-41 Duration Is a Static IRR Measurement ........................................... 4-42

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Interest Rate Risk Management

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Future Cash Flows Assumptions ........................................... 4-43 Focus on Current Position .......................................................... 4-44 Duration Masks Dispersion ............................................................ 444 Duration Calculations Exclude a Material Component of

Interest Rate Risk ........................................................................... 4-45

Duration Summary ............................................................................. 4-46

Chapter 5 Economic Value Simulation What Is Economic Value Sensitivity Simulation? ............................... 5-1 MV, PV, and EV .............................................................................. 5-2 We Use PV When MV Is Not Available ...................................... 5-2 PV Ofien Does Not Equal MV ..................................................... 5-3 Economic Value of Equity ............................................................... 5-4 Economic Value Sensitivity ............................................................. 5-5 A Note on Equity Value Terminology ............................................. 5-7 How Does Economic Value Sensitivity Simulation Differ from Duration-Based Economic Value? ................................................... 5-8 Using Economic Value of Equity Sensitivity Simulation to Measure IRR ....................................................................................... 5-10 Exhibit 5.]: Typical Bank .......................................................... 5-11 Using Real-World EVE Models in Real Banks .............................. 5-13 Dealing with Assumptions .............................................................. 5-15 Discount Rates and Yield Curve Smoothing ...................................... 5-16 Introduction to Yield Curve Smoothing ......................................... 5-17 What Is Yield Curve Smoothing? .............................................. 5-18 Choosing a Smoothing Method ...................................................... 5-19 Linear Yield Curve Smoothing....................................................... 5—19 Cubic Spline Yield Smoothing ....................................................... 5-20 Exhibit 5.2: Example of a Cubic Spline Calculation .................. 5-21 Maximum Smoothness Forward Rates ........................................... 5-21 What Smoothing Technique Should You Use? .............................. 5-22 Exhibit 5.3: Contrasting Smoothing Methods ............................ 5-23 Exhibit 5.4: Average Error in Estimating 7-Year Swap Rates 5-24 Evaluating the Rate Sensitivity of EVE ............................................. 5-25

XX

Contents

EVE Sensitivity

— Dispersion...-.................................................... 5-25 Exhibit 5.5: Economic Value of Equity ..................................... 5-26 Exhibit 5.6: Economic Value Sensitivity of Assets, Liabilities, and Equity .................................................................................. 5-28 Exhibit 5.7: Economic Value of Equity Sensitivity ................... 5-29 Plus or Minus? A Note on Arithmetic Signs .............................. 5-29 Exhibit 5.8: Sample Output of Economic Value Simulation Model ....................................................................... 5-30 Uneven Outcomes .......................................................................... 5-31 Relating the Rate Sensitivity of the Economic Value to the Rate Sensitivity of Net Income ................................................. 5-32 The Conceptual Relationship Between EVE and EAR .............. 5-32 The Practical Relationship Between EVE and EAR .................. 5-34 EVE and EAR Treatments of New Business .................................. 5-38 Exhibit 5.9: The Impact of Runoff, Rollover, and Growth Over Time .................................................................................. 5-38 The Impact of Omitting Rollover and Growth is Often Misunderstood Two Points of View ........................................ 5-39 Using EVE Sensitivity Simulation to Achieve Other Management Goals ......................................................................... 5-41 FAS 107...................................................................................... 5-41 FAS 115...................................................................................... 5-42 Product Pricing and Marketing................................................... 5-42 Advantages of EVE Sensitivity Simulation........................................ 5-43 Captures Interest Rate Risk from All Time Periods ....................... 5-43 Provides a Specific and Understandable Measure of Rate Risk Exposure................................................................................. 5-44 Focuses on the Rate Risk in the Bank’s Current Position .............. 5-44 Can Readily Be Used to Focus on Changes in Rate Exposure at the Product Level........................................................................ 5-44 Can Capture Option Risk ................................................................ 5-45 Can Capture Yield Curve Risk ....................................................... 5-45 Can Capture Basis Risk .................................................................. 5—45 Can Reflect Rate Sensiu'vity Over a Wide Range of Rate Scenarios ......................................................................................... 5-46 Can Capture Rate Risk Obscured by Accrual Accounting ............. 5-46 Meets Regulatory Expectations ...................................................... 5-46 Can Be Integrated with Other Management Information Systems ........................................................................................... 5-47

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Interest Rate Risk Management

Disadvantages of EVE Sensitivity Simulation ................................... Managing EVE Sensitivity Can Increase Earnings Volatility ........ In Most Applications, EVE Ignores the Impact of Reinvestment and New Business .................................................... EVE Does Not Provide Any Information About the Timing of Rate Risk Exposures ...................................................... Assumptions Require Careful Development, Analysis, Increased Controls, and Testing ..................................................... Use of Discount Rates Can Introduce Additional Measurement Errors .............................................................................................. Accurate Assumptions of Volume Changes Caused by Embedded Options Must Be Accurate ........................................... EVE May Fail to Capture a Material Amount of Interest Rate Risk Exposure ........................................................................ Value at Risk ...................................................................................... Three Difi‘erent VaRs ..................................................................... Exhibit 5.10: Strengths and Weaknesses of VaR Methods ........ VaR Problems and Limitations....................................................... Exhibit 5.1 I: VaR for Three Hypothetical Portfolios................. Exhibit 5.12: Cumulative VaR for Three Hypothetical

Portfolios .................................................................................... Stress Testing .............................................................................. Converting EVE to VaR ................................................................. EVE and VaR Summary .....................................................................

5-47 5-47 5-48

5-48 5-48

5-49 5-50 5-51 5-51

5-52 5-54 5-55 5-57 5-58 5-59 5-60 5-61

DIFFICULT VOLUMES

Chapter 6 Measuring the Rate Risk of Indeterminate Maturity, Administered Rate, and Putable Deposits So, How Important Is Deposit Rate Risk?............................................ 6-2 Exhibit 6.1: EAR Sensitivity to Indeterminate Maturity Deposit Repricing Assumption ..................................................... 6-4 Exhibit 6.2: EAR Sensitivity to Indeterminate Maturity

Deposit Decay Assumption .......................................................... 6-5

Contents

Exhibit 6.3: EVE Sensitivity to Indeterminate Maturity Deposit Decay Assumption .......................................................... 6-6 A Summary: The Sensitivity of Measured IRR to Indeterminate Maturity Deposit Assumptions ......................................................... 6-7 Estimating the Maturity and/or Repricing of Indeterminate Maturity Deposits ................................................................................. 6-7 Maturity Assumptions Vary I-Iugely ................................................. 6-8 Exhibit 6.4: Illustrative Indeterminate Maturity Deposit Decay Rates and Average Lives ................................................... 6-9 An Overview of Quantitative Tools for Calculating Indeterminate Maturity Deposit Runoff Rates and Average Lives ....................... 6-10 Method One: Decay or Ath'ition Analysis ...................................... 6-12 Calculating Deposit Decay or Attrition ...................................... 6-12 Exhibit 6.5: Illustration of Simple Decay Analysis .................... 6-13 Exhibit 6.6: Example Attrition Measurements ........................... 6-14 Decay Analysis Limitations ....................................................... 6-14 The Influence of Changes in Prevailing Interest Rates on Changes in Deposit Volumes: A Digression ......................... 6-16 Exhibit 6.7: Indeterminate Maturity Deposit Volume Changes Transaction Accounts — Plus 200 vs. Minus 200...................... 6-19 Exhibit 6.8: Indeterminate Maturity Deposit Volume Changes Plus 200 vs. Minus 200 ......................... 6-19 Passbook Accounts Exhibit 6.9: Core Deposit Volume Changes Money Market Accounts Plus 200 vs. Minus 200 ......................................... 6-20 Reasons Why Deposit Balances Are Not Always Rate Sensitive ............................................................................. 6-20 The Influence of the Exercise of Depositors’ Options on Changes in Deposit Volumes ................................................ 6-24 Segmented Volume and Replicating Portfolios.................................. 6-26 Method Two: Segmented Volume Analysis for Estimating Deposit Maturity ............................................................................. 6-27 Using Trend Analysis to Segment Stable and Volatile Indeterminate Maturity Deposit Components — A Simple Application ................................................................. 6-29 Using Trend Analysis to Segment Stable and Volatile Indeterminate Maturity Deposit Components A More Sophisticated Application ............................................. 6-29 Exhibit 6.10: Indeterminate Maturity Deposit Trend Analysis in Savings Account Balances ...................................... 6-30

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Interest Rate Risk Management

Method Three: Simple Regression Analysis — Finding

a Floating Rate Bond with the Same Rate Sensitivity .................... 6-31

Exhibit 6.11: Coefficients for Modeling the Deposit Rate as a Function of l-Month LlBOR Rate ...................................... 6-31 Method Four: Replicating Portfolio Analysis for Estimating Deposit Maturity — The Most Common Method .......................... 6-32 Exhibit 6.12: Illustration of Simple Portfolio Construction for Replicating Portfolio Analysis .............................................. 6-33 Combining Segmentation Analysis and Replicating Portfolios ..... 6-34 Method Five: Complex Replicating Portfolio Analysis ................. 6-35 Exhibit 6.13: Constant Deposit Balances with Complex Econometric Equations............................................................... 6-36 Method Six: Replicating Portfolio Analysis The Jacobs Method......................................................................... 6-37 Exhibit 6.14: Example Replicating Portfolio Using the Jacobs Method ...................................................................... 6-38 Moving Beyond Replicating Portfolios .......................................... 6-39 Method Seven: Structural Models of Aggregate Behavior............. 6-39 Method Eight: Option Adjusted Spread ......................................... 6-40 Exhibit 6.15: Example OAS Process .......................................... 6-41 Exhibit 6.16: Example OAS Cash Flows ................................... 6-42 Estimating Deposit Maturities — A Summary ............................... 6-42 Exhibit 6.17: Comparing Methods for Quantifying Core Deposit Rate Sensitivity ............................................................. 6-43 Estimating Administered Rates for Checking and Savings Accounts ............................................................................................. 6-44 Five Administered-Rate Variables ................................................. 6-45 Caps and Floors .......................................................................... 6-45 Time Lags ................................................................................... 6-45 Beta............................................................................................. 6-46 Exhibit 6.18: Indeterminate Maturity Deposit Rate Correlation to Treasury Bill Rates Worksheet ........................... 6-47 Exhibit 6.19: Indeterminate Maturity Deposit Rate Correlation to Prime Rate Worksheet ......................................... 6-47 Administered Rate Sensitivity Summary ................................... 6-47 Exhibit 6.20: Comparative Rate Volatility ................................. 6-48 Asymmetrical Rate Changes ...................................................... 6-50 Path Dependency of Administered Rates ................................... 6-51 Dealing with Administered Rates ................................................... 6-51

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Contents

Certificates of Deposit ........................................................................ 6-53

Chapter 7

Measuring the Rate Risk of Loans and Investments Residential Mortgage Loan and Mortgage-Backed Security Prepayments ......................................................................................... 7-2 The Magnitude of Residential Mortgage Loan and Security Cash Flow Uncertainty ..................................................................... 7-2 Distribution of Cash Flow Composition....................................... 7-2 Exhibit 7.1: Annual Cash Flow from a 30-Year 8 Percent Mortgage ...................................................................................... 7-3 Exhibit 7.2: Armual Cash Received from a 30-Year Mortgage with No Prepayments ................................................... 7-4 Exhibit 7.3: Annual Cash Received from a 30-Year Mortgage with 6 Percent Prepayments Each Year ....................... 7-4 Exhibit 7.4: Annual Cash Received from a 30-Year Mortgage with 8 Percent Prepayments Each Year ....................... 7-5 Traditional Measures of Mortgage Prepayments .............................. 7-5 CPR .............................................................................................. 7-5 PSA............................................................................................... 7-6 Disadvantages of the PSA Model................................................. 7-8 Predicting the Rate Sensitivity of Prepayments................................ 7-8 Projections for Securities .............................................................. 7-9 Projection by Coupon Rate........................................................... 7-9 Exhibit 7.5: Sensitivity of PSA Forecasts to Changes in Interest Rates .............................................................................. 7-10 Exhibit 7.6: Projected Prepayments by Coupon ......................... 7-10 Vector Analysis .......................................................................... 7-1 1 Call Risk and Extension Risk ......................................................... 7-12 Call Risk and Extension Risk Are Asymmetrical ...................... 7-14 Transaction Costs ........................................................................... 7-14 Modeling Prepayments as the Exercise of Options ........................ 7-14 Multi-Factor Models ....................................................................... 7-15 A Closer Look at Loan Age ....................................................... 7-15

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Interest Rate Risk Managgrent

Exhibit 7.7: Relationship Between Prepayments and Loan Age .................................................................................... Other Causes for Residential Mortgage Loan and Security Cash Flows “Irrationality” ......................................................... Path-Dependency ............................................................................ Exhibit 7.8: Trend in Yields for 30-Year, Fixed-Rate Mortgages ................................................................................... Exhibit 7.9: Projected Prepayments by Coupon and Age Cohort ......................................................................................... Prepayment Forecasting Models .......... Pulling It All Together Other Borrower/Security Options ....................................................... Additional Prepayment Option Characteristics to Consider ........... Put Options and Lines of Credit ..................................................... Predicting Prepayments for Business Loans................................... Loan Rate Caps and Floors............................................................. Default Options and Non-Performing Assets ................................. Administered Rates on Loans — a Bank Option ............................... Floating Rates ................................................................................. Fixed Rates .....................................................................................

—

—

7-16 7-16 7-18 7-19

7-20 7-20 7-22 7-22 7-23 7-23 7-24 7-25 7-26 7-26 7-28

Chapter 8 Rate Changes: Deterministic Scenarios and Stochastic Models Essential Questions About Rate Changes to Be Modeled.................... 8-1 Selecting a Detemtinistic Rate Scenario .............................................. 8-2 Other Issues for Determinsitic Rate Scenarios ..................................... 8-5 The Size of Possible Rate Changes .................................................. 8-6 Instantaneous Rate Shocks vs. Ramps............ 8-8 Parallel vs. Nonparallel Rate Changes .............................................. 8-9 Exhibit 8.1: Parallel Shifis of Yield Curve ................................... 8-9 Exhibit 8.2: Nonparallel Rate Cycle Shifts (with an inverted yield curve) ................................................................... 8-11 Exhibit 8.3: Nonparallel Rate Cycle Shifis (without an inverted yield curve) ................................................................... 8-12

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Contents

Using Principal Components Analysis to Define Non-Parallel Rate Changes ............................................................. 8-12 Exhibit 8.4: Estimated Net Income at Risk (Amounts in millions) ................................................................................. 8-13 Exhibit 8.5: Yield Curve Twist June 30, 2004, and June 30, 2005.............................................................................. 8-14 Evaluating Multiple Rate Change Scenarios .................................. 8-15 Exhibit 8.6: Variance in the Yield Curve ................................... 8-16 Exhibit 8.7: Level Factor (Shifi) ................................................ 8-16 Exhibit 8.8: Slope Factor (Twist) ............................................... 8-17 Future Rate Changes, Statistical Tools, and Term Structure Models ................................................................................................ 8-20 Simple (Non-Stochastic) Term Structure Models .......................... 8-20 Duration, Parallel Shins, and Implied Forwards ........................ 8-21 Exhibit 8.9: Implied Forward Yields .......................................... 8-22 Exhibit 8.10: Distribution of Rate Changes by Size (period of low volatility) ............................................................ 8-25 Exhibit 8.11: Normal and Fat-Tailed Distributions of Rate Changes .............................................................................. 8-26 Introduction to Stochastic Term Structure Models ......................... 8-28 Exhibit 8.12: Steps for Stochastic Evaluation ............................ 8-28 Types of Term Structure Models ........................................................ 8-29 Exhibit 8.13: Selected Term Structure Models .......................... 8-30 Analytical Solutions ....................................................................... 8-30 From Analytical to Numerical Solutions .................................... 831 Monte Carlo Simulation ................................................................. 8-32 Finite Difference Methods .............................................................. 8-34 Binomial Lattices............................................................................ 8-35 Exhibit 8.14: A Simple Binomial Lattice ................................... 8-36 Bushy Trees .................................................................................... 8-37 Trinomial Lattices .......................................................................... 8-37 Exhibit 8.15: A Simple Trinomial Lattice .................................. 8-38 Parameters for Term Structure Model ................................................ 8-39 Volatility ......................................................................................... 8-39 Exhibit 8.16: A Simple Binomial Lattice with 1.5 Percent Volatility .................................................................. 8-40 Drift ................................................................................................ 8-40 Mean Reversion Speed ................................................................... 8-41 Arbitrage ......................................................................................... 8-42

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Interest Rate Risk Management

Understanding Term Structure Model Parameters ......................... 8-42 Calibrating Parameters ................................................................... 8-42 Historical Volatility Curve Approach ........................................ 8-43 Exhibit 8.17: Variance in Canadian Govemment Interest Rates .............................................................................. 8-44 Advanced Volatility Curve Approach ........................................ 8-45 Exhibit 8.18: Implied Mean Reversion Speed ............................ 8-46 Implied Parameters from an Observable Yield Curve ................ 8-46 Fitting Parameters to Volatility-Sensitive Instruments .............. 8-47 Parameter Estimation for Multi-Factor Models ......................... 8-48 Choosing a Term Structure Model ..................................................... 8-48

Chapter 9 Selecting and Installing AL Models Modeling Process ................................................................................. 9-2 Exhibit 9.1: Model Process Flow Chart ....................................... 9-3 Ten Key Features of Asset/Liability Models ........................................ 9-3 1. Extent of Aggregation of Information Concerning the Bank’s Current Position ................................................................... 9-4 2. Manual vs. Automated Input of Information Concerning the Bank’s Cur-rent Position ................................................................... 9-5 Transferring Accounting Data into the Simulation Model ........... 9-6 Bank Needs and Simulation Model Sophistication ...................... 9-6 3. Ability to Capture Product Option and Basis Risk ....................... 9-7 Simulating the Exercise of Embedded Options ............................ 9-8 Criteria for Selecting Product Options Capabilities ................... 9-10 Basis Risk ................................................................................... 9-11 4. Number and Choice of Rate Scenarios ....................................... 9-12 5. Features for Facilitating Realism of Rate Scenarios ................... 9-13 6. Level of Output Detail Provided ................................................ 9-16 Detail Reports ............................................................................. 9-16 Comparative Reports .................................................................. 9-17 Management Reports .................................................................. 9-1 8 Deviations from Bank Policy ..................................................... 9-18 7. Risk Measurement Methodologies ............................................. 9-18

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Contents

8. Regulatory Compliance Issues for Interest Rate Risk Models ............................................................................................ 9-18 Thrift Institutions ........................................................................ 9-19 Commercial Banks ..................................................................... 9-20 Bank Examiner Guidelines ......................................................... 9-22 9. Easy “What-If" Modeling........................................................... 9-26 10. Applicability to Other Management Goals ............................... 9-27 Budgeting ................................................................................... 9-27 Investment Portfolio Management ............................................. 9-28 Required Financial Disclosures .................................................. 9-28 Product Pricing ........................................................................... 9-29 Using Data from Call Reports .................................................... 9-29 Option-Adjusted Spreads, Monte Carlo, and Other Advanced Modeling Features .............................................................................. 9-30 Rate Scenarios: Stochastic and Term Structure Modeling Capabilities ..................................................................................... 9-3 1 Capability to Model Prepayments and Other Embedded Options ........................................................................................... 9-34 Option Adjusted Spreads ............................................................ 9-34 Prepayment Models .................................................................... 9-35 Advanced Modeling Summary ....................................................... 9-36 Integrating Model Techniques ............................................................ 9-36 Selecting a Rate Risk Model .............................................................. 9-38 Identifying Your Rate Risk Model Requirements .......................... 9-38 Evaluating Interest Rate Risk Models ................................................ 9-40 Installing Interest Rate Risk Models .............................................. 9-46 Appendix 9A: A Guide to ALM Software ......................................... 9-49 Appendix 9B: ALM Outsourcing and Consulting Vendors ............... 9-53 Appendix 9C: Required Model Features, Functions, and Characteristics .................................................................................... 9-57

Chapter 10 Using Models and Managing Model Risk Managing Model Risk ........................................................................ 10-1 Model Flaws, Model Errors, and Model Obsolescence .................. 10-2

xxix

Interest Rate Risk Management

Exhibit 10.1: Eight Sources of Model Risk ................................ 10-3 Data and Assumption Inputs .............................................................. 10-4 Data Describing the Bank’s Current Position................................. 10-4 Exhibit 10.2: Cash Flow Over Time ........................................... 10-5 The Impact of Data Aggregation .................................................... 10-6 Common Risk Characteristics .................................................... 10-6 Match to Bank’s Risk Exposure Profile ..................................... 10-7 Information About Future Activity ................................................. 10-7 Incorporating Assumptions for Future Business: The Good, the Bad, and the Surprising ...................................... 10-8 What Is Best Practice Modeling Methodology? ........................... 10-10 What Is Best Practice Model Governance? .................................. 10-11 Exhibit 10.3: Best Practice Model Governance ....................... 10-12 Understanding the Accuracy of Model Output................................. 10-12 Managing the Integrity of Simulation Models: Benchmarking, Backtesting, and Validation.............................................................. 10-13 Three Processes for Model Validation ......................................... 10-13 What Is Backtesting? .................................................................... 10-14 Controlling Data Quality .............................................................. 10-16 Controlling, Validating, and Backtesting Assumptions ............... 10-19 Exhibit 10.4: Percentage Change in EVE from the Base Case EVE......................................................................... 10-22 Limitations of Interest Rate Risk Models ......................................... 10-24 Limited or No Capture of External Variables ............................... 10-25 Weak Links ................................................................................... 10-25 Overly Detailed Models................................................................ 10-26 Using Models to Maximize Risk Management Benefits .................. 10-27 Creating Logical Scenario Groupings .......................................... 10-27 The Inter-Related Components of Scenarios ............................ 10-28 Scenario Selection .................................................................... 10-28 Improving Model-Generated Management Reports ..................... 10-29 What Is Needed? ......................................................................- 10-30 What Is Not Needed? ............................................................... 10-31 Improving Management Confidence in IRR Modeling................ 10-31 Internal Control Checklist for IRR Models ...................................... 10-33

Contents

Chapter 11 Interest Rate Risk Measurement Summary The Scope of Typical Rate Risk Measurement: Missing Pieces ........ 11-2 The Rate Sensitivity of Noninterest Income and Noninterest Expense: Volume and Value Affects .............................................. 1 1-3 The Size of Noninterest Cash Flow Streams Can Be Material ...................................................................................... “-4 Exhibit 1 1.1 : Trend in Net Noninterest Expense........................ “-4 Some Noninterest Cash Flows Are Highly Rate Sensitive ......... 11-5 Exhibit 1 1.2: Net Income Sensitivity with and Without Mortgage Origination Fee Income ............................................. 11-6 The Value of Cash Flows Is Rate Sensitive Even When the Volume Is Not ...................................................................... 11-7 Including Both Noninterest Income and Noninterest Expense: The Optimal Solution ................................................................. 11-9 The Second Best Solution ............................................................. 11-10 More Missing Pieces: Franchise Value ........................................ “-11 Core Deposits and Core Deposit Intangibles ............................ 1 1-12 Other Sources of Franchise Value ............................................ 11-13 Summary of Included and Excluded Elements............................. “-13 Exhibit 11.3: Primary Components of a Firm’s “Value” ......... 11-14 The Impact of Credit Risk ................................................................ “-14 Interest Rate Sensitivity of Credit-Related Expenses ................... 11-15 Exhibit 11.4: Relationship Between Interest Rates and Loan Delinquency ............................................................................. 1 1-16 Exhibit 11.5: Default Adjusted VaR ........................................ 11-17 Counter-Intuitive Impact on EVE of Changes in Credit Quality .......................................................................................... 11-17 Limits to the Science: Inherent Uncertainty in Rate Risk Measurement .................................................................................... 1 1-18 The Imprecision of Position Data and Assumption Errors ........... 11-20 Assumption Sensitivity ................................................................. 11-22 A Case Study ............................................................................ “-22 Exhibit 11.6: Example of EVE Sensitivity with the Addition of a Deposit Life Rate Sensitivity Assumption ......... 11-23

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Interest Rate Risk Management

Exhibit 11.7: Example of EVE Sensitivity with the Addition of a Loan Prepayment of an Assumption ................................. Exhibit 11.8: Example of EVE Sensitivity Making Small Changes in Deposit Life and Loan Prepayment Assumptions ............................................................................. Measurement Solutions: What Works and When............................. Capturing the Four Components of IR ....................................... Exhibit 1 1.9: Capturing the Four Components of IR ............. Measurement Techniques at a Glance .......................................... Exhibit 1 1.10: Comparisons of Four Interest Rate Risk Analysis Techniques ................................................................. .............. What Is Best Practice? ......................................... Measurement Summary ................................................................ Exhibit 11.11: Suitability of Aitemative IRR Measurement Approaches ............................................................................... Rate Risk Measurement from 10,000 Feet ...................................

11-24

1 1-26 11-26 “-26

11-27 11-27 11-28

”-30 1 1-31

1 1-32 11-33

IRR MANAGEMENT POLICIES & STRUCTURES

Chapter 12 ALM Policies, Management Structures, and Risk Limits An Overview of AL Management ...................................................... 12-1 The Scope of IR Management ..................................................... 12-2 IRR Management as a Six-Step Process......................................... 12-2 Exhibit 12.1: Six Elements of IR Management ....................... 12-3 IRR Policy .......................................................................................... 12-5 Why Do We Need a Formal IRR Policy?....................................... 12-6 The Elements of an Effective ALM or IR Policy ........................ 12-7 Frequency and Method for Monitoring Interest Rate Risk Exposure ..................................................................................... 12-8 Rate Risk Exposure Limits ......................................................... 12-9 Clear Identification of Authority/Responsibility ...................... 12-13

Contents

Reporting .................................................................................. 12-16 Acceptable and Unacceptable Courses of Action for Managing Interest Rate Risk .................................................... 12-18 Measures to Take to Monitor Compliance with the IRR Policy ................................................................................ 12-20 Measures to Test the Accuracy of Data, Assumptions. and Calculations Used in the Rate Risk Measurement Process ...... l2-20 Measures to Test the Accuracy of Estimated or Projected Exposure to Changes in Prevailing Interest Rates .................... 12-22 Measures to Test the Effectiveness of Rate Risk Management Activities ............................................................. 12-22 Regulatory Compliance ............................................................ 12-24 Policy Coordination .................................................................. 12-26 Other Provisions Suitable for ALM or IRR Policies ................ 12-27 Making the IRR Policy Efi‘ective ................................................. 12-27 IRR Policy Flaws...................................................................... 12-27 Management Structure...................................................................... 12-30 Exhibit 12.2: IRR Authority/Responsibility ............................. 12-31 ALCO ..................... 12-32 Asset/Liability Management Committee ALCO‘s Overall Mission ......................................................... 12-32 ALCO Functions and Responsibilities ..................................... 12-34 Exhibit 12.3: Rate Risk Management Action Plan from November 21, 200x ALCO Meeting .............................. 12-37 ALCO Membership .................................................................. 12-38 Making the ALCO Effective .................................................... 12-39 Exhibit 12.4: Characteristics of Inefl'ective AL Committees 12-40 ALCO Meeting Topics ............................................................. 12-44 Exhibit 12.5: ALCO Agenda Sample State Bank for June 7, 20XX ............................................................................ 12-44 Setting and Using IRR Exposure Limits .......................................... 12—45 Exhibit 12.6: The IR Limit-Setting Process........................... 12-47 The Independent Variable: Selecting the Rate Change to Analyze ..................................................................................... 12-47 The Dependent Variable: Selecting Management’s Target .......... 12-48 Exhibit 12.7: Use of Market Value vs. Income Risk Limits 12-49 Focus on Income and Equity at Risk — But Not Equally ........ 12-50 Estimating the Bank’s Risk Appetite ............................................ 12-51 Exhibit 12.8: Risk Appetite ...................................................... 12-52 Risk Appetite In Theory — Top-Down Approaches ................ 12-52

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Interest Rate Risk Management

Exhibit 12.9: Application of VaR to Quantify Capital Required for Unexpected Losses ............................................. 12-53 Exhibit 12.10: Selecting Minimum Capital Level Based on Target Rating....................................................................... 12-54 Bottom-Up Approaches ............................................................ 12-55 Synthesis ................................................................................... 12-55 Risk Appetite in Practice .............................................................. 12-56 Exhibit 12.11: Understanding Risk Appetite as a Set of Constraints ........................................................................... 12-57 Exception for Liquidity Risk .................................................... 12-59 Risk Appetite Summary ........................................................... 12-59 Connecting Risk Appetitive Concepts to Interest Rate Risk Limit Setting ................................................................................. 12-60 Exhibit 12.12: Probable N11 Outcomes .................................... 12-62 Exhibit 12.13: Portfolio Value Change Distribution ................ 12-62 Set a Loss Limit .......................................................................... 12-62c Outliers ................................................................................... 12-62c Using VaR for Limits ............................................................. 12-62d Multiple Limits ....................................................................... 12-62d Exhibit 12.14: Format for Multiple IRR Exposure Limits 12-62e Tracking Actual Exposures vs. Limits ................................... 12-62e Exhibit 12.15: Comparisons of Risk Limits and Measured Exposures ................................................................................ 12-62f Using Sublirnits ...................................................................... 12-62g Exhibit 12.16: IRR Exposure Limits and Sublimits ............... 12-62h Ineffective IRR Limits............................................................ 12-62h Appendix 12A: Guidelines for Drafting Your Rate Risk Policy ................................................................................................ 12-63 Appendix 12B: Sample Rate Risk Management Policy for Placid County Bank .................................................................... 12-70 Appendix 12C: Policy Review Worksheet ..................................... 12-101

Contents

Chapter 13 ALM Decision Making, Implementation, and Oversight Introduction to Rate Risk Management Issues ................................... 13-1 Exhibit 13.1 : The Six Steps of IRR Management ...................... 13-1 Decision Making ................................................................................ 13-2 Selecting a Risk Management Philosophy: Aggressive vs. Conservative Risk Exposure Management Practices ..................... 13-2 A Framework for Understanding Aggressive vs. Conservative IRR Management............................................................................ 13-3 Exhibit 13.2: IRR Exposure Variables Matrix ........................... 13-3 Exhibit 13.3: Probable Results from Alternative Approaches to Rate Risk Management .......................................................... 13-5 The Influence of Measurement and Management Quality on Decision Making ............................................................................ 13-6 Understanding What “Risk Neutral” Really Means ....................... l3-7 The Case for Active Management of Interest Rate Risk .............. 13-10 Recognizing the Time When a Change in the Bank's Risk Exposure Is Needed ...................................................................... 13-1 1 The Risk Continuum ................................................................ 13-12 The Impact of Confidence Risk Targets Are Not the Same as Risk Limits ............................................................................... 13-12 The IRR Decision-Making Process ............................................ 13-14a Determine Your Rate Outlook ............................................... 13-14a Exhibit 13.4: Five Steps for Sound Decision Making .............. 13-15 What Scenario Should Management Focus On? ...................... 13-16 Exhibit 13.5: Projected EAR for Sunshine Community Bank ......................................................................................... 13-17 Exhibit 13.6: Rate Scenario Probability Assignments .............. 13-18 Exhibit 13.7: Probability Distribution of Rate Scenarios ......... l3-19 Exhibit 13.8: Probability-Weighted Simulation Results .......... 13-19 Decide on an IR Position ....................................................... 13-20 Exhibit 13.9: Sample ALCO Report (12-month history of position-taking, expressed as % of limit) ................................. 13-22 Determine the Basic Implementation Strategy and Delegate Implementation Responsibility ................................................. 13-23

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XXXV

Interest Rate Risk Management

Exhibit 13.10: Revised Probability-Weighted Simulation Results ...................................................................................... Flawed Decision Making.............................................................. The Non-Decision .................................................................... Wishful Thinking ..................................................................... Delayed Decisions .................................................................... Requirements for Good Decision Making ................................ Implementation of Rate Risk Management Decisions ..................... Flawed Implementation ................................................................

13-24 13-24 13-24 13-26 13-26 13-26 13-27 13-29 Requirements for Good Implementation ...................................... 13-30 Be Prepared to Change Course ..................................................... 13-30 Watch Out for Increased Risk Exposures Created in the Course of Reducing Existing Risk Exposures .............................. 13-31 Implementation Must Include Communication ...... Oversight and Testing ................................................. IRR Oversight Objectives ....................................... Internal Controls ........................................................................... 13-34 Management Reporting ................................................................ 13-36 Backtesting ....................................................................................... 13-37 Objectives of Backtesting and Tracking ....................................... 13-38 Inherent Limitations of Backtesting ............................................. 13-39 Testing and Tracking in Spite of the Limitations ......................... 13-42 Normalized Net Interest Margin................................................... 13-45 Exhibit 13.1 1: Normalized or Recurring Net Interest Income for Simple State Bank (for the month of May)......................... 13-46 Rate/MixNolume Analysis .......................................................... 13-47 Exhibit 13.12: Decomposition of Variances Between Forecast and Actual Net Income .............................................. 13—48 Exhibit 13.13: Margin Variance Analysis ................................ 13-49 Oversight Challenges ........................................................................ 13-50 Lack of Standards to Test Compliance Against ........................... 13-50 Lack of Independence in Testing .................................................. 13-52 Regulatory Expectations for Managing Model Risk ........................ 13-53 Some Perspectives on Managing Interest Rate Risk ........................ 13-56

Contents

IRR MANAGEMENT TACTICS

Chapter 14 Managing Interest Rate Risk Without Using Off-Balance Sheet Derivatives Introduction ........................................................................................ 14-1 Risk Management Strategies .............................................................. 14-1 Exhibit 14.1: Strategies for Managing Rate Risk ....................... 14-2 Risk Minimization Tactics ................................................................. 14-2 Four Groups of IRR Management Tactics ......................................... 14-3 IRR Avoidance Tactics ....................................................................... 14-4 Strategic Asset and Liability Selection Decisions .......................... 14-4 Product Design and Marketing ....................................................... 14-5 Origination for Sale ........................................................................ 14-5 Limits of IR Avoidance Tactics ................................................... 14-5 IRR Reduction Tactics ....................................................................... 14—6 Exhibit 14.2: Overview of Tactics for Managing Mismatch Risk ............................................................................................. 14-7 Using Securitization for IR Management .................................... 14-9 Limitations on IR Reduction Tactics ......................................... 14-10 Critical Impact of Customer Preferences on Rate Risk Management Strategies and Tactics ................................................. 14—1 1 Controlling IRR in Customer Business at the Source .................. 14-11 Controlling IRR in Customer Business After It Is Incurred ......... 14-12 Isolating Rate Risk by Product Type and Then Managing Rate Risk by Marketing ................................................................ 14-13 Exhibit 14.3: Products Ranked by Economic Value Sensitivity ................................................................................. 14-14 Exhibit 14.4: Products Ranked by Economic Value Sensitivity ................................................................................. 14-15 Introduction to Hedging ................................................................... 14-16 Two Types of Hedging: Value and Cash Flow ............................ 14-18 Hedging Does Not Require Derivatives ....................................... 14-18 Hedging Without Off-Balance Sheet Derivatives: Concepts and Issues ...................................................................................... 14-18 xxxvii

Interest Rate Risk Management

Defensive Hedging of IR from Core Bank Activities ................ 14-19 Natural (On-Balance Sheet) Hedges ................................................ 14-20 Potentially Confusing Differences in Natural Hedge Terminology ................................................................................. 14—2 1 Natural Hedging Is Not the Same as Balance Sheet Matching....................................................................................... 14-23 Risk Reduction Tactics Employing Natural (On-Balance Sheet) Hedges .............................................................................................. 14-24 Flexibility and Diversification...................................................... 14-26Influencing Customer Preferences to Promote Natural Hedging ........................................................................................ 14-27 Operational Weaknesses Associated with Natural or On-Balance Sheet Hedging .......................................................... 14-28 Summary .......................................................................................... 14-29

Chapter 15 Hedging with Off-Balance Sheet Derivative Instruments Should You Use Derivative Hedge Instruments to Manage IRR? ..... 15-2 Advantages of Using Derivatives ................................................... 15-2 Prerequisites for Using Derivatives ................................................ 15-3 Disadvantages of Using Derivatives........................................... 15-5 Chapter Map ................................................................................... 15-5 Key Definitions and Issues ................................................................. 15-6 What Are Derivatives? ................................................................... 15-6 Key Facts About Derivatives .......................................................... 15-7 Key Accounting and Regulatory Definitions ................................. 15-8 Use of the Term in an Important Regulation.............................. 15-8 Use of the Term in an Important Accounting Rule .................... 15-8 What Is a Derivative Hedge Instrument? ...................................... 15-11 What Is an End User? ................................................................... 15-12 Exchange-Traded vs. Over-the-Counter Derivatives ................... 15-13 Building Block Components of All Financial Instruments .......... 15-14 Differences in Risk vs. Reward Exposures................................... 15-15 Two-Sided Interest Rate Risk ................................................... 15-16

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Contents

Exhibit 15.1: Risk and Reward of Holding a Typical Long Position ........................................................................... Exhibit 15.2: Risk and Reward of Holding a Typical Short Position ........................................................................... Exhibit 15.3: A Simple Hedge Position: Long Cash — Short Futures ............................................................................ One-Sided Interest Rate Risk ................................................... Exhibit 15.4: Asymmetry of Gain and Loss Long a Call ........ Exhibit 15.5: Asymmetry of Gain and Loss Long a Put .......... Macro vs. Micro Risk Management ............................................. Micro Hedging ......................................................................... Macro Hedging......................................................................... Major Off-Balance Sheet Derivative Hedge Instruments ................. Forward Contracts ........................................................................ Futures Contracts .......................................................................... Futures Pricing Conventions .................................................... Margin Requirements ............................................................... Options ......................................................................................... Exhibit 15.6: Rights and Obligations of Options Buyers and Sellers Buyer...................................................................... Defining Option Value ............................................................. Understanding Changes in Option Prices and Delta ................ Options Pricing Conventions .................................................... Option Types ............................................................................ Introducing the Exotic Option .................................................. Interest Rate Swaps ...................................................................... Exhibit 15.7: Diagram of Cash Flow Types and Directions for a Fixed/Floating Interest Rate Swap ................................... Exhibit 15.8: Diagram of Individual Cash Flows for a Fixed/Floating Interest Rate Swap ........................................... Swap Transaction Structure and Terms .................................... Typical Swap Transactions ...................................................... Exhibit 15.9: Before the Swap .................................................. Exhibit 15.10: After the Swap .............................................. Alternatives to Plain Vanilla Swaps ..................................... Swap Market Participants......................................................... Swap Market Structure ............................................................. Swap Documentation ............................................................... Advantages of Swaps ...............................................................

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15-16

15-17 15-17 15-18 15-19 15-19 15-20 15-20 15-21 15-22 15-22 15-23 15-24 15-24 15-25

15-26 15-27 15-28

15-30 15-31 15-31 15-33 15-34 15-34 15-34

15-36 15-37 15-38 15-39 15-41 15-41 15-43 15-44

Interest Rate Risk Manage_ment

Disadvantages of Swaps ........................................................... Caps, Floors, and Collars .............................................................. Caps .......................................................................................... Floors ........................................................................................ Collars ...................................................................................... General Characteristics of Caps, Floors, and Collars ............... Exotic Caps .............................................................................. Hedge Instruments Summary ....................................................... Exhibit 15.11: Notional Amount of Holdings of Selected Derivative Types for US. Commercial Banks ......................... IRR Management Tactics Using Off-Balance Sheet Derivative Hedge Instruments ............................................................................ Using Interest Rate Swaps to Manage Gap/Mismatch Risk ......... Base Case Without a Swap ....................................................... Exhibit 15.12: Asset/Liability Management Example: Base Case Net Interest Income ......................................................... Impact of an Interest Rate Change ........................................... Exhibit 15.13: Asset/Liability Management Example: Net Income with 100 BP Drop ........................................................ Base Case with a Swap ............................................................. Exhibit 15.14: Asset/Liability Management Example: Base Case Net Interest Income with Swap ........................................ Impact of an Interest Rate Change Afier the Swap .................. Exhibit 15.15: Asset/Liability Management Example: Net Income, Including Swap, with 100 BP Drop............................ Effect of the Swap on the Bank’s Gap Position ....................... Exhibit 15.16: Asset/Liability Management Example: Interest Rate Sensitivity Gap Table .......................................... Exhibit 15.17: Asset/Liability Management Example: Market Value Table for Base Case ........................................... Efl'ect of the Swap on the Bank’s Economic Value of Equity ....................................................................................... Exhibit 15.18: Asset/Liability Management Example: Economic Value Table for Base Case ...................................... Exhibit 15.19: Asset/Liability Management Example: Economic Value After 100 BP Drop ........................................ Exhibit 15.20: Asset/Liability Management Example: Economic Value with the Swap ...............................................

xl

15-44 15-46 15-46 15-47 15-48 15-48 15-49 15-50 15-51 15-52 15-52

15-53

15-53 15-54

15-54 15-55 15-56 15-57

15-57 15-59

15-59 15-59 15-60

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15-61

15-62

Contents

Exhibit 15.21: Asset/Liability Management Example: Economic Value with the Swap Alter 100 BP Drop ................ 15-63 Using Caps to Manage Gap/Mismatch Risk ................................. 15-63 Using Interest Rate Swaps to Manage Basis Risk ........................ 15-64 Exhibit 15.22: Comparison of the Prime Rate and Six-Month CD Rates ................................................................ 15-65 Exhibit 15.23: Prime/CD Spread Risk Position ....................... 15-66 Exhibit 15.24: Using a Prime/CD Basis Swap to Hedge Risk ........................................................................................... 15-66 Exhibit 15.25: Illustration of How a Basis Swap Locks in a Spread ....................................................................................... 15-67 Exhibit 15.26: Illustration of How a Prime/CD Basis Swap Hedges Basis Risk .................................................................... 15-67 Using Options to Manage Basis Risk ........................................... 15-68 Exhibit 15.27: Illustration of Cash Flows from a 4 Percent LIBOR Cap .............................................................................. 15-69 Exhibit 15.28: Illustration of Cash Flows from a 6.50 Percent Prime Cap .................................................................... 15-69 Exhibit 15.29: Illustration of How a Prime/CD Basis Swap Hedges Basis Risk .................................................................... 15-70 Using Swaps to Manage Yield Curve Risk .................................. 15-71 Using Caps and Floors to Manage Option Risk ........................... 15-72 Adjusting for Reality ................ 15-72 Hedging in an Imperfect World Using Broker/Dealers for Derivatives Transactions ..................... 15-76 Managing Risks of OE-Balance Sheet Derivative Hedges .............. 15-77 Credit Risk .................................................................................... 15-77 Liquidity Risk ............................................................................... 15-78 Transaction or Operational Risk ................................................... 15-80 Compliance Risk .......................................................................... 15-81 Legal Risk ..................................................................................... 15-81 Derivatives Disclosure Requirements .............................................. 15-81 Requirements of FAS 107 and FAS 119 ...................................... 15-82 Required Disclosures ................................................................ 15-83 Disclosures That Banks Are Encouraged to Make ................... 15-85 Hedge Accounting Requirements Under FAS 133........................... 15-86 Applicability of Hedge Accounting .............................................. 15-87 The Simple Essence of the Complex Accounting .................... 15-91 Fair Value Hedges ........................................................................ 15-91 Cash Flow Hedges ........................................................................ 15-94

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xli

Interest Rate Risk Management

Accounting for Gains and Losses for Fair Value Hedges ........ 15-95 Hedge Effectiveness ..................................................................... 15-96 Establishing the Method to Be Used ........................................ 15-98 Assessing the Effectiveness of Fair Value Hedges .................. 15-98 Assessing the Effectiveness of Cash Flow Hedges .................. 15-99 A Shortcut Method for Swap Hedges ........................................... 15-99 Hedging Portfolios of Similar Items ........................................... 15-100 Derivatives Disclosure Requirements ........................................ 15-101 Hedge Accounting Summary ...................................................... 15-102 Exhibit 15.30: FAS 133 Hedge Accounting Requirements... 15-103 Summary ........................................................................................ 15-105

IRR IN CONTEXT

Chapter 16 Perspectives Interest Rate Risk in a Nutshell .......................................................... 16-2 What Are the Drivers of Interest Rate Risk? .................................. 16-2 How Much Risk Do We Have? ...................................................... 164 How Much Risk Are We Willing to Accept? ................................. 16-5 What Are We Willing to Do to Lessen Exposure? ......................... 16-6 What Constraints on Action Does the Bank Have? ........................ 16-6 What Degrees of Freedom for Action Does the Bank Have? ......... 16-7 Interdependencies: Rate Risk Does Not Stand Apart ......................... 16-7 IR and Earnings ........................................................................... 16-8 Exhibit 16.1: Mismatch or Gap Profits....................................... 16-9 Exhibit 16.2: Option Profits ..................................................... 16-10 Another Issue for Banks Using Funds Transfer Pricing........... IRR Management and the Timing of Earnings......................... The Impact of GAAP Accounting Rules .................................. IR and Credit Risk ..................................................................... IR and Liquidity Risk.................................................................

xiii

16-11 16-11 16-12 16-13 16~15

Contents

Exhibit 16.3: Rate Sensitivity of Asset Cash Flows for a Sample Bank ............................................................................ Exhibit 16.4: Influences of Discretionary Cash Flows ............. Exhibit 16.5: The Dynamics of Interest Rate Changes on Liquidity Risk and Interest Rate Risk ...................................... IR and Capital ............................................................................ IR and Strategic Planning .......................................................... IRR and Multinational Banks ....................................................... IR and Bank Holding Companies .............................................. Focus on the Big Picture................................................................... Exhibit 16.6: Interest Rate Risk Measurement and

16-17 16-18 16-19 16-20 16-20 16-20 16-21 16-22

Management ............................................................................. 16-24 It’s About Management ................................................................ 16-26

Glossary

xliii

Interest Rate Risk Manage_ment

Chapter 1 An Interest Rate Risk Management Overview

Risk and Financial Institutions ............................................................. [-1 What Is Risk? ................................................................................... 1-1 Types of Risk .................................................................................... 1-2 Credit Risk .................................................................................... 1-2 Liquidity Risk............................................................................... [-3 Interest Rate Risk ......................................................................... 1-3 Operations Risk ............................................................................ 1-4 Legal Risk .................................................................................... 1—4 Reputation Risk ............................................................................ [-4 Exhibit 1.1: Risks Inherent in the Business of Banking as Seen by the Federal Reserve ........................................................ 1-5 Exhibit 1.2: Risks Inherent in the Business of Banking as Seen by the Comptroller of the Currency ..................................... 1-5 What Is Interest Rate Risk Management? ........................................ l-5 The Focus Is on Interest Rate Risk/Market Risk .......................... [-6 Interest Rate/Market Risk Is Neither Simple nor Undifferentiated............................................................................ l -7 Primary Components of Interest Rate Risk ...................................... 1-7 Repricing Risk .............................................................................. 1-7 Basis Risk ..................................................................................... 1-8 Yield Curve Risk ........................................................................ l-ll Option Risk ................................................................................ 1-12 Secondary Components of Interest Rate Risk ................................ 1- 12 Exhibit 1.3: Estimated Components of Interest Rate Risk for a Typical Bank When Interest Rate Volatility Is Low .......... 1-13 Exhibit 1.4: Estimated Components of Interest Rate Risk for a Typical Bank When Interest Rate Volatility Is High ......... 1-13 Measurement Risk ...................................................................... 1-13 Reporting Risk............................................................................ 1-15 People Risk ................................................................................. l-15 Decision Process Risk ................................................................ 1-15 Summary of Interest Rate Risk Components .................................. 1-15 Managing Interest Rate Risk .............................................................. 1-16

Interest Rate Risk Manggement

Exhibit 1.5: Interest Rate Risk and Its Components ................... Unavoidability of Interest Rate Risk .............................................. The Relative Importance of Interest Rate Risk............................... Effect on Credit and Liquidity Risks .............................................. Effect on Profitability ..................................................................... Measuring, Monitoring, and Controlling Interest Rate Risk .......... Elements and Structure of Asset and Liability Management ............. Information Requirements .............................................................. Management Committee ................................................................. IRR Management Policy ................................................................ Role of Bank’s Treasury Department .............................................

1-17 l-18

1-19

1-20 1-21 1-22 1-23 1-24 1-25 1-25 1-26

Chapter 1 An Interest Rate Risk Management Overview

What exactly is risk? What exactly is interest rate risk? How much interest rate risk does the bank have? Is it too much? If it is too much, how do we decrease it? How much does it cost to reduce the exposure? Do we profit from the risk exposure? If so, is the amount of profit worth the risk? It is noteworthy that it is difficult to give a single, short, simple answer to any one of these questions. Indeed, that very difficulty is a topic that underlies some of the key issues that are considered in this book.

RISK AND FINANCIAL INSTITUTIONS What Is Risk?

Risk. The term has always been used somewhat casually to mean the chance that events will not unfold the way we expect. Every banker knows what that means. If we make a loan, there is some risk that the borrower will not pay us back. We call that credit risk. Many events, including changes in prevailing interest rates, can have more than one potential outcome. The future is uncertain. But risk is not the same as uncertainty. Some uncertain outcomes are risky while others are not. Risk is the possibility that an uncertain outcome or event might have an undesirable consequence. In the extreme, the most undesirable consequence is bank failure. Of course, bank failure is just one possible undesirable consequence and not all possibilities are equally probable. Banks, thrills, and credit unions are primarily financial intermediaries. Banks — and we use this term to describe all financial intermediaries rent money from depositors who want it back on demand or at maturity dates rarely more than a few years in the future. Bankers then lend or invest that money in a variety of assets with maturities as long as 30

—

years. Economists call the latter activity “maturity transformation." In the process of performing these basic functions, a bank takes credit risk

Interest Rate Risk Management

because it has an obligation to repay the depositors regardless of whether or not its own loans are repaid. The maturity transformation process exposes banks to liquidity risk. Also, banks accept interest rate risk because the timing and size of changes in the rates that they receive from their assets rarely match the timing and size of rate changes for their liabilities.

In other words, what we have just defined as credit risk, liquidity risk, and interest rate risk are inherent in the core economic function of banks as financial intermediaries. And, while those are ofien seen as the three most important risks, they are not the only risks faced by financial institutions.

Types of Risk Inconveniently, different observers tend to define and name the risks inherent in the business of banking somewhat differently.

In fact, as summarized in Exhibits 1.1 and 1.2, for risk-based examination purposes, the Federal Reserve Board of Governors has defined six risks while the Office of the Comptroller of the Currency (OCC) has defined nine risks. The Federal Reserve definitions are more concise and are summarized below together with a few comments explaining how they relate to the OCC’s definitions:l

Credit Risk The risk to earnings or capital that, in the words of the Federal Reserve, “arises from the potential that a borrower or counterparty will fail to perform on an obligation." Usually, but not always, the obligation in question is a requirement to make interest or principal payments. Sometimes called default risk, the failure to make required payments

I.

All quotations of Federal Reserve definitions are taken from page 1 of “Federal Reserve Guidelines for Rating Risk Management at State Member Banks and Bank Holding Companies,“ an attachment to Federal Reserve publication SR 95-51 (SUP), November 14. 1995. All quotations of OCC definitions are taken from pages 18 through 22 of the “Bank Supervision Process" booklet in the Comptroller ': Handbook, April 1996.

I-2

An Interest Rate Risk Muggernent Overview

reduces the value of equity securities, debt securities, and loans. In the

extreme, credit defaults eliminate all or almost all of the value in loans or

securities. Both the OCC and the Federal Reserve list credit risk as one of their defined risk types for risk-based examinations. The OCC definition is almost exactly the same as the Federal Reserve definition quoted above. Credit risk exposure is found in all activities where success depends on the performance of a counterparty, issuer, or borrower. Credit risk arises any time a financial institution extends, commits, invests, or otherwise exposes its funds through actual or implied contractual agreements, whether reflected on or off the balance sheet. Liquidity Risk

Liquidity risk is the risk that not enough cash will be generated from either assets or liabilities to meet deposit withdrawals or contractual loan fundings. The Federal Reserve uses a broad definition: “... the potential that an institution will be unable to meet its obligations as they come due because of an inability to liquidate assets or obtain adequate funding (referred to as ‘funding liquidity risk’), or that it cannot easily unwind or offset specific exposures without significantly lowering market prices because of inadequate market depth or market disruptions (‘market liquidity risk.’).” The OCC defines liquidity risk as “... the risk to earnings and capital arising from a bank's inability to meet its obligations when they become due, without incuning unacceptable losses.” Interest Rate Risk

Interest rate risk (IR) is the risk that changes in prevailing interest rates will adversely affect assets, liabilities, capital, income, and/or expense at different times or in different amounts. In a nutshell, it is the potential of a reduction in earnings and/or capital caused by changes in market rates of interest. The Federal Reserve calls this market risk and defines it as “... the risk to a financial institution’s condition resulting from adverse movements in market rates or prices, such as interest rates, foreign exchange rates or equity prices.” Within that definition, the Federal Reserve clearly views interest rate risk as just one component of market risk. The OCC definition of interest rate risk is “... the risk to earnings or

Interest Rate Risk Management

capital arising from movements in interest rates.” The OCC definition is a bit narrower than the Federal Reserve definition since it defines “price” risk as a separate risk. The OCC defines price risk as “... the risk to earnings or capital arising from adverse changes in the value of portfolios of financial instruments.” Since such adverse changes generally result from changes in prevailing interest rates, price risk is essentially the same as interest rate risk. In this manual, we will consistently use the term “interest rate risk" in the broader sense, as defined in the first sentence of this paragraph.

Operations Risk Operations risk is the risk that errors made in the course of conducting business will result in losses. The Federal, Reserve call this “operational risk” and defines it with specific details: “Operational risk arises from the potential that inadequate information systems, operational problems, breaches in internal controls, fraud, or unforeseen catastrophes will result in unexpected losses." The OCC calls this “transaction risk" and defines it as “... the risk to earnings or capital from problems with service or product delivery.”

Legal Risk The risk arising “from the potential that unenforceable contracts, lawsuits or adverse judgments can disrupt or otherwise negatively affect the operations or the condition of a banking organization." The OCC uses a slightly narrower definition for what it calls “compliance risk." They define compliance risk as “. .. the risk to earnings or capital arising from violations of, or nonconfonnance with, laws, rules, regulations, prescribed practices, or ethical standards.”

Reputation Risk

This is the risk to camings or capital arising from, in the words of the Federal Reserve, the possibility “that negative publicity regarding the institution’s business practices, whether true or not, will cause a decline in its customer base, trigger costly litigation, or result in revenue reductions.” The Federal Reserve and the OCC define reputation risk in almost exactly the same way.

An Interest Rate Risk Management Overview

Exhibit 1.1 Risks Inherent in the Business of Banking as Seen by the Federal Reserve

∙∙∙ ∙∙∙

Six Risks Defined by the Federal Reserve

Credit risk Liquidity risk Market risk

Operational risk Legal risk

Reputation risk

Exhibit 1.2 Risks Inherent in the Business of Banking as Seen by the Comptroller of the Currency

∙∙ ∙∙ ∙

∙∙ ∙

∙

Nine Risks Defined by the OCC Credit risk

Liquidity risk Interest rate risk Price risk

Foreign exchange risk Transaction risk

Compliance risk

Strategic risk Reputation risk

What Is Interest Rate Risk Management?

Clearly, each of the risks surrunarized in the preceding paragraphs is a topic in its own right. Credit risk alone is the subject of numerous books, articles, courses, and commentary. Each risk deserves and receives

Interest Rate Risk Management

focused attention. Well run financial institutions have separate policies for credit risk, liquidity risk, and interest rate risk. (Although these policies sometimes have different names. For example, credit risk may be addressed in a “loan" policy since lending is the main source of credit risk for most banks.) More importantly, well-run financial institutions have procedures for monitoring the most important risks and limits on how much risk they are willing to hold.

Unfortunately, risk management cannot be entirely segmented. In this and later chapters of this manual, we will discuss how risks interrelate. As we will see, some bank activities transfonn one type of risk into another. And, as we will also discuss, management of exposures to different types of risk often requires coordination.

Conceptually, asset/liability management (ALM) is simply the name we use to describe the coordinated management of all of the financial risks inherent in the business of banking. In other words, ALM is the process of balancing the management of separate types of financial risk to achieve desired objectives while operating within predetermined, prudent risk limits. Accomplishing that task requires coordinated management of assets, liabilities, capital and off-balance sheet positions. Therefore, in the broadest sense of the term, ALM is simply the harmonious management of cash, loans, investments, fixed assets, deposits, short-term borrowings, long-term borrowings, capital, and offbalance sheet commitments. This is clearly one of the most important responsibilities for senior managers. But it is not a simple task. Asset/liability managers must help defme rate risk management goals, measure rate risk exposures, evaluate rate risk exposures, recommend strategies and actions that help achieve bank goals, help implement approved rate risk management strategies, and help evaluate the effectiveness of prior rate risk management activities.

The Focus Is on Interest Rate Risk/Market Risk Notice that we prefaced the definition of ALM with the word “conceptually." The truth is that ALM is oflen used to define or describe something more narrow. Sometimes, it is used as a synonym for interest rate risk management. Sometimes, it refers to only the measurement and management of interest rate risk and liquidity risk. Sometimes, it is used

An Interest Rate Risk Mamement Overview

to describe the management of assets such as investment securities and liabilities. An example of this is borrowings that we might describe as noncustomer driven.

In this manual, we will only refer to credit risk incidentally in the course of our discussions. Credit risk largely, but not entirely, stands alone. Furthermore, credit risk deserves and receives separate treatment in separate manuals. We will also give little, if any attention, to strategic and reputation risks. Our focus is mainly on interest rate risk. Interest Rate/Market Risk Is Neither Simple nor Undifl’erentiated Resist the temptation to rush into the measurement of rate risk exposures on your balance sheet and then immediately undertake some actions to alter that apparent risk exposure. It is far too easy to miss key elements of your rate risk exposure and therefore measure your rate risk

incorrectly.

In the following paragraphs, we begin to examine the complexity of interest rate risk by defining and explaining four primary and four secondary components, or segments, of interest rate risk. In Chapter 2, we will explore two completely different frameworks for viewing rate risk. Following those discussions, Chapters 3 through 11 will take an indeptlr look at how we can measure and monitor rate risk exposures.

Primary Components of Interest Rate Risk Interest rate risk has various sources; it is not simply the risk from rates rising or falling. In fact, we can identify four sources of interest rate risk:

Repricing Risk The risk of rates moving up or down; also called duration, gap, or mismatch risk. Repricing risk is the most familiar form of interest rate risk. It is the risk of adverse consequence from a change in interest rates that arises because of differences in the timing of when those interest rate changes affect an institution's assets and liabilities. For example, if a bank makes a five-year fixed-rate loan that is funded by a six-month certificate of deposit (CD), it exposes itself to repricing risk every six months when the cost of funds for the CD resets while the yield on the

I-7

Interest Rate Risk Management

loan remains fixed. Essentially, mismatch risk is caused by either borrowing short term to fund long-term assets or by borrowing long term to fund short-term assets. The former causes trouble when rates rise, the latter when rates fall. As discussed in later chapters, mismatches exist in the current balance sheet as a result of historical transactions not yet matured. At the same time, mismatches are also created in current transactions from the maturity of historical business and from new business. It is commonly assumed that almost all IRR takes the form of mismatch risk. This can be a serious misconception. As discussed below, other types of interest rate risk also are very important. When interest rates are volatile, mismatch risk may represent 80 or 90 percent of total rate risk. However, in periods such as the second half of 2004 and most of 2005, when short-term rates rose slowly while long-term rates remained essentially flat, it is likely that less than half of all interest rate risk results from yield curve or mismatch risk. Basis Risk

The risk of rates for some instruments changing more or less than rates other instruments. Basis risk is the risk of adverse consequence resulting from unequal changes in the difference —— the spread — between two or more rates for different instrtrrnents with the same maturity. Banks, especially consumer-oriented banks, typically incur basis risk because the rates paid on their liabilities are determined differently than the rates received from their assets. The interest expense for liability instruments such as CDs rarely changes by the same amount as interest income received from loans or investments.

for

Basis risk can be illustrated with an example. Suppose that Sample State Bank makes an adjustable-rate residential mortgage loan. The loan rate changes, or resets, annually to be 170 basis points over the one-year US. Treasury security rate. The initial loan rate is 8 percent. Now suppose that the bank funds this loan with a one-year CD issued on the same day the loan is funded. The initial CD rate is 6 percent. Further suppose that the bank is able to renew the one-year CD each year for the life of the mortgage at the then-prevailing CD rate. In this example, Sample State Bank has no repricing or mismatch risk from this transaction since both the asset and liability reprice annually. (To keep things simple, we are 1-8

An Interest Rate Risk Management Overview

ignoring that loan payments change the size of the mortgage asset during the course of each year while the size of the CD remains the same.) While there is no repricing risk, Sample State Bank does have basis risk. In some years, the one-year Treasury rate may increase by a larger amount than increases in CD rates or may decrease by a smaller amount than decreases in CD rates. For example, in year two, the Treasury rate is 100 basis points higher, but the CD rate is only 90 basis points higher, so the first year spread of 200 basis points (8 percent minus 6 percent) widens to 210 basis points (9 percent minus 6.90 percent). In years when these two types of changes occur, Sample State Bank will enjoy a fatter spread than it had contemplated when the transactions were first made. On the other hand, in some years, the change in the one-year Treasury rate may increases by less than the increases in one-year CD rates or may decrease by more than the declines in one-year CD rates. When this is the case, Sample State Bank will suffer from smaller spreads than it contemplated when the transactions were first made. For example, in year three, the Treasury rates fall by 120 basis points while the CD rates fall by only 100 basis points. As a result, the loan rate falls from 9 percent to 7.80 percent, but the CD rate only falls from 6.90 percent to 5.90 percent. Thus, in year three, the 190 basis point spread is 10 basis points smaller than the original spread. What causes basis risk? Or, in other words, why do spread relationships change? Rate risk analysts and managers need to consider three distinct causes:

∙

∙

First, rates for some instruments, for example, Treasury and LIBOR rates, are very sensitive to changes in the supply and demand for those instruments in actively traded markets. On the other hand, rates for other instrtunents, such as bank savings accounts, are relatively insensitive to changes in markets. As we will discuss in Chapter 6, savings and other bank core deposit rates tend to change by smaller amounts and with time lags.

Second, spreads change as credit risk perceptions change. When

investors are not particularly worried about potential defaults, rates for instruments with credit risk, such as corporate and municipal bonds, tend to be at small spreads over risk-free Treasury rates. On the other hand, when market investors are more

Interest Rate Risk Management

∙

concerned about default risk, spreads widen to reflect credit risk premiums. For example, in the late summer and fall of 1998, capital markets were roiled by the near failure of a heavily indebted hedge fund and the collapse of the Russian ruble. During a four-month period from July through October, one-year Treasury yields fell by about 120 basis points. At the same time, yields for Baa corporate securities rose by about 3 basis points. Few examples illustrate basis risk better. Third, banks face basis risk during periods when rates are low simply because of rate compression. Rates paid for deposits are never going to be negative. Thus, when NOW or savings rates fall to low levels, they become less sensitive to additional rate reductions. In other words, if savings rates are currently 5 percent and prevailing market rates fall by 100 basis points, experience tells us that we might expect savings rates to fall by 20 or 25 percent basis points. But if savings rates are currently 2 percent and prevailing market rates fall by 100 basis points, experience tells us that we might expect savings rates to fall by 0 to 15 basis points. Low core deposit rates tend to reduce sensitivity. Clearly, each of these three sources of basis risk are important to different

degrees, depending upon the rate being considered and upon prevailing circumstances. Therefore, an understanding of which of these causes may be driving basis risk in a particular situation can be helpful.

Basis risk is not trivial. In fact, basis risk typically comprises an estimated 2 to 50 percent of the losses to earnings or capital from typical changes in interest rates. This very wide range in the estimated importance of basis risk is attributable to two factors. First, the relative impact is considerably smaller during periods when interest rates change by very large amounts. For this reason, it is unfortunate that most of the attention given to IR in most banks — both by those who measure it and those who manage it is devoted to repricing or mismatch risk. Second, basis risk is much larger in some banks, especially retail banks, than in others.

—

Unfortunately, one of the most common tools used to measure interest rate risk in smaller financial institutions gap analysis — does not

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I-lO

An Interest Rate Risk Management Overview

readily capture basis risk. Regulators are increasingly focusing on basis risk, however. Yield Curve Risk The risk of short-term rates changing by more or less than the change in long-term rates. Also called yield curve twist risk, yield curve risk is the risk of adverse consequences resulting from unequal changes in the spread between two or more rates for different maturities for the same instrument. For example, when prevailing interest rates fall, the rates for one-year Treasury notes may fall by a larger amount than the change in the rates for five-year Treasury notes. (Short-term rates are often more volatile than intermediate- and long-term rates.) This is different from basis risk, which results when rates are different for different instruments of the same maturity.

We can better envision yield curve twist risk by considering an example. Suppose that the Not As Savvy As It Thinks (NASAIT) Bank makes a floating-rate mortgage loan. The loan rate resets monthly based on the one-year Treasury rate. NASAIT Bank wants to avoid both mismatch risk and basis risk, so it match-fitnds this loan with a floating-rate CD that pays interest based on the one-month Treasury rate. The bank in this example is not as savvy as it thinks because it is still exposed to interest rate risk from unequal changes in the one-month and one-year Treasury rates. If prevailing rates rise but one-year rates increase by more than one-month rates, the bank's spread from this transaction increases. Similarly, if prevailing rates rise but one-year rates change by less than the change in one-month rates, the bank’s spread from this transaction

decreases.

Studies of yield changes indicate that, for noncallable, US. Treasury obligations, as much as 85 to 90 percent of the weekly changes in yields are attributable to changes in the shape of the yield curve, while only 15 to 20 percent of the weekly changes are attributable to changes in the overall level of prevailing rates. Of course, those numbers ignore basis risk, because they only apply to Treasury securities, and they ignore option risk, because they are based on changes in noncallable securities. For a bank as a whole, yield curve twist risk is estimated to comprise 5 to 10 percent of total interest rate risk.

Interest Rate Risk Management

Option Risk

The risk that rate changes prompt changes in the amount or maturity of instruments. Technically, embedded options are put or call options given or sold to holders of financial insu'uments. In banking, these are more familiarly known as borrower options to prepay loans and depositor options to make deposits, withdrawals, and early redemptions. Option risk arises whenever bank products give customers the right, but not the obligation, to alter the quantity or the timing of cash flows. The risk of embedded options can be seen in residential mortgages. Most bank residential mortgage loans give borrowers the right to prepay the loans in whole or in part at any time. These loans prepay rapidly during periods when prevailing interest rates have fallen below loan rates. When prevailing interest rates have risen above loan rates, these loans prepay very slowly, if at all. (Embedded options are further discussed in Chapters 2, 6, and 7.) Option risk is not an insignificant component of IR either. Embedded option risk is estimated to comprise 20 to 25 percent of all interest rate risk in average banks. However, the relative

impact of option risk is probably much larger for banks with large consumer loan and deposit portfolios. Losses resulting from option risk are also larger during periods when changes in prevailing interest rates are large.

The approximate distribution of these primary sources of interest rate risk can be seen in Exhibits 1.3 and 1.4. Secondary Components of Interest Rate Risk The primary components of interest rate risk are not the only sources of rate risk. Interest rate risk must be managed and controlled. To do this, you must first measure and report it. The process of managing interest measurement rate risk entails its own risks. There are four such risks risk, reporting risk, people risk, and decision process risk. We call these “secondary” sources of interest rate risk. Secondary IRR arises from a number of different bank activities. These risks are discussed in the

—

following paragraphs.

An Interest Rate Risk Management Overview

Exhibit 1.3 Estimated Components of Interest Rate Risk for a Typical Bank When Interest Rate Volatility Is Low

∙ OPea'

3k.

∙

Exhibit 1.4 Estimated Components ofInterest Rate Risk for a Typical Bank When Interest Rate Volatility Is High 20%

45%

10% Beasts RISK

−

Il/Ieasurement Risk

To monitor, control, and manage risk, you must accurately measure it. There are three types of measurement risk: model risk, raw data risk, and assumption risk.

I-l3

Interest Rate Risk Management

Model risk. Models are used to measure the magnitude and direction of adverse consequences expected to result from changes in prevailing interest rates. If these models are wrong, then the measurement of risk will be wrong. This, in turn, could lead to incorrect decisions. For example, if a model predicts that earnings will increase when rates go down, but earnings actually decrease, your actions may increase rather than decrease risk.

We can illustrate model risk with the following example: Suppose you use your model to measure your bank’s exposure to changes in prevailing rates and find that net interest income will be lower if interest rates rise and higher if rates decline. To offset this risk, you sell longtenn US. Treasury bonds. The sale proceeds are used to reduce borrowing of overnight fed funds. Then firrther suppose that interest rates subsequently drop, but your model‘s measurements were wrong and earnings fall instead of rising as expected. You should have kept the Treasury bonds to add more income after the fall in interest rates. In this case, mis-measurement of interest rate risk resulted in the wrong decision to sell Treasury bonds. This decision exacerbated risk and ultimately resulted in lower earnings. Raw data risk. Any incorrect input to a model will, of course, yield incorrect output. For example, the wrong maturity schedule for CDs will result in incorrect measurements of interest rate risk. It is important to periodically scrub, or assess the integrity of, database applications. Acceptable procedures include sampling comparisons of system data with loan or deposit documents, regular reconciliation of systems data to the general ledger, and tracking (with follow-up research when necessary) of summary data statistics to spot material changes in the reported data from prior periods. Assumption risk. Incorrect assumptions will also yield incorrect measures. You must, for example, make assumptions about the amount of new loan and deposit business, the characteristics of that business (fixed vs. variable), the term of that business, the amount of long-term, low-rate core deposits on the books, and the sensitivity of money market deposit rates to changes in the fed funds rate. Measurements of risk can be highly sensitive to these assumptions. For example, a 1 percentage

An Interest Rate Risk Management Overview

point error in the effect of rising interest rates on money market deposit balances could result in very material error in risk measurement. Reporting Risk

Incorrect reporting, through error or fraud, of information used to make decisions will result in suboptimal decisions.'Decision makers, typically the asset/liability management committee (ALCO), will rely on risk measurements as reported. These reports must not only be correct but also clearly understood by the users. Regarding reporting, providing a clear understanding of the risk position is just as important as providing correct information. Failure to do so will stall, if not paralyze, decision making.

People Risk Models, assumptions, and techniques aside, it is people who manage and measure risk. Not surprisingly, those with insufficient skills will not perform these activities effectively. Turnover will interfere with risk measurement and management if knowledgeable employees are not ready to succeed departing personnel. During an exam, regulators will assess the caliber of personnel assigned to running the models, measuring the risk, evaluating hedging strategies, and performing other activities related to interest rate risk.

Decision Process Risk Risk management decisions must be timely, executed quickly, and use all available information. A decision process that fails to support these objectives will result in suboptimal risk management activities. Failure to use all available information or to consider the firll range of possible outcomes could result in certain risks being identified, measured, and monitored, but not controlled.

Summary of Interest Rate Risk Components The effects of interest rate changes are complex. The amount and timing of rate changes impacts mismatch risk. Differences between changes in short- and long-term rates (yield curve risk) impact the bank's risk exposure. Varying amounts of change in different interest rates (basis

l-lS

Interest Rate Risk Manament

risk) impacts the bank risk exposure. And the influence of rate changes on customer decisions to prepay loans, add funds to savings accounts, draw down on loan commitments or withdraw funds has a huge impact. In other words, the bank’s rate risk exposure is not simply driven by four or eight types of changes. The types of changes are interdependent. Furthermore, the timing of their impact can ebb, flow, and overlap. Rather than viewing these risk components as separate risk pools, we should view them as a single risk pool whose level is constantly churned

by eight different influences.

Exhibit 1.5 summarizes the major sources of primary and secondary risks that comprise interest rate risk.

MANAGING INTEREST RATE RISK

In the broadest sense, asset/liability management is about administering all of a bank’s assets, liabilities, and off-balance sheet claims in ways that govem elements of the bank’s credit risk, IR, and liquidity risk on behalf of meeting the bank’s goals. In reality, however, both the focus and the practice of asset/liability management is primarily the management of IR. And-thus, this manual is mainly about managing IRR.

Before tackling the subject, you should put it in perspective. The following four important observations will help keep IRR in perspective:

∙ ∙

∙ ∙

IR is unavoidable. IR is usually the least risky of the risks banks take in their roles as financial intermediaries. IRR, while separate from credit risk and liquidity risk, has interdependent causes and consequences.

Acceptance of large IRR exposures is not essential to a bank's profitability.

I-l6

An Interest Rate Risk ManflLement Overview

Exhiblt 1.5 Interest Rate Risk and Its Components Risk Interest Rate Risk

Primary Risk 1. Repricing 2.

Basis

3.

Yield Curve

4.

Option

Secondary Risk 1.

Measurement

∙

Model

∙

Assumption

∙

Raw Data

2.

Reporting

3.

People

4.

Decision Process

Definition

The risk of adverse consequences resulting from changes in prevailing interest rates Risk that directly affects the bottom line

The risk resulting from differences between the timing of rate changes The risk from unexpected changes in the spread between two or more different rates The risk from unexpected changes in the spread between two or more rates of different maturities The risk of adverse consequences fi’om customer decisions to exercise options in products, such as the option to prepay a loan Risk that errors in the interest rate risk management process result in less than optimal decisions The risk of suboptimal decisions resulting from incorrectly measuring the amount of interest rate risk The risk of incorrectly measuring the amount of interest rate risk due to inaccurate interest rate risk models The risk of entering incorrect data in the interest rate risk models The risk of using incorrect assumptions in the interest rate risk models The risk of incorrect reporting of interest rate risk The risk of insufficient skills and expertise in the employees responsible for managing interest rate risk The risk of untimely, slowly executed, and/or improperly communicated decisions that fail to use all the available information

Source: Adapted from Risk Management for Banks: A Guide Compliance (Sheshunofl‘. I996).

l-l7

to

Regulatory

Interest Rate Risk Management

Unavoidability of Interest Rate Risk As a financial intermediary, a bank accepts credit risk, liquidity risk, and IRR as the vital essence of the economic function it provides. Accepting these risks is standard. As the Federal Reserve notes in its Commercial Bank Examination Manual: “Accepting this risk is a normal part of bankin and can be an important source of profitability and shareholder value." This could be considered the banking industry’s contribution to the economy. In fact, these risks cannot be eliminated without. eliminating the need for banks. Throughout much of the 19805 and early 19905, US. money center banks experienced a variety of serious problems. To a great degree, the underlying roots of those problems stem from major US. and international businesses finding ways to manage credit risk, liquidity risk, and IRR without banks. Disintennediation — the process by which banks lose some financial intermediary business — is the result.

The first important issue is that IRR is unavoidable because it is inherent in banking. As long as banks have assets that are not identical to their liabilities, they will have IRR. While innovations in products and rate risk management have created opportunities to reduce rate risk exposure, the risks have not been managed away entirely. Interest rate risk is a major and inseparable part of their business. They cannot avoid it. In fact, changes affecting the financial industry over the past several decades have increased the amount of IR that bankers must manage. Chief among these are the development of liability management in the 19605, the significant increase in interest rate volatility experienced since the mid-19705, and the explosive growth in new financial products, such as mortgage-backed derivative securities, in the 19805. Moreover, not just the quantity of IR has increased but the complexity of IRR management as well. Deregulation, the development of new financial tools for measuring IRR, and the increase in financial products available to manage it all make controlling IRR much more complicated.

2.

Interest Rate Risk Management, Section 4090.1, Commercial Bank Examination Manual, Federal Reserve Board of Governors, November 1996, page I.

l-lB

An Interest Rate Risk ManaE‘nent Overview

Effective management of IRR is both more difficult and more important than it used to be. The Relative Importance of Interest Rate Risk

Another very important issue is that IRR is not the most threatening risk to which banks are exposed in their capacity as financial intermediaries. Far fewer bank failures result from IRR than from other problems. In 1992, one major money center bank estimated that 85 percent of banking risk arose from credit risk, 10 percent from operational risk, and only 5 percent from IRR. A 1991 Federal Reserve Bank staff article pointed out that:

[T]he more than 1,200 bank failures in the past decade demonstrate that the principal risk to commercial banks is credit risk. Although other risks −− such as operating risk, foreign can prove costly and must be exchange risk, and IR controlled, they are dominated in most cases by the threat of credit losses on loans. This situation could change, of course, as the nature of banking evolves. Indeed, even in the past, interest rate movements have produced significant losses at some banks and have caused others to increase risk in other areas to offset problems caused by rate movements.3

—

A more recent comment published by the OCC confirms that regulators continue to view credit risk as more important than interest rate risk: ...credit risk traditionally has been, and continues to be, considered the most significant risk. However, changes in the structure of bank balance sheets and the use of more complex on- and off-balance sheet products to manage interest rate risk exposures has increased the importance of interest rate risk.(sic)‘

3. 4.

J.V. Houpt, and J.A. Embersit, “A Method for Evaluating Interest Rate Risk in U.S. Commercial Banks," Federal Reserve Bulletin. August l99l, page 628. OCC, Questions and Answers for Advisory Letter 95-]: Interest Rate Risk, June 20, 1995. page 2.

l-l9

Interest Rate Risk Management

As banks change practices to cope with disintermediation and other pressures affecting their profitability, new products and services are becoming more widespread. Some of the changes involve alterations in traditional loan and deposit products that give customers more options. Other changes involve adding complex, option-laden securities to investment portfolios. Even though credit risk remains more important, both of these types of changes support the OCC opinion that the importance of IR is growing. Effect on Credit and Liquidity Risks

Although credit risk and liquidity risk are separate topics, they both are related to IR. Changes in credit risk, liquidity risk, and IR can have interdependent causes and consequences. Bankers even transform IRR into credit risk. For example, a bank can shift the exposure to interest rate changes from its own balance sheet to a borrower‘s balance sheet by giving a borrower with steady cash flow a floating-rate loan instead of a fixed-rate loan. In doing so, the banker has reduced IRR, but increased credit risk. (The bank in this example reduces its IRR if having a floating-rate loan does the better job of matching the timing of interest rate changes in its sources of funds with the repricing of a floating-rate loan. Credit risk is increased in this example because the borrower assumes the risk of maintaining income sufficient to make loan interest payments that increase as rates rise.) Furthermore, controlling IRR often involves administering certain variables, such as:

∙

∙ ∙

∙ ∙

Interest rates offered on deposits Interest rates charged on loans Acceptance of credit risk

Mix between loans and investments Composition of loan and investment portfolios

Management of these variables clearly affects not only IRR, but also liquidity and credit risk. Thus, while IR is the primary focus of

l-20

An Interest Rate Risk Management Overview

asset/liability management, it cannot be examined in isolation. This manual considers the interplay between IR and credit risk, liquidity, capital, and other management issues. Effect on Profitability

To keep our understanding of IR in perspective, we must make one final, critical observation. Many observers correctly point out that interest rate risk is inherent in banking, but then proceed to the false conclusion that financial institutions cannot make money unless they take significant IRR. Neither the past experiences of banks nor economic analysis supports such a conclusion. Many banks have remained profitable with only modest exposures to IR, while many others have suffered grievous losses from excessive exposures. There is no economic justification for banks to take large amounts of IRR. Any investor who wants to speculate on interest rates could do so far more efficiently than by buying bank stocks.

While we recognize that IR is inescapable, it is important to avoid the mistake of drinking that accepting large IRR exposures is essential to a bank’s profitability. This might be true if bankers could predict future interest rates with perfect accuracy, but obviously they cannot.

Traditionally, bankers have been able to profit from what amounts to making bets on future rate changes. Sometimes called “positioning” or, less often, “interest cycle management,” this is the practice of changing a bank's balance sheet to take advantage of expected changes in interest rates. For example, if interest rates are historically high, bank managers might buy more long-tenn, fixed-rate investments to lock in higher yields. It is important not to confuse moderate and well-managed exposures to interest rate risk with imprudent rate speculation. In periods when interest rates are highly volatile, large exposure to interest rate fluctuations is a proven recipe for disaster. Attempts to earn large profits from expected changes in market rates led to large losses at First Chicago and First Pennsylvania in the 19705 and at First Bank Systems in the 19805. Aggressive positioning typically needs to be restricted to securities trading accounts, but even then it must be prudently managed.

l-2l

Interest Rate Risk Management

Attempting to profit from interest rate changes is further discussed in Chapter [3. That chapter also addresses appropriate size limits for interest rate risk positions as well as essential policy and management controls. Chapters 14 and 15 include in—depth discussions on managing risk positions. Measuring, Monitoring, and Controlling Interest Rate Risk

Interest rate risk is unavoidable even in banks that do not take rate positions. Consumers and businesses use banks because bankers take this risk; it is what they are paid to do. But bankers cannot consistently increase profits by taking more risk. Instead of saying that bankers are paid to take risks, it is more accurate to say they are paid to manage risks. Successful bankers manage risks — they understand, measure, monitor, and control risks.

—

this is what bank Measuring, monitoring, and controlling risk management is all about. AsseU’liability managers must address the

following questions:

∙

∙

∙ ∙

What is the bank’s current IRR exposure? This is often, but not always, defined to be the change in profits or capital resulting from an immediate change in prevailing interest rates of 100 to 300 basis points, called a “rate shock.”

Is the bank adequately rewarded for the risks taken? What changes in current profits and capital can result from unhedged or unreserved IRR?

How does the bank’s apparent vulnerability to changes in profits and capital resulting from risk exposures compare to its desired vulnerability?

Banks and savings associations are required by law to manage their exposure to interest rate risk. (The Federal Deposit Insurance Corporation Improvement Act of 1991 (FDICIA) amended section 39 of the Federal Deposit Insurance Act to add these requirements.) The OCC, the Federal Reserve (Fed), the Federal Deposit Insurance Corporation (FDIC), and the Office of Thrift Supervision (OTS) have jointly issued

I-22

An Interest Rate Risk Management Overview

standards for safety and soundness to implement this and other requirements. These rules specify that financial institutions should “manage interest rate risk in a manner that is appropriate to the size of the institution and the complexity of its assets and liabilities.” As the regulatory requirements imply, the actions required to manage IRR are quite different for institutions in different situations. We can consider this issue in two parts. First, the measurement of interest rate risk exposure must vary. Large institutions can cost-justify more sophisticated, and presumably more accurate, measurement models. Some institutions, regardless of size, hold assets, liabilities, or offbalance sheet instruments that expose them to potential material losses in the event of adverse changes in interest rates. These institutions require more accurate measurement procedures. Other institutions can use cruder measurement tools. See Chapters 3 through 5 for discussions of alternative IRR measurement techniques. Second, the actions that financial institutions can consider using to manage their IRR exposure will also vary, depending on their size or complexity. Various alternatives for appropriately managing interest rate risk are discussed in Chapters 14 and 15.

ELEMENTS AND STRUCTURE OF ASSET AND LIABILITY MANAGEMENT Interest rate risk is not new to banking. Rate risks, along with liquidity risks and credit risks, have always been present. However, relatively

recent increases in interest rate volatility, deregulation, and new products

have thrust IRR into the spotlight. The combination of these changes did not create IRR per se, but they have forced banks to create a more structured approach to IR management. This more structured approach has evolved in the last two decades and has become known as asset and liability management, or ALM.

5.

Standards for Safety and Soundness and Interagency Guidelines Establishing Standards for Safety and Soundness; Final Rule and Proposed Rule. Federal Register, Vol. 60, No. l3|,Monday, July 10, I995, pages 245,679—135,680.

l-23

Interest Rate Risk Management

Even though the phrase “asset liability management” is ofien used to rate risk management," this is less than ideal nomenclature. True asset/liability management must consider more than just the interest rate risk of assets and liabilities. It should also consider liquidity risk and credit risk in those positions. Moreover, true interest rate risk management must consider the rate risk from fee income businesses and off-balance sheet positions not just the rate risk in assets and liabilities. So, in a very real sense, ALM is much more than IRR management. mean “interest

—

Interest rate risk management is neither a precise nor single technique. It is a detailed approach or combination of approaches that varies from bank to bank. We have said that successful bankers understand, measure, monitor, and control risks. IRR management is both the fiamework and the tool kit for performing these tasks.

IRR management necessarily involves nearly every nook and cranny of banking. If mismanaged, it will be the principal (although not sole) cause of fluctuations in the net interest margin, the amount of interest income less interest expense. Management of the net interest margin, in turn, requires management of:

∙ ∙ ∙ ∙ ∙ ∙

Rates paid on liabilities Rates charged on loans Loan, deposit, and investment volumes

Mix between loans and investments Mix between types of loans and deposits

Other related bank management issues

Information Requirements

IRR management obviously requires a major investment in the collection and processing of information. Knowledge of the repricing and cash flow characteristics of assets, liabilities, and off-balance sheet commitments is necessary. Management of IR also requires information external to the bank, such as infomration on prevailing interest rates, the shape of the I -24

An Interest Rate Risk Management Overview

yield curve, capital market hedging instruments, and regulatory requirements. (These topics are discussed later in this manual.) The information-intensive nature of rate risk management is one reason the growth of IR management techniques has closely paralleled advances in the information-processing capabilities of computer hardware and software. Rate risk managers often function at the nerve centers of their banks. As noted above, the management of loan and deposit pricing, asset/liability portfolio volumes, and the mix of assets and liabilities within portfolios all influence a bank‘s exposure to IRR, and all are, in turn, influenced by that exposure. In the course of collecting and analyzing information for IR management, those responsible must work closely with virtually every key department in the bank. In addition, rate risk management decisions may be implemented by other portfolio managers or may affect the decisions of those managers. Obviously, such close interrelationships require good working relationships between IRR management personnel and other bank managers.

Management Committee More significantly, the interrelationships described above require close coordination between departments within the bank. For this reason, banks almost always have an ALCO. The ALCO undertakes a variety of IR management activities. Because of its wide-ranging scope and its significant influence on bank decisions, the ALCO invariably includes representatives of senior management. In a very significant sense, the ALCO becomes a formalized senior management decision-making forum.

IRR Management Policy Flaming, organizing, and controlling IRR are all management tasks carried out by more than one individual, even in small banks. To contribute toward ensuring the safety and soundness of the bank, you will need an interest rate risk policy. Not only is this an important element of asset/liability management structure and a good business practice, formal IRR or ALM policies are required by most bank regulators. The IR policy is a written, formal policy approved by a bank’s board of directors.

Interest Rate Risk Management

IRR policies typically include numerous specific requirements for the creation and operation of the ALCO. The policy also may address the creation and operation of the bank department or staff that measures and monitors rate risk. Most importantly, the IRR policy sets the guidelines for defining how much risk the bank will accept and how that risk will be controlled. Interest rate risk management policy requirements are further discussed in Chapter 12. Role of Bank’s Treasury Department

In small banks, the chief financial officer usually handles interest rate risk management as a part-time responsibility. In large and medium-sized banks, entire departments, often called treasury departments, are responsible for measuring, monitoring, and controlling IRR. These departments reflect the wide scope of rate risk management. Their staffs collect and analyze the data and maintain the models that lie at the heart of interest rate risk management techniques. In addition, treasury staff members ofien become liaisons and sometimes, coordinators between different areas within the bank. For many large and medium-sized banks, treasury departments also serve as the logical choice for creating and managing funds transfer pricing systems. Funds transfer pricing systems are basically developments of cost accounting that allow managers to isolate the income and expenses

associated with separate activities within the bank. But in the process of achieving that goal, funds transfer pricing systems almost always buy funds from providers and sell funds to users at rates that allocate IRR. The treasury department is often allocated all of the identifiable IRR. Obviously, much of the IRR incurred in separate areas of the bank is offset by the actions of other areas. That amount of risk is in effect “netted out" at the treasury department. The treasury department may then deal with the remaining risk in any combination of the following three ways:

∙

It may encourage some change in the bank’s management of loans, investments, or deposits to increase the amount of risk that is offset within the bank. This is the process of creating or managing what are called “natural hedges." Often, this is done through the ALCO.

l-26

An Interest Rate Risk Management Overview

∙ ∙

It may use financial instruments, principally interest rate swaps or futures, to hedge some or all of the remaining risk. This is often monitored by the ALCO and is always done within policy guidelines.

It may elect to retain some or all of the remaining risk. This, too, is usually monitored by the ALCO and is always done within policy guidelines.

In the course of managing and hedging IRR, treasury departments may employ traders who deal in a wide variety of short-term funds, financial futures, options, and swaps, and sometimes even foreign currency futures, options, and swaps. In large banks, treasury traders deal in such instruments in often successful efforts to produce trading profits.

l-27

Interest Rate Risk Mamement

l-28

Chapter 2 Defining and Quantifying Interest Rate Risk

The Influence of Rate Volatility on Rate Risk ..................................... 2-1 Exhibit 2.1: Change in Average Monthly Rates lO-Year CMT and 3-Month T-Bill ............................................... 2-2 Rate Volatility Is an Occasional Event ............................................. 2-3 The Impact of Rate Volatility ....................................................... 2-3 What the Volatility Requires ............................................................ 2-4 Coping with Rate Volatility .............................................................. 2-5 It’s All About Cash Flow ..................................................................... 2-5 Exhibit 2.2: Known and Unknown Cash Flow Elements ............. 2-7 Uncertain Cash Flows ....................................................................... 2-8 Principal Cash Flows .................................................................... 2-8 Interest Cash Flows ...................................................................... 2-9 Cash Flow Summary .................................................................. 2-10 Exhibit 2.3: Principal and Interest Cash Flow Matrix ................ 2-11 Focus on the Net Cash Flows ..................................................... 2-1 1 Embedded Options: Most Important Risk Management Challenge 2-l2 Some Definitions ........................ 2-12 Puts, Calls, Caps, and Floors Put and Call Options ................................................................... 2-13 Caps, Floors, and Collars ........................................................... 2-13 Bank Products and Customer Options ............................................ 2-14 Exhibit 2.4: Embedded Options in Common Retail Bank Products .................................................................. 2-15 Understanding Key Option Characteristics .................................... 2-16 In-the-Money and Out-of-the-Money Options ........................... 2-16 The Option Time Value .............................................................. 2-17 European-Style and American-Style Options ............................ 2-18 Understanding Option Exercise...................................................... 2-18 Changes in Prevailing Rates Drive Most Option Decisions ....... 2-18 Changes in Prevailing Rates Do Not Drive All Option Decisions .................................................................................... 2-19 Suggestions for Measuring Rate Risk from Embedded Options ....................................................................................... 2-21 Embedded Options: Risk Measurement Challenge ........................ 2-22

—

2/10

2-i

2110 Interest Rate Risk Management

Two Ways to Understand Interest Rate Risk...................................... 2-23 Accounting Perspective Defined .................................................... 2-24 Exhibit 2.5: Illustration of How a Change in Rates Impacts Earnings .................................................................... 2-25 Economic Perspective Defined....................................................... 2-25 Exhibit 2.6: Illustration of How a Change in Rates Impacts Economic Value ......................................................................... 2-26 How Interest Rate Risk Affects Profits —- A Sample Calculation ...................................................................................... 2-26Exhibit 2.7: Sample Balance Sheet on January 1 ....................... 2-27 Exhibit 2.8: Sample Income Statement on December 31 ........... 2-27 Exhibit 2.9: Sample Balance Sheet on December 31 ................. 2-28 Effect on Noninterest Income and Expense.................................... 2-29 How Interest Rate Risk Affects Equity .......................................... 2-29 Exhibit 2.10: December 31 Balance Sheets from an Accounting Perspective .............................................................. 2-30 Exhibit 2.11: December 31 Balance Sheets from an Economic Perspective ................................................................ 2-31 Accounting Perspective vs. Economic Perspective ........................ 2-32 Advantages and Disadvantages ...... 2-32 Accounting Perspective Economic Perspective Advantages and Disadvantages......... 2-33 Best Use for Each Perspective .................................................... 2-34 Different Audiences Different Points of View ...................... 2-34 Exhibit 2.12: Different Perspectives on Interest Rate Risk ........ 2-35 Summary ............................................................................................ 2-35

—— —

Chapter 2 Defining and Quantifying Interest Rate Risk

THE INFLUENCE OF RATE VOLATILITY ON RATE RISK Interest rate risk (IR) is not caused by high interest rate levels. Nor is it caused by low prevailing rates. Instead, rate risk is a function of rate volatility. When interest rates are stable, interest rate risk is not much the more than a minor concern. In those periods, rate risk exposures do potential for lower earnings and capital resulting from rate changes not lead to actual losses of significant size. Conversely, when interest rates are unstable, rate risk is a major concern. It is precisely during periods of rate volatility that the potential for adverse outcomes from rate risk exposures is most probable.

——

Before the late 19705, few bankers gave much thought to interest rate risk. Certainly, the practice of “borrowing short and lending long” was considered risky. But few addressed the topic of monitoring, measuring, or managing interest rate risk. To the contrary, many banks and the entire savings and loan industry filled their balance sheets with fixed-rate loans, including 30-year residential mortgages and intermediate-term investments. At the same time, they funded those assets with short-term certificates of deposit (CD5), savings accounts, and other sources of funds that were sensitive to changes in prevailing interest rates.

In fact, it is an understatement to say that before the late 19705, few bankers paid any attention to interest rate risk. As we have already observed, most of the tools for measuring and managing IRR have been developed only in the last 20 years. In reality, many large banks undertook significant actions from the mid-19605 to the mid-19705 that largely ignored interest rate risk. For example, liability management — the practice of relying on sources of short-term (ovemight to one year) borrowed money to fund asset growth was developed, refined, and spread by large banks during this period. Bankers paid a high price for these actions, as we can see from the trends shown in Exhibits 2.1 and

—

2.2.

2/10

2-1

2/10 Interest Rate Risk Management

Exhibit 2.1 Change in Average Monthly Rates lD-Year CMT and 3-Month T-Bill lO-Year CMT Change In Average Monthly Rate! 10 Year CMT

15m ‘00-

68:1.Points

l

II

I

tin.

I. III .til..Ii LILil' 1' I'll t

'1" I

19131900195219“tmrmtmrmrmtmrmmmmmm

3-Month T—Bill

Point:

ut n a B

5

J-Monih T-BIII

IONIMINIWIHIWIWIWZIWIHIWWNWMM

2-2

Defining and Quantifying Interest Rate Risk 8/09

Rate Volatility Is an Occasional Event Exhibit 2.1 shows monthly changes in the average yield for a 10-year US. Treasury bond from 1979 through December 2008 and the monthly changes in the average yield for three-month US. Treasury bills from 1979 through December 2008. Notice that volatility was very high in the early 19805 but significantly less after the mid to late 805.

The Impact of Rate Volatility An example, using historic interest rates, clearly shows the impact of rate volatility. Assume that a bank had steadily accumulated assets with yields similar to the 30—year Treasury bond yield over the decade from 1969 to 1978. The highest yield before 1979 was about 8.75 percent, while the lowest yield afier 1969 was about 5.75 percent. For simplicity’s sake, let’s estimate that the average yield for that decade was about 7.50 percent. If the bank acquired its assets in relatively similar amounts throughout that decade, its portfolio of assets might have yielded 7.50 percent by the end of 1978. Now imagine that the bank funded those assets with liabilities at a cost comparable to the three-month Treasury bill rate. (Actually, no bank would have a cost of deposits quite that low, and no bank would have all of its deposits repricing every three months.) At the beginning of 1978, the bank would have been funding its 7.50 percent assets with liabilities that cost about 6.25 percent. Accordingly, the bank would have had a positive spread of about 1.25 percent.

Next, consider the rate changes for the subsequent years. Suppose the bank grew its assets by a total of 20 percent in 1979 and 1980 and that those new assets had an average yield of 10.50 percent. In such a case, by the end of 1980, the bank might have increased its average yield on assets from 7.50 percent to about 8.10 percent. However, by the end of 1980, our imaginary bank had a cost of funds of about 15 percent. In other words, by the end of 1980, the bank would have had a negative spread of about 6.90 percent! Even though savings and loan associations and banks actually had considerable amounts of deposits that were far less volatile than the three-month Treasury bills used in this example, many actually found themselves in just this predicament. That problem

8/09 Interest Rate Risk Management

did not go away until late 1982, and it came back — although in a milder in 1984. form

—

What the Volatility Requires

The rate volatility evidenced in Exhibit 2.1 leads us to two very important conclusions. First, and by far the most important, is that failure to monitor, measure, and manage a bank’s exposure to interest rate changes can be a very costly mistake. Such failures led to the losses and destruction of capital in the early 19805 that devastated the savings and loan industry and severely hurt many banks. Second, periods of significant rate fluctuations are less common than periods with more stable trends. Thus, the importance of IR management for any bank is clearly greater in the relatively rare periods of high interest rate volatility than it is in more normal times. The huge negative spreads that savings and loan managers were faced with after 1978, together with the significant increase in deposit insurance coverage in the mid-19805, forced the managers of those institutions to attempt to grow out of their problems. The essence of their strategy was simple.

Assume that you were managing a savings and loan association that had total assets of $10 million at the beginning of 1979, and that those assets had an average yield of 7.50 percent. During 1979 and 1980, you tripled the size of the S&L by adding $20 million of new assets. You could have added new 30-year Treasury bonds with an average yield of 10.50 percent, in which case, by the end of 1980, the average yield on your assets would have been 9.50 percent. Or, you could have added new commercial mortgages with yields averaging 14 percent, which by the end of 1980, would have given you an average yield on your assets slightly higher than 12 percent. Either of these alternatives is considerably better than the 8.10 percent yield earned by the bank in the previous example, which grew by only 20 percent in that period.

By the end of 1982, when three-month Treasury bill rates were about 8 percent, an S&L association that had successfully adopted a growth strategy could have restored itself to a situation in which its interest spread was again positive. Many associations did just that. Unfortunately, the large growth of high-yield assets primarily comprised 2-4

Defining and Quantifying Interest Rate Risk 10/08

high-risk commercial mortgages. Losses on those mortgages eventually destroyed more S&Ls than were destroyed earlier by the high interest rates. Thus, the experiences of the 19805 are a vivid illustration of both interest rate risk and how IRR can lead to unacceptable credit risk. Coping with Rate Volatility

The volatile rate experiences of the late 19705 and early 19805 caused a major revolution in bank management. Tools for monitoring, measuring, and managing interest rate risk that were undreamed of before that time have become common in little more than a decade. Simulation modeling, duration analysis, hedges, and swaps are just a few of the innovations. All of those and many others are discussed later in this manual. Along with these innovations has also come a much better understanding of the strengths and weaknesses of the tools bankers now use for monitoring, measuring, and managing interest rate risk. These tools are discussed at length later in this manual. IT’S ALL ABOUT CASH FLOW

Why does rate volatility increase the risk of lower earnings and/or lower capital? The answer to that question goes to the heart of interest rate risk and liquidity risk. (It is also relevant to credit, strategic, compliance, and reputation risks.) Consider these basic truths and the sequence in which we list them: 1.

Unlike almost all other types of businesses, the assets and liabilities of banks are primarily composed of financial instruments.

2.

Most financial instruments are contracts that create a right or obligation to receive or deliver cash at some point in time. Investment securities, loans, and other financial instruments carried as assets on the bank’s balance sheet represent claims to receive cash from other parties. Deposits, borrowings, and other financial instruments carried as liabilities on the bank’s balance sheet represent claims by others that will require the bank to pay cash. (Other types of financial instruments are contracts that

2-5

10/08 Interest Rate Risk Management

create a right or obligation to receive or deliver another financial instrument or commodity such as options and futures.)

Whether the cash flows from financial instruments are called “principal,” “interest," or something else, we do net always know 'when they Will occur. Nor do we always know the amount of individual cash flows. (Recall our introductory discussion of option risk in Chapter 1.) We may, for example, not know how big a future loan prepayment will be nor when it will occur. Similarly, we may not know how large a deposit withdrawal may be nor when it may occur.

In many cases, the uncertain timing or amount of future cash flows is related to changes in prevailing interest rates. For example, when market rates of interest fail, loan prepayments tend to accelerate.

Exhibit 2.2 illustrates the combinations of known and unknown elements. For each of the four combinations of the two elements, consider the following characteristics and examples:1

1. Christian Kronseder, Credit Suisse, November 2004.

2-6

Dcfininn and Quantifying Interest Rate Risk l0/OB

Exhibit 2.2 Known and Unknown Cash Flow Elements

Am ount

n wo k u n wo k unknown

known

Time/Maturity

∙∙

1. Time known/amount unknown Stochastic cash flow Modelling of price along contract value continuum Examples include margin calls, European options, and share dividends. 2. Time unknom’arnount unknown Stochastic cash flow Modelling of time behaviour along contract value continuum Worst case for a cash flow Examples include basically all products that have an American option type of behaviour (e.g., deposits). 3. Time unknown/amount known Stochastic cash flow Time unknown can mean:

∙ ∙∙

∙∙

2-7

10/08 Interest Rate Risk Management

— —

Starting date exists from whenever a cash flow can happen. Cash flow can happen anytime. Modelling of time behaviour. It is not granted that the cash flow events have the same probability. Examples include traveller’s checks and loans with flexible down payments. 4. Time known/amount known Deterministic cash flow Examples include coupon payments, interest payments, and swaps.

∙

∙ ∙∙

—

Asset/liability management — particularly interest rate risk and liquidity risk management — therefore focuses on cash flows. Liquidity risk managers focus on the amount and timing of all future cash flows. Rate risk managers focus on the amount and timing of interest rate sensitive cash flows. Uncertain Cash Flows

What do we mean when we say that we do not always know the amount or the timing of some cash flows; or when we say that some cash flows are uncertain? To answer that question, let’s take a closer look at the nature of cash flows from financial instruments.

Principal Cash Flows

Principal is the name we use for the remaining balance owed on a loan by a borrower or on a security by its issuer, exclusive of any accrued interest. For a nonamortizing security, the principal amount is usually the par value. For a loan or an amortizing security, the principal amount is the cm'rent balance or current face value. When we consider principal cash flows, we can divide principal payments into three groups or types. These are: or scheduled principal payments that have unchangeable, legally binding cash flows in predetermined

l. Contractual

2-8

Defining and Quantifying Interest Rate Risk 10/08

amounts that must be made on predetermined days. A nonamortizing, noncallable bond has a par amount that must be paid by the issuer on the maturity date. A CD has a face value that must be paid by the issuing bank on the maturity date.

Contractual or scheduled principal payments that may be altered under the terms of the financial instrument. For these instruments, the principal cash flow or flows are contractually scheduled but not contractually binding. Options, as we will discuss in the next section, pemrit one party to alter the timing or amount of the scheduled cash flows. Examples include a loan that may be prepaid, a bond that may be called, or a CD that may be redeemed prior to maturity. (The fact that some of these options may require fees or penalties does not eliminate the possibility that they may occur.)

Cash flows not contractually specified. The best example of this type of principal cash flow is the “maturity" of a checking or savings account. The cash flow occurs whenever the depositor withdraws the funds.

Interest Cash Flows When we consider interest cash flows, we can also divide them into three groups or types. These are: l. Fixed rates. Interest payments calculated based upon contractually fixed rates. Many loans and most certificates of deposit specify fixed rates of interest.

2. Administered rates. Interest payments calculated based on administered rates. Those interest rates that the bank or other payer is contractually permitted to change whenever and by what ever amounts it desires. An example would be the rates paid on savings accounts. Regrettably, these rates are sometimes called variable rates. That term is regrettable because it is too easily confused with the very different floating rates. Floating rates. Interest payments calculated based upon an index that periodically resets. The index might be a Treasury or LIBOR

2-9

10/08 Interest Rate Risk Management

(London Interbank Offered Rate) rate. Often, the floating rate is based on a contractually specified sum of the current value for the index rate plus some defined spread. Floating rates may reset daily, monthly, quarterly, or on any other contractually agreedupon frequency.

Note that contractual caps or floors can efieaively convert a floating-rate instrument into a fixed-rate instrument. Once the rate for a floating-rate instrument reaches the cap or floor level, it ceases to float until and unless prevailing rates change direction. Cash Flow Summary All financial instruments have both interest and principal cash flows. (For a zero coupon security, the “interest" cash flow is discount.) We can therefore view the three types of principal cash flows and the three types of interest cash flows as a matrix (Exhibit 2.3). Some example instruments with these types of cash flows are shown in the exhibit matrix.

Defining and Quantifying Interest Rate Risk 10/08

Exhibit 2.3 Principal and Interest Cash Flow Matrix Principal Cash Flows

1;

Fixed Rate

Contractually Binding

Contractually Scheduled but Not Binding

Treasury notes

Fixed-rate,

Unscheduled

residential

mortgages

a

∙∙ "'

5

Administered Rate

Savings accounts

Flouting Rate

Understanding the cash flow characteristics of bank’s assets, liabilities, and off-balance sheet commitments is the first step in understanding both interest rate risk and liquidity risk. Understanding how the amount or timing of those cash flows may vary with changes in prevailing market rates of interest is the second step. Evaluating the interest rate risk for all instruments with cash flows in the far left column of Exhibit 2.3, especially those in the top lefi box, is straight forward. For example, duration analysis, a measurement tool described in Chapter 4, is well suited to these instruments. However, the task is more difficult for instruments with cash flows in the middle and right-hand columns. Those instruments have option risk. Our discussions in the next section of this chapter provide more background on option risk. Then, in later chapters, we focus on the practical problems of measuring the option risk in deposit and loan products. Focus on the Net Cash Flows

Financial instruments all have interest rate or market risk. Indeed, entire books discuss the market risk of marketable investment instruments. And, as we will discuss in later chapters, many of the tools that rate risk

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10/08 Interest Rate Risk Management

managers use to quantify rate risk exposures were first developed for measuring the risk of individual investment instruments.

Rate risk managers, nevertheless, must focus on the bank’s overall or net risk exposures. The simple fact is that the risk that some cash flows may be earlier than expected may be partially or completely ofi‘set by the risk that some cash flows may occur later than expected. The risk that some may be larger than expected may be offset by the risk that others are smaller. And, most importantly, the fact that the amount or timing of some cash flows is altered by a given change in rates is likely to be at least partially offset by other changes prompted by the same rate change.

Focusing on the overall or net position is the goal of the various risk measurement methods that we will explore in Chapters 3 through 5.

EMBEDDED OPTIONS: MOST IM'PORTANT RISK MANAGEMENT CHALLENGE In Chapter 1, we defined option risk, basis risk, and yield curve twist risk. Recall that those are three of the four primary components of IR. Option risk, as we just observed, arises from the two types of uncertain cash flows — interest or principal. But option risk can also be found in some floating-rate instruments. When instruments with floating rates have caps on how high they can go or floors limiting how low they can go, those instruments have option risk. In addition, administered rates and floating rates ofien create both basis risk and yield curve twist risk. Evaluating the interest rate sensitivity for instruments with cash flows in the middle and far right-hmd columns of the table in Exhibit 2.3 therefore requires material assumptions. Indeed, as we will discuss in the following chapters, the measured level of rate risk exposure is ofien highly sensitive to those assumptions. Since option risk, and the assumptions about option exercise that are incorporated into the measurement of our rate risk exposures, is so critical, it is a good idea to spend some time learning more about key option characteristics. Puts, Calls, Caps, and Floors −− Some Definitions

The attributes of bank products that make rate risk measurement messy are product features, mainly: puts, calls, caps, and floors. In this section,

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Defining and Quantifyigg Interest Rate Risk 10108

we will discuss how the existence of these contractual features in bank products impacts rate risk measurement. But first, it is helpful to defme just exactly what these product features are.

Put and Call Options

Options are contracts between two parties. In that sense, they are no different than simpler f'mancial instruments such as bonds and loans. The distinguishing characteristic of options is that they give the holder the but not the obligation to buy or sell the underlying right commodity or financial instrument.

—

—

Rights to buy something at a fixed price in the future are call options. Rights to sell something at a fixed price in the future are put options. Calls and puts are distinct types of option instruments. The buying or selling of a call does not involve the buying or selling of a put. Similarly, the buying or selling of a put does not involve the buying or selling of a call.

Caps, Floors, and Collars A cap is an agreement in which the writer guarantees the buyer that a variable rate of interest will not exceed a specified rate for a specified period of time. If the relevant interest rate stays sufficiently below the cap level, the cap buyer benefits from having smaller interest rate payments. A cap, then, functions as an insurance policy against higher interest rates.

A floor is the opposite of a cap. It obligates the writer to reimburse the buyer in the event that a variable rate of interest falls below a specified level. In essence, a floor insures against lower interest rates. A collar combines a cap and a floor. A collar locks the buyer into a band of variable interest rates that cannot exceed a cap nor fall below a floor. The interest rate will float freely between those two levels, within the collar. While a cap gives the buyer protection against higher interest rates, the buyer gives up the benefit if interest rates go below the floor level.

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Bank Products and Customer Options

Put, call, cap, and floor contracts can be purchased as distinct contracts. Indeed, these financial contracts are ofien purchased by banks to hedge interest rate risk exposures. In Chapter 16, we will focus on how these and other derivative contracts can be used to manage interest rate risk. In that context, the option contracts are part of a risk manager’s solution tool kit. However, in a different context, these contracts are not risk management solutions. When puts, calls, caps, and floors are incorporated within traditional bank products, they are part of the risk exposure problem. Puts, calls, caps, and floors “built into” bank products are referred to as “embedded options.” For most bank AL managers, traded options are far less important than embedded options. Many bank products include contractual provisions that give either the bank or its customer the right to buy or sell something from the other party at a predetermined price. The “something” that is bought or sold is money. Most of these options give the holder the right to increase, reduce, or payoff the loan or deposit balance. Others give the holder the right to change or prevent changes in the interest rates paid or charged. Perhaps the most obvious example is the contractual right of a residential mortgage loan customer to prepay his or her loan. This contractual prepayment right is a call sold by the bank. When the customer prepays his or her loan, the debt is being called.

Many of the embedded options in retail banking will be discussed in subsequent chapters. They include the right of many borrowers to prepay their flxed- or administered-rate loans. Other embedded options are equally common but not often viewed as financial options. These include customers’ rights to add to fixed— or administered-rate liabilities by making deposits to open-end deposit accounts such as savings and interest-bearing checking accounts. They also include customers’ rights to add to fixed-rate assets by drawing funds under open-end credit arrangements such as credit cards and lines of credit. Over the past few decades, banks have significantly expanded the number and the types of financial products for sale to consumers. For example, instead of two types of mortgage loans — fixed rate and borrowers can now choose from a range of products floating rate

—

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Defining and Quantifying Interest Rate Risk 10/08

which may have floating rates for some period of time and then fixed rates or those that have fixed rates for some period of time and then floating rates. Embedded options materially affect the products’ interest rate sensitivity. The proliferation of these products materially complicates the rate risk exposure of the whole bank. The tremendous complexity of common bank products is shown in Exhibit 2.4. Checking and savings accounts, for example, have four embedded options in each product: puts, calls, caps, and floors. The put option is the depositor’s right to withdraw his or her funds. Actually, since funds may be withdrawn in full or in part and at one time or in many transactions, each account has a series of puts. Similarly, the depositor’s right to add more funds to her checking or savings account constitutes a series of call options. The same deposit product has an implied floor. No matter how low market rates fall, banks still pay some amount of interest to these depositors. Floors may be as low as l or 2 percent, but they exist. Finally, the same deposit products have an implied cap. No matter how high market rates get, banks seem to stop raising the rates paid on these accounts at some level. In the 19905, the implied cap on savings accounts seems to be around 5 to 7 percent. The puts and calls in checking and savings accounts are embedded options. The implied caps and floors result because the rates are administered rates set by the bank. Many loan products also have more than one type of embedded option. For example, a floating-rate loan tied to the bank's prime rate includes the bank’s option to administer the rate in its favor — at best a cap option — and the borrower’s option to make prepayments — a series of call options.

Exhibit 2.4 Embedded Options in Common Retail Bank Products FIXED-RATEAND LAGGING-RATE PRODUCTS

BANK PRODUCT Fixed-rate loan Credit line Credit card Checking and savings Checking and savings

OPTION Form Prepayment Draw down Draw down Additional deposit Withdrawal

2-15

_

TECHNICAL Dsscnmrox Sold call Sold put Sold put Sold call Sold put

10/08 Interest Rate Risk Management

Exhibit 2.4 Embedded Options in Common Retail Bank Products (cont.) FLOATING-RATE AND ADNIINISTERED—RATE PRODUCTS TECHNICAL DESCRIPTION OPTION Form Rate ceiling Sold cap Rate floor Long floor Rate ceiling Long cap Rate floor Sold floor

BANK Pnonucr Variable-rate loan Variable-rate loan Checking and savings Checking and savings

Source: James Westfall, “Managing Interest Rate Risk in Retail Loan and Deposit Products,“ a presentation made at the BA] Asset/Liability and Treasury Management Conference, Oct. 7-9, 1991, Washington, DC, as subsequently modified by L. Matz. Used and adapted with the pcmrission of Mr. Westfall.

Understanding Key Option Characteristics Before we address the risk measurement challenges of embedded options, we need to consider a few more characteristics of option contracts and embedded options.

ln-the-Money and Out-of-the-Money Options

When we defined put and call options, we noted that these confiacts give their holders the right to buy or sell at a specified price. We call that price the “strike price.” When you buy options, you are buying the right to buy or sell at a preset price level. A 102 strike price means a call holder can buy the underlying instrument at a price of 102 no matter what actual price levels prevail in the future. The single most important determinate of whether or not an option will be exercised is whether or not the exercise of the option will financially benefit the holder. This, in tum, depends upon how the strike price in the option compares to prevailing market prices. The difference between the strike price and the current market price is the option’s intrinsic value. If the option currently has intrinsic value, we say that the option is “in the money.” If it doesn’t, we say that it is currently “out of the money.” Call options are said to be in the money if the strike price is lower than the current market price, called the spot price, for the underlying

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Defining and Quantifying Interest Rate Risk 10/08

instrument. When the strike price of a call option is lower than the spot price, the owner can exercise the option to purchase the underlying instrument at a price that is less than it would cost to purchase it at the same time at the spot price. In other words, a call option that is in the money is valuable to its owner because it allows the option owner to purchase the underlying financial instrument at a price that is less than its current market price. A call option with a strike price that is above the current market price is said to be out of the money.

Put options are said to be in the money if the strike price is higher than the spot price, for the underlying instrument. When the strike price of a put option is higher than the spot price, the owner can exercise the option to sell the underlying instrument at a price that is higher than the sales price that could be realized if the underlying instrument was sold at the same time at the spot price. In other words, a put option that is in the money is valuable to its owner because it allows the option owner to sell the underlying financial instrument at a price that is higher than its current market price. A put option with a strike price that is below the current market price is said to be out of the money. For example, if the option gives the holder the right to prepay a 6 percent loan when prevailing rates are 4 percent, the option has intrinsic value. That option is in the money. On the other hand, if the option gives the holder the right to prepay a 6 percent loan but prevailing rates for new loans are 8 percent, the option currently has no value. That option is out of the money. The Option Time Value Evaluations of stand-alone options also focus on time remaining before the option expires. Options also have a time value in addition to any intrinsic value. An option that has no intrinsic value now may move into the money later if prevailing market rates or prices change. Clearly, the more time remaining before the expiration of the option, the more opportunity for the option to either get into the money or get more deeply into the money.

For economic approaches to measuring interest rate risk, such as economic value at risk (EVE), time value is also important for evaluating embedded options. (Valuing options will be discussed in Chapter 16.) 2-l7

10/08 Interest Rate Risk Management

However, for accounting-based measures of rate risk, such as earnings at risk (EAR), the time value of an embedded option is not too relevant. The embedded option simply goes away when the loan or deposit goes away. European-Style and American-Style Optiom

It is also important to notice that the definition of an option given near the beginning of this section used the somewhat vague phrase “in the future” to describe when the right to buy or sell may be exercised by the holder. Actually, options have two difi‘erent types of exercise times, sometimes called styles. These are known as “American options” or “American-style options” and “European options” or “European-style options.” American options can be exercised at any time or anytime between a defined start date and a defmed expiration date. European options, on the other hand, can be exercised only on a single day. This seemingly arcane difference is hugely important to rate risk managers. European-style options can be valued with analytical formulae. American-style options are harder to value and their value can really be only approximated. Almost all embedded options are American-style options. The holder of a savings account, for example, can add new funds or withdraw funds at any time as long as the account is open. The holder of a residential mortgage loan can prepay at anytime during the life of the loan. Understanding when an American-style option might be exercised is not a trivial problem.

Understanding Option Exercise Of course, the main challenge for rate risk managers is understanding when the holder of an option will elect to use the option. When will loans prepay? When will deposits be withdrawn?

Changes in Prevailing Rates Drive Most Option Decisions

Options with intrinsic value are likely to be exercised while those that have none are not likely to be used.

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Defining and Quantifyinggterest Rate Risk 10/08

In a rising rate environment, a put option becomes more valuable. When prevailing rates rise, the owner of a put for a fixed-rate savings account can exercise her option to decrease her balance invthat account by making a withdrawal. She will then have less money on deposit at a rate that became less attractive when prevailing rates ros'e. Similarly, when rates rise, the owner of a put for a fixed-rate bank line of credit can exercise his option to increase his holding of that loan by obtaining an additional draw down of loan funds under the line of credit. He will then have borrowed more money at a rate that became more attractive when prevailing rates rose. Conversely, puts are less valuable when prevailing rates fall. In a falling rate environment, a call option becomes more valuable. When prevailing rates fall, the owner of a call option for a fixed-rate savings account can exercise her option to increase her balance in that account by making a deposit. She will then have more money on deposit at a rate that becomes more attractive when prevailing rates fall. Similarly, when rates fall, the owner of a call option for a fixed-rate bank loan can exercise his option to decrease his holding of that loan by making a paydown or a prepayment of the loan. He will then have borrowed more money at a rate that becomes less attractive when prevailing rates fall. Conversely, calls are less valuable when prevailing rates rise. Changes in Prevailing Rates Do Not Drive All Option Decisions

One of the reasons that analysis of consumer-related financial products is so complex is because of the issue of the so-called “irrationality” of consumers. This is not in any way intended to describe the mental state of bank customers. Instead, “irrationality” is just a term used by economists to describe decisions not motivated purely by fmancial gain. For example, auto loans and residential mortgages are often repaid just because borrowers decide to trade current homes or cars for new homes or cars. Some bankers refer to the five D5: death, divorce, destruction, default, and departure (relocation). All of the five Ds are reasons other than changes in interest rates that lead consumers to prepay their loans. (In the case of default, a liquidation or charge-off “prepays” the loan.)

Perhaps the most prominent example of “irrational” option exercise is mortgage loan prepayments. Mortgages are often prepaid when current 2-l9

10/08 Interest Rate Risk Management

mortgage rates are higher than the borrower's mortgage rate, and many borrowers fail to prepay even when rates have fallen far below the rate on their loan. As a working assumption, the hypothesis that borrowers are not very intelligent runs contrary to the assumptions behind all developments in modern financial theory over the 20 years since the Black-Scholes options formula was fast published. The perception of “irrationality" is simply a shorthand description for the fact that lenders and academic researchers do not have enough data to “see through” the individual loan or pool data to understand why the individual borrowers’ behavior is more rational than it appears at first glance. Ifthey could “see through" the data, the failures to exercise in-the-money prepayment options would be seen to have many perfectly understandable causes. In some cases, for example, the borrower may be too busy. In some cases, the borrower may be temporarily unemployed and therefore unable to qualify for a new, lower rate loan.2

The need to deal with hard-to—explain consumer behavior is essential for accurate risk management in the insurance, investment management, and banking industries. Insurance companies must deal with the reality that some traditional life insurance policy holders will cancel their policies in return for the surrender value when interest rates rise, “putting” the policy back to the underwriter. Investment managers who suffer poor performance know that some customers of the firm will “put” their ownership in a mutual fund back to the investment management company. Bankers who make home equity loans know that some of these loans will be “called” by the borrower. Bankers also know that some time deposit customers will ‘put” the deposit back to the bank and are willing to pay an early withdrawal penalty when rates rise in order to earn more on their funds. Without dealing with the degree of “irrational” consumer behavior behind these products, institutions cannot measure their risk exposure accurately.3

2.

Adapted from Kenji Irnai and Donald R. van Deventer, Financial Risk Mathematics: Applications to Banking, Investment Management and Insurance, Chapter 13, “h-rational FJrercise of Fixed Income Options,” May 20, 1996.

3.

Adapted from Kenji Irnai and Donald R. van Deventer, Financial Risk Mathematics: Applications to Banking, Investment Management and Insurance, Chapter 13, “Irrational Exercise of Fixed Income Options," May 20, 1996.

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Defining and Quantifying Interest Rate Risk 10/08

Suggestionsfor Measuring Rate Riskfiom Embedded Options As we will discuss, there are lots of different ways to view and measure rate risk exposures. Regardless of which approach you employ, you are going to have to make some major assumptions about the exercise of embedded options. The relationship between changes in prevailing interest rates and the exercise of customer options is ambiguous. Interest rate changes are not the only drivers of option behavior.

In general, risk managers should structure option assumptions and model parameters with the following four guidelines in mind: 1. Clearly the most important driver of option exercise is the intrinsic value or “moniness” of the option. Considerable care must be taken to reflect that fact that high rate environments will see more withdrawals from savings accounts and fewer loan prepayments. Obviously, floating rate loans with caps will be more likely to “cap out" in high rate scenarios. Conversely, savings deposits and loan prepayments will increase in low rate environments. Floors become a risk measurement issue then, too.

Assumptions about option exercise should reflect transaction costs. For example, the option to prepay a fixed rate, 8 percent mortgage is not likely to be exercised when prevailing rates fall to 7.75 percent. The out-of-pocket costs to refinance the loan are likely to exceed the intrinsic value. Even if the out-of-pocket costs do not quite exceed the intrinsic value, the bother of refmancing is an intangible but real cost. Some simulation models permit the rate risk analyst to employ a “fill in the blank" transaction cost factor that modifies the assumed exercise of embedded prepayment options.

Assumptions about option exercise should also reflect prevailing economic conditions. For example, high rates ofien mark the turn in economic cycles from boom to recession. At those cyclical peaks, business deposits tend to be drawn down while consumer loan refmancings are reduced as some borrowers encounter financial problems. Some simulation models permit the rate risk analyst to defme “macro factors” that modify the assumed exercise of embedded prepayment options.

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10/08 Interest Rate Risk Management

4. The exercise of many embedded options are strongly or weakly influenced by prior rate history. For example, the first time prevailing rates fall to 6 percent, it is highly probable the an 8 percent loan will prepay. However, the third or fifth time that prevailing rates rise above 8 percent and then fall below 6 percent, it is not very likely that an 8 percent loan will prepay. If the borrower did not exercise his or her prepayment option the first few times it fell deep into the money, he or she is unlikely to exercise it on subsequent occasions when the option falls deep into the money. This phenomena, called “path dependency," is discussed in more detail in Chapters 7 and 8. Embedded Options: Risk Measurement Challenge

IRR managers must clearly recognize five important facts about embedded options: 1. First, many of the most widely used bank products contain significant option risk features. As we observed in Chapter 1, between 20 percent and 50 percent of all US. bank assets and liabilities have been estimated to incorporate embedded options. And embedded options have been estimated to comprise 20 percent to 25 percent of the total IRR in banks. This is especially true for banks that focus on consumer loans and deposits. Retail banks, regardless of size, often have large holdings of loans and deposits subject to prepayment or early redemption. Second, too many rate risk measurement processes fail to deal effectively with the risks posed by embedded options. Even when they' are addressed, they are usually addressed ineffectively. Measuring the risk exposure from embedded options is too often a serious weakness introducing large errors into measurement processes that are robust in every other way. We review examples of this in Chapter 4’s discussion of duration analysis.

Third, failure to manage option risk can pose a serious fmancial threat. Losses can result from either the failure to manage option risk or from ill-advised attempts to manage perceived IRR without properly considering options risk.

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Defining and Quantifying Interest Rate Risk 10/08

4.

Fourth, embedded options are more important in some rate environments and less important in others. Embedded options usually work in favor of the customer and against the bank. Even though individual bank customers are ofien financially unsophisticated, as a group, bank customers have shown a strong inclination to exercise embedded options in bank products at the best time for themselves and, therefore, at the worst time for the bank.

5. While an understanding of how options are exercised in response to changes in prevailing interest rates is very helpful to rate risk managers, it is not suflicient. Other influences. such as transaction costs, need to be considered.

In our discussions of income simulation, duration analysis, and economic value simulation, we note a number of weaknesses for each of these approaches to measuring IRR. Naturally, the focus in those discussions is on the specific methodology under consideration at the time. While the strengths and weaknesses of each specific rate risk measurement method should be understood, it is equally important to understand that some serious weaknesses are not inherent in the specific risk measurement approach used. Instead. these serious analytical problems are inherent in the business of banking. In other words, attributes of specific bank products and services, especially retail bank products and services, diminish the accuracy of even the best IRR measurement methods. In subsequent chapters, we will first focus on specific rate risk measurement tools and then on risk measurement problems specific to deposits, loans, and off-balance sheet positions. In each case, embedded options are the source of the bulk of the risk. Accordingly, the general discussions of embedded options in this chapter should be considered as just an introduction to the measurement and product-specific discussions in the following chapters. TWO WAYS TO UNDERSTAND INTEREST RATE RISK

How is interest rate risk best defined? And how do we quantify it? We have defined interest rate risk in general terms as the possibility that changes in prevailing market rates of interest will cause a reduction in

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10/08 Interest Rate Risk Management

bank eamings, bank capital, or both. And, we have identified changes in either the amount of future cash flows, the timing of future cash flows, or both as the link between changes in prevailing rates and adverse impacts on earnings or capital.

Now we can begin to get more specific. In this section, we define how we can describe and quantify the risk. Rate risk can be analyzed from two quite different perspectives. IRR can be defined by the effect it has on profits. We can describe this as the accounting perspective. Altemately, IRR can be defined by how it affects the capital value, or, more precisely, the economic value of the capital of the bank. We can describe this as the economic perspective. Each perspective has advantages and disadvantages, but both are useful. Accounting Perspective Defined

Most often, interest rate risk is defined and measured in terms of its impact on profits. The measure of IR is defined as the quantity by which earnings increase or decrease as a result of interest rate changes. So in this sense, earnings exposure is the measure of interest rate risk. This concept can be viewed as a process or as a sequence of changes. Exhibit 2.5 illustrates the sequence. (The asset and liability cash flows referenced in the exhibit include loan prepayments and deposit account withdrawals. These are examples of the option component of interest rate risk.)

If earnings exposure is the measure of IRR, changes in the net interest margin are the link that connects changes in interest rates and changes in earnings. The impact of interest rate changes on earnings is almost entirely affected through changes in the net interest margin. As we shall see, this perspective on IR is an accounting perspective. It captures the change in earnings that results from changes in prevailing interest rates.

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Defining and Quantifying Interest Rate Risk l0/08

Exhibit 2.5 Illustration of How a Change in Rates Impacts Earnings Flrst Stage

Third Stage

Second Stage Changes in rates earned from

adjtnlable rate

assets and new assets

Change

interest rates

Changes in

.

prevatltng

—§

\l

3:321:11of interest

income

Chan es 'n

mc amount 8 I

rates paid on

' “9"???”

of interest expense

rate

ltabtltttes and

new liabilities

Fourth Stage

→ '“F°’"°-

Change in

net interest 1

Income.ne

capital, etc.

Changes in the amount and timing of asset and liability cash flows

Economic Perspective Defined

A second way to define interest rate risk is in terms of its impact on the true capital value of the bank. This impact is usually described as the change in the economic value of the bank’s equity. This definition looks at IRR from an economic perspective. It captures the change in the economic value of the bank even though that change is not reflected in the bank's accounting books and records. This concept can be viewed as a process or as a sequence of changes. Exhibit 2.6 illustrates the sequence. (In addition to the changes shown, noninterest income and noninterest expense may also be affected by changes in prevailing rates. This issue is explored in Chapter 11.)

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Interest Rate Risk Management

Exhibit 2.6 Illustration of How a Change in Rates Impacts Economic Value Flrst Stage

/

Thlrd Sage

Second Stage

Changes

.

appropriate

discount rates

—>

Fourth Stage

Changes in the present value

or

asets

_

Change in net

interest

or Economic Value Of Equity

Change In prevailing

present value

rates

Changes in the amount and liming ol'asset —)

3““ “MW cash flows

5:32;:value of

liabilities

How Interest Rate Risk Afi‘ects Profits — A Sample Calculation

To see exactly how we define and measure interest rate risk from an accounting perspective, consider two examples. First, suppose that a bank, ABC Bank, begins a year with one asset, one liability, and some initial capital. The asset is a $1 million investment in a five-year US. Treasury note that yields 5 percent. The liability is a six-month bank CD in the amount of $900,000 that pays interest to the depositor at an annual rate of 3 percent. The initial capital is $100,000. Exhibit 2.7 shows what the bank’s balance sheet looks like on January 1. At the end of six months, ABC Bank is able to renew the CD at the same rate for a second six-month term. Thus, after 12 months, the bank’s income statement on December 31 will look like the statement in Exhibit 2.8.

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Defmigg and Quantifying Interest Rate Risk

10/08

Exhibit 2.7 Sample Balance Sheet on January I

Assets U.S. Treasury note

$1,000,000

Mm

Total assets

Liabilities Certificate of deposit

↨ 900,000

Total liabilities

$ 900,000

Capital

5

Capital Total liabilities and capital

100,000

$1,000,000

Exhibit 2.8 Sample Income Statement on December 31 Paying 3 Percent

Interest income ($1,000,000 x .05)

$50,000

Less: Interest expense ($900,000 x .03)

(27,000)

Net income before taxes

$23,000

Exhibit 2.8 shows that ABC Bank earrts a net profit before taxes of $23,000. The net interest margin is calculated by dividing the taxable equivalent net interest income by the average earning assets. Note that only earning assets, not total assets, are used to calculate the net interest margin. For ABC Bank, the net interest margin is $23,000 divided by $1 million, or 2.30 percent.

Now consider the alternative shown in Exhibit 2.9. Here, ABC Bank has the same balance sheet as shown above, but assume that when the CD matures at the end of the first six months, the bank can renew it only for

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Interest Rate Risk Management

a second six-month term at an interest rate of 4 percent. ABC Bank’s income statement afier 12 months would then look like the statement in

Exhibit 2.9.

Exhibit 2.9 Sample Balance Sheet on December 31

Six-Month Renewal at 4 Percent Interest income ($1,000,000 x .05)

$50,000

Less: Interest expense

($900,000 x .03) x (.5)

(13,500)

($900,000 x .04) x (.5)

(18,000)

Total interest expense

(31,500)

Net income before taxes

$18,500

At the 4 percent CD rate, the bank’s profit before taxes is only $18,500. Its net interest margin, calculated by dividing $18,500 by $1 million, is only 1.85 percent.

A comparison of these two calculations reveals the specific interest rate exposure of a bank with this balance sheet composition. The bank has $1 million in assets that do not change their rate of return (i.e., what the bank eams) for five years. The bank also has $900,000 in liabilities that change their cost every six months. The remaining $100,000 has no accounting cost. Because ABC Bank has assets that reprice less frequently than its liabilities, we say that it is liability sensitive. ABC Bank can also be considered to have a negative gap. Because ABC Bank’s balance sheet is liability sensitive, its earnings fall when interest rates rise. When we compare the net income shown in Exhibit 2.8 with the net income shown in Exhibit 2.9, we can calculate that a 1 percentage point increase in CD rates causes the bank’s net income to fall by $4,500 ($23,000 less $18,500). If the CD rate had

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Defining and Quantifying Interest Rate Risk 10/08

fallen to 2 percent at the time of renewal, the 1 percent decrease in rates would have caused the bank’s net income to rise by $4,500.

We can use a number of alternative methods to describe the IRR to the bank with the balance sheet used in these exhibits. For example, if interest rates do not change, the $23,000 net income earned could be considered a “base case.” We could then describe the effects of a 1 percent change in interest rates by saying that such a change would cause a $4,500 or 19.57 percent change in the bank’s eamings. While a 19.57 percent increase in earnings would be nice, a 19.57 percent reduction in earnings is material. Our sample bank therefore has a fairly large and almost certainly tmacceptable quantity of interest rate risk — it is too liability sensitive. Effect on Noninterest Income and Expense

In the exhibits above, we have defined and measured interest rate risk according to its impact on bank earnings. But in our calculations, we

examined only the changes in the bank’s net interest margin that resulted from a change in interest rates. Bank earnings, in both the accounting and economic senses, comprise more than just interest income and interest expense, the net interest margin. The accounting perspective does not end with the net interest margin. A stable net interest margin is not the only goal for asset/liability (AL) managers, even when managers are only concerned about the current year’s earnings. Earnings also comprise noninterest income, principally fee income, and noninterest expense. Both of these categories may also increase or decrease as a result of changes in interest rates. For example, customers who have the choice of keeping minimum balances in their checking accounts or paying fees may choose to keep high balances and avoid fees when rates are low, and to keep low balances and pay the fees when rates are high. The noninterest expense of provisions for loan losses is a second example of a nonmargin change that can be related to changes in prevailing interest rates. This issue is discussed in Chapter 11.

How Interest Rate Risk Affects Equity To see exactly how we define and measure interest rate risk from an economic perspective, reconsider the two examples discussed above. Exhibits 2.8 and 2.9 both have the same starting balance sheet shown in 2-29

10/08 Interest Rate Risk Management

Exhibit 2.7. However, their ending balance sheets are not the same because the income the bank earned during the year was not identical in the two examples. Exhibit 2.10 depicts what the two ending balance sheets look like fi'om an accounting perspective as of December 31. The two difl'erent balance sheets show that, as of December 31, the book value of equity was $123,000 in the first example, but $118,500 in the second example. The difl‘erence of $4,500 represents a 3.7 percent decrease in equity.

Exhibit 2.10 December 31 Balance Sheets from an Accounting Perspective

No Change

+ 100 Basis Points

Assets Cash

$ 23,000

$ 18,500

U.S. Treasury note

1,000,000

1 000 000

$1,023,000

$1,018,500

↨ 900,000

↨ 900,000

$ 900,000

$ 900,000

$ 100,000

$ 100,000

23,000 123,009

18,500 1 18,500

$1,023,000

$1,018,500

Total assets

Liabilities Certificate of deposit

Total liabilities Capital Capital Retained earnings Total capital

Total capital and liabilities

For the economic perspective, we want to consider the economic value of equity. In the first column shown in Exhibit 2.10, interest rates are the same at the end of the year as they were at the beginning of the year. Therefore, in this case, the economic value of equity is the same as the book value.

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Definingand QuantifyinLhiterest Rate Risk 10/08

In the second column shown in Exhibit 2.10, however, interest rates rose by 1 percent on June 30. In this example, the market or economic value of the CD as of December 31 is the same as its book value. This is because when prevailing rates rose 1 percent, the rate on the CD rose by 1 percent. But the market value for the U.S. Treasury note changes — as of December 31, the U.S. Treasury note still has four years of remaining life. It pays interest at a rate of 5 percent, but since prevailing rates have risen by 1 percent, potential buyers will pay a lower price so that they can receive a yield of 6 percent. The price necessary for a four-year investment with a coupon rate of 5 percent to give a yield of 6 percent is 96.4921. That means that in the second example, the market value of the U.S. Treasury note on December 31 is $964,921. With that knowledge, we can calculate the economic value of equity as shown in Exhibit 2.1 1. Exhibit 2.11

December 31 Balance Sheets from an Economic Perspective Assets Cash U.S. Treasury note Total assets

No Change

3 23,000 1,000,000

$ 18,500

964 21

W

mam;

3 900,000 $ 900,000

↨ 900,000 $ 900,000

$ 100,000

$ 64,921

23,000 123 000 $1,023,000

$ 983,421

Liabilities

Certificate of deposit Total liabilities

Capital Capital Retained earnings Total capital Total capital and liabilities

+100 Basis Points

18,500 83,421

Thus, from an economic point of view, the impact of a 1 percent increase in interest rates on our hypothetical bank is a decline in the economic value of equity. If interest rates do not change, the economic value of equity is $123,000 as of December 31. If rates rise by 1 percent, the economic value of equity is $83,421. The difl‘erence of $39,579 represents a 32 percent decrease in equity.

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Interest Rate Risk Management

Notice that for Exhibit 2.11, the economic value of the Treasury note is the same as its market value. This is true for instruments that are traded in active markets. However, most bank assets and liabilities are composed of instruments that are not actively traded. If we had chosen to illustrate a loan asset rather than a T-note, we would have had to calculate an economic vaIUe for that asset. The same is true if we had chosen to illustrate a longer term CD that would, because of its term, not be repriced to the current market rate level within the one-year time period used in the illustration. In short, we cannot rely on market values to measure the impact of rate changes on equity. In the real world, we need methods for calculating the economic value of assets and liabilities. These methods will be discussed in Chapters 4 and 5.

Accounting Perspective vs. Economic Perspective As illustrated above, interest rate risk can be viewed from two different but complementary perspectives:

∙ ∙

The accounting perspective defines and quantifies interest rate risk as the change in earnings caused by a change in interest rates. This is the traditional accounting perspective.

The economic perspective defines and quantifies interest rate risk as the change in the economic value of equity that occurs as asset portfolio values and liability portfolio values rise and fall with the changes in interest rates.

Neither of these perspectives provides the sole, correct view of interest rate risk. And each has advantages and limitations that must be understood. Accounting Perspective

— Advantages and Disadvantages

The one important advantage of the accounting perspective for the asset/liability management analyst is that the numbers this perspective uses best match the numbers that most people use. For the most part, boards of directors, industry analysts, and regulators look at reported earnings and the book value of the bank’s balance sheet. Even though market values are used for trading account assets and in footnotes to fmancial reports, it is the accounting perspective that most people rely

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Defining and Quantifying Interest Rate Risk 10/08

on. Changes in the reported earnings affect a bank’s cost of funds, its liquidity, its ratings, and its stock value. Therefore, measurements of interest rate risk that relate that risk to changes in reported profits are relevant.

But the accounting perspective also has a number of disadvantages, the most significant of which is that it focuses the asset/liability analyst on only the near-term efl‘ects of changes in interest rates. If we had a bank that had as its only asset a 30-year U.S. Treasury bond and as its only liability a five-year CD, an analysis of interest rate risk from an accounting perspective would show that there is zero interest rate risk in the first year. That is clearly incorrect. The sample bank has a large exposure now to changes in interest rates, even though the impact of this exposure on the bank's earnings does not begin until the end of the fifth year. Furthermore. the exposure lasts for 25 years! (Other weaknesses in the accounting perspective are discussed in Chapter 3.) Economic Perspective

—

Advantages and Disadvantages

The one important advantage of the economic perspective for the asset/liability analyst is that it focuses on the sensitivity of the economic value of equity to changes in prevailing interest rates. This provides a comprehensive measurement of interest rate risk. In addition to reflecting the sensitivity of all assets and liabilities, it reflects the sensitivity of all embedded options and other important influences on value that are not captured by accounting conventions. Embedded options are discussed in Chapter 7, and influences not captured by conventional accounting methods are discussed in more detail in Chapters 3 through 7. Equally as important, the economic perspective reflects those sensitivities across the full maturity spectrum of the bank's assets and liabilities. But the economic perspective also suffers from a number of disadvantages. One major disadvantage is the fact that the sensitivity of the economic value of equity to changes in prevailing interest rates can tell the asset/liability analyst a lot about the quantity of interest rate risk, but nothing about its timing. Managers need to know IRR timing as well as the quantity. Steps undertaken to reduce risk in year one may be different from steps undertaken to reduce risk in year five.

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10/08 Interest Rate Risk Management

A second major weakness in the economic perspective is that it is subject

to a large number of practical problems and must rely on a considerable number of subjective assessment factors. It is relatively easy to calculate the market value of a bond with a fixed rate of interest and a fixed maturity. It is considerably more difficult and far less objective to calculate the economic value of a savings account with no fixed maturity and a rate that bank management can change from time to time. Many of the problems with the economic perspective are discussed in more detail

in Chapters 5 through 7.

Best Usefor Each Perspective Clearly, the accounting and economic approaches to defining and measuring interest rate risk are complementary. The main strengths of each at least partially ofi’set their primary weaknesses. The accounting perspective focuses on the impact of interest rate risk on the reported earnings of the bank. It tells the asset/liability manager a lot about both the timing and the magnitude of the changes in income resulting from changes in prevailing interest rates. The economic perspective captures more information and reflects all time periods. Three methodologies — duration-based economic value of equity, economic value of equity simulation modeling, and value at risk —— employ economic perspective: to measure interest rate risk.

After all is said and done, approaches that may be described as using the accounting perspective are the best for identifying short-term interest rate risk, while approaches that use the economic perspective are best for identifying long-term IRR. As noted earlier in this chapter, there is no single answer, no magic solution, for IR management.

Drfi'erenl Audiences

—

— Difi‘erent

Points of View

—

Different people inside and outside of the bank all share an interest in the bank’s rate risk exposure. However, they have distinctly difl'erent perspectives and therefore focus on different aspects. These disparate points of view also influence preferences for accounting-based or economic-based measures. Exhibit 2.12 summarizes these differences.

Defining and Quantifying Interest Rate Risk lO/OB

Exhibit 2.12 Different Perspectives on Interest Rate Risk Constituency

Focus

IRR Concerns

Shareholders and Stock

Factors affecting share price:

Impact of [RR management on share price multiple is a function of:

Analysts

Creditors and

Rating.

Agencres Regulators

∙.

. ∙

— —

Current earnings Future earnings (growth and WWW)

[RR component of current and projected earnings Confidence in future JRR results — Downside and upside possibilities Shareholders seem to be more tolerant of [RR than analysts are.

Factors affecting solvency: Capital (book and

economic) Earnings stability

What is the downside risk to current and future earnings and capital? What as-yet-tmrecognized IRR effects are embedded in today's bflance sheet?

Factors affecting stability of the banking system and of individual institutions: Capital (book and economic)

∙ .

Seem to lie between shareholders and creditors re risk tolerance.

Growing emphasis on measures of economic value.

Earnings stability

Source: J. Kimball Hobbs

Why is this divergence of views important? Because without it, we could never understand why some banks have different views toward risk and why they favor accounting or economic-based measurement approaches. In addition, these different points of view help explain other important rate risk management decisions. We will address these disparate needs as they apply to bank policies, management decisions about rate risk exposures and limits, and the impact of rate risk on bank credit ratings and stock prices.

SUMMARY More than anything else, you should take away two insights from the issues discussed in this chapter.

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10/08 Interest Rate Risk Management

1. Both accounting and economic measures of rate risk provide valuable insights into the bank’s risk exposure. These are not competing tools; they are complementary tools.

2. Both earnings and value changes are driven by the impact of changes in prevailing rates on the size of asset and liability positions and on the composition of assets and liabilities Rate changes cause cash flow changes. Some of the cash flow changes result from contractual provisions in the instruments, for example, floating rates. Other cash flow changes result from the combination of contractual provisions and customer behaviors, such as loan prepayments. Understanding the direct and indirect impacts of rate changes on cash flows is the key to measuring rate risk. Altering the net cash flow impact of rate changes is the key to managing interest rate risk.

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Chapter 3 Income Simulation

An Improved IRR Measurement Approach .......................................... 3-1 What Is Income Sensitivity Simulation? .......................................... 3-2 Prerequisites for Superior Income Simulation .................................. 3-3 Understanding the Simulation Process Dynamics .......................... 3-10 Understand the Dangers and Benefits of Simulating Future Business and Risk Management Actions ........................................ 3-10 Exhibit 3.1: Illustration of the Simulation Process ..................... 3-11 Income Simulation Inputs, Processes, and Outputs ............................ 3-12 Income Simulation Inputs: Data and Assumptions ........................ 3-13 Income Simulation Outputs: Summary Tables and Graphs ........... 3-15 Exhibit 3.2: ABC Bank Projected Earnings Under Nine Difi‘erent Rate Scenarios ............................................................ 3-16 Exhibit 3.3: ABC Bank Change in Earnings Under Nine Difiemnt Rate Scenarios ............................................................ 3-17 Exhibit 3.4: ABC Bank Percent Change in Eamings Under Nine Different Rate Scenarios .................................................... 3-17 Uneven Outcomes ...................................................................... 3-18 Earnings at Risk vs. the Rate Sensitivity of Risk-Neutral Earnings ...................................................................................... 3-19 Stunmary Reports Depicting Changes Over Time ..................... 3-19 Exhibit 3.5: Cumulative EAR Caused by a 200 bp Rate Change ........................................................................................ 3-21 Exhibit 3.6: Trend in Net Income: Actual Plus Four Projected Scenarios .................................................................... 3-21 Exhibit 3.7: Quarterly Trend in EAR ......................................... 3-22 Using Income Simulation to Evaluate IRR ........................................ 3-23 Dollar Dispersion ........................... 3-23 Evaluating Bankwide Risk Percentage Deviation from Base Case ............................................ 3-24 Evaluating How the Constituent Elements Contribute to the Overall Risk Level.......................................................................... 3-25 Risk by Product .......................................................................... 3-25 Exhibit 3.8: Forecasted Changes in Asset Yields and Liability Costs (for a 200 basis point rate increase) ................... 3-26

—

2/09

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2/09 Interest Rate Risk

Management

Risk by Information Source ....................................................... 3-27 Exhibit 3.9: Components of Expected Cash Flows .................... 3-27 Using Income Simulation to Manage IRR ...................................... 3-28 Advantages of Income Simulation Modeling..................................... 3-28 Specific Measure of Rate Risk Exposure ....................................... 3-28 More Accurate Reflection of Reality .............................................. 3-29 Focus on Changes That Count ........................................................ 3-30 3-30 Focus on Management’s Reactions to Changes Flexibility in Reflecting Rate Shifts for Difi‘erent Maturities......... 3-30 Flexibility in Reflecting Basis Changes in Different Instruments ..................................................................................... 3-3 1 Integration with Other Management Information Processes .......... 3-32 Disadvantages of Income Simulation Modeling ................................ 3-32 Assumptions Require Careful Development, Analysis, Increased Controls, and Testing ..................................................... 3-33 Assumptions Can Intentionally or Inadvertently Understate Risk Exposures ............................................................................... 3-33 More Complex Interest Rate Risk Management ............................ 3-34 Understatement of Long-Term Interest Rate Risk .......................... 3-35 Limited Number of Alternatives May Not Capttu'e the Full Extent of the Bank’s IRR Exposure ............................................... 3-36 Accuracy May Be Impaired by Limited Incorporation of Interrelations Between Variables .................................................... 3-37 Summary ............................................................................................ 3-38

3-ii

Chapter 3 Income Simulation

Rate risk analysts must be able to measure interest rate risk (IRR) using methods that accurately capture changes in the volume and timing of the multiple cash flows and diverse interest rate changes that occur in banks.

AN IMPROVED IRR MEASUREMENT APPROACH What are the requirements for a better IRR measurement approach? El First, the measurement system must enable you to understand the size and direction of your bank’s interest rate exposure under a variety of interest rate scenarios. This is true whether you use simulation modeling to measure the risk of a change in net income or other measures of IR exposure, such as the change in the economic value of equity (discussed in Chapter 5).

Second, the system must readily and accurately capture all of the important data for volumes, maturity dates, repricing dates, and hidden options that accurate rate risk measurement requires. This is not simple. It requires a great deal of data from many different operational areas within each bank. Third, the data must be used in ways that clearly focus attention on the critical variables. If the analysis indicates an unacceptable level of IRR, you must be able to identify which variables are

responsible. Forum, the system must be dynamic. It must facilitate easy and accurate accommodation of all of the new loans, new deposits, withdrawals, repayments, and other changes. We know that such changes will occur even though we cannot predict exactly how much will change or exactly when it will change.

2/09 Interest Rate Risk

[I

Management

Filth, the system must be able to reflect that changes in prevailing interest rates affect different assets and liabilities in different ways. As we have discussed, both the timing and the amount of the changes in rates paid or received on bank products respond differently to the same change in prevailing interest rates.

In short, bank managers need a rate risk management system that combines the advantages of management-adjusted gaps, dynamic gaps, and beta-adjusted gaps without all of the disadvantages of gap reports. Income simulation analysis accomplishes most of these goals far better than gap analysis. In fact, income simulation analysis captures the dynamic aspects of short-term bank IRR better than any other alternative. In Chapter 2, we saw that IRR can be viewed from two different but complementary perspectives. The traditional accounting perspective defines and measures IRR as the change in earnings caused by a change in interest rates. This perspective provides the best view of short-term IRR exposure. The economic perspective defines and measures IRR as the change in the economic value of equity caused by a change in interest rates. This perspective provides the best view of long-term IRR exposure. Income simulation modeling, like gap analysis, provides an accounting perspective for IR. Economic approaches are discussed in Chapters 4 and 5. What Is Income Sensitivity Simulation?

Income simulation modeling is a tool for measuring rate risk exposure. The simulation process produces a set of income projections. Comparisons of those projections enable rate risk managers to measure and analyze the sensitivity of income to potential future changes in prevailing interest rates. Perhaps the single most distinguishing characteristic of income simulation modeling as an asset/liability management tool is that it is forward looking. Income simulation modeling, like forecasting, looks at alternative futures and the potential effects of those futures. In this sense, income simulation modeling is unlike gap analysis and duration analysis. Both of those approaches concentrate on accurately measuring where the

Income Simulation 2/09

bank is now. Income simulation modeling evaluates the IRR arising from both a bank’s current position and its forecast of future business.

Because of the very nature of their business, banks have highly developed systems for historical accounting. Bankers usually know their prior performance and current condition with great accuracy; however, they are often less familiar with the world of projections, forecasts, and simulations. Historically, banks have used prospective accounting only to prepare budgets. Since budgeting requires many of the same assumptions about future interest rates and asset and liability volumes, some banks use the same software package to prepare budgets and to measure IRR. The goal of income simulation modeling is to forecast how net interest income, and therefore net income, varies in response to changes in prevailing interest rates. In other words, we are not as concerned with the projected amount of net income as we are with the sensitivity of that amount. This is often referred to as earnings at risk, or EAR.

Prerequisites for Superior Income Simulation Before we conduct an income simulation, answer the following four preliminary questions. (We can successfully perform a simulation analysis knowing the answers to only the first three of the four questions discussed in the following paragraphs, but it is more useful if we address all four.) 1. What is our base case? The amount of interest rate risk exposure measured by income simulation, as we have just observed, is referred to as EAR. We calculate earnings at risk by subtracting the projected earnings after a projected change in prevailing interest rates from the projected earnings absent a change in prevailing rates. In other words, the EAR is the difl'erence between a change projection and a base projection. two projections

—

The base projection, usually called the “base case," should be selected carefully. It is the reference point against which EAR is measured. As one author suggested, the base case is like the “you are here” sign on a map. You can’t know how far you are from where you want to be unless you know where you are. While there are many alternatives and variations for the selection of a base case

2/09

Interest Rate Risk Management

starting point, three main choices are described in the following paragraphs. (Note that these three choices consider the base case as a single choice. However, as we will discuss later in this chapter, we will actually have a base case rate scenario and a separate base case “business” scenario describing asset and liability volumes.) Bank Case I: No Change in Rates or Volumes. The base case can be an income projection that assumes absolutely no changes in prevailing interest rates, no changes in customer preferences, no changes in bank products or prices, no changes in bank competition or market conditions, and no changes in bank strategies. This is sometimes referred to as the static case or static scenario. Many banks like to use a “no change” base case. They consider it a “pure” standard of comparison against which EAR can be calculated. In effect, a “no change" base case isolates all changes in the amount of measured EAR.

Rate risk managers using a “no change” base case need to be careful not to ignore some biases in this scenario. The “no change in rates or volumes” scenario is not as pure as it may seem. For one thing, it ignores all future changes in deposit and loan volumes, which are inevitable, ofien material, and often linked to changes in prevailing rates. (This point is also addressed in the two alternative approaches to choosing a base case, which are discussed next.) A second bias in the “no change” base case arises from the slope of the yield curve. Short-term interest rates are almost always lower than long-term rates, yield curves almost always have an upward slope. (We call such a slope “positive.”) At the same time, it is extremely unlikely that your bank has a perfectly risk-neutral balance sheet at all times. You may be asset sensitive. Most of the time, most banks are at least a little bit liability sensitive. When yield curves have a positive slope, an asset-sensitive bank will always earn less just because it is borrowing liabilities at a longerterrn (higher rate) point in the yield curve than it is investing its assets. For the same reason, when yield curves have a positive slope, a liability-sensitive bank will always earn more just because it is borrowing its liabilities at a shorter-tenn (lower rate) point in the yield curve. The combination of the rate risk exposure in your

3-4

Income Simulation 2/09

current balance sheet and the current slope of the yield curve will almost always mean that the “no change” base case incorporates some rate positions.

This does not mean that a “no change” base case is a bad choice. It simply means that comparisons between the “no change" base case and exposure positions that we will calculate later are not pure comparisons. They are impure in the sense that we cannot say that 100 percent of the difference between the net income in our “no change" base case and the net income in our subsequent projection is the measure of our rate sensitivity. Some rate sensitivity is also in the base case. Bank Case 2: The Most Likely Change in Rates and Volumes. Altemately, some banks feel that it is misleading to use a “no change” base case. These bankers argue that EAR should measure only the change in earnings caused by a change in prevailing rates. According to this argument, it is okay for secondary effects, such as changes in customer behavior, to be included in EAR because those changes are prompted by the change in prevailing rates. It is not okay, according to this argument, to include changes, such as the normal grth in loans and deposits, that have nothing to do with a change in prevailing interest rates. Bankers following this line of reasoning usually prefer to use a base case that might be described as the “most likely” earnings scenario.

A “most likely“ base case may be derived in several different ways. One technique is to examine historical changes in bank assets, liabilities, income, and expense. Some historical changes are the result of trends that can be expected to continue, while other changes are not likely to recur. Bank Case 3: The Budget as the Base Case. A more elaborate “most likely” base case scenario can be created by incorporating the present position with the changes expected by the managers of each revenue- and expense-generating activity in the bank.

Of course, an elaborate “most likely" base case scenario is a lot like a budget. In fact, many bankers prefer to use their budget forecast as the base case. This has two advantages. First, the

3-5

2/09 Interest Rate Risk

Management

budget process already includes well—developed procedures for capturing the changes planned by revenue and expense managers. Second, when the budget is used as a base case, projections of EAR are also projections of how much changes in prevailing rates will alter budgeted net income. Unfortunately, there is one problem with using the bank’s budget as the base case scenario. When preparing their budgets, many banks incorporate their expectations for future interest rates into their budget projections rather than assuming no change in rates. For these banks, the budget already has a rate change scenario “cooked in.” Therefore, if they calculate EAR by subtracting the projected change in eamings after a change in prevailing interest rates from the projected earnings in the base case, they are really measuring the EAR caused, in part, by the difl‘erence between the rate change in the base case and the rate change in the projected rate-change scenario. In other words, when the base case scenario incorporates expected rate changes, measruements of EAR are most difficult to interpret. 2. What time horizon do we want? Income simulation analysis tends to focus on the cumulative one-year gap. This is even more true for income simulation. Bankers and bank analysts pay close attention to annual earnings when they consider bank profitability. If a change in prevailing interest rates causes a bank to sufl‘er a decline in earnings in one month that is offset by an improvement in earnings in the following month, few will mind. In such a situation, the increase or decrease in earnings caused by the rate change may even be fully or more than fully offset by other eamings changes caused by other rate changes or by other factors. Consequently, the bank’s earnings for the year may not even reflect the consequences of a one-month decline caused by a change in prevailing interest rates. 0n the other hand, a change in prevailing interest rates that causes a bank to suffer a decline in earnings for one year will be noticed even if it is ofi‘set in the following year. Throughout this chapter, the discussions and exhibits generally use a one-year time horizon.

3-6

Income Simulation 2/09

No matter how good a job our income simulation does in capturing the bank's exposure to changes in prevailing interest rates during a one-year time period, it is important to remember that none of the bank's intermediate-ten'n or long-term interest rate risk is captured in that horizon. Some proponents of income simulation argue that this is not tremendously important because management needs to focus on the one-year horizon. That conclusion is too simple, however. Even though management should focus on a one-year horizon, it would be foolish to ignore potentially major adverse effects just because they are not yet — within that horizon. Other proponents of income simulation argue that the one-year horizon is not overly limiting because management has more time and more strategic alternatives available to deal with longer-term problems. That conclusion is also too simple. No amount of time or flexibility is adequate to plan for a problem that we don’t yet

—

know exists.

In reality, the amount of interest rate risk not captured by an income simulation using a one-year horizon may or may not be material. We cannot know this until we look. Therefore, it is prudent to look. This can be done in a number of different ways. Some bankers use income simulations with longer horizons of two to five years. This enables them to focus on the one-year rate risk exposure while still obtaining information on longer-term exposures. This approach suffers from two related difficulties. First, the assumptions used in income simulation become increasingly dubious as they are applied to customer behavior and bank actions in increasingly distant time periods. Second, sometimes it is difl'rcult to consider the relative priorities and dangers of short- and long-term rate exposures.

A variation of the multiyear time horizon approach minimizes both of those problems. Some banks simulate the interest rate risk for each year in the next five years. Then they discount the measured EAR for future years to calculate the present value for each EAR quantity. (When this is done, the discount rates should reflect the time periods but should not be adjusted for the rate changes or rate shocks used in the simulations.) Since the discount process

2/09 Interest Rate Risk Management

produces progressively smaller present values for the same quantity, as the quantities move further and further into the future, this technique gives a greater weight to short-term exposures and a smaller weight to longer-term exposures. It is a good way to use income simulation for capturing and evaluating both short-term and intermediate-term exposures. A third approach, which is discussed later in this manual, is to use income simulation to capture rate risk exposures within a one-year. horizon and to use an economic approach to measure interest rate risk exposures over all time periods. The use of two methods is recommended by bank regulators and is common in larger banks. 3.

What changes in interest rates do we want to examine? Undoubtedly, one of the most valuable features of income simulation modeling is the capability to examine the sensitivity of net income to a variety of possible future interest rate changes. Obviously, some bank management strategies are more lucrative in rising rate environments, while others are more lucrative in falling rate environments. Instead of only studying the changes in income that might result from one given change in prevailing interest rates, banks can model the effects of different future rate scenarios. The simplest applications of income simulation modeling reflect the effects of rate shocks. A rate shock is a one-time, instantaneous increase or decrease in all interest rates. Banks ofien model plus and minus 200 and 300 basis point rate shocks. To do a rate shock analysis, we assume all interest rates change by the amount of the shock. For example, in a 300 basis point increase rate shock, the prime rate is increased from whatever rate it is at the time of the modeling to a rate that is 300 basis points higher. Note that while the rate changes in a rate shock analysis occur instantaneously, the bank’s deposits, loans, and investments are not affected by those rate changes until the first repricing date of each instrument. For example, prime rate loans may reprice immediately, but CDs

reprice at maturity.

Income Simulation 2/09

Of course, income simulation modeling need not apply simple assumptions about uniform increases or decreases in interest rates. Models can and should be used to study much more realistic projected changes. For example, instead of studying the changes in income that might result from a change that affects interest rates for all financial instruments equally, a bank can model the effects of a change that affects rates on some assets and liabilities more than it affects rates on others (this is basis risk). Thus, income simulation modeling can be used to more realistically show larger changes in more sensitive rates. Similarly, instead of studying the changes in income that might result from a change that affects short-term and Iong—tenn rates by the same amount —— a parallel yield curve shift — a bank can model the effects of more realistic changes in which rates for some maturities change by larger amounts than rates for other maturities (this is yield curve risk).

Many banks model the effects of three different rate scenarios: a rising rate scenario, a no-change rate scenario, and a falling rate scenario. Banks that use a base case scenario that is not the no change in rates scenario often model the effects of four different rate scenarios: rising rates, falling rates, no change in rates, and the base case. Some banks choose to examine more than one rising and falling rate case and, therefore, use even larger numbers of future rate scenarios. In Chapter 8 we discuss how to select potential rate changes to model. What changes in business conditions do we want to examine? Measuring EAR requires more than just modeling the impact of changes in prevailing rates on projected net income. It is also necessary to recognize that both bank customers and bank product managers make different decisions in different interest rate environments. Customer behavior is difl‘erent in different rate environments. For example, in high-rate environments, residential mortgage borrowers may prefer adjustable-rate loans, but in lowrate environments, they may prefer fixed-rate loans. Customer behavior also changes in response to different bank pricing and marketing decisions. For example, in a rising rate environment, the bank may not raise the rate it pays to savings passbook depositors as fast as it raises rates it pays for certificates of deposit (CDs). In

2109 Interest Rate Risk Management

response, customers may move some deposits from savings accounts into higher yielding certificates. As this example illustrates, rate risk analysts need to consider difi'erent bank behaviors in different rate environments in addition to differences in customer behavior in different rate environments. Accurate measurement of EAR requires the simulation of different business strategies as well as difl‘erent rate environments.

Understanding the Simulation Process Dynamics

At its most simple, the simulation process has just three steps. First, we select some interest rate scenarios to evaluate. Second, we run the simulation model to calculate the impact of the rate scenarios on our assets and liabilities. Third, we evaluate the range or sensitivity of net income calculated for the set of rate scenarios. However, the real benefits of income simulations are realized when we use simulations more dynamically. Exhibit 3.1 illustrates this process. Notice that the process can be seen as a loop. In the first part of the loop, the business scenarios for assets and liabilities and the selected rate scenarios are used to produce a simulation analysis that indicates a set of net income outputs. As we just discussed, the business condition assumptions should be tailored to fit the conditions associated with a particular interest rate scenario. Then, in the second part of the loop, the sensitivity of net income is compared with management’s desired limits or targets. If any of the scenarios result in undesirable projected outcomes, the bank can plan on making changes in its customer business or in its discretionary funding or hedging activities to alter its projected exposure. Understand the Dangers and Benefits of Simulating Future Business and Risk Management Actions The incorporation of new business, funding, and hedging strategies is a key characteristic of income simulation modeling. It is also both a major advantage and a major weakness of this tool. The benefits of including future changes are clear and compelling. A static analysis implicitly assumes that the current book of business runs off. Ignoring the volumes of renewed, rolled over, and replaced assets and liabilities can introduce huge errors. Furthermore, as we have also observed, it is simply

3-10

Income Simulation 2/09

unrealistic to assume that bank managers will not make different strategic business decisions in dramatically different interest rate environments. Exhibit 3.1 Illustration of the Simulation Process

Selected Interest Rate Scenarios

Changes in rates paid on adjustable rate instruments and

Selected Business Scenarios

Changes in asset and liability ‘ volumes and mix

new instruments

−∙ Sets of projected Simulatons

net income for the various scenarios

Seleted Hedging Scenarios

One offsetting weakness is that projections of new business, changes in funding strategies, or future risk management activities require assumptions which, in turn, introduce unavoidable errors. It is very hard to predict future business accurately. Moreover, errors in new business assumptions for various loans and deposits do not necessarily come close to canceling each other out. Sometimes errors iir future business assumptions have the net effect of overstating rate risk exposure. Managers can then take actions in the belief that they are reducing their exposure when in fact their actions actually increase their risk exposure. Sometimes anticipated future business has rate risk characteristics that offset the rate risk exposures in current positions and thus masks the

2/09 Interest Rate Risk Management

extent of the bank's current risk exposure. In those circumstances, the assumption errors for new business can leave the bank vulnerable because managers may see the need for risk reduction measures. Because future business assumptions are more prone to error, the reliability of measured risk is diminished.

incorporating projections for new business and future funding is not just a source of inevitable assumption errors. In some instances, future business goes so far as to include prudent future risk reduction or

hedging activities. This can result in the disquieting effect of measured risk always residing within limits by definition.

INCOME SIIVIULATION INPUTS, PROCESSES, AND OUTPUTS Over a dozen sofiware vendors offer income simulation models. (Models are also available to calculate the interest rate sensitivity of equity, an economic perspective on IRR discussed in Chapter 5. Some sofiware packages ofl‘er both measurement approaches.) The essential functions of all these income simulation software packages are roughly the same, but they have major differences in methodologies, features, and ease of use. in essence, the core of any income simulation model is nothing more than a giant set of simple arithmetic operations. For example, if we currently have $100,000 invested in an asset that earns 8 percent for the next six months, and we project that the interest rate for that asset will be 9 percent for the subsequent six months, our projected gross interest income from that asset for the next year will be $8,500. (First we multiply the $100,000 by 0.08 and then divide that result by two, since we only earn the 8 percent for half the year. Then we multiply the $100,000 by 0.09 and divide that result by two. Next, we add the results from the two six-month periods.) After we repeat this sort of calculation for every group of investments, loans, and deposits included in the model, an income projection will pop out.

What we might call “low-end models” require the user to come up with his or her own projections for volume changes resulting from the impact of rate changes on customer loan and deposit volumes. They also require the user to come up with his or her own projections for changes in the shape of yield curves, difi‘erences between yield curves for different

3-12

Income Simulation

products, and other rate dynamics. At the other extreme, a handful of “high-end models" use complex mathematics to evaluate the affect of options, yield curve dynamics and other variables. A more complete discussion of modeling sofiware is in Chapters 9 and [0.

Income Simulation Inputs: Data and Assumptions Regardless of whether you use a basic or advanced model, the actual simulation of net income requires a great deal of information. Users must information obtain factual information about the current position about currently outstanding assets and liabilities. Users must generate a forecast of expected future activity. For both current and anticipated business, we need to know the balances, the rates, and the maturity or repayment terms. More accurate analysis requires additional information such as interest rate caps on loans and about the current position more information about forecasted balances — such as changes in deposit withdrawals and loan prepayments.

—

—

—

New business volume forecasts can be particularly difficult. Growth

rates, for example, should be consistent with rate scenarios. If rates rise by 200 or 300 basis points from current levels, customer demand for new loans is likely to be considerably lower than it would be in the sort of economic conditions that might prevail if rates fell to 200 or 300 basis points below current levels. Scenario analysis, discussed earlier in the

chapter, addresses this concern.

On the other hand, new business rate forecasts are less important. Most with the important exception of savings accounts and new business other administered rate deposit products — is added at currently prevailing market rates. Therefore, except for administered rates, any changes in the spread relationships between products tend to be more important than changes in the rates themselves.

—

A sense of proportion is critical. More detailed inputs can improve accuracy. But excessive detail is ofien not worth the time and effort it takes to obtain the information and input it into your model. We can illustrate this point by considering how two different banks treat their mortgage pass-through securities. At one extreme, the Simple Bank models all of its MBS pass-throughs with a single set of prepayment assumptions. Simple Bank employs an 8 percent CPR in their flat-rate 3-13

Interest Rate Risk Maggement

assumption, a 12 percent CPR for its down 200 basis point rate scenario and a 6 percent CPR for each rising-rate scenario. Even if those CPR levels are completely appropriate for its average MBS, the Simple Bank will not capture the potentially significant rate sensitivity of its MBS assets very accurately. lts higher coupon pools are likely to prepay more perhaps much more rapidly. At the same time, its lower rapidly coupon MBS pools are likely to prepay more slowly.

—

The Simple Bank would achieve far more accurate results by modeling groups of MBS pools separately. It might, for example, group the pools by coupon. In that case, prepayment assumptions for M385 with coupons between 7 and 8 percent would be different fi'om the prepayment assumptions for MBSs with coupons between 8 and 9 percent. On the other hand — and this is a key point — the extra accuracy that can be obtained by modeling each MBS instrument individually is not worth the time and cost. Consider, for example, a practice used by Detail Bank. The Detail Bank models each MBS pool individually. The Detail Bank owns numerous MBS pass-through pools that have similar coupon rates and similar contractual maturities. A 25-year mortgage and a 30-year mortgage with the same coupon rate will both prepay at very similar rates. Both have most of their prepayments in the first 60 months. The Detail Bank is not making much improvement in its measurement of rate risk by modeling those instruments separately. The same is not true for CMOs. Since CMO structures tend to vary considerable from one instrument to the next, even when they are both described as the same type, more accuracy often results from modeling them individually. Therefore, if both of our example banks hold material amounts of CMO instruments, the Simple Bank is missing risk in those instruments while the Detail Bank finds that its extra effort results in much more accurate risk measurement. In short, more detail may or may not provide a material improvement in forecast accuracy. Rate n'sk modelers must apply a well-considered sense of proportion.

You can maximize the insights from EAR analysis by modeling changes in volume and mix that are driven by changes in interest rates. The most sophisticated applications of income simulation modeling use scenario analysis. (it may be more accurate to call it strategy analysis.) Scenario

Income Simulation

analysis allows the bank to incorporate a wide range of assumptions to produce the most realistic possible estimates of all of the changes that really occur when interest rates change. Scenario analysis can and should be used to reflect that neither bank customers nor bank managers want the same amounts of loans and deposits in different interest rate scenarios. Instead of studying the changes in income that result from the impact of future interest rate changes on the bank’s current level and mix of assets and liabilities, scenario analysis can model the effects of rate changes on a variety of possible future levels and mixes of business. For example, a rising rate simulation might forecast less growth in loans and more growth in CDs than a falling rate forecast. (Such an assumption represents one example of changes in consumer preferences.) Exhibits 3.2, 3.3 and 3.4 all reflect alternative business scenarios. Income Simulation Outputs: Summary Tables and Graphs

All of the income simulation software packages produce detailed reports of projected assets, liabilities, income, and expense for every interest rate scenario created by the asset/liability (AL) analysts. The reams of detailed information in sets of balance sheets, income statements, and comparative analysis reports for each interest rate scenario modeled are fine for IRR analysts, but not for bank decision makers. The simulation model’s output should also include tables and graphs that summarize the IRR assessment. These are very useful to rate risk managers who must present explanations of their bank’s IRR exposure to senior managers and directors. Exhibit 3.2 is a sample summary table. In spite of the fact that it is much briefer than a full set of financial reports, there is a huge amount of management information available from this table. Start by reading across the base case-strategy line. On this line, we can see the bank’s exposure to changes in interest rates. This is the IRR in the bank’s current position. The bank’s base case business strategy positions the bank to be slightly liability sensitive. If interest rates rise, net income will decrease, and if they fall, it will increase.

Note that bank managers are not limited to the three interest rate scenarios shown in the three columns of Exhibit 3.2. It is just as common, if not more common, to show four rate scenarios: most likely, rising rates, flat rates, and falling rates. (Note that the rising and falling

Interest Rate Risk MaEgement

interest rate scenarios represented by the first and third columns are actually examples of simple rate shocks.) Obviously, managers are not limited to modeling the effects of just three different business strategies, such as those listed on the left side of Exhibit 3.2. (Note that business strategy 1 and business strategy 2 are examples of scenario analysis.) However, employing three different strategies is adequate and probably the most common usage.

Exhibit 3.2 ABC Bank Projected Earnings Under Nine Different Rate Scenarios Projected Net Income for the Bank (amounts in thousands) Rising Interest Rate Scenario

Flat Interest Rate Scenario

Declining Interest Rate Scenario

up 200 bp

no change

down 200 bp

Business strategy 1:

$2,550

$2,450

$2,400

Base case strategy:

$2,400

$2,500

$2,650

Business strategy 2:

$2,300

$2,600

$2,850

Earlier in this chapter we observed that the projected changes in net income, rather than the amount of projected net income, was more illuminating. We referred to the projected change in net income resulting the sensitivity of net income from a change in prevailing interest rates as the amount of earnings at risk. Exhibit 3.3 restates the same information shown in Exhibit 3.2. However, in Exhibit 3.3, we see only the changes in earnings the EAR. Reporting the EAR rather than the absolute amounts has two advantages. First, it is easier to see the impact of the different rate scenarios and the different business strategies in Exhibit 3.3 than it is in Exhibit 3.2. Second, the relative changes may be more accurate than the absolute amounts because many of the errors that will occur in the assumptions or in the data will pollute the flat-rate base case and some or all of the other projections in equal amounts. To the extent that errors affect both numbers in equal amounts, the change between the two numbers —— the measured EAR is unaffected by the errors.

—

—

—

—

3-I6

Income Simulation

Exhibit 3.3 ABC Bank Change in Earnings Under Nine Different 'Rate Scenarios Earnings at Risk (amounts in thousands)

Rising Interest Rate Scenario

Flat Interest Rate Scenario

Declining Interest Rate Scenario down 200 bp

up 200 bp

no change

Business strategy 1:

+50

—50

—100

Base case strategy:

- 100

-0-

+150

Business strategy 2:

—200

+100

+350

Not surprisingly, it is often more useful to show the asset/liability management committee (ALCO) the EAR expressed as percentages rather than dollars. We can see a restatement of the EAR from dollars in Exhibit 3.3 to percentages in Exhibit 3.4. Exhibit 3.4

ABC Bank Percent Change in Earnings Under Nine Different Rate Scenarios Earnings at Risk Rising Interest Rate Scenario

Flat Interest Rate Scenario

Declining Interest Rate Scenario

up 200 bp

no change

down 200 bp

Business strategy 1:

+2%

-2%

-4%

Base case strategy:

-4%

-0-

+6%

Business strategy 2:

—8%

+4%

+14%

Note that the percentages shown in Exhibit 3.4 are in round numbers. We choose not to show hundredths, or even tenths, of percentage points because of the inherent imprecision in these projected outcomes. After all, if any of the many assumptions used to calculate our earnings at risk

Interest Rate Risk Management

are even a little bit inaccurate, our projected outcomes are likely to be more than a few tenths or hundredths of a percentage point inaccurate. Using round numbers focuses us on the approximate magnitude of the EAR without implying a false degree of precision.

Uneven Outcomes As we observed above, the base case business scenario shows that the bank is slightly liability sensitive. Note that even though rates are projected to rise and fall by an identical 200 basis point move, the resulting $100,000 decrease in income is smaller than the resulting $150,000 increase in income. In other words, the notional changes are asymmetrical. Rising rates hurt this bank, but they hurt it to a smaller extent than falling rates help it. Asymmetrical outcomes are typical.

We can identify two reasons for the asymmetrical projections. The first is the benefit that the banks receive from being liability sensitive. Recall that a liability-sensitive bank is, on average, borrowing short and lending or investing long. Accordingly, the liability-sensitive bank benefits from the spread that it receives from the difference between short- and longterrn rates. As we have observed, yield curves almost always slope that is, long-term rates are almost always higher than shortupward terrn rates. We call this a positive or upward sloping yield curve. As long as yield curves have a positive slope and rates do not increase, banks can make more by borrowing short and lending long by being liability sensitive. But borrowing short and lending long is costly when rates rise. We can see this in the decrease in net income projected to result from increases in rates. However, the amount of the loss resulting from an increase in rates is slightly offset by the advantage of borrowing short and lending long.

—

—

The second reason for asymmetrical projections is that there are embedded or hidden options in the bank’s loan and deposit portfolios. Consider mortgage loans. Many borrowers prepay their loans. Some prepayments are due to mortgages being refinanced at lower rates. Obviously, more refinancing occurs when rates fall and less when rates rise. As a result, more existing fixed-rate assets are lost in falling rate environments. Of course, other embedded options in other bank products can affect IRR exposure in the opposite way. (This problem is discussed in Chapters 2, 6, and 7.)

3-18

Income Simulation

Earnings at Risk vs. the Rate Sensitivity of Risk-Neutral Earnings When we examine reports such as those shown as Exhibits 3.3 and 3.4, the EAR. For we focus on the measured sensitivity of earnings example, we can look at Exhibit 3.4 and see that a 200 basis point increase in prevailing rates will cause a 4 percent decrease in our net income if everything else stays the same. That is an accurate and useful way of viewing these model results. For this example bank’s risk-neutral strategy, its earnings at risk are indeed 4 percent for a 200 basis point rate shock. Keep in mind, however, that the sensitivity of projected earnings, the EAR, is not quite the same as the change in earnings from a risk-neutral position. In other words, we can’t look at the data in Exhibits 3.3 and 3.4 and say that for the base case strategy, earnings will be 4 percent less in the event of a 200 basis point rate increase than they would be if the bank had zero exposure to interest rate risk. The measured 4 percent rate risk sensitivity is the projected change from the selected base case. Even if that base case is a “no change in rates" scenario, it is not a rate risk-neutral scenario.

—

A “flat rate,” “no change in rates” base case is not a risk-neutral position for two reasons. First, as we noted earlier, the bank’s current balance sheet almost certainly has some degree of net exposure to IR. We don’t start from a risk-neutral balance sheet. We start with open positions that have some net exposure. Second, even the base case business strategy scenario has explicit or implicit assumptions for loan prepayments, deposit withdrawals, new business, etc. New activity creates new positions or alters our starting positions.

The fact that we are not measuring the change from a risk-neutral position is not a problem. It is merely a small but important point that _needs to be kept in mind when income simulation reports are analyzed. We simply need to remember that earnings at risk is the measured sensitivity of the eamings in a base case that includes some degree of rate sensitivity already.

Summary Reports Depicting Changes Over Time

We can also point out another important distinction about the presentation. Exhibits 3.2, 3.3, and 3.4 are tables. They are easy to read because our sample bank is modeling only three different rate scenarios

Interest Rate Risk Manggement

—

rising, flat, and falling — and is reporting the change in net income at only one point in time (i.e., after one year). If the bank chose to model more than four or five scenarios or net income at more than one point in time, a graph would be preferable to a table. Graphs are particularly valuable because they allow us to view a bank’s IRR exposure at different points in time. They reflect the dynamic nature of the bank’s exposure to interest rate risk. Exhibit 3.5 depicts a bank’s exposure to a 200 basis point change in interest rates. This bank's exposure is shown over six calendar quarters. Unlike the tabular format used in the previous exhibits, the graph in Exhibit 3.5 reveals much more detail for three of the nine scenarios. The extra detail is the time dimension —— the changes that occur during the course of the bank’s one-year time horizon. Of course, to illustrate this additional information about the temporal trend on a two-dimensional graph, we can only examine the set of projected changes for one rate scenario at a time. Nevertheless, it is often useful to look at the trend in our projected rate risk exposure over the time period. In Exhibit 3.5, we can see that the size of the net income exposure at the end of one year is different from the size of the net income exposure at other points in time. While this is hardly surprising, the graph's value is that it shows that the changes in the size of the exposure for different time periods are not uniform. With the graph, we can gain some meaninng insights into the dynamics of the bank's IRR exposure. Graphs reveal more information and may therefore be more useful to ALCOs than tables. Some ALCOs use both.

A more complex time series is illustrated in Exhibit 3.6. On the left side of that exhibit, the trend in net income for the most recent four quarters is graphed, while on the right side, projected net income under four separate rate scenarios is shown. Following these lines to their far right ends, we see that the highest net income is projected under the bank‘s budget. The next highest is the projected net income under the bank’s rising rate scenario. The static rate scenario, no change in current rates, produces the third best net income forecast. Notice that the four scenarios depicted in Exhibit 3.6 showlthe forecasted trends in net interest income. This format could just as easily be used to show the trend in net income. However, as we observed about the tables

3-20

Income Simulation

look

shown as Exhibits 3.2, 3.3, and 3.4, it is often much more helpful to at the percent deviation between the base case and each forecast scenario.

Exhibit 3.5 Cumulative EAR Caused by a 200 bp Rate Change Not Interest Income 200

00

O1

02

03

04

OS

06

Rates Risa No Change Rates Fall

Quarters

_._

_._

Exhibit 3.6 Trend in Net Income: Actual Plus Four Projected Scenarios

Net Interest Income 50

45 40 35 30

UGI

25

20

3-21

Interest Rate Risk Management

The graph shown as Exhibit 3.7 is simply a different way of representing the same types of trends. In this graph, each of the four lines represents the difference, expressed as a percentage, between a flat-rate scenario and a rate-shock scenario. The four lines are for two rising rate shocks — up 100 bp and up 200 bp — and two falling-rate-shock scenarios. Unlike the trend report illustrated in Exhibits 3.5 and 3.6, the trends shown in 3.7 are just the quarterly trend the estimated amount of the current EAR as of each quarter not the cumulative change. Rate risk analysts could easily adapt a presentation format like the one shown in Exhibit 3.6 to just show the quarterly trend. Conversely, IRR analysts could just as easily adapt a presentation format like the one shown in Exhibit 3.7 to show the cumulative data.

—

—

Exhibit 3.7 Quarterly Trend in EAR

“M

Percent Deviation from Flat-Rate Scenario lard-p at M95 char 11 I'm Rat: Sta-aria by Queue

0]

+400 −

or

−∙ ∞ −∙−

∞ −∙−∙↑∞

∆

o:

0:

OJ

ea

as

as

or

on

Source: Janney Montgomery Scott, LLC, Asset/Liability Services

As Exhibit 3.7 illustrates, reviewing the trends can be very helpfiil. Note, for example, that if prevailing rates fall by 200 basis points, the bank in that example forecasts earnings that will be 12 percent lower than if rate

Income Simulation

remain unchanged. However, by the sixth quarter, that exposure is forecasted to decline to 4 percent and by the seventh quarter it is forecast to decline to zero. If the bank only looked at its EAR for one year, it might choose to reduce an exposure that seems to disappear nine months into the second year. An understanding of the forecast trends can clearly help decision makers evaluate which risk exposures require attention.

Today’s projections for EAR in future quarters are merely simulations based on the best current data and assumptions. Those inputs are subject to some important limitations that we will discuss in Chapters 10 and 11. Since projections for the next few quarters are more likely to be accurate than projections for quarters in the more distant future, your evaluation of forecasted trends should give more weight to the near future than you give to the distant firture. For this reason, you should also pay attention to how your forecasted levels of EAR change with successive forecasts. In other words, it can be helpful to know if the amount of EAR at risk projected this quarter for the second quarter of year 200x are growing or shrinking in subsequent projections as we get closer to the second quarter of that year. USING

INCOME SIMULATION T0 EVALUATE IRR

Whether we look at tables of projected balance sheet and income statement changes or summary graphs, additional focus is required to evaluate the forecasted rate risk exposures. Rate risk managers must evaluate the forecasted exposure for the bank as a whole. In the following paragraphs, we will summarize two techniques for evaluating the whole. In addition, rate risk managers must be able to evaluate which constituent elements contribute the most to the risk exposure. An ability to “drill down" into the forecast is also essential.

Two measurements are commonly applied to evaluate the degree of risk evidenced by measurements of income volatility such as those shown in Exhibits 3.3 and 3.4.

Evaluating Bankwide Risk -— Dollar Dispersion One measure is the dispersion, which is the range or spread of the changes. For example, in the base case strategy shown in Exhibit 3.2,

3-23

Interest Rate Risk Management

projected net income ranges from a decline of $100,000 if rates rise to an increase of $150,000 if rates fall. The magnitude of this range is the dispersion. For the base case, the dispersion is $250,000. As a percentage of the base case flat interest rate scenario projected net income of 82.5 million, the dispersion is 10 percent. This is high, since maximum acceptable dispersion is ofien considered to be 5 percent or even 2 percent of budgeted net income. However, the amount of income volatility that is desirable for each bank varies. (Interest rate risk tolerance levels, a major topic in itself, is discussed in Chapter 12.)

Percentage Deviation from Base Case A second technique for evaluating net income volatility is to measure EAR as a percentage. In Exhibit 3.3, one example is the $200,000 decrease in net income that is projected if business strategy 2 is followed in a rising rate environment. That $200,000 change is equivalent to 8 percent of the budgeted income in the base case strategy assuming flat interest rates. If the rising rate scenario used in that example were considered highly likely, then an 8 percent change in net income might be deemed an unacceptable risk. On the other hand, if the rising rate scenario used in that example were considered too big to be probable, then an 8 percent change in net income might be deemed an acceptable risk.

In the process of measuring the interest rate risk captured by income simulation models, notice how important a base case is to the analysis of the output. Any indicated net income volatility is more meaningful when it can be related to net income predicted in the base case. In the examples shown in Exhibits 3.2 and 3.3, the base case strategy in the flat interest rate environment is considered to be the base case. This would almost certainly correspond to the bank’s budget. When a changing interest rate scenario is considered most probable, the base case scenario in a projected most likely rate scenario is the base case that corresponds to the bank's budget. (As noted above, many banks use four rate scenarios: most likely, rising rates, flat rates, and falling rates.) In each situation, the base case is a vital standard against which the other scenarios and cases are measured.

3-24

Income Simulation

Evaluating How the Constituent Elements Contribute to the Overall Risk Level In Chapter 2 and at various other points in this manual, we have observed that the bank’s net exposure to changes in prevailing rates is far more important than the riskiness of individual positions or portfolios. After all, there is no need to be concerned about the rate risk from two-year, fixed-rate loans if that risk is offset by the risk from two-year, fixed-rate CDs. Nevertheless, rate risk managers need to understand which instruments or portfolios contribute to the bank’s net exposure. For example, if the bank forecasts a large drop in net income resulting from a 200 basis point rate shock, it can be very insightful to understand which assets or liabilities contribute the most to this exposure. Rate risk analysts must be able to “drill down" into the data. Tools that help guide “drilling down“ can be very helpful.

Risk by Product

Comparing the changes in asset yields and liability costs is one tool for highlighting the extent to which constituent parts contribute to the overall risk. Exhibit 3.8 illustrates this approach. The incomplete sample data shown in that exhibit enables two types of comparisons. First, we can compare changes within a balance sheet category. Notice, for example, how the sample report indicates that MBS securities experience a much larger yield decline than Treasury securities. Second, we can compare changes between balance sheet categories. Notice, for example, how the change in loan yields (1.78 percentage points) is significantly larger than the forecasted change in securities yields (1.09 percentage points). Note that a complete evaluation of yield and cost sensitivity requires infomration, like that shown in Exhibit 3.8, for more than just the singlerate change scenario used in that illustration.

3-25

Interest Rate Risk Management

Exhibit 3.8 Forecasted Changes in Asset Yields and Liability Costs (for a 200 basis point rate increase)

Instrument T

Yield/Cost

After Rate

Initial Yield/Cost

Total Assets

Securities T

7.47 6.13 8.05

Other Loans

Consumer I/L HELOC Residential

Commercial Other assets Total Liabilities

NOW

MMDA Insured CDs Jumbo CDs Fed firnds

FHLB Other

Other Liabilities

3-26

Percentage Point

Income Simulation

Risk by Information Source Banks using EAR models should also evaluate the components of projected asset and liability volumes in future time periods. How much of the change in each category results from contractual cash flows? How much from assumptions for roll-over or renewal? How much from assumptions for new

business? An example is shown in Exhibit 3.9.

Exhibit 3.9 Components of Expected Cash Flows

∙ ≡

fiififiiiiili! Ice-armamDIb-an-aai

Imm— Obi-MM!“

As the exhibit illustrates, future business, roll-over, and renewal assumptions can contribute much more to projected earnings changes than the contractual portions of cash flows modeled.

In addition, past forecasts or risk estimates should be compared with actual results as one tool to identify any potential shortcomings in modeling techniques. Such comparisons are known as back testing and are discussed in Chapter 11.

3-27

Interest Rate Risk Management

Using Income Simulation to Manage IRR The capacity to evaluate and compare the bank’s projected interest rate risk exposure in alternative business scenarios is a key benefit of income simulation. The IR exposure created by a bank’s current position is not changed until something is done to change the projected volume, mix, rates, and characteristics of assets and liabilities in the future. Our sample bank in Exhibits 3.2, 3.3, and 3.4 has two altemative business strategies to alter its current IRR position. Strategy 1 shifts the bank to an assetsensitive posture. If it implements this strategy, the simulation predicts that net income will increase if rates rise. The bank projects that it will only increase income by $50,000 over the base case flat scenario if it correctly positions itself for an increase in interest rates. On the other hand, because of positively sloping yield curves, the simulation projects that the bank stands to lose $100,000 if it positions itself for rising rates but rates actually fall.

Alternatively, strategy 2 increases the bank‘s existing liability sensitivity. If the bank implements this strategy, the simulation predicts that net income will increase if rates fall. The bank projects that strategy 2 will increase income by $350,000 if it correctly positions itself for a decrease in interest rates. On the other hand, it stands to lose $200,000 if it positions itself for falling rates but rates actually rise.

ADVANTAGES OF INCOME SIMULATION MODELING At the beginning of this chapter we observed that income simulation analysis captures the dynamic aspects of short-term bank IRR better than any other altemative. In fact, income simulation analysis offers a number of significant advantages to IR managers. Seven of these advantages are discussed below.

Specific Measure of Rate Risk Exposure

Income simulation modeling provides a specific measure of rate risk exposure rather than a crude proxy to quantify risk. That is, it measures a specific amount of change in the bank’s net interest margin or in its net income rather than merely a mismatch. Income simulation thus expresses rate risk exposure in a way that is useful to decision makers. Bank boards

3-28

Income Simulation

of directors, industry analysts, and regulators pay close attention to reported earnings. Even though net income is hardly the sole point of reference for anyone reviewing bank performance, it is definitely one of the most common and familiar. Changes in reported earnings affect a bank’s cost of funds, liquidity, ratings, and stock value. Therefore, measurements of IR that relate that risk to changes in reported profits are relevant.

More Accurate Reflection of Reality Income simulation modeling mirrors reality better than other rate risk measurement approaches. Clearly, it requires a great number of assumptions, and this is often interpreted as a disadvantage to the approach. Even the Office of the Comptroller of the Orr-rency (OCC), the primary regulator of national banks, cites the “myriad of assumptions" required for income simulation modeling as a limitation of this approach.l But in reality, all rate risk measurement approaches employ major assumptions. Income simulation may appear to employ more assumptions than other approaches to measuring IRR, but this appearance is somewhat deceptive. In other approaches, many assumptions are not apparent but are actually implicit in the analysis. For example, static gap analysis does not really avoid the need to make assumptions about new business, it merely assumes that there is no new business. Economic value of equity sensitivity analysis, as we will see in Chapter 5, does not really avoid the need to make separate assumptions about yield changes for different instruments or different terms. Income simulation may be less objective than rate risk measurements that make uniform, hidden, or oversimplified assumptions. On the other hand, it is much more realistic. The beauty of income simulation is that the assumptions are explicit and not buried. Consequently, managers can more easily evaluate how much of the indicated exposure is real and how much is an artifact of the measurement tool.

I.

Comptroller of the Cun'ency, “Interest Rate Risk" in the Comptroller's Handbook, .lune I997, page 87.

3-29

Interest Rate Risk Management

As we discussed earlier in this chapter, incorporating assumptions about both rate changes and volume changes — is core deposit changes particularly critical for accurate estimates of rate risk exposure.

—

Focus on Changes That Count Income simulation modeling forces rate risk analysts to focus on changes that really make a difference to the risk assessment. As we have observed, many assumptions used in income simulation modeling are predictions of customer behavior. They attempt to capture the interaction between rate changes and changes in customer preferences for loan and deposit products. Clearly, this is an impossible task. Changes in customer preferences for loans and deposits are subject to many variables, including the current interest rate environment, competition, and economic conditions.

But customer behavior does change. As we have repeatedly observed, the best example is loan prepayments they speed up when rates fall and slow when rates rise. As imperfect as it may be, income simulation modeling is the best tool for dealing with difficult volumes such as consumer loans and core deposits. For the same reasons, it is also the best tool for dealing with hard-to-predict interest rates such as the administered rates for core deposits and prime-based loans. (The low elasticities of core deposit rates are discussed in Chapter 7.) Income simulation forces you to focus on important changes that can really make a difference in the measured IRR exposure.

—

Focus on Management’s Reactions to Changes Customer behavior is not the only change that affects IRR exposure. It is hardly realistic to assume (as many rate risk measurement approaches do) that bankers will not make management changes in response to changes in prevailing interest rates. Income simulation modeling can capture the interaction between rate changes and management reactions to those changes.

Flexibility in Reflecting Rate Shifts for Different Maturities One of the most important advantages of income simulation modeling is the flexibility to reflect the fact that short- and long-term interest rates do

Income Simulation

not change by the same amounts at the same time. Consider yields for U.S. Treasury instruments. Graphically, we can express this assumption as an upward or downward shift in a yield curve without any change in the shape of that yield curve. For all points on the curve, the gap analysis assumes that any changes are identical. (We call such a shift a “parallel"

shift in the yield curve.)

Parallel yield curve shifts are rare. Rate risk measurement methods that assume parallel shins can lead to IR measurements that are materially misleading. Assume, for example, a bank owns a floating-rate investment that pays interest at a rate tied to the one-year U.S. Treasury note. The rate resets monthly. The bank is funding the security with floating-rate deposits. The deposit rate also resets monthly, but is tied to the overnight federal funds rate. While both the asset and the liability have floating rates that reset monthly, it is a mistake to conclude that there is no IRR. If the rate for overnight funds rises by 200 basis points, the rate for oneyear U.S. Treasury obligations will probably rise by fewer than 200 basis points. The bank will probably experience a decline in income. While the above example may seem unusual, the underlying problem is short-term interest rates e usually far more volatile than conunon ent approaches that assume long-term interest rates. Rate risk meas parallel yield curve shifts will always be less accurate than those that do not. Thus, if we want to measure our exposure to adverse consequences from changes in interest rates, a more accurate rate shock scenario would be a nonparallel shift in the yield curve.

—

Income simulation models can easily accommodate rate change forecasts that assume nonparallel yield curve shifts. Different rates are used for different maturities. Other rate risk measurement approaches can capture nonparallel changes in yield curves, but not always as easily as income simulation models. Because of its flexibility, income simulation modeling is the best IRR measurement approach to realistically reflect the way interest rates actually change. Flexibility in Reflecting Basis Changes in Different Instruments

Not only do interest rates change in different amounts for different maturities, they change in different amounts for different instruments. Historical analysis clearly demonstrates that most rates do not move up 3-31

Interest Rate Risk Management

or down in unison. For example, if the yield for three-month U.S. Treasury securities moves up by 100 basis points, the yields for A-rated corporate bonds of identical maturity may move up by more or less than 100 basis points. Part of the reason for this problem is called basis risk. By using different interest rates for different instruments, simulation modeling can reflect changes in basis.

Gap analysis, in contrast, implicitly assumes that when interest rates change, the rates for all instruments change at the same time. Again, flexibility that simulation modeling provides makes it the best IRR measurement approach to realistically reflect the way interest rates actually change. Integration with Other Management Information Processes Last, but not least, income simulation analysis can be closely integrated with other management information processes in the bank. Two principal examples are the budgeting and business planning processes. For example, income simulation analysis allows IRR managers to model different management strategies in different interest rate environments. This makes it a useful interface between rate risk management and strategic planning and budgeting. The research and analysis needed to develop the assumptions used in income simulations are the same input required for longer term planning and forecasting. Income simulation provides planning, discipline, and structure.

Banks can also test plans before they implement them. A plan that works well in one rate environment may still not be the right plan if it works unfavorably in another.

DISADVANTAGES OF INCOME SIMULATION MODELING

The seven advantages just described make income simulation modeling an attractive tool for rate risk managers. Nevertheless, income simulation modeling also has some disadvantages of which managers should be aware. Six of these are discussed below.

3-32

Income Simulation

Assumptions Require Careful Development, Analysis, Increased Controls, and Testing As we have already observed, many authorities continue to suggest that the major disadvantage of income simulation modeling is that it is too dependent on assumptions. Certainly, income simulation modeling is assumption dependent. However, all measurement methods are assumption dependent. The distinguishing characteristic of income simulation is not its dependency on assumptions, but that the user can easily modify the assumptions used because, unlike the other approaches, income simulation does not employ assumptions that are implicit in the technique itself. It is a distinguishing benefit of income simulation modeling that such flexibility with assumptions allows it to mirror reality more accurately than other techniques.

The real problem is not assumption dependency per se. Instead, the real problem is that it is hard to develop good assumptions. And, even after sound assumptions are developed, more work is required to test, update, and manage their use. Specific issues that should be considered are discussed in Chapters 6, 7, and 1 1. Controlling and testing assumptions is discussed in Chapter 10. Assumptions Can Intentionally or Inadvertently Understate Risk

Exposures

The fact that income simulation permits rate risk managers to reflect potential future changes is, as we have already noted, both a strength and a weakness. The errors that can be introduced by assumptions for future business are not the only problem. As we have also discussed, many future actions will vary in different rate environments. We might, for example, make different funding and risk management decisions in high rate environments than in low rate environments. While it can be more accurate to reflect these differences, it can also mask the true extent of the rate risk exposure. Simulations that include actions that might be undertaken to reduce the bank's rate risk exposure change the conditions for which the original rate risk exposure was projected. As we noted earlier, assumptions used in income simulations can include prudent future risk reduction or hedging activities. In this way, some of the assumptions used in the 3-33

Interest Rate Risk Management

simulation actually mask some or all of the current rate risk exposure. In the extreme, this can result in the disquieting effect of measured risk always residing within limits by definition.

Assumptions that result in the masking of risk may be an inadvertent effect of the bank’s efforts to evaluate the most realistic business scenarios. Unfortunately, they can also be deliberate understatements of risk. Income simulation modeling can be called less objective than other rate risk measurements, if by “less objective" one means “more easily. manipulated.” Both the Federal Reserve and the OCC have published comments about income simulation's lack of objectivity. They correctly observe that if the IRR measured by an income simulation model did not fall within policy limits, the assumptions used in the income simulation could easily be adjusted until the measured risk fell within policy limits. The problem does not lie with the tool, but is actually a fault of some users. Managers who are more concemed with producing favorable results than with measuring correctly can indeed manipulate income simulation models more easily than they can other measurement techniques. This cannot be prevented as long as dishonest managers exist. It can, however, be controlled. Specific suggestions for policing the integrity of income simulations are discussed in Chapter 10. More Complex Interest Rate Risk Management

Income simulation models can complicate IRR management. While it is great to know that a bank’s income forecast is as accurate as possible, such a forecast may not provide the best information needed to manage

IRR. Often it is hard to separate the effects of rate changes from the effects of changes in business strategies or customer behavior. Thus, while the income simulation model can be more realistic, it can also be less revealing. It can be difficult to isolate the effects of interest rate variables alone. Interest rate changes do not occur in a vacuum. This problem is addressed in retroactive analysis of historical performance by using a technique called “normalized” analysis. (Normalized analysis is discussed in Chapter 13.) However, for prospective analysis and management, it does make rate risk management more difficult. For example, many of the hedging ideas mentioned in Chapters 14 and I6 assume that managers have identified specific quantities of IRR exposure. The problem is not that income 3-34

Income Simulation

—

simulation modeling is too inaccurate for risk managers on the contrary, it can be the most accurate measurement tool for short-term IRR. The problem is not one of accuracy, but one of clarity.

Understatement of Long-Term Interest Rate Risk Most importantly, income simulation modeling understates the magnitude of long-term IRR. One OCC publication summed up the problem succinctly: “... banks that use simulation models with horizons of only one or two years do not fully capture their long-tem'r exposure."z Income simulation modeling focuses the AL management analyst on only the near-term effects of changes in interest rates. It falls to capture the IRR that arises from bank assets and liabilities that do not mature, reprice, or change in volume within the time period being modeled. In Chapter 2, we considered the example of a bank that had as its only asset a 30-year U.S. Treasury bond and as its only liability a five-year CD. An income simulation of this bank’s earnings would show absolutely no sensitivity to changes in interest rates. Even if interest rates doubled, the bank would be completely unaffected. But clearly, it would be false to conclude that this bank has zero IRR. The bank would have a large exposure to changes in interest rates, an exposure existing now, even though its impact on earnings would not begin until the end of the fifth year. And furthermore, this impact would last for 25 years!

Because income simulation modeling focuses on the near-term (usually one year) effects of interest rate changes and ignores economic value risk, it can completely fail to identify potentially large long-term risks such as “time bombs.” Over the years, many banks accumulate what one observer has named IRR “time bombs" in their balance sheets. We can illustrate this problem with an example. Suppose that two years ago, in a lower interest rate environment, a bank accumulated a significant amount of deposits in a portfolio of low-rate CDs. The original maturity of those CDs was four years. Now, two years later, the bank uses an income simulation model to capture its IRR. Those relatively low-rate CDs do not appear to represent any exposure to an adverse result arising from a

2.

Comptroller of the Currency, "Interest Rate Risk" in the Comptroller's Handbook, June 1997, page 88.

Interest Rate Risk Managflrent

change in interest rates because they do not mature or reprice for another two years. But this appearance is incorrect. The bank is benefiting from a situation that will not last. Every day, the bank gets closer to'the time when it will have to replace those CDs at a higher cost. This is a time bomb not captured in income simulation analysis.

Time bombs may be favorable or unfavorable. They may involve individual assets or liabilities, or groups of assets or liabilities. It does not matter whether they result from positions intended to influence IRR or from random activities or decisions made without regard for IR.

Interest rate risk arises from a bank's cumulative asset and liability positions. Banks will always have many assets and liabilities with maturity or repricing dates more than one year in the future. Income simulation models or any other measurement tool that focuses on will always fail to capture the changes expected in one year or less full extent of banks’ IRR. As we discuss in Chapters 4 and 5, many banks use income simulation analysis together with duration analysis or economic value of equity analysis to capture both short- and long-term exposures to interest rate risk, while other banks combine the present values of net income simulations for future years.

—

—

Even though income simulation, as an accounting approach to measuring interest rate risk, is inherently better at capturing short-term rate risk exposures than intermediate- and long-term exposures, this weakness is not always as big as it seems. As noted earlier in this chapter, some banks employ income simulation modeling that does capture both their short-term and their intermediate-term rate risk exposure. Limited Number of Alternatives May Not Capture the Full Extent of the Bank’s IRR Exposure

Income simulation modeling, as we have considered it in this chapter, creates a small number of alternative projections that managers can then

compare. For example, Exhibits 3.2, 3.3, and 3.4 show comparisons of nine different income simulations. Banks that use four alternative interest rate scenarios, such as most likely, rising rates, flat rates, and falling rates, together with three altemative business scenarios, run a total of 12 different income simulations.

3-36

Income Simulation

Certainly, nine or more income simulations are far better than only one or two. Performing analyses on a small number of business strategies with only a few different scenarios for plus or minus changes in rates severely restricts the decision-making information available to management. For example, for their rising and falling rate scenarios, many banks model highly improbable rate shocks. Rate shocks are very large, immediate shifts in interest rates. (See Chapter 8 for a discussion of choosing rate changes to model.) If rate shocks are used, management does not have the advantage of analyzing more probable interest rate shifis. On the other hand, if probable rate shifts are modeled, management does not have the advantage of looking at less likely rate changes. Even if a risk has a low probability of occurring, it may nevertheless be a large risk that management might want to consider in contingency planning. However, even 9 or 12 simulations may be inadequate. For example, a bank with significant holdings of callable investments and pre-payable loans may have very little rate risk exposure in declining, stable, or moderately rising rate scenarios but very material rate risk exposure if rates rise by 200 or 300 basis points. This is a particularly relevant problem if prevailing rates fell after those investments or loans were added. (If rates fell after those assets were acquired but before the time of simulation analysis, the call or prepayment options are currently out of the money. Therefore, a small increase in prevailing rates is much less likely to trigger the options than a large increase.)

Accuracy May Be Impaired by Limited Incorporation of Interrelations Between Variables

Our discussions of income simulation techniques so far in this chapter have included only a few rough approximations of the connections between variables. For example, earlier in this chapter we observed that a rising rate simulation might forecast less growth in loans and more growth in CDs than a falling rate forecast. Many variables are connected. Loan prepayments are the most obvious example. As we have previously observed, loans prepay faster after rates have fallen and slower after rates have risen. Many variables in our interest rate simulation models will change in interrelated ways. (The changes are highly correlated.) Unless we capture these interrelationships in the assumptions used to generate

3-37

Interest Rate Risk Management

model inputs, the model’s output will not be accurate. This disadvantage is far more applicable to the relatively simple simulation models used by most banks than it is to the complex models that track individual cash flows using detailed data extracted from the investment, loan, and deposit accounting systems.

SUMMARY Many aspects of income simulation modeling are surprisingly simple. We usually model a relatively small number of straightforward interest rate scenarios. We usually also model the changes in groups of investments, loans, and deposits rather than in each individual asset and liability. We obtain results expressed in the familiar, easy-to-understand terms of net interest income and net income. But the process is actually more complex than it seems.

In particular, the usefulness of the output is highly dependent on the accuracy of the input. Accurate assumptions are crucial. The usefulness of any answer depends on the degree of accuracy in the assumptions and the degree of accuracy in the calculations. The accuracy of the change in net income predicted by the model is equally dependent on the accuracy of the benchmark level of net income and the accuracy of the interest rate changes predicted to influence net income. For all of these reasons, the time horizon used in income simulation modeling is critical. Clearly, there is a relationship between the degree of confidence for interest rate and business activity forecasts and the time frame used. Short-tenn forecasts are more likely to be accurate than long-term forecasts. The further that assumptions and forecasts project out in time, the more they will diverge from the actual events that subsequently occur.

In spite of its shortcomings, income simulation modeling is probably the single best approach for measuring IRR. We can say this for two reasons: 1. Income simulation does the best job of meeting the requirements set forth in the beginning of this chapter. It enables us to understand the size and direction of a bank’s interest rate exposure under a variety of interest rate scenarios. When used rigorously, it

Income Simulation

captures all of the important data for volumes, maturity dates, repricing dates, and hidden options required for accurate rate risk measurement. Because the outcome is so obviously based on explicit assumptions, it focuses attention on the critical variables. It captures the effects of the inevitable changes caused by new loans, new deposits, withdrawals, repayments, and other changes. It can be used to reflect the important fact that changes in prevailing interest rates affect different assets and liabilities in different ways.

2. Income simulation expresses the quantity of IR in terms readily understood by senior bank managers and is easily incorporated into budgets and strategic plans. When we use income simulation models to analyze the effects of a certain size change in prevailing interest rates, we can reasonably say that we are 95 percent confident that changes in prevailing interest rates cannot cause more damage than a 5 percent reduction in our net income for the next year. (The amount of such a change is discussed in Chapter 8.)

Nevertheless, income simulation modeling is only one tool in the rate risk manager’s tool kit. Rate risk managers who want a complete picture of their bank’s IRR exposure ofien combine income simulation with other approaches. They use income simulation to measure short-term rate risk, but also use an economic approach to capture longer term rate risk. Chapters 4 and 5 consider economic approaches to measuring IRR.

3-39

Interest Rate Risk Management

3-40

Chapter 4

Duration and Convexity

What Is Duration Analysis? .................................................................. 4-1 Measuring the Dollar Weighted Average ......................................... 4-3 Measuring the Weighted Average of the Present Value ................... 4-3 Exhibit 4.1: Macaulay Duration for a 6 Percent F ive-Year Bond∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 4-4 Exhibit 4.2: Macaulay Duration for a 12 Percent Seven-Year Bond ......................................................................... 4-5 Using Duration ..................................................................................... 4—5 Comparing Maturities with Weighted Averages and Durations....... 4-6 Exhibit 4.3: Cash Flows of Assets with Five-Year Maturities ..... 4-7 Exhibit 4.4: Cash Flows Weighted Averages and Durations ............................................................................... 4-8 Characteristics of Duration ............................................................... 4-9 Modified Duration .............................................................................. 4-10 Calculating Modified Duration....................................................... 4-1 1

—

Convexity ........................................................................................... 4-12 Exhibit 4.5: Rate Sensitivity of a 6 Percent lO-Year Treasury ...................................................................................... 4-13 Positive Convexity .......................................................................... 4-15 Exhibit 4.6: Price/Yield Relationship 6 Percent lO-Year Noncallable Bond ....................................................................... 4-15 Negative Convexity ........................................................................ 4-16 Exhibit 4.7: Price/Rate Relationship 5.5 Percent 30-Year FNMA Pool ................................................................................ 4-16 Characteristics of Convexity .......................................................... 4-17 Convexity Describes Duration Errors That Only Become Material for Large Changes in Rates .......................................... 4-17 Convexity Describes Duration Errors in Particular Directions ................................................................................... 4-17 Convexity Is More Material for Longer Term Instruments Than for Shorter Term Instruments ............................................ 4—1 8 Exhibit 4.8: Comparative Convexity ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 4-18 Convexity Is More Material for Amortizing Instruments .......... 4-19

6/08

4-i

6/08

Interest Rate Risk Management

Exhibit 4.9: Volatility Comparison Between a lO-Year Treasury Bond and a 12-Year Mortgage Pass-Through Bond .................................................................... 4-20 Adjusting Duration to Compensate for Convexity ......................... 4-20 Limitations of Macaulay and Modified Duration ............................... 4-21 Effective Duration, Option Adjusted Duration, and Partial Duration.............................................................................................. 4-24 Effective Duration and Empirical Duration 4-25 Effective Duration and Option-Adjusted Duration......................... 4-26 4-27 Key Rate Duration Exhibit 4.10: Key Rate Duration Table ...................................... 4-28 Partial Duration .............................................................................. 4-28 Applying Duration to Measure IRR for the Entire Bank.................... 4-29 Calculating Duration of Equity∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 4-30 Understanding Changes in Duration of Equity ............................... 4-31 Key Rate Duration for the Whole Bank ......................................... 4-33 Exhibit 4.11: Key Rate Duration Graph ..................................... 4-33 An Empirical Alternative ................................................................ 4-33 Positive and Negative Durations .................................................... 4-34 Capturing the Duration of All Cash Flows ..................................... 4-35 Advantages of Duration...................................................................... 4-35 Captures Interest Rate Risk from All Time Periods ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 4-36 Expresses the Measured Quantity of IR as a Single Value ∙∙∙∙∙∙∙∙∙∙ 4-37 Expresses the Measured Quantity of IRR as a Change in a Well-Understood Variable ........................................................... 4-37 Captures IRR Obscured by Accrual Accounting Methods ............. 4-3 8 Facilitates Segregation of Rate Risk Components .......................... 4-39 Disadvantages of Duration ................................................................. 4-39 Managing Dtu'ation Can Increase Earnings Volatility .................... 4-39 Duration Relies on the Unlikely Assumption That All Rates Change at the Same Time ..................................................... 4-40 Duration Ignores Basis Risk ........................................................... 4—40 Duration Is Difficult to Calculate for Products with Administered Interest Rates ............................................................ 4-41 Duration Is 3 Static IRR Measurement ........................................... 4-42 Future Cash Flows Assumptions ........................................... 4-43 Focus on Current Position ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 4-44 Duration Masks Dispersion ............................................................ 4-44

—

4-ii

Duration and Convexity

6/08

Duration Calculations Exclude a Material Component of Interest Rate Risk ........................................................................... 4-45 Duration Summary ............................................................................. 4-46

4-iii

6/08

Interest Rate Risk Management

4-iv

Chapter 4

Duration and Convexity

One of the best known tools for measuring long-term interest rate risk (IRR) is duration analysis. In fact, in the mid-19805, some experts felt that this was the single solution for capturing the quantity of interest rate risk exposure. Today, we know better.

Duration analysis measures the time that assets and liabilities have remaining before they reprice. In a sense, duration analysis is a far more sophisticated (albeit more complicated) way of doing what gap analysis attempts to accomplish. Duration analysis provides an IR manager with a single measure of a bank’s rate risk exposure. It has many of the same advantages and disadvantages as gap analysis, with some notable exceptions. Unlike gap and income simulation analysis, however, duration analysis is not an accounting approach to interest rate risk measurement. It is an economic approach. As noted in Chapter 2, economic approaches offer some important advantages to users.

As we explore in this chapter, duration is an excellent measure of rate risk in instruments or portfolios with known cash flows and small rate changes. Duration is less useful for measuring the firm’s total rate risk. However, you can value duration as much for the concepts and vocabulary as you do for its use as a risk measurement metric.

WHAT IS DURATION ANALYSIS? The concept of duration analysis originated in bond portfolio management and was first proposed in 1938 by Professor Frederick Macaulay. Macaulay wanted to measure the timing of cash flows from bonds. He quantified a well-known but not well-understood phenomenon measuring the balancing point after which a bond's return remains practically unchanged no matter what happens to interest rates.

—

Duration can be thought of as an explanation for the seemingly confusing way that bond prices change in response to changes in prevailing interest

4-1

Interest Rate Risk Management

rates. We can illustrate this phenomenon with a simple example: Suppose that we buy a five-year bond today at a yield of 6 percent. The bond pays interest semiannually. Now suppose that rates rise to 8 percent the bond is tomorrow. The value of our bond falls. That makes sense worth less a day later because investors can get 8 percent on new bonds. Each year for five years, an investor can get 2 percentage points more interest on a new bond than we will get for the bond we bought the day before. So, does the value of our bond decline by 2 percentage points each year, or a total of 10 percent of the principal? No, absolutely not» Never. It declines by less. The actual loss will be just a bit more than 8 percent of the principal.

—

A 2 percent per year increase in rates produces less than a 10 percent decrease in the value of the bond because the total amount of yield that we lose is really less than 2 percent per year. It is less because every six months we can reinvest the interest. If rates had remained at 6 percent, the reinvested interest would earn 6 percent, so the total return for the five years would be 6 percent. However, since rates rose to 8 percent, we can now reinvest the interest that we receive at 8 percent. Accordingly, our total return for our five-year investment will be slightly more than 6 percent. Our opportunity to reinvest the cash flow from the interest payments partially offsets the loss resulting from the increase in rates. So what is duration? One way to view duration is as the balancing point for a series of cash flows. One author described it as that “sweet spot” that lies somewhere between the day you bought the bond and the day that it matures, where the bond’s return remains practically unchanged no matter what happens to interest rates.l Others have called it the “center of gravity” of cash flows. Let's take a closer look at that balancing point. The five-year bond in the above example can be viewed as a series or a row of 10 cash flows. The first nine cash flows are the first nine semiannual interest payments. Payment one is received in 6 months, payment two is received in 12 months, and so on, until payment nine is received in 4 1/2 years. The

1.

ED. Granite, “Bond's Duration ls Handy Guide on Rates," Wall Street Journal (Apr. 19, 1993), page CI.

4.2

Duration and Convexity

tenth and final payment consists of the last semiannual interest payment plus the entire amount of the principal. Measuring the Dollar Weighted Average

Look at the bond described above and answer the following question: If we buy the bond today, when do we get our money back? We can give three answers to this question. The most common answer is that we get our money back in five years when the bond matures. That answer is not entirely accurate, since relatively small amounts of money are received earlier with each semiannual interest payment. A more accurate answer might be that we get our money back in about 4.42 years. This is more accurate because it is the dollar weighted average of the 10 cash flows. It is dollar weighted because the time remaining until each of the 10 cash flows is received is multiplied by the amount of each cash flow. Then the 10 products are added up. The sum of the 10 products is divided by the sum of the 10 cash flows. The result is the dollar weighted average time remaining until all the cash is received.

Measuring the Weighted Average of the Present Value Duration uses a more sophisticated methodology than the simple dollar weighted average life. The dollar weighted average time until we get our money back is not the most accurate way to find the sweet spot or balancing point described earlier. Such an average ignores the time value of money. We can use a more sophisticated way to answer the question of when we get our money back. Cash flow received in the near future is more valuable than cash flow received later. Instead of a simple dollar weighted average of the cash flows, we can calculate a present value weighted average. Such an average is the duration of the bond. For our five-year bond in the above example, the duration is about 4.39 years. In other words, the present value weighted average of the 10 cash flows is 4.39 years. The present value (PV) for each of 10 cash flows in this example can be seen in the third column in Exhibit 4.1. Duration involves four simple calculations:

1. Determine the amount of each individual cash flow due to be received in the future.

4-3

Interest Rate Risk Management

2. Determine the time remaining until each cash flow is received.

3. Calculate the present value of each future cash flow.

4. Divide the sum of the weighted present values for the cash flows by the sum of the present values. While the calculation of duration for mortgage-backed securities (MBSs) with many payments can be tedious, computers make short work of this task. For instruments with semiannual cash flows, such as most fixedrate investments, a more simplified calculation that weights the present values of each cash flow by the number of the semiannual compounding periods can be used. This simple method is shown in Exhibit 4.1.

Exhibit 4.1 Macaulay Duration* for a 6 Percent Five-Year Bond (par amount $100, paying interest semiannually) Semiannual Period

1 2 3 4 5 6 7 8 9 10

Macaulay duration

Cash Flow

3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 103. 0 130

2883:)!

PV of Cash Flow 2.91262 2.82779 2.74542 2.66546 2.58783 2.51245 2.43927 2.36823 2.29925 76.64167

Period X PV

2.91262 5.65558 8.23626 10.66184 12.93915 15.07470 17.07489 18.94584 20.69325

766.41670 87861083

= 4.39

or 878.61/2(100) = 4.39

"‘ This formula is oversimplified and will work only for semiannual cash

flows.

Duration and Convexity

Another simplified method for an instrument with only one cash flow each year is illustrated in Exhibit 4.2: Exhibit 4.2 Macaulay Duration* for a 12 Percent Seven-Year Bond

(par amount $10,000, paying interest annually)

Year 1 2 3 4 5

Cash Flow 1,200 1,200 1,200 1,200

Weighted

P.V. of Cash Flow

Period Times P.V.

Cash Flow

at 10 Percent

1,200 2,400 3,600 4,800

1,090.91

991.74 901.58 819.62

1,090.91 1,983.48 2,704.74 3,278.48

6,000

7

1,200 1,200 11,200

78,400

745.11 677.37 5,747.37

3,725.55 4,064.22 40,231.59

TOTAL

18,400

103,600

10,973.70

57,078.97

6

"

7,200

Weighted Average Maturity = 103,600/18,400 = 5.63 years Macaulay Duration = 57,079/10,974 = 5.20 years This formula is oversimplified and will work only for annual cash

flows.

The time remaining until maturity is not an accurate measure of interest rate sensitivity. Neither is the dollar-weighted average time remaining until we receive all of the cash flows. Duration is an accurate measure of the bond’s sensitivity to interest rate changes. It is the measure of the balancing point where the price risk of the principal equals the reinvestment risk of the periodic cash flows.

USING DURATION Now that we know what duration is, we can apply the concept to help us understand investments. Actually, we can use duration to help our understanding of investments in two different ways. First, duration helps 4-5

Interest Rate Risk Management

us compare securities. For example, a yield comparison of two securities with the same duration is far more meaningful than a comparison of two securities with the same maturity dates but different durations. Second, duration can help us understand the price sensin'vity of an investment. These concepts are discussed in the following paragraphs.

Comparing Maturities with Weighted Averages and Durations So far, we have considered the duration of a bond that pays interest semiannually and principal at maturity. Actually, duration can be applied to measure the interest rate sensitivity of any stream of cash flows. The number of the cash flows is not a limiting factor. Furthermore, there can be one principal cash flow and many interest cash flows, or any

combination of principal and interest cash flows.

Consider three sample assets, A, B, and C. All have contractual maturities of five years. Asset A is a zero coupon bond; asset B, a U.S. Treasury note that pays interest semiannually; and asset C, a consumer installment loan. The cash flows from these three assets are displayed in Exhibit 4.3. As expected, 100 percent of the cash flow from asset A appears in year five because it is a zero coupon bond. Most of the cash flow from asset B is also in year five, since no principal is received until maturity. However, the semiannual interest payments received over the life of the note produce some cash flow in the first four years. All of the cash flow from asset C is distributed over the five-year life because the bank receives both principal and interest each month over the life of the loan.

Exhibit 4.4 depicts the same three assets, with lines added that show the dollar weighted average life of the cash flows and, for the U.S. Treasury note and consumer loan, the durations of the cash flows. As we have already observed, the simple average of the cash flows does not reflect the time value of money. Duration analysis provides us with a weighted average by discounting the cash flows. The weightings are based on the relative present values of the cash flows. This gives us a much more accurate measure of a bank‘s [RR exposure.

Duration and Convexig

Exhibit 4.3 Cash Flows of Assets with Five-Year Maturities Percent ot cash Flow 100

'6

80-

E

co

{—9

«-

E

a

”r

at

2

Yen's

4

5

Percenrct Cash Flow 100 30

Note,

B

T E S A yrusae T .S U

60

rstnlaeuImnyaimPeS g

O

o

E

a3 5a I0

Porcontol Cash Ftou

80,-

so 40

E

20

e

o

5

g

0

You:

Source: IL Harrington. Asset and Liability Management by Banks (Paris: Organization for Economic Cooperation and Development, 1987), page 168.

4-7

Interest Rate Risk Management

Exhibit 4.4 Cash Flows — Weighted Averages and Durations Percent 0! Cash Flow

∞

aE

Datum = Wm“! Average Lute

3'3 '

a

Burma'- = 5Y0“

S. U

40

E

-

N

∙

0

1

2

3 Years

4

5

Percent at Cash Flow

mo 80

,eto.SNU

Drruon (”Yeas

wumroa Average Lrto

4 33V...

launimsetSnemyaP

Inters Treasuy

B

TES A

60

Percent d cw- Flow 100

—

−

O

83

C

ASET

m!!!

InstalmeCour

naoL

Bullion 268 was Wormtsd Average Ulc a

Source: R. Hanington. Am and Liability Managemmt by Banks (Paris: Organization for Economic Cooperation and Development, 1987), page 169.

4-8

Duration and Convexity

Characteristics of Duration

Calculating duration can be a bit complex, but the principles underlying it are easily understood. Five general observations, or properties, hold true for all duration measurements: a cash flow is paid or received, the greater the duration. A $100 cash flow that occurs in 24 months has a greater duration than a $100 cash flow that occurs in 12

I. The longer the time until months.

The incremental increase in durationfalls dramatically as the time final maturity lengthens. For a three-year security with a 10 percent coupon rate, paying interest semiannually has a duration of 2.66 years. Compare that with an otherwise identical four-year from three years security. By extending the maturity one year the duration extends by 0.73 years to 3.39 years. to four years On the other hand, if we extend the maturity by one year from the duration only extends by 0.52 years. four years to five years A 100-year bond has a drn'ation of less than 12 years.

to

—

—

—

—

The higher the reinvestment rate of interest, the shorter the duration. A $100 cash flow that occurs in 24 months with an interest rate of 8 percent has a lower duration than a $100 cash flow that occurs in 24 months with an interest rate of 4 percent. (However, for MBSs, the change in prepayments caused by changes in interest rates more than offset the change in duration caused by changes in the reinvestment rate.) The more the duration varies from zero, the greater the interest rate sensitivity. The IR of a bond with a duration of 50 months is greater than the IRR of a bond with a duration of 30 months. That is true even if the bond with the 30-month duration. has a contractual maturity that is greater than the bond with the 50month duration. Duration is additive. The durations of individual instruments can be combined to determine overall durations of portfolios. The durations of portfolios can be combined to determine the overall durations of banks. (This property is discussed in the next section.)

4-9

Interest Rate Risk Management

MODIFIED DURATION

The goal of rate risk measurement is to quantify a bank's interest rate sensitivity. We want to know how much exposure we have to an adverse consequence from a change in prevailing interest rates. Macaulay duration quantifies our exposure. But is it meaningful? For example, Macaulay duration analysis can tell us that the duration of an asset is four a concept explained later years. If we know that our duration of equity in this chapter is 3.5 years, would we know whether this is an acceptable exposure, a slightly unacceptable exposure, or a totally unacceptable exposure? No. Macaulay duration does not quantify our exposure in a meaningful way. Macaulay duration only gives us a proxy that represents our interest rate risk.

—

—

To get a better understanding of how we can use the duration of equity to measure the bank‘s sensitivity to interest rate changes, we need to introduce another concept modified duration. (Modified duration is sometimes called “Hicks duration” because this improvement to a year Macaulay’s measure was developed by Hicks in 1939 after Macaulay.) The modified duration improves the accuracy of the Macaulay duration by adjusting it to reflect the effects of interest compounding. Clearly, different instruments pay interest at different frequencies. (1n Exhibits 4.3 and 4.4, asset A pays interest only at maturity, asset B pays semiannual interest, and asset C pays monthly interest.) Since all instruments do not compound interest in the same way, the modified duration is more accurate than the Macaulay duration, as we see in the calculation below.

—

—

In essence, modified duration is a measurement of sensitivity. (Economists refer to this as price elasticity.) It measures the percentage change in the value of an instrument for each 1 percent change in prevailing interest rates. For example, an instrument with a modified duration of four years will experience a 4 percent decline in value if interest rates rise by 1 percent. Similarly, an instrument with a modified duration of two years will experience a 2 percent decline in value if interest rates rise by 1 percent. Instnrments that are more sensitive to changes in prevailing interest rates have higher modified durations than instruments that are less sensitive.

4-10

Duration and Convexity

The simple relationship between the price sensitivity of an instrument and its modified duration that was illustrated in the examples discussed in the previous paragraph can be described by a formula:

Percentage price change = —Du.ration X Change in rates Thus, when we use an example of a 1 percent interest rate increase resulting in a 4 percent decline in the value of a bond with a four-year modified duration, we can express that relationship in the above formula as:

Percentage price change = —Duration x Change in rates

Percent price change = —4-year duration x 1 percent change in rates Percentage price change = —4 X 1 Percentage price change = —4 When investors, broker/dealers, or other market observers and participants use the term “duration," they are almost always referring to the modified duration rather than to the Macaulay duration.

Calculating Modified Duration Modified duration can be calculated in three steps: 1. Divide the yield of the instrument by the number of times per year that the interest is compounded.

2. Add the number 1 to the result from step one. 3. Divide the Macaulay duration by the result calculated in step two.

If the number of compounding periods per year is K, then the formula for calculating modified duration could be written as:

Modified duration

=

4-Il

Macaulay duration (1 + (yield / K))

Interth Rate Risk Management

(Note that for continuous compounding, modified duration equals

Macaulay duration.)

In the introduction to Macaulay duration at the beginning of this chapter, we used an example of a five-year bond that pays interest semiannually at a rate of 6 percent. In the section discussing present value weighted average, we saw that the bond had a Macaulay duration of 4.39 years, as shown in Exhibit 4.1. By applying the formula for the modified duration given above, we would determine the bond’s modified duration as. follows: Modified duration

=

May—influ— (l + (yield / K))

Modified duration =

_4-39_ (1 + (.06 2))

Modified duration =

439 1.03

Modified duration =

427

We can then describe the resulting modified duration in two ways. We can say that for that bond, the duration is 4.27 years. However, we can also say that for each 1 percentage point change in prevailing rates, the value of this bond will change by 4.27 percent. This is a highly useful measure. However, it is not entirely accurate. At this point, we can only say that modified duration provides a rough estimate of the percent change in value that results from a change in prevailing rates. CONVEXITY

At first glance, it might seem that modified duration is the perfect tool for both investors and rate risk managers. Unfortunately, duration is neither a completely accmate nor a stable measure of rate sensitivity. That is why, at the end of the prior section, we said that modified duration only provided a rough estimate of the price sensitivity.

4-12

Duration and Convexity

We can see the difference between rate sensitivity measured by an instrument’s duration and its actual price sensitivity in an example. The table in Exhibit 4.5 shows the changes in the price for a noncallable bond resulting from four possible changes in prevailing interest rates. Exhibit 4.5 Rate Sensitivity of a 6 Percent lO-Year Treasury

Percentage

Change in Prevailing Interest Rates

Yield

Price

-200

4.00

116.35

—100

5.00

107.79

7.79

no change

6.00

100.00

no change

+100

7.00

92.89

(7.11)

+200

8.00

86.41

(13.59)

Change in Price

16.35

The modified duration of a 6 percent 10-year Treasury note is 7.44 years. Therefore, if modified duration is an accurate measure of interest rate sensitivity, we should expect a one percentage point change in prevailing rates to cause a 7.44 percent change in the price of this security. As the far right column reveals, this is not the case. The actual rate sensitivity is difl‘erent. The actual change in price resulting from a 1 percentage point increase in rates is not 7.44 percent. Instead, it is 7.11 percent. And, the actual change in price resulting from a 1 percentage point decrease in rates is 7.79 percent rather than 7.44 percent. In other words, for the security illustrated in Exhibit 4.5, a decrease in prevailing rates increases the price more than the modified duration predicts. And an increase in prevailing rates depresses the price by less than the modified duration predicts. Duration is not a completely accurate measure of rate

sensitivity.

What do we mean when we say that duration is not a stable measure of rate sensitivity? Simply put, the magnitude of rate sensitivity changes as yields or prevailing rates change The lack of stability just described can also be seen in Exhibit 4.5. As we observed, a 1 percentage point

4-13

Interest Rate Risk Management

decrease in prevailing rates produces a 7.79 percent decrease in the price for the security in that illustration. Note, however, that a 2 percentage point change in prevailing rates does not lead to a decrease that is twice as large. Doubling the 1 percentage point change in rates would be 15.58 percent. The actual change, however, is 16.35 percent. In other words, duration is not merely an inaccurate measure of rate sensitivity it is a proportionate measure of a disproportionate phenomena.

Duration measures of that Treasury note's sensitivity to changes in prevailing rates reveal a proportionate relationship between the size of change in prevailing rates and the size in the changes in the price of that note. So the change in value that results from a decline in prevailing rates from, say, 10 percent to 9 percent, is the same as the change in value of that same bond if prevailing interest rates fall from 5 percent to 4 percent. In technical terms, the problem is that duration analysis assumes a linear relationship between changes in rates and changes in market value. But price/yield relationship does not change proportionately. As we will see, it is nonlinear. The difi‘erence between rate sensitivity measured by an instrument’s duration and its actual price sensitivity is called “convexity.” For more mathematically inclined readers, convexity is the sum of the weighted average of the squares of the time to maturity of each cash flow plus one half of the weighted average of the time to maturity of each cash flow. The weights in that formula are the present values of each cash flow.

Think of convexity as the margin of error in the interest rate sensitivity measured by duration. If convexity is low that is, if the price/yield duration is fairly accurate and relationship is close to a straight line fairly stable. In that case, the duration of an instrument calculated when interest rates are at 10 percent will not be much different from the duration of the same instrument calculated in a 5 percent interest rate that is, if the environment. On the other hand, if convexity is high price/yield relationship is clearly curved — duration is unstable. In that case, the duration of an instrument calculated in a 10 percent rate environment will be different from the measured duration for the same instrument calculated in a 5 percent rate environment.

— —

—

Actually, the curved price/yield relationship described by convexity can differ from the straight line in either of two distinct ways. When the 4-14

Duration and Convexity

curve rises up fi'om a tangent straight line, we call say that the price/yield relationship has positive convexity. When the curve falls down fi'om a tangent line we say that the price/yield relationship has negative

convexity.

For noncallable bonds, convexity is always positive. The same is definitely not true for callable bonds or most mortgage-backed bonds. These instruments have negative convexity. Both of these relationships are discussed and illustrated in the following paragraphs. Positive Convexity

Exhibit 4.6 illustrates positive convexity. The straight line shown in Exhibit 4.6 illustrates the price/yield relationship as measured by duration. In other words, the interest rate sensitivity of the Treasury bond’s price would exactly match the straight line if duration was an accurate measure of rate sensitivity. The curve in Exhibit 4.6 shows the true price/yield relationship. In other words, the actual interest rate sensitivity of that bond is illustrated by the curve. Exhibit 4.6 Price/Yield Relationship 6 Percent lO-Year Noncallable Bond Price 180

140 120

100

1%

2%

3*

4%

5"

6% 7% Yield

85

9%

10$

11$

12‘

For the Treasury bond shown in Exhibit 4.6, the price at very low and very high yields exceeds the price indicated by the straight line. In this relationship, the curve is said to slope upwards. We call this positive convexity.

4-15

Interest Rate Risk Management

Negative Convexity

Exhibit 4.7 illustrates negative convexity. The straight line shown in Exhibit 4.7 illustrates the price/yield relationship as measured by duration. In other words, the interest rate sensitivity of that mortgage security’s price would exactly match the straight line if duration was an accurate measure of rate sensitivity. The curve in Exhibit 4.7 shows the true price/yield relationship for that mortgage security. In other words, the actual interest rate sensitivity of that bond is illustrated by the curve.

Exhibit 4.7 Price/Rate Relationship 5.5 Percent 30-Year FNMA Pool

m \ I13

no

‘

105

\

I”

\\

°°

∙

\—

a:

W

∙

4")

CW0?! YIOH

∞

200

300

For the GNMA bond shown in Exhibit 4.7, the price at very low and very high yields is less than the price indicated by the straight line. In this relationship, the curve is said to slope downwards. We call this negative convexity.

4-16

Duration and Convexity

Characteristics of Convexity

Rate risk managers need to understand how convexity impacts the amount of rate sensitivity measured by duration. This is true for the investment instruments used as examples so far in this chapter. It is an application equally true for the net duration of the bank as a whole of duration that we will explore later in this chapter.

—

In a nutshell, four characteristics of convexity influence the reliability; as well as the usefulness, of duration measures-of interest rate sensitivity. These four key characteristics are considered in the following paragraphs.

Convexity Describes Duration Errors That OnIy Become Materialfor

Large Changes in Rates

Let‘s begin by examining the size of the error in duration. Duration is an accurate measurement of the price sensitivity of a cash flow stream only for small changes in interest rates. Duration becomes increasingly inaccurate as prevailing rates move above or below the coupon rate of the bond. Look at the middle sections of the graphs shown in Exhibits 4.6 and 4.7. Notice that, in that region, both of the curves follow the straight lines fairly closely. (This is only true for the center portion of graphs — just above and just below the 6 percent coupon rate of the bonds.) The assumption of a linear relationship between yields and prices does not make a material difference for small rate changes. We see significant differences only for the larger rate changes. In other words, duration is a fairly accurate measure of interest rate sensitivity for small changes in prevailing rates. However, duration clearly becomes a less and less accurate measure of rate sensitivity as the cumulative amount of change in prevailing rates builds up either above or below the original rate level.

Convexity Describes Duration Errors in Particular Directions Second, consider the direction of the error in duration. Take another look at Exhibit 4.6. A decrease in prevailing rates is reflected by movement from right to left on either the line or the curve. Similarly, an increase in prevailing rates is reflected by movement to the left. Now, look at the far left side of the graph. In that region of the graph, duration understates the

4-17

Interest Rate Risk Management

rate sensitivity. When prevailing rates fall significantly, duration understates the rate sensitivity. Now look at the far right side of the graph. When prevailing rates rise significantly, duration overstates the price sensitivity. The direction of the duration error — overstating rate sensitivity when rates are high and understating rate sensitivity when rates are low — is always true for instruments with positive convexity. In other words, it is true for all noncallable instruments. Notice, however, that in Exhibit 4.7, the price sensitivity indicated by the duration line on the left side of that graph overstates the true rate sensitivity.

Convexity Is More Materialfor Longer Term Instruments Thanfor Shorter Term Instruments Convexity is also more material for long-term bonds and less material for short-term bonds. In Exhibit 4.5, we saw that a 100 basis point change in rates for a 10-year Treasury note with a modified duration of 7.44 years changes the price by about 35 basis points more than expected in one direction (7.79 minus 7.44). And, as we also saw in that example, the same size rate change in the opposite direction changes the price by about 33 basis points more than modified duration predicts (7.43 minus 7.11). The sum of those changes is 68 basis points. A comparison of the convexity for a range of shorter and longer term bonds is shown in Exhibit 4.8.

Exhibit 4.8 Comparative Convexity

Treasury

Duration

Convexity

2-year

1.88

0.05

3-year

2.56

0.08

5-year

4.32

0.22

lO-year

7.44

0.68

30-year

13.45

2.71

4-18

Duration and Convexity

As Exhibit 4.8 illustrates, the convexity for a short-term security is negligible. However, for a longer term security, it is material.

Convexity Is More Materialfor Amortizing Instruments

MBS investments, as the comparison of Exhibits 4.6 and 4.7 illustrates, can have much more convexity than other fixed-income investments. Why is the duration of MBS investments more sensitive to changes in the discount rate? The answer is that mortgage-backed securities have larger periodic cash flows. A bond with interest and principal cash flows that are received by investors well before maturity will produce more dollars to be reinvested than a bond that only pays out interest cash flows before maturity. Thus, the duration of the bond with principal and interest cash flows is more sensitive to changes in the interest rate earned when the monthly cash flows are reinvested. That is why most MBS bonds have more convexity than other bonds. Duration slides up or down as rates change. Duration for mortgage-backed bonds slides up or down more than duration for other types of fixed-income investments.

Exhibit 4.9 highlights how the negative convexity of an MBS passthrough investment represents more volatility than the smaller and positive convexity of a noncallable Treasury bond. In this example, a Treasury bond with 10 years remaining to maturity is compared with an MBS pass-through pool with an assumed life of 12 years. Note that for a 200 basis point increase in rates, the price of the Treasury declines by 11.48 percent, while the price of the MBS declines by 13.78 percent. For a 200 basis point decrease in rates, the price of the Treasury increases by 13.66 percent, while the price of the MBS increases by 16.39 percent. (These are not the same bonds used for Exhibits 4.5, 4.6, and 4.7.)

If the differences between the price changes for the MBS and the Treasury in Exhibit 4.9 seem small, remember that these value changes are only the changes resulting from the use of different discount rates in the duration calculation. In other words, the changes shown for the MBS in Exhibit 4.9 only reflect changes in the value of the bond. In run, these changes echo changes in the reinvestment income caused by higher or lower interest rates. Our point here is that the changes in value displayed in Exhibit 4.9 do not reflect the additional volatility resulting from increases or decreases in prepayment rates that would almost certainly occur with such shifts in prevailing rates. This is why it is important to 4.19

hrterest Rate Risk Management

remember that convexity is an accurate means of quantifying just one component of MBS volatility. It captures the reinvestment volatility, but not the prepayment volatility.

Exhibit 4.9 Volatility Comparison Between a 10-Year Treasury Bond and a lZ-Year Mortgage Pass-Through Bond Basis Point Change in Prevailing Rates

Bond Equivalent Yield

Percentage Change in T-Bond Price

Percentage

Price

200

11.61

88.517

-1 1.48%

-13.78%

150

11.11

91.207

-8.79%

-10.11%

100

10.61

94.013

-5.99%

-6.59%

50

10.1 1

96.942

-3.06%

-3.21%

0

100.000 103.193

0

0

-50

9.61 9.11

3.19%

3.35%

-100

8.61

106.529

6.53%

7.18%

Change in MBS Price

-150

8.11

110.015

10.02%

11.52%

-200

7.61

113.659

13.66%

16.39%

Adjusting Duration to Compensate for Convexity

In a nutshell, convexity makes duration inaccurate for large shifts in interest rates, for longer term investments, and for instruments that have embedded options. To compensate for this problem, the price sensitivity formula discussed earlier in this chapter can be adjusted to incorporate convexity. The first formula, using modified duration to describe interest rate sensitivity, was shown as:

Percentage price change = —Duration x Change in rates The formula, revised to reflect convexity, is:

Percentage price change = (~Duration x Change in rates) + l/z (Convexity x Change in ratesz)

4-20

Duration and Convexity

Unfortunately, convexity is not a stable measure either. Like duration, convexity depends on the level of interest rates. Furthermore, the price sensitivity formula incorporating both modified duration and convexity still does not work well for certain financial instruments with embedded options when those options are deep in the money. Embedded options in general and the concept of in-the-money options are discussed in Chapter 2.

LIMITATIONS OF MACAULAY AND MODIFIED DURATION As we noted above, convexity makes duration inaccurate for large shifts in interest rates, for longer term insh'uments, and for instruments that have embedded options. Adjusting duration for convexity only partially fixes these deficiencies. Subsequent discussions in this chapter will present more accurate duration measures. But before we ttu'n' to those measures, it will be helpful to recap the limitations of both Macaulay and modified duration.

Macaulay and modified duration calculations use a single discount rate. This key assumption introduces two separate problems: 1. Managing a moving target. The measured duration changes every time a change in prevailing interest rates prompts us to employ a different discount rate. Like present value analysis, duration analysis depends heavily on the discount rate used in the calculation. Difl‘erent rate assumptions produce difl'erent answers. The following example illustrates this problem. A bank buys a U.S. Treasury bond that has exactly 10 years remaining until maturity. At today’s interest rates, the bond has a duration of seven years. But if rates rise tomorrow, the duration the bank measures tomorrow will be slightly shorter than seven years. And if rates fall tomorrow, the duration the bank measures tomorrow will be slightly longer.

In reality, there is not a single duration value for a given cash flow stream. Different interest rate environments produce different duration values for the same cash flow stream. Accordingly, the real interest rate sensitivity of any asset or liability is not a single duration value. Duration slides up or down as rates change.

4-21

Interest Rate Risk Management

Such changes in duration are not much of a problem for many bank assets and liabilities. For example, the duration of a 10-year noncallable bond would not shrink below 7 years unless rates rise above 9 percent. The duration of that same bond would not exceed eight years unless rates fall to less than 3 percent.2 For many bank investments and CDs, duration changes will not make much difference in the measured interest rate sensitivity.

But this is not the case for most bank loans, callable investment securities, or mortgage-backed investments. For these instruments, duration can change very significantly as prevailing interest rates change. Understand that, for this issue, the greater sensitivity of these instruments is not a result of convexity. It is not due to the fact that some or all of the cash flows are optional. (That is a separate problem.) Instead, the extra sensitivity we are describing here results from the fact that these instruments simply have larger periodic cash flows. To understand why the duration of these instruments is more sensitive to changes in the discount rate, take another look at Exhibits 4.3 and 4.4. Asset B, a five-year bond, has comparatively minor cash flows in the first four years just the semiannual interest payments. Changes in the discount rate used to weight those cash flows do not produce major changes in the duration of the asset because those cash flows are relatively small. But for asset C, the five-year loan, the annual cash flows are all equal. So a change in the discount rate used to weight those cash flows can easily produce a major change in the weighted average time remaining until maturity.

—

In short, the value of any future cash flow is obviously different in different rate environments. 2. Flat yield curves. Applying a single discount rate to all cash flows regardless of when they occur assumes a flat yield curve. This is rarely the case. Yield curves are almost always upward sloping long-term rates are almost always higher than short-term rates. That means, to be accurate, we should use higher discounts for cash flows occurring in later years than the discount rates we

—

2.

ED. Granite, “Bond’s Duration Is Handy Guide on Rates,” Wall Street Journal (Apr. 19, 1993), page C11.

4-22

Duration and Convexity

apply to cash flows occurring soon. Neither Macaulay nor modified duration reflect the term structure of rates. Macaulay and modified duration implicitly assume that changes in prevailing interest rates all occur in the same amounts for all rnattuities parallel yield curve shifts. In reality, short-term interest rates are almost always more volatile than long-term rates. Furthermore, parallel yield curve shifi assumptions usually overstate the changes in long-term interest rates. Therefore, since duration and market value of equity analysis are most influenced by long-term changes, they effectively magnify the error of the parallel yield curve assumption.

—

Most importantly, both Macaulay and modified duration assume that the amount or the timing of cash flows does not change with changes in prevailing rates interest rates. As we have discussed, this is simply not true for many types of financial instruments including most bank consumer loan assets and significant consumer deposit liabilities. Duration and modified duration are not accurate for instruments, such as residential mortgage loans, that have embedded options. The simplest illustration of this problem is a callable bond. If prevailing rates are above the coupon rate of a bond callable at par, the bond is not likely to be called. In that case, its duration will be based on the present values of all of the interest cash flows to maturity plus the principal cash flow at maturity. However, if prevailing rates are below the coupon rate of a bond callable at par, the bond is likely to be called. In that case, its duration will be based on the present value of only the interest payments that will be received until the call date plus the principal cash flow received on the call date.

Floating rate investments and loans with options can create a particularly interesting problem. In theory, a floating rate instrument should be very easy for rate risk analysts to evaluate. The rate risk analyst simply treats the floating rate instrument as if it were a fixed-rate instrument with a “maturity date" equal to the first repricing date. Viewing a floating rate instrument in that way makes perfect sense if its coupon rate truly adjusts to whatever current market rate prevails on the repricing date. However, many floating rate loans and securities have caps and floors. The caps or

4-23

Interest Rate Risk Management

floors may be periodic limits on the size of the rate change on any one adjustment date. Or they may be lifetime limits that are maximum or minimtun levels for the coupon rate. Cap and floor options can prevent the instrument’s coupon rate fi'om resetting to current market rate on the adjustment date. Therefore, the duration of floating rate instruments with options can be quite a bit longer than the time until the first reset date.

Limitations of Macaulay and modified duration also make hedging difficult. We can illustrate this problem with an example. Suppose we purchase a lO-year U.S. Treasury note with a 6 percent coupon rate. We purchase the note on the date of issue at par. The modified duration of that note is 7.44 years. At the same time, we fund that note with a zero coupon CD that has a modified duration of 7.44 years. If rates rise flour 6 percent to 10 percent, the modified duration of the Treasury note falls to 6.89 years, but the modified duration of the zero coupon CD only falls to 7.30 years. In other words, a 4 percent change in prevailing rates changes the duration and the prices of the two instruments by different amounts. A transaction that seems to be perfectly hedged at one rate level is not perfectly hedged at a different rate level. Because the convexity of the two instruments is different, the changes in the two instruments that result from large rate changes will also be different.

EFFECTIVE DURATION, OPTION ADJUSTED DURATION, AND PARTIAL DURATION The limitations of Macaulay and modified duration have not escaped the attention of quantitatively oriented risk experts. Starting in the 19705, they have developed a number of more complex duration measures. Improved versions of modified duration include Fisher-Well duration and Bierwag-Kaufman duration. These duration metrics resolve one or two of the four limitations discussed in the preceding section.

We might begin with the assertion that effective duration is a method for calculating duration more accurately. However, that is not entirely true. So, let’s begin with the fact that difi'erent texts use the term “efl'ective duration” differently. Adding to the resulting confusion, a number of other duration names are often used interchangeably. In the following

4-24

Duration and Convexity

paragraphs, we will examine each of the major types of effective duration.

Effective Duration and Empirical Duration

One of the most common definitions of efl'ective duration is: “A duration measure that does allow for changes in cash flows as yields change...”3 While this is a completely accurate definition, it is also a broad definition. And, in its breadth, it actually covers several different duration measures.

Earlier in this chapter, we noted that modified duration was a measure of the weighted average time for receiving the cash flows from a financial instrument. We considered an example and found the modified duration to be 4.27 years. At the same time, we observed that for the same example bond, for each 1 percentage point change in prevailing rates, the value of this bond will change by 4.27 percent. Modified duration, in other words, is a measure of a financial instrument’s price volatility. But, as we have just discussed, modified duration fails to capture the price

volatility accurately.

What if we simply back into a duration measure by using an observable price change? Suppose that prevailing rates rise by 1 percentage point and, in response, the price of callable bond X falls by 2 percent. (Actually, at any one time, the change in prevailing rates is likely to be smaller so we would have to multiply the observed price change to get the price change associated with a 1 percentage point change. Furthermore, as we noted earlier for modified duration, the measured duration is more accurate for smaller rate changes.) We can then conclude that the accurate duration of bond X is 2 percent or 2 years. That duration for callable bond X incorporates all of the factors that contribute to its price volatility. We can therefore conclude that it allows for changes in cash flows associated with changes in rates. This measure thus meets the general defmition of effective duration.

3.

Fabozzi, Frank. Chapter 11 “Price Volatility Measures: Duration," Fixed Income Mathematics. page 174.

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Interest Rate Risk Management

When effective duration is calculated by “backing into” the “real" duration as described here, we call it the empirical duration. We can express this in a formula similar to the two previous price sensitivity formulas: Effective or Empirical duration

=

Price change Change in rates

Note that the result of the above formula must be multiplied by 100 to convert it to a percentage.

Empirical duration is obviously of limited use because it requires

knowledge of actual price changes. What we want to know is how much price change (how much interest rate sensitivity) will result from a change in rates. Since this formula uses the price change and the change in rates to quantify the effective duration, we cannot use it to predict or estimate rate sensitivity. Instead, we can only use it after the fact to “back into” the “real” duration. However, there is one important application of empirical duration that we will discuss later in this chapter. Altemately, the term “effective duration” is used by some practitioners as a synonym for “option-adjusted duration.” Effective Duration and Option-Adjusted Duration

combine the effective duration formula described in the paragraph with option-adjusted spread (OAS) methodology, variant of effective duration is known as “option-adjusted Option-adjusted duration incorporates the expected durationshortening effect of an issuer’s embedded call provision. It is also called adjusted duration.‘1

When we preceding we get a duration."

Here is an illustration of option-adjusted duration.’ The current market price for MBS X is 103-10. If prevailing interest rates fall by 50 bp, we

4.

Eric Benhamou “Duration for Callable Securities Swaps Strategy," London, FICC, Goldman Sachs Intemational, tmdated.

5.

Lakhbir Hayre, editor, Salomon Smith Barney Guide to Mortgage andAsset-Backed Securities, Chapter 1, “A Concise Guide to Mortgage Backed Securities” page 41.

4-26

Duration and Convexity 6/08

project that the price of MBS X will increase to 103.93. On the other hand, if prevailing rates rise by 50 bp, we expect the price to fall to 102.08. For all three rate levels, the OAS is a constant 85 bp. option adjusted duration = 100 times (the change in price) divided by the original price option adjusted duration = 100 X (103.93 — 102.08) + 103.31 option adjusted duration = 1.8

The option adjusted duration for this bond is 1.8 years or 1.8 percent. That compares with a modified duration of 1.16 years for the same MBS. Notice that two of three prices used in the above example did not come from observed market prices. Instead they came from OAS models. These models depend on assumptions for a number of variables, such as rate volatility, and are therefore not often exactly correct. For this reason, the actual empirical duration will usually not be the same as the optionadjusted duration. Nevertheless, option-adjusted duration is more accurate than modified duration.

Option-adjusted duration provides significant improvement over modified duration because the OAS input reflects the fact that expected

cash flows fi'om many financial instruments will fluctuate as interest rates change. More precisely, option-adjusted duration accommodates interest-sensitive cash flows by taking into account the change in the timing of the option exercise that results from the change in prevailing interest rates.

However, the option-adjusted duration does not remove all of the limitations we discussed earlier for modified duration. Option-adjusted duration still relies on assumptions for parallel yield curve shifts and no changes in the OAS.

Key Rate Duration As we have noted more than once, short-term rates tend to be more volatile than long-term rates. Changes in prevailing interest rates almost never impact all maturities in equal amounts. Key rate duration addresses the impact of nonparallel shifts in the yield curve. It does this by

4-27

Interest Rate Risk Management

6/08

isolating the change in the rates for one maturity point on the yield curve

at a time. This is also referred to as “reshaping duration.”

Sometimes, key rate duration is only calculated for two points on the the change in a short-term rate, such as the l-year yield, yield curve and a change in a long-term rate, such as the 10-year yield. More comprehensive applications identify 10 or 11 key points and calculate the effective duration at each point. The actual calculation of key rate duration is almost the same as we discussed earlier for empirical duration. The only difference is that we use a change in yields for one particular maturity point while holding all other yields the same.

—

Risk managers can calculate effective or empirical duration for a change in each of a series of points and then combine the results in a table similar to a repricing gap report. An example is shown as Exhibit 4.10. Partial durations done in a set like this will sum to a value that is usually close to the overall empirical duration.

Exhibit 4.10 Key Rate Duration Table

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Partial Duration

Key rate duration, as described in the previous paragraph, is one example of partial duration. In fact, some users consider the terms to be synonymous. Partial duration is more accurately defined to be a duration

4-28

Duration and Convexity 6/08

calculation for which one variable is changed while all other variable are held constant. In our discussion of key rate duration, we considered calculating effective or empirical duration for a change in the yield for a single maturity point while holding yields for all other points on the yield curve constant. That is partial duration. In addition, we can calculate an option-adjusted duration changing a variable such the OAS while holding all other variables constant. That too can be considered to be an application of partial duration.

APPLYING DURATIONTO MEASURE IRR FOR THE ENTIRE BANK For IRR managers, the importance of duration is its usefulness in assessing the interest rate exposure of entire bank balance sheets. Since duration concepts are easier to grasp when we consider how they apply to individual bonds, the examples in this chapter examine individual bonds. But as an asset/liability management tool, the real value of duration lies in the simple fact that it applies equally to individual instrtunents and whole portfolios of assets and liabilities.

After the durations of individual bank assets and liabilities have been determined, those values can be combined to calculate the bank’s overall interest rate risk. If the sum of the durations of all of the assets is roughly the same as the sum of the durations of all of the liabilities, then the bank has very little IRR. In such a case, the effects of a change in interest rates on bank assets are offset by the effects of the same change in interest rates on bank liabilities. The actual calculation of a bank‘s duration of equity involves just a few more steps. First, you must calculate weighted averages for all assets and then add them together. For this purpose, weightings are determined by the percentage of the individual assets to the total. In other words, the duration of an asset that comprises two percent of total assets is given twice as much weight as the duration of an asset that comprises one percent of total assets. You can do this for each individual asset, but banks normally do it for groups of similar assets. The duration of all automobile loans, for example, would be calculated for an entire group of auto loans as if they were just one asset. The same is done for liabilities.

4-29

6/08 Interest Rate Risk Management

Since capital is excluded from this calculation, one other calculation is necessary to reflect the fact that the amount of the assets is larger than the amount of the liabilities (assuming, of course, that the bank has at least some capital). The total of the weighted averages for the liabilities is further weighted by multiplying it by the percentage of assets funded by liabilities.

Once these calculations are done, you must subtract the total of the weighted averages for the liabilities from the total of the weighted averages for the assets. The difference is the duration of the bank’s entire portfolio. This is usually called the duration of equity or DoE. The duration of equity is sometimes referred to as the “portfolio value of equity” or the “economic value of equity.” However, as we discuss in Chapter 5, those names, especially economic value of equity, are more commonly used to refer to something slightly different than the DoE. In order to promote clarity, we will therefore use only the name DoE. Calculating Duration of Equity

In a nutshell, duration of equity views the bank’s equity as if it were a bond. This “bond” has a stream of obligations for future cash inflows. Those are the cash-in flows from the bank’s assets. It also has a stream of obligations for future cash outflows. Those are the cash-out flows fiom the bank’s liabilities. When we calculate the present value weighted average for the asset cash flows and reduce that total by the total of the present value weighted cash flows from the liabilities, we have calculated the duration of the equity “bond.” We can express this a bit more simply in the following formula:

If: DA = the sum of the weighted average durations for the bank’s assets

DL = the sum of the weighted average durations for the bank’s liabilities DoE = the duration of the bank’s equity Then:

DoE = ((DA times total assets) - (DL times total liabilities» + equity

4-30

Duration and Convexity 6/08

Consider an example. A bank has $100 of assets with a weighted average duration of three years. It has $92 of liabilities with a weighted average duration of two and one half years. Duration of equity for this bank is 8.75 years, using the above formula:

DoE = ((DA times total assets) — (DL times total liabilities» + equity DoE = ((3 x 100) — (2.5 x 92)) + 8

DoE = (300 — 230) − − 8 DoE = 70 + 8 DoE = 8.75

Understanding Changes in Duration of Equity Once we know the duration of equity, we can use that measurement to calculate how a change in interest rates might afl‘ect the bank’s equity value.

The link between the duration for portfolios and the total change in the economic value of equity is expressed in the following formula:

If: CE = the percentage change in the duration of equity

D = duration CR = the change in prevailing interest rates

Then: CE=—Dx CR

x

100

(The minus sign in the formula is necessary because there is an inverse relationship between changes in interest rates and prices. In other words, interest rate increases cause price decreases and vice versa.) So, if the duration of equity is 1.24 years and we want to quantify the change in equity that might result from a 200 basis point increase in prevailing rates, we apply the formula like this:

4—31

6/08 Interest Rate Risk

CE=-l.24 X .02

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CE=-l.24 X2 CE=-2.48

Similarly, the percent change in equity resulting from a 3 percentage point decrease in prevailing interest rates +3.72. Sometimes we need a measure of IR that conveys our exposure in dollars. Oflen, senior officers, directors, and others simply find it easier to grasp risk exposures expressed in dollars rather than years or percentages. Fortunately, duration can readily be converted into a measure of dollars at risk. Simply multiply the percentage change in the duration of equity by the amount of equity. If, for example, the bank has $10 million in equity and a duration of equity of 1.24 years, we have

already calculated that it would lose 2.48 percent of its equity if prevailing rates rise by 2 percentage points. Therefore, if prevailing rates rise by 2 percentage points, the bank might expect to see a $248,000 reduction in equity. Of course, risk managers don’t just want to measure the current level of risk exposure, they also want to consider the impact of management changes in the risk exposure. Suppose, for example, we want to evaluate the impact of selling a $20 bond with a duration of .5 and reinvesting the proceeds in a short-term bond with a duration of 1.5. We could recalculate the duration of assets to reflect the change and then recalculate the DoE. But there is a faster way to evaluate the change. All we need to do is to multiply the $20 by the change in its duration and then divide by the amount of equity.‘5 So, if equity is 10, the change in DoE will be: change in DoE = 20 x ((5 - 1.5) +10)

change in DoE = 20 X (3.5 +10)

change in DoE = 20 X 0.35 change in DoE = 7

6.

The author wishes to thank Mr. I. Kimball Hobbs for pointing this out.

4-32

Duration and Convexity 6/08

Key Rate Duration for the Whole Bank The key rate duration example shown earlier as Exhibit 4.10 clearly shows a bank-wide view of assets, liabilities, and off-balance sheet exposures. A graphical presentation of the same data can be seen below inExhibit4.11.

Exhibit 4.11

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Notice that unlike the single duration of equity number, the key rate duration information illustrated in Exhibits 4.10 and 4.11 reveals the time horizons for the risk exposures. An Empirical Alternative

An alternative method of calculating the duration of equity uses the economic value of equity (EVE) produced by simulation models and is discussed in Chapter 5. This alternative, economic value sensitivity simulation modeling, has some important advantages over the durationbased measurement discussed above. Consequently, it is now much more common than duration-based measurements. We can calculate an empirical measure for duration of equity by using the information from EVE simulations. Suppose for example, that an EVE simulation model (like those discussed in Chapter 5) indicates the economic value of the bank’s equity will fall 0.9 percent in response to a 20 basis point increase in rates but will fall by 0.8 percent in response to

4-33

6/08 Interest Rate Risk Management

a 20 basis point decrease in prevailing rates. To calculate the empirical duration of equity using this data, we execute the following two steps:

1. Average the change from the increase and decrease rate scenarios. In our example, we average 0.9 percent and 0.8 percent. The result is 0.85 percent.

2. Adjust the average change in the duration of equity to see the equivalent change resulting from a 100 bp shift in rates. (We could have simply started with a 100 bp change. However, duration is' more accurate for a smaller change.) In our example, we used a 20 bp rate shift so we want to multiply the duration of equity value, 0.85, by 5. The result is 4.25. Duration of equity for the bank in our example is therefore 4.25 percent.

While this is an easy and quick way to calculate DoE, risk managers should pay attention to the EVE simulation results rather than this duration value. It is far more important to evaluate the risk indicated by changes in EVE in response to a wide range of changes in prevailing rates. This is because the impact of embedded options is only fully revealed when large changes in rates are modeled. Positive and Negative Durations

The same inverse relationship that exists between changes in bond prices and changes in interest rates also applies to duration of equity. When the duration of assets is longer than the duration of liabilities, the duration of equity is a positive number. In other words, a bank with long-term assets funded by short-term liabilities will have a positive duration of equity. (In Chapter 3, we called such a bank “liability sensitive”) For a bank with a positive duration of equity, the market value of its equity will increase if rates decline and decrease if rates rise. The opposite is also true. When the duration of assets is shorter than the duration of liabilities, the duration of equity is a negative number. In other words, a bank with short-term assets fturded by long-term liabilities will have a negative duration of equity. (In Chapter 3, we called such a bank “asset sensitive”) For a bank with a negative duration of equity, the

4-34

Duration and Convexity 6/08

market value of its equity will decrease if rates decline and increase if rates rise.

Capturing the Duration of All Cash Flows It is important for a bank to capture the duration of all of its cash flows, not just the cash flows generated from its assets and liabilities. Like gap and income simulation analysis, duration is almost always applied only to interest-bearing assets and interest-bearing liabilities and the cash flow generated from those instruments. In other words, almost all interest rate risk measurement focuses on the net interest margin. Duration is a useful tool, especially for evaluating the rate risk exposure in specific fixed-rate assets and liabilities that have known maturities and known cash flows. However, when cash flows are not known with certainty, duration measures become approximations that are only as good as the underlying estimates. Furthermore, the duration methodology itself introduces actual or potential errors. As a result, duration can never be more than a useful proxy for interest rate risk exposure. This is particularly true when duration is used to measure risk for the bank as a whole, rather than for specific items on the balance sheet, as well as when duration is used to measure rate risk exposure to large changes in prevailing rates.

In the final pages of this chapter, we will consider some serious limitations of duration as it applies to bankwide risk measurement. Although duration is a useful tool when we know what it does best and when it is most accurate, it is a misleading tool when used without an awareness of its limitations.

ADVANTAGES OF DURATION At the beginning of this chapter we observed that duration analysis is often the best tool for capturing long-term interest rate risk. In fact, duration analysis ofl‘ers a number of significant advantages to IR managers. Five specific advantages are discussed below.

4-35

6/08 Interest Rate Risk Management

Captures Interest Rate Risk from All Time Periods Duration captures interest rate risk in all time periods, not just in the next 12 months. It incorporates all of the future cash flows fi'om a bank’s current assets and liabilities. This is a significant improvement from the gap and income simulation approaches to IRR measurement that we considered in Chapter 3. Gap models can capture most, or even all, of the future period mismatches in current assets and liabilities and can be constructed with buckets extending into as many future periods as desired. However, gap analysis does not measure the IRR of long-term positions with anything near the accuracy of duration analysis. This is because, tmlike gap, duration recognizes that cash now is more valuable than cash later. Income simulation models are usually used to measure IRR for only one year. Income simulation also can be extended to include longer periods, but it is not practical to simulate as far into the future as the maturity of the bank’s longest asset or liability. In contrast, duration analysis shows the efl'ects of changes in rates on the present value of all future earnings, not just on next year’s book earnings. Duration analysis offers a more comprehensive approach to measuring interest rate risk because it incorporates the entire spectrum of a bank's repricing mismatches.7

In Chapter 3, we observed that one disadvantage of income simulation

modeling is that it can completely fail to identify potentially large longterm risks represented by what one observer has named IRR “time bombs" in their balance sheets. Large changes in a bank's exposure to

interest rate risk can be caused by the sudden maturity or repricing of significant amounts of assets or liabilities. If such time bombs occur more than one year in the future, they will probably not be captured by income simulation analysis. Duration analysis captures time bombs regardless of when they occur.

7.

J.V. Houpt and J.A. Embersit, “A Method for Evaluating Interest Rate Risk in U.S. Commercial Banks," Federal Reserve Bulletin (August 1991), page 627.

4-36

Duration and Convexity 6/08

Expresses the Measured Quantity of IRR as a Single Value Duration produces a single measure of interest rate risk, which facilitates rate risk management. Duration analysis not only incorporates all of the future cash flows from a bank’s current assets and liabilities, it also distills the IRR from those assets and liabilities into a single number. This number can be the duration in years, or it can be the percentage change in portfolio value of a bank’s equity for any given change in prevailing interest rates.

There are three related advantages to having IRR from so many diverse cash flows distilled into a single measure:

∙

∙ ∙

It makes the extent of a bank’s total IRR quite clear.

It permits easy comparison of a bank’s current IRR exposure to previous or future exposures. Since the measure is created by adding the durations of portfolios

or of individual assets and liabilities, it can readily be examined as an aggregate or in pieces.

Income simulation analysis provides a single measure of current IRR exposure, but duration provides a total exposure value that is readily broken into components. If a duration is unacceptable, managers can easily review and analyze the durations of the individual asset and liability portfolios that together comprise the total bankwide duration. Gap analysis segments total IRR exposure into smaller units, or time buckets, that managers can individually analyze, but these buckets are less useful than groups of assets or liabilities. Only duration analysis gives managers the advantages of a single number that is clear both as a total measurement and when subdivided into workable components. Duration is easy to use.

Expresses the Measured Quantity of [RR as a Change in a WellUnderstood Variable

Duration emphasizes market value changes. Except for bond, currency, and derivatives traders, every bank manager alive today has spent his or her entire working career in an accrual accounting world. (Accounting

4-37

6/08

Interest Rate Risk Management

rules for market value disclosures in footnotes and for mark-to-market accounting of investments are beginning to change this environment.) We are used to focusing on profits as the “bottom line.”

In theory, equity value should be more important. After all, the stockholders, not the managers, own the business. Since the stockholders benefit from higher stock prices, the economic or market value of the firm is more important than its bottom line net income. Duration analysis, as we have seen, can measure interest rate risk in terms of potential change in economic or market value. Thus, duration is a measure of risk that expresses that risk in a theoretically more

meaningful way.

Captures IRR Obscured by Accrual Accounting Methods Unlike gap analysis and income simulations, duration analysis correctly reflects the interest rate risk inherent in the reinvestment of cash flows. This is easiest to see if we consider zero coupon bonds. Suppose that a bank has just one asset, a five-year zero coupon bond purchased to yield 10 percent to maturity. The bank also has one liability, a five-year certificate of deposit (CD) that pays interest monthly at an annual rate of 8 percent. Traditional gap analysis would show that this bank has no IRR. Both the asset and the liability reprice in five years. But this is clearly inaccurate. Even though the principal cash flows are exactly matched, the interest cash flows are not. If interest rates rise, the opportunity cost of paying the CD interest monthly for 59 months before the interest income is received will be greater than if interest rates stay the same or fall. Since duration incorporates both income and principal cash flows, it avoids this problem. For most banks, income simulation analysis would correctly show that the bank described in the above example is asset sensitive, but it would understate the degree of asset sensitivity because most income simulation models capture data from the bank’s accounting system. For generally accepted accounting principles (GAAP) purposes, a prorated portion of the interest income that will be earned from the zero coupon bond is accrued monthly. Consequently, an income simulation model that obtained data for this asset fi'om the bank’s accounting system would recognize income (the 2 percent spread between the asset yield and the liability cost) each month. Most models would then treat that income as a

4-38

Duration and Convexiy 6/08

cash flow stream in which each income cash flow is reinvested in all months after the month in which it is earned. This cash flow stream is more valuable in higher rate environments and less valuable in lower rate environments. But no interest income is received from the zero coupon bond until it matures. If interest rates change, it is not the value of the 2 percent annual income stream that will change, but the value of the entire 8 percent stream of liability interest payments. Because duration is based on the present values of the actual cash flows, it would show the true degree of asset sensitivity in this example bank.

Facilitates Segregation of Rate Risk Components As we discussed in Chapter 1, interest rate risk has four primary components. Duration measures can be used to separately quantify the rate risk arising from gap or mismatch risk and the rate risk arising from option risk. The mismatch risk is mainly what is measured by duration alone, whereas the option risk is mainly what is measured by convexity.

DISADVANTAGES OF DURATION The five advantages just described make duration analysis seem an attractive tool for rate risk managers. Unfortunately, duration analysis also has significant disadvantages that limit its utility. Early in our discussion of duration, we listed four serious limitations of both Macaulay and modified duration. Risk managers using either one of those tools should consider that earlier list of limitations together with the disadvantages discussed in the following paragraphs. Risk managers using effective duration need only consider the following disadvantages.

Managing Duration Can Increase Earnings Volatility If rate risk managers use duration measurements to manage rate risk, they can increase the volatility of reported bank earnings. This can occur when managers take steps in one accounting period to reduce risks that will actually be incurred in future accounting periods. This can easily happen because the single measure of overall interest rate risk provided by duration does not provide any information about the temporal nature of that risk. In other words, duration may tell us that we will suffer a 5 percent decrease in portfolio equity if rates rise by 2 percent, but it does

4-39

6/08 Interest Rate Risk Management

not say whether that change results from mismatches in this year’s cash flows or some other year’s cash flows.

The sensitivity of equity duration to changes in prevailing interest rates can tell the rate risk analyst a lot about the quantity of interest rate risk, but it says nothing about its timing. Managers need to know timing as well as quantity. Steps undertaken to reduce a risk in year one may be different from steps undertaken to reduce a risk in year five. This difficulty can be reduced if DOE measures are supplemented with key. duration information.

Managers can easily increase can-rings volatility as a result of steps taken to reduce IRR exposure. In the long run, this volatility may not matter — indeed, it may be a small price to pay for better risk management. But in the short run, it presents a problem. Duration Relies on the Unlikely Assumption That All Rates Change at the Same Time

Duration implicitly assumes that all rate changes occur at the same time. That assumption is unlikely at best. Corporate bond rates do not necessarily rise and fall at the same time as U.S. Treasury bond rates. CD rates do not necessarily rise and fall at the same time as commercial paper rates. Changes in prime-based loans ofien lag behind changes in Treasury rates. Changes in rates paid on core deposits ahnost always lag behind changes in rates paid for capital markets instruments. Duration approaches to measuring rate risk completely fail to capture such timing differences. Duration Ignores Basis Risk

Duration implicitly assumes no basis risk. In previous discussions of both gap and income simulation analysis, we saw that changes in interest rates rarely affect interest rates for all instruments by the same amount. Changes in the spreads (the interest rate differences) between instruments increase or decrease daily. Income simulation models can easily accommodate rate change forecasts that assume changes in spreads, but duration analysis cannot.

Duration and Convexity 6/08

The inaccuracies that result from applying such an assumption to spread relationships can be significant. One commentator put it this way: Whatever rate of interest is chosen as a representative market rate, it will invariably diverge, over time, from other rates. Duration measures the sensitivity of the price of assets and liabilities to changes in the general level of rates of interest; it does not show how a bank will be affected by changes in relative rates of interest.“

Duration-based approaches to IR measurement cannot readily reflect such spread changes. As it can for nonparallel rate changes. duration can capture some effects of this common reality if we use different discount rates for different instruments. But this approach is also, at best, cumbersome. Ofien, the improvement in the accuracy of IR measured is not enough to justify the extra analytical work. Duration Is Difficult to Calculate for Products with Administered Interest Rates Duration is difficult to apply to retail loans and deposits. As the discussion of gap analysis and income simulation in Chapter 3 shows, many loans and deposits have indeterminate repricing dates. We do not know, for example, when interest rates paid on savings accounts will change. Since we do not know when these assets and liabilities will reprice, we can only estimate the duration of these accounts. Also, since for many banks the quantities of assets and liabilities with indeterminate maturities comprise major portions of the balance sheets, the estimates can have a major influence on their total duration of equity calculation. As a result, their duration measurement of total interest rate risk may be susceptible to errors.

The impact of this problem is reduced but not eliminated by concentrating on the changes in the economic value of equity. If the assumptions are the same, the change in duration of equity value that results from a change in interest rates may be more accurate than the

8.

R. Harrington, “Aims and Methods,” Asset and Liability Management by Banks (Paris: Organization for Economic Cooperation and Development, 1987). page 170.

6/08 Interest

Rate Risk Managgme'nt

absolute level of risk measured by the duration of equity alone. Unfortunately, focusing on the change rather than on the absolute level of risk cannot eliminate all of the errors caused by faulty assumptions for repricing times. We calculate the duration for each instrument by using the present value to weight the cash flow. The present value is clearly sensitive to the assumption made for the discount rate. (It is also sensitive to the

assumption made for the time remaining until repricing, but that variable is eliminated if we focus only on the change — we are holding the time until repricing assumption constant.) We could use the same discount rate for each rate change scenario, but this assumption would ignore the differences in reinvestment income available in difl‘erent interest rate environments. If we alter the discount rate that we use to reflect difierent prevailing rates in our analysis, errors in the assumed time until repricing will produce incorrect measurements of interest rate risk. Regardless of whether we change the discount rate to reflect different reinvestment rates in different interest rate environments, duration analysis still has problems with administered-rate bank products. Experience has shown that administered rates, such as the prime rate and the rates paid for savings and negotiable order of withdrawal (NOW) accounts, do not change when prevailing interest rates change. There are time lags. Experience has also shown that administered rates do not change by the same amounts as prevailing rates change. There are dampening efl‘ects. Furthermore, there may be implied ceilings for core deposit interest rates. Duration analysis fails to capture the dynamics affecting the changes in administered interest rates. Both of these problems, indeterminate maturity dates and administered interest rates, reduce the accuracy of duration-based IRR measurements. (Both of these problems are discussed in Chapters 6 and 7.) Since for many banks, assets and liabilities with indeterminate maturities or administered rates comprise major portions of their balance sheets, this weakness can lead to significant misstatements of interest rate risk. Duration Is a Static IRR Measurement

Perhaps the most serious weakness of duration-based approaches to IR measurement is that they are static measures in a dynamic world. 4-42

Duration and Convexity 6/08

Duration implicitly assumes that all of a bank’s future cash flows are known. Unfortunately, this is not the case. At best, we know all of the future cash flows from the assets and liabilities that we hold today. Tomorrow, things will certainly be different. We have already discussed the problems that arise because durationbased measurements of IRR fail to capture all of the rate risk caused by volume changes and interest rate changes. Other factors can also cause major changes in fiiture cash flows. Changes in bank markets, competition, products, marketing, strategic planning, and economic conditions can materially affect asset and liability levels. Future Cash Flows — Assumptions

Duration-based approaches to risk measurement actually include the following implied assumptions about future cash flows:

∙

∙ ∙

∙ 9.

Macaulay and modified duration analysis assume that known cash flows from principal payments or from maturities will occur when they are contractually scheduled to occur. Actually, prepayments accelerate these cash flows. Duration analysis assumes that all cash flows are reinvested in the same instruments. Actually, principal payments or maturing balances are often reinvested in other uses or reborrowed from other sources.9

Duration analysis assumes that changes in interest rates will not prompt changes in customer behavior. Actually, additions and withdrawals from savings accormts are just two examples of common bank cash flows that are not predictable. Duration analysis assumes that changes in interest rates will not prompt changes in the management of the bank. Actually,

Olson Research Associates, Inc., Community Bank Guide to Asset/Liability Management Policies (Washington, D.C.: American Bankers Association, 1991). page 25.

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management strategies and tactics often differ in different interest

∙

rate environments.

Duration analysis assumes that there are no incremental changes in bank assets and liabilities. Actually, banks constantly gain or lose market share for loans and deposits in the markets that they serve.

Focus on Current Position Duration-based measurement of IRR focuses on accurately measuring where a bank is now. Even though it does not always accurately capture a bank’s current IRR exposure, its failure to accurately reflect future exposure is more significant. Income simulation modeling evaluates the interest rate risk arising both from a bank’s current position and from its forecast of future business. Duration looks only at interest rate risk in the current position. By ignoring future changes that affect that risk, it fails to accurately measure real exposure to future rate changes.

The consequence of this problem can be serious. Consider this: the changes between today’s balance sheet and tomorrow’s balance sheet will probably be inconsequential, and the changes between today’s balance sheet and next month’s balance sheet will probably be small, but the changes between today’s balance sheet and the balance sheet two years from today will probably be significant. In the near term, the future cash flows from all existing positions at that time are much more like future cash flows from the existing positions now. In the long term, the future cash flows from all existing positions at that time are unlikely to resemble the future cash flows fiom the existing positions. Duration purports to be the best IRR measurement system for capturing long-term rate risk. This is true only to the extent that the future resembles the present. Duration Masks Dispersion

Single duration of equity measures mask the dispersion of individual asset and liability durations. Any given duration value can result from a set of cash flows with a high dispersion of maturities or from a set of cash flows with a low dispersion of equity values.

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Duration and Convexity 6/08

For example, Narrow National Bank owns two bonds. One has a duration of 36 months and the other has a duration of 48 months. Since both bonds are for the same amount and both have the same coupon rate, the duration of Narrow National’s portfolio is 42 months. At the same time, Broad State Bank also has two bonds in its portfolio. One has a duration of 3 months and the other has a duration of 8] months. Again, since both investments are the same size and have the same coupon rate, the duration of Broad State’s portfolio is 42 months. Both banks have investment portfolios with the same duration, even though Narrow National has a low dispersion and Broad State has a high dispersion.

On a static basis, the fact that the single value for duration for a portfolio or a bank masks the dispersion of the individual durations that comprise that single value is irrelevant to the rate risk manager. The rate risk is the same. If rates immediately rise or fall, two portfolios or two banks with identical durations of equity will benefit or suffer to the same extent, regardless of the dispersion of their asset and liability durations. However, the same is not true over time. On a dynamic basis, rate risk managers must consider the effects of dispersion. This can be seen in the above example. In this case, approximately 3 months after Broad State's investment portfolio was calculated to be 42 months, it will jump to something near 78 months. (The passage of time causes one of its investments to mature while the duration of the other shortens slightly.) At the same time, 3 months afier Narrow National‘s investment portfolio was calculated to have a duration or 42 months, it will still be roughly 39 months. Clearly, the dispersion masked by the single duration measure for Broad State’s portfolio obscures the vital need for its rate risk managers to actively manage its rate risk. Duration Calculations Exclude a Material Component of Interest Rate Risk

Duration analysis is almost always used to measure the interest rate risk of assets and liabilities on the balance sheet and their related cash flows. Thus, the interest income cash flow streams from assets and the interest expense cash flow streams from liabilities are included in the measured duration of equity. In other words, the bank’s exposure to adverse consequences from future changes in'prevailing rates is measured for its net interest margin as well as the principal amounts of its assets and

liabilities.

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Rate Risk Management

But to the extent that duration analysis is applied only to the net interest margin, it severely overestimates interest rate risk. This can be a major weakness. For example, if such an analysis shows that a bank is perfectly balanced and apparently has no interest rate risk, the bank is actually exposed to falling rates. This is because the duration of equity calculation discounts only the cash flows associated with the net interest margin, without including the big negative cash flow from the net noninterest expense. Noninterest income is almost always just a small fraction of net interest expense. Therefore, net noninterest expense is almost always a material cash outflow. This problem is discussed in more detail in Chapter 11. Rate risk managers should not fail to include this cash flow

in their analysis.

DURATION SUMIVIARY At first glance, duration appears to be the key that unlocks the door to superior IRR measurement. Its heavy use of mathematics and sophisticated analytical concepts gives it an aura of accuracy. The beguiling simplicity of its output gives it great appeal to senior managers and regulators. Unfortunately, duration loses some of its attractiveness after close scrutiny.

One advantage of duration often cited is that it can summarize the interest rate risk of an entire bank in a single number. That advantage is of very little use if the single number is wrong. For large changes in prevailing rates, the single number is wrong. For banks that have significant holdings of core deposits and loans subject to prepayment, the single number is, at best, a close approximation. For changes in basis risk, the single number is wrong. At the same time, it is a mistake to ignore duration analysis. Duration proponents regard it as a superior method for understanding interest rate risk. Correctly, duration proponents cite the fact that it not only includes long-term interest rate risk ofien ignored by other IRR measurement systems, but also reflects the time value of money. Incorrectly, proponents cite the advantage of duration as an “objective" measure because it does not require as many assumptions. But as we have seen, duration contains implicit assumptions that greatly oversimplify reality. Duration also fails to reflect embedded options that are included in

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Duration and Convexity 6/08

income simulation models through the latter’s subjective assumptions. One critic of duration analysis summed up its value this way: ...the expectations of the duration theory’s power fall considerably short of what it can do in reality. The facts are that it assumes away elusive economic variables, disregards the possibility of change, and ignores the inherent complexity of the problem. Duration can be a useful analytical technique, but it is neither a universal tool nor a magic shield against interest rate rrsk.ro

-

This may be too critical an opinion of duration. For example, it does not give duration credit for capturing longer term interest rate risk, which income simulation ignores. 0n the whole, however, it is correct to say that duration can be a helpful analytical technique, but it is too flawed to be used as the sole measure of interest rate risk.

As we have repeatedly observed, there is no single answer, no magic solution, for IRR management. Duration can be used as a supplement to income simulation modeling to capture some of the interest rate implications of large, long-term positions. However, a far better technique for capturing long-term risk is discussed in Chapter 5. Duration can also contribute to asset/liability management, acting as a useful tool for rate risk managers engaged in hedging specific instruments. (This type of hedging is discussed in Chapter 16.)

10. C. Gilmore and J. Hunter, “Duration — Magic Number or Misleading Indicatofl," Bank/Asset Liability Management, June 1987, page 2.

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Chapter 5 Economic Value Simulation

What Is Economic Value Sensitivity Simulation? ............................... 5-1 MV, PV, and EV .............................................................................. 5-2 We Use PV When MV Is Not Available ...................................... 5-2 PV Often Does Not Equal MV ..................................................... 5-3 Economic Value of Equity ............................................................... 5-4 Economic Value Sensitivity ............................................................. 5-5 A Note on Equity Value Terminology ............................................. 5-7 How Does Economic Value Sensitivity Simulation Differ from Duration-Based Economic Value? ................................................... 5-8 Using Economic Value of Equity Sensitivity Simulation to Measure IRR ....................................................................................... 5-10 Exhibit 5.1: Typical Bank .......................................................... 5-11 Using Real-World EVE Models in Real Banks.............................. 5-13 Dealing with Assumptions .............................................................. 5-15 Discount Rates and Yield Curve Smoothing ...................................... 5-16 Introduction to Yield Curve Smoothing ......................................... 5-17 What Is Yield Curve Smoothing? .............................................. 5-18 Choosing a Smoothing Method ...................................................... 5-19 Linear Yield Curve Smoothing....................................................... 5-19 Cubic Spline Yield Smoothing ....................................................... 5-20 Exhibit 5.2: Example of a Cubic Spline Calculation .................. 5-21 Maximum Smoothness Forward Rates ........................................... 5-21 What Smoothing Technique Should You Use? .............................. 5-22 Exhibit 5.3: Contrasting Smoothing Methods ............................ 5-23 Exhibit 5.4: Average Error in Estimating 7-Year Swap Rates 5-24 Evaluating the Rate Sensitivity of EVE ............................................. 5-25 EVE Sensitivity Dispersion ....................................................... 5-25 Exhibit 5.5: Economic Value of Equity ..................................... 5-26 Exhibit 5.6: Economic Value Sensitivity of Assets, Liabilities, and Equity .................................................................................. 5-28 Exhibit 5.7: Economic Value of Equity Sensitivity ................... 5-29 Plus or Minus? A Note on Arithmetic Signs .............................. 5-29

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2110 Interest Rate Risk Management

Exhibit 5.8: Sample Output of Economic Value Simulation Model ....................................................................... Uneven Outcomes .......................................................................... Relating the Rate Sensitivity of the Economic Value to the Rate Sensitivity of Net Income ................................................. The Conceptual Relationship Between EVE and EAR .............. The Practical Relationship Between EVE and EAR .................. EVE and EAR Treatments of New Business .................................. Exhibit 5.9: The Impact of Runoff, Rollover, and Growth

5-30 5-31 5-32 5-32 5-34 5-38

Over Time .................................................................................. 5-38 The Impact of Omitting Rollover and Growth is Ofien Misunderstood — Two Points of View ........................................ 5-39 Using EVE Sensitivity Simulation to Achieve Other Management Goals ......................................................................... 5-41 FAS 107...................................................................................... 5-41 FAS 115...................................................................................... 5-42 Product Pricing and Marketing................................................... 5-42 Advantages of EVE Sensitivity Simulation........................................ 5-43 Captures Interest Rate Risk from All Time Periods ....................... 5-43 Provides a Specific and Understandable Measure of Rate Risk Exposure................................................................................. 5-44 Focuses on the Rate Risk in the Bank’s Current Position .............. 5—44 Can Readily Be Used to Focus on Changes in Rate Exposure at the Product Level ........................................................................ 5-44 Can Capture Option Risk................................................................ 5-45 Can Capture Yield Curve Risk ....................................................... 5-45 Can Capture Basis Risk .................................................................. 5-45 Can Reflect Rate Sensitivity Over a Wide Range of Rate Scenarios ......................................................................................... 5-46 Can Capture Rate Risk Obscured by Accrual Accounting ............. 5-46 Meets Regulatory Expectations ...................................................... 5-46 Can Be Integrated with Other Management Information Systems ........................................................................................... 5-47 Disadvantages of EVE Sensitivity Simulation ................................... 5-47 Managing EVE Sensitivity Can Increase Earnings Volatility ........ 5-47 In Most Applications, EVE Ignores the Impact of Reinvestment and New Business .................................................... 5-48 EVE Does Not Provide Any Information About the Timing of Rate Risk Exposures ...................................................... 5-48

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Assumptions Require Careful Development, Analysis, Increased Controls, and Testing ..................................................... 5-48 Use of Discount Rates Can Introduce Additional Measurement Errors .............................................................................................. 5-49 Accurate Assumptions of Volume Changes Caused by Embedded Options Must Be Accurate ........................................... 5-50 EVE May Fail to Capture a Material Amount of Interest Rate Risk Exposure ........................................................................ 5-51 Value at Risk ...................................................................................... 5-51 Three Difl‘erent VaRs ..................................................................... 5-52 Exhibit 5.10: Strengths and Weaknesses of VaR Methods ........ 5-54 VaR Problems and Limitations....................................................... 5-55 Exhibit 5.1]: VaR for Three Hypothetical Portfolios................. 5-57 Exhibit 5.12: Cumulative VaR for Three Hypothetical Portfolios .................................................................................... 5-58 Stress Testing.................................................................................. 5-59 Converting EVE to VaR ................................................................. 5-60 EVE and VaR Summary ..................................................................... 5-61

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5-iv

Chapter 5

Economic Value Simulation

What is your balance sheet really worth? How much of that value might be lost as a result of adverse changes in future interest rates? These are questions that were introduced when we discussed economic vs. accounting perspectives in Chapter 2. The focus of Chapter 4 was on the balance sheet. After carefully evaluating both gap analysis and duration analysis, we found a lot of value in their objectives, but some serious limitations in their accuracy.

In this chapter, we will focus on a tool called “market value” or “economic value” sensitivity simulation. As we will see, this is another economic perspective on interest rate risk. Later in the chapter, we will also take a brief look at a closely related risk measure known as value at risk (VaR). Just as duration was touted as an ideal solution in the mid19805, economic value of equity (EVE) and VaR were widely viewed as ideal solutions in the mid-19905. The truth is that these tools offer important advantages. They enable risk managers to model the impact of future rate changes on balance sheet values in ways that are far more complete, accurate, and insightful than earlier tools. Yet, as we will also see, even though these tools are far more beneficial, they are not perfect solutions. Readers should also View the information discussed in this chapter with Chapter 11’s key perspectives on the applications of these important tools.

WHAT IS ECONOMIC VALUE SENSITIVITY SIMULATION? Rate risk analysts applying economic measures to quantify rate risk require some measure of “market values” or market value sensitivity. In

some cases, observable market prices can be used to value financial instruments. However, for most bank assets and liabilities, there are no

observable market prices because the instruments are rarely, if ever,

traded. Thus for the vast majority of bank-owned financial instruments, we apply mathematical tools to infer either the value or the sensitivity of

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Interest Rate Risk Management

the value. (Duration and VaR analysis infer the sensitivity of financial instruments. EVE or “market value” analysis infers a “market value.")

Economic value measures of risk start with “market values.” Unfortunately, not all financial instruments can be valued the same way. The risk in traded instruments is defined as the price volatility of the instrument. It is often described in terms of how much the price might change (the value of an 01) or by the duration of the instrument. Both descriptions are perfectly suited to the needs of financial instrument traders. Neither is well suited to the needs of bank risk mangers. Indeed, two huge problems loom over the application of market risk valuations to problem of a bank’s overall exposure to interest rate risk (IRR).

∙

∙

First, bank risk managers have to focus on the impact of large changes in prevailing rates on portfolios full of loans and deposits with embedded options. When we examine the price sensitivity of these loans and deposits in response to large changes in rates, the accuracy of duration and other price sensitivity measures is seriously degraded by the negative convexity created by the options. (Negative convexity was discussed in Chapter 4.) Second, there simply are no observable market prices for the vast mqiority of bank assets and liabilities.

MV, PV, and EV Without observable market prices, financial analysts and risk managers

apply mathematical tools to infer market prices and price sensitivity. Of course, these same tools can be applied to instruments that have observable market prices. In those cases, we are able to verify the accuracy of the inferred prices. But the further we move away from observable prices and price changes resulting from observed rate changes, the squishier the implied market value sensitivity numbers become.

We Use PV When MV Is Not Available

The present value (PV) of any financial instrument is determined by three simple things:

Economic Value Simulation 2/10

1. The first variable is the amount of cash flow. For a discount security, such as a Treasury bill, the amount of the cash flow is the principal received at maturity. For a loan, on the other hand, there may be dozens or hundreds of cash flows providing a cumulative cash flow stream. Obviously, more cash is more valuable than less cash. 2. The second variable is the timing of the cash flows. A five-year, zero coupon bond has a single cash flow at the end of the five-year term. A 30—year mortgage has monthly principal and interest payments. Obviously, cash received sooner is more valuable than cash received later. 3.

The third variable is the discount rate that we apply to measure the difference in value between cash received soon and cash received later. Value is clearly sensitive to the choice of discount rate.

—

These three concepts identifying the cash flow, identifying the timing, and selecting a discount rate to calculate present value are well known to students of finance.

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PV Oflen Does Not Equal MV Seems simple, but it isn’t. Consider the following influences on PV and MV: 1. A diversified group of car loans, credit card loans or mortgage loans usually has a market value well in excess of the sum of the present values of each loan in the group. 2. A seasoned loan generally has a higher market value than new loan but PV calculations do not reflect seasoning.

3.

Options embedded in investments, loans, and deposits can make it hard to quantify the amount and timing of future cash flows in future rate environments. For these instruments, the calculated PV is dependent upon assumptions about the instrument’s cash flows.

4. At the same time, decisions about the discount rate can materially impact the calculated value.

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Interest Rate Risk Management

For these reasons, we have to be very careful about using the term “market value” to describe inferred market values. That does not mean that “market value” or “economic value” analysis is useless. Far from it. Market value analysis, properly applied, can be extremely insightful. In this chapter, our focus is on how we can use the inferred values to quantify the bank’s IRR exposure. Later in this chapter, we will also consider the discount rate problem in detail. Then, in subsequent chapters, we will examine the option problems. Economic Value of Equity

The simple value concepts just described can be applied to the bank as whole. As we saw in the previous chapter, duration of equity is one way to do just that. Economic value of equity sensitivity simulation is another.

In a nutshell, EVE sensitivity simulation simply calculates present values (PV) for all of a bank’s cash flows. That is all there is to it. Assets generate cash inflows. Liabilities mandate cash outflows. In its simplest form, the formula is:

EVE = PV of all asset cash flows minus the PV of all liability cash flows

The present values of all of the cash flows owed to the bank are mainly the sum of the present values of the cash flows that will come to the bank in the future from its current investment and loan assets. These include both principal and interest income. Similarly, the present values of all of the cash flows that the bank owes to others are mainly the sum of the present values of the cash flows that will be paid in the future for the bank’s current deposits and borrowings. These include interest expense as well as principal. In some cases, such as for a loan or deposit payable on demand, the future may be tomorrow. In other cases, such as for a long-term loan, the final cash flow may be many years in the future. Some banks may also wish to include cash flows from oE-balance sheet positions. However, for most banks, those cash flows tend to be comparatively minor. We may also choose to incorporate the impact of nonbalance sheet cash flows such as noninterest income and expense. The merits of including those cash flows are discussed in Chapter 11.

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Economic Value Simulation 2/10

The difl‘erence between the total present values of cash flowing into the bank and the total present values of the cash flowing out of the bank in the future is the net value owned by the stockholders. We might call it the bank’s equity value. However, such a name would be confusing since it is neither the accounting (book) value of equity nor the stock market value of equity. While a variety of names are used, in this chapter we refer to the net present value of equity as the “economic value of equity” or EVE.

Economic Value Sensitivity The focus of economic value simulation is not on EVE itself. Instead, the focus is on changes in EVE or, more specifically, on the sensitivity of EVE. Calculating EVE sensitivity is a simple, three-step process:

1. Calculate EVE using currently prevailing interest rate levels.

2. Calculate EVE under one or more dtfl'erent interest rate environments or scenarios. The alternative rate scenario should reflect all interest rate-dependent factors such as changes in the amount and the timing of cash flows that might be associated with economic activity when rates are at levels that are included in the particular scenario. As we will discuss in Chapter 8, rate scenarios may be selected to be realistic or unrealistic. 3. Subtract the difirence. This is the quantity of EVE sensitivity. It may be expressed as a dollar amount or as a percent of the base case EVE from step one.

Example: For the first step, suppose that the present value of all expected cash flows from assets for Simple Bank is $80,000. As of the same date, the present values of all of the expected cash flows from liabilities are $78,000.

Since EVE equals the PV of assets minus the PV of liabilities, EVE = $2,000.

Now, for the second step, recalculate all of the cash flows assuming that prevailing interest rates increase by 100 basis points. (Note that the cash flows from the principal amounts of the assets and liabilities do not

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change let because market rates are 100 basis points higher. Nor do the interest income and interest expense cash flows from fixed rate assets and liabilities. The only changes will be in the amounts. and therefore the present values, of the variable rate interest income and interest expense.) Assume that under the higher rate scenario, EVE = $2,025.

Thus for the third step we can calculate that the change in EVE is $2,000 minus $2,025 or -25. The percent change in EVE is -25/2,000 or -1.25 percent.

The essence of this technique is to quantify the sensitivity of EVE to changes in prevailing interest rates. Economic value sensitivity simulation is the process of generating multiple calculations of cash flow present values for a range of alternative future interest rate levels. We might call this change or sensitivity in EVE the economic value at risk; however “value at risk” has a much more specific meaning that will be explored later in this chapter. Economic value simulation modeling is a tool for measuring rate risk exposure. The simulation process produces a set of economic value of equity projections. Comparisons of those projections enable rate risk managers to measure and analyze the sensitivity of economic value to potential future changes in prevailing interest rates.

Since EVE is the difference between the present values of all future cash inflows and outflows, it is essentially the net present value of all future earnings from the bank’s current balance sheet. Indeed, if we could do an accurate projection of future net income, the sum of the present values for net income in all future periods would almost equal the economic value of equity. (Later in this chapter, we will discuss why the sum of the present values for all future net income will not exactly equal the economic value of equity.)

EVE sensitivity can therefore be thought of as a barometer of future eamings “weather.” This barometer that tells us if the bank’s long-term earnings capacity is “stormy” (potentially volatile if future rates are volatile) or “calm” (potentially stable no matter what happens to future rate levels).

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Economic Value Simulation

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The core beauty of EVE sensitivity simulation is that we can obtain more accurate and insightful measures of risk. EVE simulation allows more accurate reflection of rate-dependent cash flows. These include changes in adjustable-rate instruments, in prepayment rates for amortizing instruments, and in caps and floors. EVE simulation also allows more accurate and more flexible reflection of future interest rates. In particular, we can use different discount rates for short-, medium-, and long-term cash flows. Conceptually, this is simple stuff. Only the application details are complex. A Note on Equity Value Terminology We call this present value approach to measuring long-term interest rate sensitivity “market value” analysis or the economic value of equity. This

is terminology that makes sense for financial instruments like traded securities. For example, the net present value of all of the cash flows from a noncallable, fixed-rate U.S. Treasury note is indeed equal to its market price when the present value is calculated using a discount rate that reflects currently prevailing rate levels. However, many bank assets and liabilities are not actively traded and therefore do not have current market prices. Furthermore, the net present values for many loans and deposits must be calculated using estimates for their maturity dates, interest rates, and other cash flows. For many years, the difference between what we now call the economic value of equity and other, inconsistent uses of the term “market value,” was reflected by using the term “market value of portfolio equity” (MVPE). The Office of Thrifi Supervision (OTS) helped to popularize this term by using it to describe the capital position of a savings and loan association in Thrift Bulletin 13. (TB-13 was the first specific regulation of interest rate risk for federal financial institutions.) Subsequently, the OTS recognized that the term “market value” was a bit misleading. At that time, it began using the term “net portfolio value” (NPV) instead. However, NPV is also less than ideal. Among other problems, NPV is used in other contexts to mean “net present value.”

In short, you may see the terms market value, market value of portfolio equity, or MVPE in reference books, articles, and other regulatory pronouncements. You may see the terms net portfolio value of equity or NPV in publications directed toward savings and loan associations. The 5-7

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Interest Rate Risk Management

newer terminology is “economic value of equity” or EVE. The key point to remember is that all of these terms refer to the same thing.

How Does Economic Value Sensitivity Simulation Differ from Duration-Based Economic Value?

Actually, as observed in Chapter 4, two different methods can be used to calculate the EVE and the sensitivity of that value to changes in prevailing interest rates. One method, the topic of Chapter 4, is to apply_ duration analysis, sometimes called “dollar duration,” “duration MVPE,” or “net duration analysis.” In Chapter 4, we used the term “duration of equity." The other method, the topic of this chapter, is a more direct application of present value analysis, sometimes called “market value analysis” or “net present value analysis.” For reasons discussed below, we refer to this second method as economic value of equity sensitivity simulation. The two methods are similar in that both use present value calculations to derive market values. However, the applications of these two methods are quite different.

Consider an example. Suppose that we apply the duration of equity (DoE) method described in Chapter 5 and calculate that the Simple Bank has a DoE of 1.25 years. Since this was determined from a modified duration calculation, we also know that the “value” of equity should increase by 1.25 percent if prevailing interest rates fall by 100 basis points or decrease by 1.25 percent if prevailing rates rise by 100 basis points.

Now, return to the simple EVE calculation in the previous section. In that example, we calculated that the sensitivity of the economic value of equity for the Simple Bank was -l.25 percent. In other words if prevailing interest rates rose by 100 basis points we calculated that EVE would fall by 1.25 percent. So, here is the question: Should DoE and EVE sensitivity reveal identical rate risk exposure for the same bank at the same time? After all, that is exactly the case for the Simple Bank in this example.

The answer is that in concept, DoE and EVE sensitivity can calculate identical rate risk exposure for the same bank at the same time but in practice we should never expect to see identical results.

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Economic Value Simulation

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Economic value of equity sensitivity simulation is a significantly different and far more sophisticated approach to measuring the sensitivity of equity value to changes in interest rates. Even though, like duration of equity, it employs present value calculations, it is more flexible and more accurate than duration when applied to the whole bank. Economic value of equity sensitivity simulation differs from duration in at least three significant ways:

I. The first, and the most important, difference between duration of equity and economic value of equity simulation is that the values of “equity” calculated by economic value of equity sensitivity simulation are scenario specific. That is, each cash flow, each asset, and each liability has a different market value for every rate scenario considered by the IRR analyst. Duration, as it is most commonly calculated, uses one discount rate. Economic value of equity sensitivity simulation applies different discount rates for each scenario. For example, if we have a floating-rate loan that has a current coupon rate of 10 percent, economic value of equity sensitivity simulation might use a 10 percent discount rate to analyze a no-change-in-rates scenario, an l1 percent discount rate for a 1 percent rising rate shock scenario, a 12 percent discount rate for a 2 percent rising rate shock scenario, and so on. A second distinguishing feature of economic value of equity sensitivity simulation is that it can employ different discount rates to reflect the term structure of interest rates. In other words, next month’s payment due from an installment loan can be discounted with a short-term rate, while the payment due 60 months from now — from that same loan can be discounted with an intermediateterm discount rate. The use of different discount rates for shortand long-term cash flows prevents economic value of equity sensitivity simulation from being restricted by the unrealistic assumption of parallel yield curve shifts. This is another way in which EVE can be applied to avoid a problem that impairs the accuracy of duration measures. Like income simulation, economic value of equity sensitivity simulation is far more realistic than gap analysis or duration of equity. The term structure of interest rates is a basic element for interest rate risk. EVE sensitivity analysis captures this risk element. Duration only captures it at the instrument level not at the cash flow level.

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Interest Rate Risk Management

3. The third distinguishing characteristic of economic value of equity sensitivity simulation is that it can model difl‘erent cash flow assumptions in different rate scenarios. For example, a scenario that models the effects of a 200 basis point (bp) increase in rates can, and should, use a different assumption for mortgage loan prepayments than a scenario that models the effects of a 200 bp decrease in rates. Unlike duration analysis, economic value of equity sensitivity simulation can be used to reflect the changes in customer and bank behavior you can expect under difi‘erent rate scenarios. This also makes economic value of equity sensitivity simulation, like income simulation, far more realistic than gap analysis or duration of equity.

USING ECONOMIC VALUE OF EQUITY SENSITIVITY SIMULATION TO MEASURE IRR

In the introduction to this chapter, we observed that the basic concepts of EVE simulation were simple but that the application details were complex. Now we want to lift the lid and begin taking a look at those application details. We will begin with a simple case study. Later in this the limits, chapter, we will consider some more advanced topics problems, and complications. Then we will explore a few advanced applications that address some of those limits, problems, and complications. Readers may f'md it helpful to note now that the same simple case study introduced here will be revisited in Chapter 11 when we address those additional issues.

—

A simple application of economic value of equity sensitivity simulation is shown in Exhibit 5.1. This example illustrates how the concept works.

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Economic Value Simulation 2/10

Exhibit 5.1 Typical Bank

Amounts Shown in Thousands

Aw: Investments

3 90,000

Dollar weighted average time to reprice or mature:

2.5 years 6.0%

Dollar weighted average yield:

Loans

310.000

Dollar weighted average to reprice or mature:

4.0 years

8.0%

Dollar weighted average yield:

$ 400.000

TOTAL ASSETS Li

'

iti

3 80,000

Demand deposits (including NOW)

2.0%

Dollar weighted average rate:

120,000

Savings deposits (including MMDAs)

Dollar weighted average rate:

4.0%

.

160.000

Certificates of deposit

Dollar weighted average time to reprice or mature:

1.5 years 5.0%

Dollar weighted average rate:

5 360,000

TOTAL LIABILITIES

Capital

40,000

TOTAL LIABILITIES AND CAPITAL

$ 400,000

Now let’s assume currently prevailing market interest rates are as follows: 4.00% overnight

6 months

4.50%

1.0 years

5.00%

1.5 years

5.50%

2.0 years

5.75%

2.5 years

6.00%

3.0 years

6.10%

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Interest Rate Risk Management

3.5 years

6.20%

4.0 years

6.30%

4.5 years

6.40%

5.0 years

6.50%

5.5 years

6.60%

6.0 years

6.70%

If we then apply these current rates as discount rates to the balance sheet of Typical Bank, we can calculate the present values for the assets and liabilities that have fixed maturities. However, at least two liability categories, demand deposits and savings deposits, do not have maturities. Accordingly, we must estimate those maturities. For purposes of this example, assume that the demand deposits mature in 2.5 years. At the same time, assume that the savings accounts mature in three years. (Refer to Chapter 6 for more information about estimating core deposit maturities.) The present values of the assets and liabilities of Typical Bank, using the prevailing interest rates shown above, are: Present value of investments

$ 90,000

Present value of loans

328,136

Present value of demand deposits

( 72,770)

Present value of savings deposits

(113,276)

Present value of CDs

(158,878)

If we add the present values of the assets and subtract the present values of the liabilities, we can calculate the economic value of equity. The economic value of equity is $73,212,205. (Note that this is not a completely correct answer, as we used some simplified assumptions to make it easy for readers to duplicate the calculations. For example, these values assume no compounding of interest; also, they assume that all interest income or expense is received or paid at the end of each year or at maturity.) Do not be misled by the apparent precision of the calculated EVE. Just because we have calculated a value to an exact dollar amount does not mean that it is accurate down to the last dollar. In fact, in Chapter 11, we

5-12

Economic Value Simulation 2/10

reexamine the rate sensitivity of Typical Bank. As we discuss in that chapter, some small and quite reasonable adjustments in our calculations can produce equity values above $75 million and below $71 million for the Typical Bank balance sheet shown in Exhibit 5.1.

The critical issue, as we noted earlier, is not the dollar amount of the calculated EVE. Instead, it is the sensitivity of that value to changes resulting from changes in prevailing interest rates. To assess the extent of Typical Bank’s exposure to adverse consequences from changes in interest rates, it is necessary to compare the economic value of equity in the current interest rate environment with projected equity values calculated with both higher and lower rates. The results of this analysis for Typical Bank can be seen in Exhibit 5.5 and are discussed in the next section. Clearly, economic value of equity sensitivity simulation is another form of' simulation modeling. Not surprisingly, income simulation and economic value of equity sensitivity simulation have similar requirements, outputs, advantages, and disadvantages. Both offer the advantages of flexibility and the capacity to analyze realistic future conditions. Both require large quantities of input. Both produce large quantities of output. Both require controls. These topics are addressed in Chapter 10. Using Real-World EVE Models in Real Banks The EVE simulation we just worked through for our Typical Bank case study is a model. You can even build it into a spreadsheet and call it a computer model. Nevertheless, it is far simpler than even the least functional, lowest cost models available to bank rate risk analysts. Using an actual EVE simulation model in a real bank is different from our case study in three ways: 1. A huge amount of data on cash flow size and timing must be obtained. Some of this data is contractually fixed. Finding that data is a mechanical process. On the other hand, some of that data is unknown. Even in our simple case study, we had to make assumptions for things like the maturity of checking and savings deposits. In a real bank, rate risk analysts must estimate or approximate a large number of unknown bits of information about

5-13

2110 Interest Rate Risk Management

the amount and timing of cash flows. Assumptions must be made and used. In subsequent chapters, we will discuss some of the most critical assumptions as well as control requirements for

assumptions.

2. Appropriate discount rates must be selected. This single topic raises a large number of important issues. As we will discuss later in this chapter, the best EVE models apply many different discount rates for each flow to reflect a lot of specific factors such as the term structure of interest rates. Quite a few other issues affect the choice of applicable discount rates as well. For example, should the discount rate applied to a loan reflect credit risk? Models adjust discount rates for the compounding fi'equency appropriate to each cash flow stream. They also interpolate interest rates (e.g., to obtain a discount rate for cash in-flow due in 50 days when we only input rates for 30 and 60 days).

Of course, the basic premise of EVE sensitivity is the examination of how future rate changes impact value. This introduces another whole set of variables. In Chapter 8, we will discuss the selection of rate-change scenarios. Many models employ very sophisticated methodologies, to consider what future rates might be and what path rates take to get from current levels to future levels.

3. Other model features such as data input, model flexibility, and analysis output can also be highly sophisticated. Many of these issues are discussed in Chapters 9 and 10. It is very important for rate risk analysts and managers to keep these topics in perspective. Too many model vendors try to daule users with sales presentations and models stressing huge choices in discount rates, snazzy model features, and more reporting options than we can describe

in a book. Notice that those bells and whistles concentrate on the second and third groups of variables in our list of three. The truth is that few of the variables in our second or third groups will impact the accuracy of your measured risk exposure as much as the variable in the first group. In other words, presentations from model vendors tend to emphasize the items listed above as if the importance of those items ranked 3, 2, and then 1 but the actual importance of those items for accurate risk management is 1, 2, and then 3.

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Economic Value Simulation 2/10

Dealing with Assumptions It is a common misconception that EVE simulation is less reliant on assumptions than income simulation. It is true that, unlike income simulations, EVE simulations do not require assumptions for new business or business scenarios. Nevertheless, reliance on assumptions is even greater in EVE sensitivity simulation than it is in income simulations. Unlike eamings simulations, EVE sensitivity simulations require assumptions about discount rates. What yield curves should be used? When rates change, how much will short-term rates change compared with long-term rates? These are just two of the issues that influence the selection of discount rates in EVE sensitivity simulations. And, also unlike earnings simulations, EVE analysis requires assumptions about the maturity of indeterminate maturity deposit accounts such as savings and money market deposit account (MMDA) balances. Like income simulation, economic value of equity sensitivity simulation depends heavily on the assumptions used in the model. For example, economic value of equity sensitivity simulations can incorporate assumptions for fast prepayments (larger early cash flows) from mortgage loans and securities in low-rate scenarios. The same simulations would then incorporate assumptions for slow prepayments (smaller early cash flows, more late cash flows) from mortgage loans and securities in high-rate scenarios. Just as in income simulation, the assumption dependency of economic value of equity sensitivity simulation is both a curse and a blessing. When assumptions are accurate, or at least realistic, the measured rate risk will be far more accurate and therefore far more useful. When assumptions are poor, the results can be worse than useless.

Rate risk analysts must give careful consideration to all of the assumptions. A few practical suggestions follow: E1

The cost of core deposits does not correlate closely with capital market rates such as U.S. Treasury security yields. (This basis risk issue is considered in more detail in Chapter 6.) It may be more appropriate to select discount rates for core deposits from secondary certificate of deposit (CD) yield curves or from Federal

2/10

Interest Rate Risk Maflgement

Home Loan Bank cost of funds data. (However, most risk managers use a single yield curve for discount rates.) E1

The maturities of savings and checking accounts are a major unknown. Some portion of these deposit balances is usually rate sensitive and can therefore be treated as short term while the rest is usually not rate sensitive. Techniques for estimating the average mattuity of these deposits or for segmenting them into groups with different estimated maturities are discussed in Chapter 6.

CI

Assumptions used in income simulation do not have to be identical to the assumptions used in EVE sensitivity simulation. For example, a bank may want to assume that core deposits are immediately repriceable in its income simulation but that they have some maturities in its economic value of equity sensitivity simulation.

DISCOUNT RATES AND YIELD CURVE SMOOTHING

As we have discussed, rate risk analysts applying economic measures to quantify rate risk require some measure of “market values" or market value sensitivity. In some cases, observable market prices can be used to value fmancial instruments. However, for most bank assets and liabilities, there are no observable market prices because the instruments are rarely, if ever, traded. Thus for the vast majority of bank-owned fmancial instruments, we apply mathematical tools to infer either the value or the sensitivity of the value. (Duration and VaR analysis infer the sensitivity of financial instruments. EVE or “market value” analysis infers a “market value.”) Calculations for inferring market values or durations require discount rates. This applies to all present value calculations applied to value cash flows. It also applies to all option adjusted spread (OAS) calculations applied to value options. Consequently, a key problem facing the rate risk analyst is what discount rate to use for valuing cash flows and options.

When we talk about valuations, we usually assume precise calculations. In reality, present value measures are far less precise than we usually

5-16

Economic Value Simulation 2/10

suppose. For example, we are normally very confident that we know the present value of $1 dollar that will be received at any specific time in the future. That confidence, however, relies on three assumptions:

∙

First we assume that we are using an appropriate discount rate. But are Treasury rates the most appropriate rates for valuations? What about swap rates? And, if Treasury rates are used, should we use coupon rates or zero coupon rates?

∙

∙

Second, we assume that we have a discount rate for each maturity to match the term of each cash flow that we wish to value. As we will discuss in more detail, this is often not the case.

Finally, we ofien want to use a forecast of future rates, rather than cru'rently prevailing rates, as the source for the valuation discount rates. Certainly, that is the case when rate risk analysts calculate EVE. Introducing a forecasted rate, by defmition, creates more error.

Introduction to Yield Curve Smoothingl

A major problem quickly arises when we begin to value cash flows. All valuation calculations start with a yield curve. If, for example, we want to calculate the value of a 1 year, zero coupon bond, we can simply calculate the present value by applying a discount rate to the single cash flow to calculate the present value. The problem is that we typically have actual interest rate information for only a handful of data points for each yield curve. We may know the rates for 5 or 20 maturities. But rates for some maturity points are inevitably missing. If, for example, we are attempting to value a loan 5 year loan with monthly principal and interest payments, we are unlikely to have observable, market discount rates that exactly match the due dates for all 60 cash flows from that loan. Furthermore, the current observed yield curves may have unreliable

1.

Major portions of this section have been adapted from Kenji Irnai and Donald R. van Deventer, Financial Risk Mathematics: Applications to Banking, Investment Management and Insurance, Version 2 of Chapter 2, “Yield Curve Smoothing.“ completed April 22, 1996.

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Interest Rate Risk Management

observations at certain maturities. Unreliable observations often result from a lack of liquidity in the market for that maturity sector. The dilemma is clear. Market interest rate data is discrete across maturities. Market interest rate data is discrete across products. Market interest rate data is discrete across counterparties. But continuity in spot and forward rates is critical for evaluation and for the application of analytical models. The solution is something called yield curve smoothing. What Is Yield Curve Smoothing?

Smoothing is the process of connecting the dots between observed interest rates for various maturities to create an interest rate for all maturities. Smoothing extracts rate data for maturities which are not market observations.

This is the most fundamental step in financial instrument valuation. Without a perfect fit to actual data and a rational shape, any analysis of the value of a portfolio can be seriously misleading. Yield curve smoothing impacts:

∙ ∙

∙

The accuracy of the fitted yield curve The estimated values of the term structure model parameters The quality of the valuation and thus of the derived risk measures and hedges

Yield curve smoothing is simple to describe but hard to do. The simple description is to draw a smooth, continuous line through observable market data points. This exercise, which seems so simple at first glance, is often the single largest source of error in fixed-income options calculations. Since an infinite number of smooth, continuous lines pass through a given set of points, called “knot points,” some other criterion has to be provided to choose among the alternatives. The most appropriate smoothing method is that which produces the smoothest possible line between observable points of primary interest and the user.

Economic Value Simulation 2/10

Choosing a Smoothing Method An infinite number of yield curve smoothing methods will connect an arbitrary number of “dots” or market data points. The best yield curve smoothing technique, meaning the one that generates the smoothest curve, varies depending on whether you look at prices, yields, or forward rates. One must apply some criteria for defining the “best“ line connecting the dots to select from these various possibilities.

Inappropriate smoothing techniques can have material impact on your results. For example, the “linear yield smoothing method” (a commonly used method) tends to generate spikes in the curve that could have significant impact on the valuation of bullet securities. For the last 30 years, market participants have used cubic splines as the leading technique for smoothing, applying it most commonly to zero coupon yield curves. (It is applied to current zero coupon rate rather than forward rates because smoothed forward rates are ofien wildly implausible.) Most users choose one of the following:

∙ ∙ ∙ ∙

Linear yield curve smoothing Cubic splines applied to prices Cubic splines applied to yields

Maximum smoothness forward rates

In the following paragraphs, we will briefly consider three methods: First we will discuss linear yield curve smoothing. Second, we will look at cubic splines, the most common smoothing tool. Then we will discuss

maximum smoothness forward rates, the tool that usually provides the most accurate results. Linear Yield Curve Smoothing

Linear yield curve smoothing is the simple process of “drawing” straight lines to connect the knot points. If, for example, we know that 30-day

2/10 Interest Rate Risk Management

rates are 4 percent and 60-day rates are 4.2 percent, we can interpolate that 45-day rates are 4.1 percent.

Linear smoothing is neither the most popular nor the most accurate smoothing tool. It is, however, the easiest to use. For that reason, market participants have often relied on this technique despite the fact that its limitations are well known:

∙ ∙

∙

Linear yield curves are continuous but not smooth; at each knot point there is a kink in the yield curve.

Forward rate curves associated with linear yield curves are linear and discontinuous at the knot points. This means that linear yield curve smoothing sometimes cannot be used with the Heath, Jarrow and Morton term structure model, since it usually assumes the existence of a continuous forward rate curve. (Term structure models are discussed in Chapter 8.) Estimates for the parameters associated with popular term structure models (like the extended Vasicek or Cox, Ingersoll and Ross models) are unreliable because the structure of the yield curve is unrealistic. The shape of the yield curve, because of its linearity, is fundamentally incompatible with an academically sound term structure model, so resulting parameter estimates are ofien implausible.

Cubic Spline Yield Smoothing

Cubic splines have historically been the preferred method for yield curve smoothing. The cubic spline approach was designed to create yield curves that are both continuous and smooth.

A cubic spline is a series of third degree polynomials that have the form: y = a + bx + cAJ+ dz} Like other smoothing methods, these polynomials are used to connect the dots formed by observable data. For example, a U.S. Treasury yield

5-20

Economic Value Simulation 2/10

curve might consist of interest rates observable at 1, 2, 3, 5, 7, and 10 years. To value a fixed-income option, we need a smooth yield curve that can provide yields for all possible yields to maturity between 0 and 10 years. A cubic spline fits a different third degree polynomial to each interval between data points (0 to 1 years, 1 to 2 years, 2 to 3 years, etc.). In the case of a spline fitted to swap yields, the variable x (independent variable) is years to maturity and the variable y (dependent variable) is yield. The polynomials are constrained so they fit together smoothly at each knot point (the observable data point); that is, the slope and the rate of change in the slope with respect to time to maturity have to be equal for each polynomial at the knot point where they join. If this is not true, there will be a kink in the yield curve (i.e., continuous but not differentiable).

However, two more constraints are needed to make the cubic spline curve unique. The first constraint restricts the zero-maturity yield to equal the l-day interest rate (e.g., the federal funds rate in the U.S. market). At the long end of the maturity spectrum a number of alternatives exist. The most common one restricts the yield curve at the longest maturity to be either straight (y"=0) or flat (i=0). There are other alternatives if the cubic spline is fitted to zero coupon bond prices instead of yields.

We can illustrate cubic spline smoothing with a simple example. Suppose that we have three knot points. We know that overnight rates are 4 percent, 1 year rates are 6 percent and 2 year rates are 3 percent. Applying cubic splines to create a continuous, smooth yield curve from those three points results in the following:

5-20a

2/10

Interest Rate Risk Management

(This page intentionally lefi blank.)

5-20b

Economic Value Simulation

Rate

Exhibit 5.2 Example of a Cubic Spline Calculation

r

0.50

I

0.70

I

I

0.90

1.10

1.30

1.50

1.70

1.90

Time

Using cubic splines does not require an understanding of the math. Users should, however, understand the characteristics of discount rates calculated using this tool. Three characteristics of cubic spline outputs are particularly important:

1. The cubic spline of yields or zero coupon bond prices often produce forward rate curves that are too volatile to be consistent with market expectations of future interest rates.

Cubic splines typically result in sharply upward or downward sloping forward rates as maturities lengthen. The cubic spline smoothing of bond prices produces forward rate curves that are consistently smoother (but less accurate) than those produced by cubic spline smoothing of yields. Maximum Smoothness Forward Rates

An alternative smoothing technique is the maximum smoothness technique. The yield curve with the smoothest possible forward rate function, consistent with observable data, is closely related to but significantly difi‘erent from the popular cubic spline approach to the

5-21

Interest Rate Risk Management

smoothing of both yields and discount bond prices. The yield curve that produces the smoothest possible forward rates consistent with given zero coupon bond prices has a quartic forward rate function that spans each time interval between observable data points. This contrasts with the cubic polynomial that is used to fit either yields or discount bond prices in the cubic spline approach. This method produces the smoothest possible forward rate curve (withf‘=0 at the longest maturity) that causes the interpolated yield curve to be totally consistent with the observable data. Risk analysts do not need to understand the formidable mathematics in order to use this too]. All that is really necessary is an understanding of when to use the tool. What Smoothing Technique Should You Use?

Market participants usually describe the “best” fitting yield curve as the smoothest. From a finance theory point of view, there are three financial terms that might be subject to the smoothing process: zero coupon bonds, zero coupon yields, and forward rates. Once smoothing is done with respect to anyone of these, one can determine the other two financial terms. It is a common observation that smoothing with respect to zero prices or zero yields can leave one with implausibly volatile forward rates, but a smooth forward rate curve never produces implausible zero

prices or yields.

In most cases, we recommend the “maximum smoothness forward rates” technique. However, sometimes, other smoothing techniques are more appropriate. For risk managers, it is critical to understand that different smoothing methods should be used for different purposes. It can be mathematically proven that:

∙ ∙

The smoothest possible zero coupon bond price function is produced by using a cubic spline of zero coupon bond prices to fit observable yield curve data. The smoothest possible continuous yield curve is produced by using a cubic spline of bond yields to fit observable yield curve data.

5-22

Economic Value Simulation

The smoothest possible continuous forward rate curve is produced by using the maximum smoothness forward rate technique to fit observable yield curve data.

Rate risk analysts can get a good feel for the differences in discount rates, and thus the variations in present values, that arise from the choice of smoothing methods. Exhibit 5.3 shows a comparison of yield curves calculated using different smoothing techniques. Exhibit 5.3 Contrasting Smoothing Methods

−

ll

marvteldcme

CSPtbltP'IO)

CSPrtce-et’Y'lol

\

CSYiddefY-O)

CSYIGHHY'I

./

3

Smooth»! Forward Rate Gum

'.|

0

l

4

SImemsIFuwnRal am Cubic an Prices tP‘IOi

funk

Price: (EC)

we sum

6

∙

nu. can)

tum: ‘1‘th Cum

3

10

∙∙ ∙ T“

∙∙

l)

Source: The Kamalnna Corporation

The comparative graph reveals several important insights. First, it is clear that each smoothing method produces slightly different forward curve so that, for any given maturity (e.g., 3 years), the discount rate may be slightly different. Consequently, the market values or OAS calculated using these discount rates will be slightly different.

5-23

Interest Rate Risk Management

∙

∙

Second, it is also clear that linear smoothing produces yield curves that are inconsistent with either all the other methods or with common experience. This is a weak tool.

Third, the other smoothing tools illustrated do not create much difference in the short term portion of the yield curve but do create significant variations for longer term yields. A comparison of six different smoothing techniques applied to seven—year rates can be seen in Exhibit 5.4. Exhibit 5.4 Average Error in Estimating 7-Ycar Swap Rates

91

l l

Max-mun Smear-ass

V

Cch Price

Cine Pica

Ceca: Yield

(Y'aO)

(P'=:>)

(Y':0)

Cube Yield (Y'=O) Emu

Lnear Smoe'rmq

Source: Charles D. Demarest. Kamakura Corporation.

In addition, it is important to realize that the differences in smoothed yield curves also depend on instrument types. For amortizing loans with no options, this is not a big issue. For zero coupon bonds where all the cash flow comes at maturity, this could be an important issue. For floating rate instruments that reset frequently, this could be a big issue.

5-24

Economic Value Simulation

Traders often apply smoothing techniques in the process of calculating current market prices. However, rate risk managers rely on smoothing to obtain discount rates for multiple, future rate scenarios. Since the maximum smoothness technique is superior for fonNard rates, this method offers the best results for risk analysis.

EVALUATING THE RATE SENSITIVITY OF EVE

As we observed above, rate risk managers need to evaluate the sensitivity of the economic value of equity to changes in prevailing rates. Rate risk managers can evaluate EVE sensitivity in two ways. Both are different views of the range, or dispersion, of the measured risk exposures. One'technique is to evaluate the range of changes in the calculated dollar amount of EVE caused by rate changes. For example, in Exhibit 5.5, we can see a range of changes in equity values — from a gain of $12,952,527 if rates fall by 200 bps, to a loss of $11,569,219 if rates rise by 200 bps. (As we observed, this bank is very liability sensitive.) If managers think that a 200 bp rate shock is an appropriate risk to evaluate, they must then decide if this roughly $24.5 million range is an acceptable or unacceptable risk. A second technique for evaluating EVE sensitivity is to evaluate the percentage of capital at risk for a range of changes. For example, the analysis indicates that Typical Bank stands to lose about 16 percent of that capital in the event of a 200 bp increase in prevailing interest rates. If managers think that a 200 bp rate shock is an appropriate risk to evaluate, they must then decide ifthis 16 percent loss is an acceptable or unacceptable risk. In the following paragraphs we will consider some key points for evaluating interest rate risk using EVE sensitivity.

EVE Sensitivity — Dispersion The interest rate risk is measured from the dispersion of equity values above and below the value produced using current or base case rates. An array of difl‘erent economic values of equity for any bank can easily be calculated any time. In its simplest form, this is accomplished by

5-25

Interest Rate Risk Management

adjusting the discount rates. For example, each point in the cmrent yield curve discussed above can be increased or decreased by 50, 100, 150, or 200 bps. If we do that, we add four lower rate yield curves and four higher rate yield curves to the currently prevailing yield curve. Thus, this technique produces nine different discount rates for each maturity (in other words, nine different one-year rates, nine different two-year rates, nine different three-year rates, etc., and all points in between). Accordingly, we can calculate nine different economic values for equity. For the Typical Bank example, these nine difi'erent values are shown in Exhibit 5.5. Exhibit 5.5 Economic Value of Equity

Interest Rate Change (in basis points)

Percent Change in EVE

Economic Value of Equity

Change in EVE (in dollars)

—200

$86,164,731

12,952,527

18%

—150

82,787,421

9,575,216

13%

-100

79,504,799

6,292,594

9%

'—50

76,313,987

3,101,782

4%

0

73,212,205

0

50

70,196,765

(3,015,439)

0%

—4%

100

67,265,073

(5,947,131)

—8%

150

64,414,622

(8,797,583)

—12%

200

61,642,986

(11,569,219)

-16%

Exhibit 5.5 shows that if interest rates fall by 200 bps, Typical Bank will experience an 18 percent increase in EVE. On the other hand, if rates rise by 200 bps, the bank will experience a 16 percent decrease in EVE. The sensitivity analysis illustrated in the far right-hand column of Exhibit 5.3 quantifies just how liability sensitive the bank really is. In fact, the sensitivity of calculated economic values to changes in interest rate

5-26

Economic Value Simulation

levels is more important and can provide more insight than the calculated economic value level itself.

Note that the EVE sensitivity measures shown here are not as accurate as it could be, for reasons that we will soon discuss. Furthermore, the asymmetrical outcomes up 18 percent and down 16 percent are not as asymmetrical as we should expect. Both of these issues are discussed in more detail in this chapter and in subsequent chapters.

—

Note that the Typical Bank illustration can be made considerably more accurate with additional assumptions. As we will discuss in chapters 6 and 7, changes in interest rates lead to changes in customer behavior. For example, if rates fall by 200 bps, loan prepayments will probably increase. Instead of an average maturity of four years, the loans at Typical Bank may have an average maturity of only three years when rates fall by 200 bps. Similarly, deposit withdrawals change when rates change. A more accurate simulation than the one shown in Exhibit 5.5 would reflect such changes.

Note that the percentages shown in the right column of Exhibit 5.5 are in round numbers. We chose not to show hundredths, or even tenths, of percentage points because of the inherent imprecision in these projected outcomes. Afier all, if any of the many assumptions used to calculate our EVE sensitivity are even a little bit inaccurate, our projected outcomes are likely to be more than a few tenths or hundredths of a percentage point inaccurate. Using round numbers focuses us on the approximate magnitude of the EVE sensitivity without implying a false degree of precision. When EVE data under a variety of rate scenarios are shown graphically, the rate sensitivity can be more clearly seen. Two graphs are shown in Exhibits 5.6 and 5.7. (Note that the data in Exhibits 5.6 and 5.7 are the same, but the data used in Exhibit 5.1 are fi'om a difl‘erent bank.)

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Interest Rate Risk Management

Exhibit 5.6 Economic Value Sensitivity of Assets, Liabilities, and Equity Percentage Change 40 ,0

0

.20

l

mg;

−−−−

∙

∙

h.

.~

/minuwrlla

u i\ \

.40

\

.eo ~80 -m-31-m-r.n-z:-ID-m-s)

o

a:

m

in

am

an

an

m

a

B 35-: Ponl Changer: ‘nterost Rates

Exhibit 5.6 shows three lines. The line that is highest at the lefi side of the graph shows the change in the total present value of the cash flows from assets. Notice that present value of the asset cash flows gains more and more value as prevailing interest rates fall. This is true for all assets. The line that is lowest on the left side of the graph shows the change in the total present value of the cash flows fi'om liabilities. Notice that the present value of the liability cash flows rises as prevailing rates rise. This is true for all liabilities. (See the upcoming section on the arithmetic sign convention for more information on this presentation of liabilities.) The middle line in Exhibit 5.6 charts the changes in the net present value of equity across the 17 different rate scenarios depicted in this graph. This is the EVE sensitivity for the bank. The graphical format used in Exhibit 5.6 allows readers to clearly see how the sensitivity of asset and liability values combine to produce the sensitivity of the EVE. This format also makes it easy to show this sensitivity over a very large range of potential changes in prevailing interest rates. The amount of EVE at risk shown in this graph is isolated in Exhibit 5.7. The formats of both Exhibits 5.6 and 5.7 work very well for conveying the sensitivity of EVE to senior managers and directors.

5-28

Economic Value Simulation

Exhibit 5.7 Economic Value of Equity Sensitivity

∙

Penman: Charon

.-

\

− i

II

II

LII

I

1

[III

1

1

4co~asa-m-rso.a:c-rso-Iuo-soosorocrsomnoaooseom

Baas Point Change In htereet Rates

Plus or Minus? A Note on Arithmetic Signs

Some readers may have been surprised when they first looked at the liability line in Exhibit 5.6. As we discussed, that line shows that the net present value for the bank’s liabilities falls when prevailing rates fall and rises when prevailing rates rise. How can that line he a correct reflection of the sensitivity of those deposits and borrowings to changes in prevailing rates? Almost all financial instruments, whether they are CDs or Treasury bonds, have positive durations. When prevailing interest rates rise, the value of a fixed-rate bond falls. So does the value of a fixed-rate CD. Conversely, when prevailing interest rates fall, the value of a fixed-rate bond rises. So does the value of a fixed-rate CD. This relationship between the value of a financial instrument and changes in rates is equally true for bank asset and liability portfolios. After all, bank asset and liability portfolios are simply collections of financial instruments.

We can see the true direction of the sensitivity of bank assets and liabilities in Exhibit 5.8, reproduced from the Comptroller 's Handbook.

5-29

Interest Rate Risk Management

Exhibit 5.8 clearly shows the same asymmetry in the change or sensitivity or the economic value of equity that we discussed in the previous section, but that is not why it is shown here. Notice that the present values for the liabilities shown in Exhibit 5.8 are all positive numbers. In order to calculate the present values of equity in that table, the present values of the liabilities are subtracted from the present values of the assets. Then notice that the changes in the present values of liabilities are positive for rate decreases and negative for rate increases. This is the exact opposite of the way that the changes in the present value of liabilities are shown in Exhibit 5.6. In Exhibit 5.6, the changes in the present values of the liabilities are shown as negative numbers. In that exhibit and in Exhibit 5.7, the sensitivity of EVE is calculated by adding the liability number to the asset value.

Neither the presentation in Exhibit 5.6 nor the one in Exhibit 5.8 is incorrect. The presentation shown in Exhibit 5.8 conforms to the order of arithmetic operations most commonly used. We normally subtract positive liability values from positive asset values to calculate equity. The presentation in Exhibit 5.6 merely switches the order of the signs simply to display the relationships in a more easily understandable way. Exhibit 5.8 Sample Output of Economic Value Simulation Model

Interest Rate Scenario (in thousands of dollars) Down 200 bp

PV of Assets

$55,000

.

Up

Up 200 bp

Down 100 bp

Base Case

100 bp

$54,000

$53,000

$52,000

$51,000

($2,500)

$1,500

$1,000

$0

($1,500)

$49,000

$43,700

$43,000

$47,000

$46,500

Change

$1,000

$700

$0

($1,000)

($1,500)

PV of Equity

$6,000

$5,800

$5,500

$5,000

$4,500

$500

$300

$0

($500)

(S 1,000)

Change pv of Liabilities

Change

Source: Interest Rate Risk, a booklet in the Comptroller 's Handbook, Table 4, page 89, June 1997.

5-30

Economic Value Simulation

Uneven Outcomes As we observed above, the base case business scenario shows that the bank is liability sensitive. As prevailing interest rates increase, projected economic values decrease. However, it is also very important to note that the size of the changes in economic value is not equal in response to equal changes in prevailing interest rates. In fact, two very important observations about the underlying elements of the bank’s interest rate sensitivity can be seen in the report data. First, an increase in rates reduces the EVE by a smaller amount than the gain in the EVE resulting from a decline in prevailing interest rates. For example, in Exhibit 5.5, a 100 bp increase in prevailing rates is projected to cause an 8 percent reduction in economic value, while a 100 bp decrease in prevailing rates is projected to cause a 9 percent increase in economic value. Rising rates hurt this bank, but they hurt it to a smaller extent than falling rates help it. Asymmetrical outcomes are typical.

Most of the time, a liability-sensitive rate risk exposure benefits a bank. Recall that a liability-sensitive bank is, on average, borrowing short and lending or investing long. Accordingly, the liability-sensitive bank benefits from the spread that it receives from the difference between short- and long-term rates. As we have observed, yield curves almost always slope upward — that is, long-term rates are almost always higher than short-term rates. We call this a positive or upward sloping yield curve. As long as yield curves have a positive slope and rates do not increase, banks can make more by borrowing short and lending long by being liability sensitive. But borrowing short and lending long is costly when rates rise. We can see this in the decrease in net income projected to result from increases in rates. However, the amount of the loss resulting from an increase in rates is slightly offset by the advantage of borrowing short and lending long.

—

The second important observation that can be found in the data shown in Exhibits 5.5, 5.6, and 5.7 is the impact of embedded options in the bank‘s loan and deposit portfolios. As we discussed in Chapter 4, options give these instruments negative convexity. The cash flows, in addition to the discount rates, vary as prevailing rates vary. The impact of negative convexity can be seen most clearly in Exhibit 5.7. Notice that economic value changes are small in response to small changes in prevailing rates.

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Interest Rate Risk Management

The amount of the EVE sensitivity tends to be roughly equal for small rate changes even though the direction or sign is obviously positive for rate decreases and negative for rate increases. This is not the case for large rates changes. As Exhibit 5.7 shows, large rate changes cause changes in economic value that are both large and asymmetrical.

In this regard, it is important to understand that the simple assumptions used for the Typical Bank example at the beginning of this chapter show much less negative convexity from embedded options than the bank really has. In other words, the examples that we have considered so far understate the asymmetrical outcomes. In Chapter 11, we revisit this example and apply more complex assumptions for loan and deposit changes. These revised outcomes illustrate the asymmetrical impact of options more clearly. The trend of changes in equity values over the 17 rate scenarios illustrated in Exhibits 5.6 and 5.7 is not unusual, but it could easily be different at different times, with different assumptions in the model, or for different banks. However, the existence of an asymmetrical relationship between EVE changes in falling rate scenarios and EVE changes in rising rate scenarios is typical. In fact, the ability to reflect such asymmetrical sensitivities is one of the attributes of economic value simulation that make it, along with income simulation, a more realistic rate risk measurement technique. Relating the Rate Sensitivity of the Economic Value to the Rate Sensitivity of Net Income

Rate risk analysts and managers can benefit from both a theoretical and a practical understanding of a comparison of EVE and earnings at risk (EAR) measures of rate risk. The Conceptual Relationship Between EVE and EAR

Conceptually, it is easy to relate the rate sensitivity of net income to the rate sensitivity of economic value. As we mentioned at the beginning of this chapter, for any single interest rate scenario, the EVE should approximately equal the present value of the annual net incomes for all future years. Suppose, for example, that we use both an income simulation model and an EVE simulation model. Both models

5-32

Economic Value Simulation

incorporate the same assumptions. Suppose we use the income model to project net income for all future years and we then take the present value of every one of those projected income amounts. If we use the same discount rates to calculate the present value that we used in the economic model, the present value of the future net incomes should be close to the calculated economic value of equity. They should be close, but not identical, and that’s an important point. It is not important because rate risk analysts or managers need to reconcile the two measures of risk — they don’t. Understanding why these two measures aren’t exactly the same is important because having a handle on the differences requires you to consider concepts that help you appreciate the nature of these two risk measures. In other words, a better understanding of how they differ will help you grasp what each measure is telling you about rate risk. (These variance issues are closely related to the discussion of economic value model weaknesses later in this

chapter.)

In a nutshell, four general problems prevent the present value of the earnings for all future time periods from equaling the EVE even when the same discount rates are used to calculate the present values.

1. Banks have more assets than liabilities. This is simply another way of stating that banks have capital. The present value of all future net income would only be exactly equal to the economic value of equity for a bank with no equity. For a bank with equity, the present values of the asset principal cash flows will exceed the present values of the cash flows from the principal values of the liabilities. If the discount rates applied to determine the present value of interest income are adjusted to reflect a cost of capital, this discrepancy can be eliminated. 2. Many banks that perform EVE analysis only include balance sheet cash flows in their EVE calculations. As we will discuss in Chapter 11, significant errors in rate sensitivity result. Some portions of noninterest income, for example mortgage servicing fees and account analysis fee income, may be rate sensitive. Furthermore, the value of noninterest income and noninterest expense cash flows is rate sensitive even if the quantity of those cash flows is not. Net income, and therefore the present values of

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Interest Rate Risk Management

future net income, will reflect net, noninterest expense. Economic value of equity calculations that only incorporate assets, interest income, liabilities, and interest expense are incomplete.

3. Earnings are calculated using accrual accounting. EVE, on the other hand, uses only cash transactions. Thus, it is significant that there can be material differences between the timing of cash flows versus the timing of income recognition. Consider a simple example: Suppose that a bank owns a five-year, zero-coupon bond. The bond was purchased at a discount. The amount of that discount represents the income that the bank will earn from the investment. In calculating EVE, the “income” is captured as a cash flow in the fifth year when the full par amount of the bond is received. Therefore, EVE includes the present value of that income cash flow discounted to the present from a date five years in the future. Net income, on the other hand, recognizes monthly accretion of the discount. Therefore, if we take the present value of the net income for each of the next five years, each one of those years has one fifth of the income from the zero-coupon investment. Consequently, even if we use the same discount rate for the present values of net income and for calculating EVE, the results will be different because the timing of the cash flow is not the same as the timing of the income.

4. As we noted earlier, EVE calculations do not include fitture business while EAR simulations certainly do. As we have also observed, this discrepancy makes absolutely no difference to the extent that future business is added at the market rates of interest prevailing at that time. However, for floating-rate instruments with caps and floors and, most importantly, for core deposits, this discrepancy will produce irreconcilable measures of rate EVE and EAR. The Practical Relationship Between EVE and EAR

So far, we have discussed the conceptual relationship between EVE and EAR. The next question is whether EVE relates to earnings at risk in practice. The answer to that question is no, not even close, for the following reason:

5-34

Economic Value Simulation

Without a doubt, the main reason is the simple fact that we don’t normally look at the sum of the present value of earning for future years. Instead, as we discussed in Chapter 3, we almost always look at earnings at risk for just one, two, or three years in the future. Just because the present value of all future earnings might equal the economic value of equity, that doesn’t mean that rate risk sensitivity of the current period’s earnings relates in any way to sensitivity of EVE. After all, as we have just discussed, the sensitivity of EVE reflects the rate risk in all periods, while the EAR is measured for just a single defined period. If the rate risk sensitivity for any one year is similar to the total risk exposure for all years it will be nothing more than a coincidence. In fact, even the direction of rate risk exposure whether we sufl'erfi‘om rising rates and benefit from falling rates or vice versa may be different for the next

—

—

year than it isfor allfixture years.

An OTS study of changes in 1993 (a year in which rates fell significantly) and 1994 (a year during which market interest rates rose sharply) found some pretty weak correlations. The OTS study found that the economic value model was not even very good at predicting the direction of the earnings rate risk exposure. When prevailing rates rose in 1994, 59 percent of thrift institutions in the OTS study experienced a decline in their net interest margins. For that group of thrifts, in early 1994, the NPV model indicated that 87 percent would experience a decline in economic value of equity if rates rose. In other words, the NPV model was directionally correct in predicting the earnings risk for 87 percent of those thrifis. On the other hand, for the tluifis whose net interest margin actually rose in 1994, the NPV model only identified 20 percent of them as being subject to an increase in economic value of equity if prevailing rates rose. In other words, the NPV model was directionally incorrect at identifying the earnings risk for 80 percent of those institutions.2 In short, it is very important to remember that your rate risk exposure for the next month, quarter, year, or two years may not even be in the same direction as the entire rate risk exposure in all of your balance sheet positions. EVE sensitivity tells us the amount of our

2.

Elizabeth Mays, "The Relationship Between Changes in S&Ls' Net Interest Income and Projected Changes in Net Portfolio Value,” Bank Asset/Liability Newsletter, June 1996, pages 5-7.

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Interest Rate Risk Management

rate risk exposure, but it tells us absolutely nothing about the timing of the risk.

A change in prevailing interest rates causes an immediate and very real change in the value of our assets and liabilities. However, that same change does not impact the earnings of the bank immediately. Instead, earnings are affected at the time that the instruments reprice. This earnings impact may occur on the day of the change in prevailing rates or many years in the future.

Knowing when earnings will be impacted can be important. It is particularly important when the measured sensitivity of EVE is high and rate risk managers want to reduce their exposure. We can see this potential problem by looking at the following example. Consider two different banks. For both banks, a 100 bp decrease in prevailing rates causes a $300 increase in their equity values. However, Bank A has fairly short-term assets and liabilities. In fact, the average life of its liabilities is something less than one year. For Bank A, a 100 bp decrease in rates causes a $400 increase in the present value of its assets and a $100 increase in the present value of its liabilities. In contrast, Bank B has longer term assets and liabilities even though, on average, its liabilities are still of a shorter term than its assets. The average life of its liabilities is something greater than one year. For Bank B, a 100 bp decrease in rates causes a $1,000 increase in the present value of its assets and a $700 increase in the present value of its liabilities. If everything else is equal, we can say that a decrease in prevailing interest rates will impact the profits of Bank A sooner than it impacts the profits of Bank B, even though the eventual impact — the on both banks impact over the life of the current assets and liabilities will be the same. This difference in the timing of the loss has important ramifications for rate risk managers acting to reduce or offset their risk exposure. Under some circumstances, a new transaction that offsets some or all of the EVE can reduce earnings this year while reducing a potential loss that would not have reduced earnings until some future year.

—

Of course, the difference between the earnings rate risk exposure in one year and the “life of the balance sheet” rate risk exposure measured by EVE sensitivity does not directly address the question posed at the beginning of this subsection. Would the sum of the present value of all 5-36

Economic Value Simulation 6/08

future earnings equal the economic value? The practical answer is still no. The OTS study identified five other factors that contribute to discrepancies between the results of the two measurement methods. The most important of those five was the fact that, during the time period studied, thrift institutions were able to retain more core deposits than the NPV model assumed and increase core deposit rates more slowly than market rates increased. (Recall that the OTS refers to economic value as NPV or net present value.) Other factors included the change in asset and liability volumes and changes in spreads. Clearly, these same five factors not just savings and loan apply to all financial institutions associations.

—

Another way of looking at the problems identified in the OTS study described in the previous paragraph is to think of them as assumption errors. When we calculate future rate risk exposure, whether we measure earnings at risk or economic value sensitivity, we must make assumptions about future rates and volume changes. Our assumptions will never be completely accurate. Assumption errors may be deliberate. For example, as we will discuss in Chapter 6, the OTS model treats core deposits as shorter term liabilities than empirical evidence, including their own, indicates. Other assumption errors are inadvertent. While both EAR and EVE models are subject to assumption errors, the ramifications of those errors tend to be more significant in EVE models. Because they need assumptions about core deposit maturities not just core deposit repricing, EVE models require more assumptions and therefore introduce more opportunity for errors. And because they incorporate all future cash flows, not just next year’s, the accumulated impact of assumption errors can be much greater in EVE models. Still, even though EVE will never be exactly equal to the sum of the present values for net income in all future years, the concept has some merit. To simplify the comparison, you might elect to project net income for just the next five years. Five years won’t capture the full economic value since some assets have longer lives than this. However, it captures most of the value. In addition, the present value of cash flows not received for more than five years will not be very large in comparison to the values of the cash flows projected for the first five years.

5-37

6/08

IntegestRateBifl Mflagement

EVE and EAR Treatments of New Business EVE calculations, as we have discussed, do not include future business loan renewals, deposit rollovers, new loans, new deposits, etc. Instead of treating the bank as a going concern, EVE calculations erode the balance sheet. In other words, this is the net present value of the bank’s current position. This does not include any value from any activity for investments, loans, deposits, or other instruments acquired in

—

the future. In effect, EVE assumes the liquidation of the balance sheet. As the OCC notes: “Often, the analytics consider only terminal cash flows (i.e., cash inflows are considered runoff and are not reinvested) so that the balance sheet is reduced to zero over time.”3 In reality, our banks do not shrink or liquidate. We do not stop all new activity as of the date that we measure EVE.

Exhibit 5.9 The Impact of Runoff, Rollover, and Growth Over Time

∙

Not Interest Income from this point is measure from tulagalust S. , 5,. 3i.

Valuatlon tPV. EV) from this point the typical "risk“ measure from

'

∙

ut ‘

.N'umarlo,I tin/against S,

S

Forecast Growth−

CF:

CW

Business Roll

Base runoff

− ∙ ∙

so

}0t’lcn a bigger assumption Huge Assumption

∙

llm pmnt'! It is “ 3113‘ Incisuring this an; uratuly uccrunry'.‘ [i am. why not‘.‘

[a Source: Mr. Tom Day.

3.

Russell, Bill, “Interest Rate Risk Measurement,” Capital Markets Quarterly Journal, June 1996, page 14.

5-38

Economic Value Simulation 6108

We can value all three of these components. For most banks, new business roll typically is 18 percent to 27 percent of current position balances. The manner in which it is modeled (from both an income and valuation view) is a significant modeling assumption, ofien poorly understood by management and external third parties. The Impact of Omitting Rollover and Growth is Often Misunderstood Two Points of View

—

—

When you consider the volume changes illustrated in Exhibit 5.9, it is both of which are wrong. The first easy to draw two conclusions incorrect conclusion is that EAR captures a fuller picture of future risk because EVE misses the IRR in all of the rollover and growth volumes. The second incorrect conclusion is that the omission of rollover and growth volumes is irrelevant because all of that future business will be booked at the then prevailing market rates. In other words, EVE assumes that all future assets and liabilities are generated at whatever market rates of interest happen to prevail at the time the current asset or liability rtms of? or the new business is booked. For example, if we have a five-year loan funded by a one-year CD, the economic value of equity calculation implicitly assrunes that after the first year, there will be a series of four successive one-year CDs, paying interest at the prevailing rates for new CDs in each of those years, funding the five-year loan. This second interpretation is important. If all new assets and liabilities are indeed generated at future market rates of interest, then they have no rate risk. In that case, excluding them from the rate sensitivity calculation does no harm at all.

In fact, our first incorrect conclusion, that that EAR captures a fuller picture of future risk because EVE misses the IRR in all of the rollover and grth volumes, is itself an overstatement. Clearly, the argument made by the second incorrect conclusion is true to some extent. Some, perhaps quite a bit, of the rollover and grth is added at market rates.

But our second incorrect conclusion, that the omission of rollover and growth volumes is irrelevant because all of that future business will be booked at the then prevailing market rates, is also an overstatement. Consider three exceptions:

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6/08 Interest Rate Risk

Management

One exception is floating rate loans and bonds. Rate risk calculations assume that floating rate instruments “mature” on their first repricing date. If those instruments have no limits on the rate reset, this assumption works because the coupon rate resets to a market rate. However, if those instruments have rate caps or floors, they will not necessarily reset to market rates.

A far more material error arises from the treatment of administered rate deposits. The omission of new, renewed, or rolled over savings and NOW and MJVIDA deposits is significant. New savings, NOW, and money market deposits are not really added at currently prevailing market rates of interest. Instead, they are added at a “blended” or “average” rate that we pay for all such deposits, regardless of when they were originated. The blended rate does change in response to changes in prevailing levels of interest rates. However, the rates, terms, and volumes of these funds change only slowly and incrementally. If prevailing rates rise or fall tomorrow, savings account rates are not likely to respond, and, if they do, will only change by a small fraction of the change in market rates. The pricing behavior of savings accounts rates does not simply lag behind changes in wholesale market rates. Nor does it simply reflect some fraction of the change in wholesale market rates. The fact is that savings and NOW account rates simply do not track changes in wholesale rates. The risk manager‘s time horizon creates a third group of exceptions. Rollover and growth volumes added afier the date of the risk measurement but before the rate risk manager’s time horizon, may be added at the prevailing market rates for the dates that the new business is generated. However, those rates are probably not the same as the prevailing rates as of the date of the time horizon. In other words, the manager interested in his or her one-year rate risk exposure, will still find the EVE is incomplete because it doesn't capture the impact of differences between rates at the time rollover and growth is booked and the prevailing rates one year from the analysis date.

5-40

Economic Value Simulation 6/08

The failure to incorporate new business activity also produces one additional anomaly. By ignoring balance sheet growth, EVE calculations exclude the present values of the future net interest income that will be generated by the net increase in the volume of new business.

Using EVE Sensitivity Simulation to Achieve Other Management

Goals

The primary purpose of using an economic value of equity sensitivity simulation model is to measure IRR by measuring the interest rate sensitivity of equity. However, some important ancillary benefits can be obtained from these models. One benefit is that the EVE data for assets and liabilities can be used for required accounting disclosures. Another benefit is that economic value sensitivities of individual asset and liability types can be used to make pricing and marketing decisions. Both applications of the data are discussed in this section.

FAS 107 The Financial Accounting Standards Board (FASB) issued its Statement of Financial Accounting Standards No. 107 (FAS 107) in 1991 to begin addressing growing concerns in the regulatory community about historical cost accounting abuses. Among other concerns, regulators felt that historical cost accounting permitted some banks to enhance profits by selling securities that had unrealized gains while continuing to hold, at historical cost levels that were greater than market values, securities with unrealized losses.

FAS 107, “Disclosures About Fair Value of Financial Instruments,” requires financial institutions to disclose, to the extent practicable, the market value of financial assets. Clearly, most investment securities have acn'vely-traded markets with readily available market prices. Just as clearly, most bank assets and almost all bank liabilities do not have actively-traded markets with readily available market prices. When market prices are not available, FAS 107 suggests calculating “the present value of estimated future cash flows using a discount rate commensurate with the risks involved." EVE sensitivity simulations have all of the required data necessary for these disclosures.

5-41

6/08 Interest Rate Risk Management

FAS 107 only requires these disclosures in financial statement footnotes. Changes in economic values do not have to be reported in income statements as changes in income or on balance sheets as changes to stockholders' equity. Instead, the footnote shows changes in fair market values and the impact of those changes on equity. In effect, the required FAS 107 disclosures are nothing more than the market values of the assets and liabilities in the no-change-in-rates scenario. FAS 115 The FASB issued FAS 115, “Accounting for Certain Investments in Debt and Equity Securities,” in 1993 as the next stage in a continuing efi‘ort to expand the use of economic value accounting. As with FAS 107, FAS 115 was adopted to address perceived inconsistencies and weaknesses in the historical cost accounting approach. FAS 115 focuses on investment activities. The rule creates three separate categories for investment securities and establishes distinctly separate accounting treatments for securities in each category. The three categories are trading, available for sale, and held to maturity.

For most banks, the main decision required by FAS 115 pertains to the assignment of investment securities as either available for sale (AFS) or held to maturity (HTM). Changes in the economic value of AFS investments must be reflected in reported capital. As a result, managers need to manage AFS holdings to maintain economic value changes within acceptable boundaries. Economic value simulation can provide managers with the data necessary to achieve that goal. Specifically, economic value simulation can provide managers with forecasts of economic values under a number of different rate scenarios. (Bond calculators can do this too, but they do it one bond and one rate scenario at a time.)

Product Pricing and Marketing The economic values for individual groups of assets and liabilities must be calculated as intermediate steps in the process of calculating EVE. We saw total economic value changes for assets and liabilities in Exhibit 5.6. In the process of generating those totals, data entered in the economic value simulation are aggregated in groups selected by the users. For example, loans may be aggregated as closed-end consumer loans, open-

5-42

Economic Value Simulation 6/08

end consumer loans, closed-end business loans, open-end business loans, and mortgage loans. (The choices needed for appropriate data aggregation are discussed in Chapter 9.)

Economic value sensitivities for each asset and liability aggregation group in the simulation can be examined and compared. Bank products can even be ranked by their economic value sensitivity. The longest-term fixed-rate assets and liabilities will have the largest economic value sensitivities. Very short-term and floating-rate assets and liabilities will generally be the least sensitive.

Comparative data on interest rate sensitivity by product can be very useful. One important application of these data can be in product pricing. For example, the rates charged for loans should include a charge for the interest rate risk. A short-term fixed-rate loan requires only a small rate risk premium. A long-term fixed-rate loan clearly requires a larger rate risk premium. The same data can be used to make marketing decisions. For example, a bank that is exposed to declining economic values for equity in rising rate environments can reduce that exposure by focusing on increasing liability products with the largest rate sensitivity or on reducing assets that have the largest rate sensitivity. This type of management activity is an example of natural hedging, a concept discussed in Chapter 14.

ADVANTAGES OF EVE SENSITIVITY SIMULATION

EVE sensitivity simulation analysis captures the dynamic aspects of long-term IRR better titan any other alternative rate risk measurement technique. In fact, EVE sensitivity simulation ofl'ers a number of significant

advantages below.

to [RR managers. Eleven of these advantages are discussed

Captures Interest Rate Risk from All Time Periods

EVE sensitivity simulation, like duration, captures interest rate risk in all time periods, not just in the next 12 months. It incorporates all of the future cash flows from a bank's current assets and liabilities. This is a

5-43

6/08 Interest Rate Risk Manggement

significant improvement from the gap and income simulation approaches to IR measurement considered in Chapter 3. Provides a Specific and Understandable Measure of Rate Risk Exposure

EVE sensitivity

simulation modeling provides a specific and understandable measure of rate risk exposure (e.g., a dollar amount of change in the bank’s EVE) rather than a crude proxy to quantify risk (e.g., gap mismatch or duration of equity). EVE sensitivity simulation thus expresses rate risk exposure in a way that is meaningful and useful to decision makers. Bank directors, industry analysts, and regulators pay close attention to equity. Even though equity is hardly the sole point of reference for anyone reviewing bank performance, it is defmitely one of the most common and familiar. Therefore, measurements of IRR that relate that risk to changes in equity value are relevant.

Focuses on the Rate Risk in the Bank’s Current Position

As noted earlier, EVE sensitivity simulation does not incorporate new business assumptions. While this detracts from the realism of the it also a disadvantage discussed in the next section projections offers an advantage. The no-change-in-rates projected economic value of equity is, in fact, a mark-to-market of the bank’s current balance sheet. It shows the net value of all of the current asset and liability positions. This can be a useful starting point for considerations of rate risk exposure.

—

—

Can Readily Be Used to Focus on Changes in Rate Exposure at the Product Level

EVE sensitivity simulation modeling can provide rate risk managers with information on the rate sensitivity of the economic or market values for a large number of specific bank products. This advantage arises from the fact that market values and value at risk for individual portfolios and products can easily be isolated in the process of projecting market or economic values for the entire balance sheet. Risk managers, in turn, can readily use this information to focus on changes in the pricing or outstanding balances of those products. By providing the information that enables managers to focus on the specific sources of rate risk, EVE sensitivity simulation improves managers’ ability to control that risk.

5-44

Economic Value Simulation 6/08

Can Capture Option Risk

EVE sensitivity simulation can reflect embedded options. It allows rate risk managers to employ different assumptions suitable to each different rate scenario. Customer behavior changes as rates change. We have previously discussed some of the major examples of rate-sensitive customer behavior, including deposit withdrawals and loan prepayments. As noted in Chapter 1, embedded options like the ones just mentioned can comprise a significant portion of total interest rate risk. EVE sensitivity simulation enables rate risk managers to capture options risk when volume and cash flow timing assumptions are selected and applied appropriately. Note the qualification in the last sentence. In order to capture option risk, you must adjust your assumptions for the size and the timing of optionrelated cash flows in each rate scenario. Can Capture Yield Curve Risk

EVE sensitivity simulation can reflect yield curve risk. One of the most important advantages of EVE sensitivity simulation modeling is the flexibility to reflect that short- and long-term interest rates do not change by the same amounts at the same time. Gap analysis and duration analysis ignore yield curve risk. EVE sensitivity simulation can capture this risk when discount rates are selected and applied appropriately. Again, note the qualification in the prior sentence. In order to capture yield curve twist risk, you must model the impact of nonparallel yield curve shifts. If you only model the impact of standard rate shocks (e.g., plus or minus 100, 200, and 300 bps) you will not see how yield curve risk impacts your balance sheet. Can Capture Basis Risk

EVE sensitivity simulation can reflect basis risk. Not only do interest rates change in different amounts for different maturities, but they also change in different amounts for different instruments. Historical analysis clearly demonstrates that most rates do not move up or down in unison. EVE sensitivity simulation, by using different interest rates for different instruments, can reflect changes in basis. Gap and duration analysis, in contrast, implicitly assume that when interest rates change, interest rates for all instruments change at the same time. EVE sensitivity simulation, like income simulation, can capture this risk. In order to capture basis 5-45

6/08

Interest Rate Risk Management

risk, you must select discount rates for each major type of instrument from appropriate yield curves for instruments of that type. However, as we discuss in Chapter 11, EVE treatment of basis risk can create perverse outcomes for bank liabilities.

Can Reflect Rate Sensitivity Over a Wide Range of Rate Scenarios EVE sensitivity simulation can be applied to measure the bank’s sensitivity to a variety of different future interest rate scenarios. Gap analysis and duration analysis cannot do this easily. Income simulation and EVE sensitivity simulation are thus more flexible and more useful to rate risk managers who, by definition, do not know future prevailing interest rates.

Can Capture Rate Risk Obscured by Accrual Accounting

EVE sensitivity simulation, like duration analysis, correctly reflects the interest rate risk inherent in the reinvestment of cash flows. This aspect of interest rate risk is not captured in gap analysis or in income simulations. This advantage applies to all assets and liabilities having cash flows that do not occur monthly but it is most significant for zero coupon bonds. Because interest income and expense are accrued monthly, income simulation models treat that income or expense cash as if it repriced monthly. (Gap analysis usually ignores all the income and expense cash flows.) Economic value sensitivity simulations apply a discount rate appropriate for the time period until the cash flow is received, and therefore implicitly include reinvestment risk that is missed by income simulations for all nonmonthly cash flows of income and expense. Meets Regulatory Expectations

EVE sensitivity simulation meets bank regulatory expectations. Both the Joint Agency Policy Statement on Interest Rate Risk, issued by the Federal Deposit Insurance Corporation (FDIC), the Federal Reserve (Fed), and the Office of the Comptroller of the Currency (OCC) in 1996, and the risk-based examination guidelines emphasize the importance of measuring IRR from an economic perspective. In addition, the regulators note that banks with significant holdings of instruments with intermediate- and long-term maturities or embedded options should be

5-46

Economic Value Simulation 6/08

able to assess the potential long-term impact of changes in interest rates. Since only economic approaches to measuring IRR capture the potential long-term impact, the regulators are essentially telling banks with those types of holdings that they must use a duration or EVE approach to quantifying their rate risk exposure. Can Be Integrated with Other Management Information Systems Last, but not least, is that EVE sensitivity simulation analysis can provide bank managers with information that helps them meet other management needs. These include market value disclosures required by FAS 107 and decisions on the allocation of investment securities between available-for-sale and held-to-maturity categories under FAS 115. As we have seen, market or economic value sensitivities to rate changes can also be used in product pricing.

DISADVANTAGES OF EVE SENSITIVITY SIMULATION The 11 advantages just described make EVE sensitivity simulation one of the two most attractive tools for rate risk managers. Nevertheless, EVE sensitivity simulation also has some disadvantages of which managers should be aware. Seven of these are discussed below. Managing EVE Sensitivity Can Increase Earnings Volatility The use of EVE sensitivity simulation in rate risk management can increase the volatility of reported earnings. This can occur when rate risk managers take steps in one accounting period to reduce risks that will actually be incurred in future accounting periods. This can easily happen because the measured EVE sensitivity is a specific quantity of rate risk exposure accrunulated from all time periods. In other words, the amount of EVE sensitivity does not provide any information about the temporal nature of the risks.

Many senior managers believe that it is a strategic error to forgo any material amount of current earnings in order to reduce rate risk that won’t occur until years in the future. This point of view is not necessarily a result of short-term focus on current earnings. It also reflects that fact that because neither the bank's future business nor its future competitive

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Management

environment are likely to be the same as the current business and competitive environment, the projected future rate risk exposure is almost certainly wrong. Future rate risk exposure may be close to the level predicted by current EVE calculations. Or, it may not. Therefore, the business justification for reducing future exposures merits close scrutiny.

In Most Applications, EVE Ignores the Impact of Reinvestment and New Business Economic value simulation rarely includes projections for new businesses. Essentially, most EVE simulations erode the balance sheet down to the final cash flows. Since the main advantage of using economic value simulation is to capture rate risk in future time periods, it is significant that it only captures future rate risk fiom present positions. As we look farther into the future, our projected economic values for equity become increasingly unrealistic. Three or five years from the date of measurement, the measured rate risk from remaining assets and liabilities may quite likely be materially different from the new risk exposures fi'om assets and liabilities subsequently acquired. This weakness is discussed at length earlier in the chapter.

EVE Does Not Provide Any Information About the Timing of Rate Risk Exposures As we discussed earlier in the chapter, EVE sensitivity measures tell us the size of the rate risk exposure in all time periods but do not provide any insights into which time periods have the risk. Indeed, as we saw in the discussion of the OTS study, a financial institution exposed to a decline in economic value in the event of rising rates may actually see an increase in income the first year following a rate increase. Without knowing which time periods are exposed, it is harder to make effective risk remediation management decisions.

Assumptions Require Careful Development, Analysis, Increased Controls, and Testing

As we have already observed, many authorities continue to suggest that the major disadvantage of EVE simulation modeling is that it is too dependent on assumptions. Certainly, EVE sensitivity simulation

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modeling is assumption dependent. However, all measurement methods are assumption dependent. The distinguishing characteristic of EVE simulation (and income simulation, too) is not its dependency on assumptions, but that the user can easily modify the assumptions used. It is a distinguishing benefit of EVE simulation modeling that such flexibility with assumptions allows it to mirror reality more accurately than other techniques. Unlike income simulations, EVE sensitivity simulation models require additional assumptions for maturities. Since the economic value sensitivities are derived from changes in economic values that, in turn, are derived from present values, every economic value calculation requires a maturity for the cash flow. As we know, core deposits have no maturities. The “maturity” of those cash flows is a guess, at best. Since these liabilities ofien comprise material portions of bank balance sheets, the assumed maturity of the underlying cash flows is a major influence on the measured quantity of risk.

The real problem is not assumption dependency per se. Instead, the real problem is that it is hard to develop good assumptions. Even afler sound assumptions are developed, more work is required to test, update, and manage their use. Along these lines, specific issues that should be considered are discussed in chapters 7 and 11. Controlling and testing assumptions are covered in Chapter 10.

Use of Discount Rates Can Introduce Additional Measurement Errors

EVE sensitivity simulation models use discount rates. This can complicate interest rate risk management by obscuring the true causes of rate sensitivity. Since the market or economic value sensitivities are derived from changes in market values that, in turn, are derived from present values, the discount rates used to calculate the present values certainly influence the results. If, for example, retail bank certificates of deposit are discounted using a discount rate derived from the U.S. Treasury note curve, the rate sensitivity of those deposits will probably be overstated. Since discount rates are, in effect, another complete set of information that must be assumed in the rate risk measurement process, it is not always clear whether the magnitude of measured rate sensitivity is

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Interest Rate Risk Management

driven by the underlying cash flows, the selection of the discount rate, or both. Errors can also result from the decisions made about the number of

discount rates to employ in the simulation. As we noted above, in order to capture basis risk, we need to employ different rates for difl‘erent instruments. In order to capture yield curve risk, we need to apply different discount rates to different cash flows from the same instrument depending upon the timing of those cash flows. We can

—

—

simplify the simulations by selecting fewer discount'rates, but that simplification reduces the accuracy of the output. 0n the other hand, the more discount rates we use, the more potential assumption errors we introduce.

Accurate Assumptions of Volume Changes Caused by Embedded Options Must Be Accurate Most banks, especially community banks, have very large holdings of loans and mortgage-backed investments that can be prepaid without penalty. They also tend to have material holdings of fixed-rate CDs that can be withdrawn before maturity, with only minor penalties for early withdrawal. Many also have adjustable-rate mortgage loans or investments with rate caps and floors.

EVE measures that fail to capture the options incorporated in these assets and liabilities will misstate their rate sensitivity. For example, the value of a fixed-rate, residential mortgage loan will decline in response to an increase in prevailing rates. Its value will fall more or less identically to the decline in value of an otherwise identical noncallable, fixed-rate loan in response to an increase in prevailing rates. However, the value of a callable loan will not increase as much as the value of a noncallable loan in response to a decline in prevailing rates. Indeed, the callable loan value may not increase at all. In other words, loans and investments subject to prepayments and calls have asymmetrical rate sensitivity; so do fixed-rate CDs that can be withdrawn before maturity. EVE models that do not include the optionality of those instruments will not capture the asymmetrical risk and will, therefore, produce misleading results. Even when the EVE model captures the oph'onality of loans, investments, and deposits, it can easily produce misleading results for

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banks that do not use carefully designed assumptions for volume changes. When rates rise, at least some fixed-rate CDs are withdrawn early. When rates fall, some fixed-rate loans are prepaid. Thus, the seemingly offsetting changes in the value of the CDs and the value of the loans are not really offsetting. In reality, the offsetting loan volume dissipates as rates fall, while the offsetting CD volume dissipates (although to a much smaller extent) as rates rise. If you use EVE to measure your IRR exposure, you must be carefiil to craft volume assumptions that reflect the option-driven changes in volumes. Otherwise, the measured rate risk exposure will be inaccurate. Of course, this requirement applies to income sensitivity models as well. However, since an EVE model is looking at the value of the cash flows from the entire life of an asset or liability, an assumption error that materially overstates the life of the instrument creates a much bigger error in an EVE model than in an EAR model.

EVE May Fail to Capture a Material Amount of Interest Rate Risk Exposure In many banks, EVE sensitivity simulation analysis is used to measure only the interest rate risk of assets and liabilities on the balance sheet and their related cash flows. Thus, the interest income cash flow streams from assets and the interest expense cash flow streams from liabilities are included in the measured EVE. That is, the bank’s exposure to adverse consequences from future changes in prevailing rates is measured for its net interest margin as well as the principal amounts of its assets and liabilities. But, as we discussed earlier, to the extent that economic value sensitivity simulation is applied only to the net interest margin, it severely overestimates interest rate risk. It effectively overstates the net interest income cash flow stream by ignoring the expense cash flow stream (mainly personnel and facilities) that must be paid in order to realize the income cash stream. And it ignores the value of the feeincome business annuities. These omissions can be a major weakness. This problem is discussed in more detail in Chapter 11.

VALUE AT RISK In a simplistic way, we might define the sensitivity of EVE as we have described it so far in this chapter, to be the value at risk (VaR). If, for

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example, a 100 bp increase in prevailing rates is projected to cause a 12 percent decrease in EVE, we might say that the bank has 12 percent of its value at risk. We might, but we don’t. Instead, VaR is used in a specific way. VaR almost always refers to a measure that combines EVE sensitivity with the probability of the change in value. VaR doesn't just consider a few changes in EVE. VaR is a more rigorous way of looking at the volatility of EVE. VaR is usually defined in statistical terms as the probabilistic bound of market value losses over a given period of time for a given level of certainty. The given period of time is called the holding period or the time horizon. The level of certainty is called the confidence interval. In other words, VaR is the maximum amount that might be lost for a given time period with a given degree of confidence.

Both the holding period and the confidence interval can be selected to fit the needs of the analyst. International bank capital standards, for example, use a 99 percent confidence interval for a 10-day holding period. Three Different VaRs

Statistically derived measures of VaR actually use three different approaches. Each produces a different resulting measured quantity of VaR. Each has fairly clear advantages and disadvantages. Banks should not use or consider buying any of the VaR models unless they understand what the model is saying when it measures value at risk. Even though they are all called VaR, different measures are inaccurate in different ways:

∙

Historical VaR calculates value at risk by comparing the actual volatility of components or risk elements within a portfolio to the historical sensitivity of those components. This provides a range or distribution of possible losses. A single VaR can then be calculated for the selected confidence level. Historical VaR is generally preferred for its ability to capture risk from unlikely events (but only to the extent that those unlikely events fall within the selected historical time period). However, the measured amount of VaR is heavily influenced by the choice of time horizon and by the volatility that occurred during that historical time

Economic Value Simulation 2/09

period. If fixture changes do not resemble the change in value that occurred during the selected time horizon, the forecast VaR will

∙

∙

4.

not be a good indicator of the real risk. As one banker explained VaR, we flip the coin often enough to be confident that we are not too wrong, as long as the future looks somewhat like the past.

Analytical or correlation VaR also compares the sensitivity of risk elements. A number of variables may influence an instrument’s value. The most obvious is the level of prevailing interest rates. Other variables may be default risk, commodity prices, equity prices, and foreign exchange rates. Although the price sensitivity of a financial instrument can be correlated with a single variable (called the instrument’s delta, or the mean-variance VaR), more accurate results compare the price sensitivity to multiple variables.

Values for portfolios of instruments are influenced by multiple variables. Accordingly, multi-variant correlation analysis is applied. The volatility for each component is then calculated using a standard matrix. This is the type of VaR calculated by some popular models, such as the one developed by J .P. Morgan. This is the least computational-intensive of the three statistical types of VaR measurements. However, this approach does not adequately reflect option risk or incorporate the risk of unlikely events. Monte Carlos simulation is widely recognized as the most powerful and flexible method for estimating value-at-risk ...."‘ Also known as empirical or simulation VaR, Monte Carlo simulation calculates VaR by modeling potential value changes for a defined time horizon over a large number of possible scenarios. Monte Carlo analysis results in thousands of simulations, perhaps as many as 10,000. Each simulation reflects a difl‘erent potential outcome. When all of the simulations are rtm, they are usually listed in order of the biggest gain to the biggest loss. A cut-off point is determined based upon the selected confidence level. The loss at that cut-off point is the amount of value at risk.

“Improved Monte Carlo Methods for Value-At-Risk,“ Risk Magazine. EnterpriseWide Risk Management Supplement, November l997.

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In addition to greater accm'acy, another benefit is that by running numerous scenarios, it is more likely to find, ex ante, a scenario that is reasonably close to realized rate moves. This greatly simplifies the banktesting exercise championed by certain stakeholders. 5 Monte Carlo does the best job of capturing option risk. Unfortunately, it is themost computational intensive of the three techniques. Each of the three VaR calculation methods has strengths and. weaknesses. Exhibit 5.10 provides a comparison of these strengths and weaknesses.

Exhibit 5.10 Strengths and Weaknesses of VaR Methods Factors

Historical VaR

Correlation VaR

Monte Carlo VaR

Easy to

Very easy

Very easy

Not at all easy

Easy to explain

Very easy

Hard

Very hard

Historical data period may be too short

Can be a problem

Can be a problem

No problem

implement

Direction

Backward looking Backward looking

Captures embedded options

Not well. Risk can be overstated or

Credit

Ignores and can therefore create

understated, depending on whether the historical period incorporates a

Forward looking_

Not well. Risk can be understated. especially when volatility is high.

Very well

Ignores

Explicitly incorporates

strong trend.

risk/default

5.

"selection bias”

Fred Poorman, "Time for Better ALM Practices?." Bank Asset/Liability Management, page 4, November 2007.

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Economic Value Simulation 8/09

Factors

Historical VaR

Correlation VaR

Computationalintensive

Not very

Least

Extremely

Other issues

Dubious assumption that the future will be like the past

Highly controversial assumption of

Subject to “model risk“ from inaccurate assumptions

normal distributions

Monte Carlo VaR

VaR Problems and Limitations A wide variety of calculation issues, such as the choice of time periods used for historical VaR calculations, impairs the accuracy of VaR measures. However, six issues merit particular attention.

1. Both historical and correlation VaR simply do not provide an accurate measure of risk for extreme conditions. This problem was most clear at the start of the 2007-2009 banking crisis: For example, some firms’ initial assessment of the true potential losses they faced were likely skewed downward by their VaR measures’ underlying assumptions and a dependence on historical data from more benign periods. Firms suggested that VaR calculations based on new market data were anywhere from about 10 percent to at least 200 percent higher compared with VaR calculations conducted using data sets reflecting earlier, and more favorable, market conditions. The increase in most firms‘ VaR calculations ranged from 30 percent to 80 percent.‘5

2. VaR doesn‘t do a good job of reflecting option risk. In statistical terms, the problem is that VaR relies on a symmetrical distribution, but options create asymmetrical distributions. As we noted above, the non-normal distribution problem is most serious for historical and correlation VaR measures, while the option risk problem is most serious for correlation VaR.

6.

Section V, B, 3, “Observations on Risk Management Practices During the Recent Market Turbulence,“ Senior Supervisors Group, March 6, 2008.

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Interest Rate Risk Management

3. For instruments and portfolios with credit risk, asymmetry of returns comes not only from optionality but also from default risk. In fact, default risk can create more asymmetry than option risk. This, too, is mainly a problem for historical and correlation VaR. 4. For portfolios with credit risk, historical VaR is also impaired by “selection bias.” The calculated VaR for the current portfolio does not include counterparties for instruments you may have held in the past but that subsequently defaulted.

5. It is also important to remember that the focus of VaR is on volatility. Recall that the amount of value at risk is some level of loss identified at a particular level of confidence for a particular distribution of volatile events. The level of generally prevailing interest rates therefore makes a difference. Volatility tends to be proportionate to the absolute level of rates. If prevailing rates are very high, a 100-basis point change is a smaller percentage and more probable than when prevailing rates are low. Furthermore, changes in volatility can lead to underestimation of risk. Roughly speaking, if markets are half as volatile, banks' risk exposure appears to be half as large as it was before the decline in volatility, even though the size and all other characteristics of the exposure are the same.

6. Perhaps the most serious deficiency in VaR as a metric for risk managers is that it reduces the risk down to a single number. This is an oversimplification and can be very misleading. Consider the three example portfolios shown in Exhibit $.11.

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Economic Value Simulation 8/09

Exhibit 5.11 VaR for Three Hypothetical Portfolios

HYPOTHETICAL PORTFOLIO VALUES Short rate mean Short rate volatility

Level of ShortTen'n Interest Rate

1.26% 1.69% 2.35% 3.71%

4.44% 7.00% 9.56% 10.29% 1 1.65%

Number of Sigmas irorn Mean -2.87 -2.65 -2.32 -1.65 -1.28 0.00 1.28 1.65

2.32 12.31% 2.65 12.74% 2.67 Slmple Standard Deviation Local Rate Sensltlvlty 1% Worst-Case Outcome

0.07 0.02

Cumulative Probability

0.10%

0.50% 1.00% 5.00% 10.00% 50.00% 90.00% 95.00% 99.00%

99.50% 99.90%

A 1 10 50 100 100 100 100 100 100 100 100 39 0 99

P°""°"° B 120 120 120 120 120 100 80 00 80 80 80 20 20 20

C 160 160 160 160 105 100 95 40 40 40 40 54 5 60

Source: Donald R. van Deventer and Kenji Irnai, Financial Risk Analytics: A Term Slructure Model Approach for Banking. Insurance and lnvesmrenl Management, McGraw-l-Iill, pages 375-376.

The three hypothetical portfolios shown in Exhibit 5.11 are designed to highlight a problem. If we use the standard deviation as our yardstick, portfolio C is the most risky and portfolio B is the least risky. If we use the sensitivity to one point on the yield curve as our yardstick, portfolio B is the most risky and portfolio A has zero risk. On the other hand, if we define our risk as the worst-case outcome expected to occur no more than 1 percent of the time, then portfolio A is the most risky while portfolio B is the least risky.

How can all three of the .VaR risk yard sticks shown in Exhibit 5.1] be correct? The truth is that each gives an accurate view of a small part of the risk, but none is an accurate view of the overall risk. The overall risk for the three hypothetical portfolios is shown in Exhibit 5.12.

8/09 Interest Rate Risk Management

Exhibit 5.12 Cumulative VaR for Three Hypothetical Portfolios Porflolio Value

O

am

can

IWI

am

WWI

”E!

”M

term.

I'M

”34“

mm

Cumulative Probabil'ny

Source: Donald R. van Deventer and Kenji Irnai, Financial Risk Analytics: A Term Structure Model Approach for Banking, Insurance and Investment Management, McGraw-Hill, pages 375-376.

Leaving aside all of the math jargon, the bottom line is that VaR is an interesting and useful tool but one that simply does not describe the full extent of a bank’s risk exposure. With just a bit of overgeneralization, we can characterize VaR as an excellent measure of risk under normal conditions. However, VaR is not all that accurate for abnormal conditions. “The problem comes for the tiny number of crises when markets move much more and, to add insult to injury, banks’ assumptions about the diversity of their portfolios are shown to be wrong. In other words, the models, says one regulator with a chuckle, are of least use when they are most needed!” Users of VaR for trading risk management learned that lesson (again) in August and September 1998 when capital markets were shocked by the 7.

“The Coming Storm," The Economist, February 19th, 2004.

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Economic Value Simulation 8/09

collapse of the Russian ruble and the near collapse of a major hedge firnd. Presumably, a return to the extreme interest rate volatility seen in the early 19805 would be the interest rate risk equivalent of such abnormal conditions.

Stress Testing Precisely because of its methodological limitations, VaR should not be used without stress testing. Weak stress testing is simply a matter of “peering into” the tails of the volatility distribution. This can be done by choosing to look at events exceeding some selected number of standard deviations. Alternatively, sophisticated math tools, such as extreme value analysis, may be applied. While looking at the extreme events in the distribution tale can be insightful, it is not the best way to stress test. As one expert observed: “The question is not: 'What risk will we get if we push out the quantiles?’ —- The answer to that question is only a matter of scaling and is therefore meaningless! Instead, the uestion is: ‘Is there a structural change that the bank should model?” In a nutshell. the problem is that risk in not linear in extreme events. A better way to stress test is to model a series of unusual events. Stress tests may model the impact of abnormal market conditions. Or they may model the change in the measured amount of VaR that occurs when some of the other simulation assumptions are pushed to extremes. For example, stress tests for correlation VaR measures include simulations in which the correlations are assumed to change dramatically. As one author noted, “There is no standard way to do stress testing. It is just a way to experiment with the limits of a risk model and to think ‘outside the box.”‘9

Stress testing is a necessary requirement for using VaR as a measure of risk exposure. But stress testing is also the antithesis of VaR. Look at it this way. The main value of VaR, as opposed to simple measures of the change in EVE, is that VaR is probabilistic. We can easily calculate how

8.

Dr. Robert E. Fiedler, in conversation with this author.

9.

Kenneth S. Leong, "The Right Approach," Value at Risk, a Risk Special Supplement, June 1996, page 14.

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much EVE might be lost if prevailing rates were to rise by, say 200 basis points. However, we don’t know whether or not to be worried by that exposure because we don’t know how likely a 200 basis point rate jump may be. VaR may let us say that there is a particular probability, say 96 percent, that we won’t lose more than X dollars in a particular time period. However, one of the reasons we do stress testing is because we know that a particular probability is not accurate for abnormal conditions. By definition, stress testing introduces extreme events or scenarios that are only limited by the imagination. While stress testing can indicate how much might be lost if the model is wrong, it doesn’t tell us anything about the likelihood that the model may be wrong. In other words, when we do stress testing, we gain insight but lose the probabilistic benefit. Converting EVE to VaR

When the EVE model is complemented with an estimate of the probabilities of the interest- rate scenarios used, the EVE model becomes a Value at Risk (VaR) model, which builds a statistical distribution of profit and losses that may occur over a specified time horizon at a given confidence level owing to movements in interest rates. The method not only measures the magnitude of the loss, but also the probability of the loss.

To convert EVE to VaR, follow these four

steps:'°

1. Start with static EVE. The calculation of the present values gives us the immediate (now) value for each given discount rate curve. 2. Model the term structure of interest rates or the yield curve. Some banks model volatility changes over time, while other banks assume volatility is constant.

10. “Range of Practices and Issues in Economic Capital Modeling," Consultative Document, Basel Committee on Banking Supervision, BS, August 2008, pages 55 and 56.

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Economic Value Simulation 3/09

—

Pick a time say one year, or five years, or 10 years — you can see what percentile a historical rate moves for the selected time period.

In the third step the economic value of assets and liabilities and the term structure of interest rates are combined to produce the final value distribution which can be used to compute VaR or economic capital.

EVE AND VAR SUMMARY At the beginning of Chapter 3, we considered five requirements for a better approach to IR measurement. A summary of these five requirements follow:

1. The measurement system must enable us to understand the size and direction of our bank’s interest rate exposure under a variety of interest rate scenarios.

The system must readily and accurately capture all of the important data for volumes, maturity dates, repricing dates, and hidden options. The data must be used in ways that clearly focus attention on critical variables. The system must facilitate easy and accurate accommodation of all new loans, new deposits, withdrawals, repayments, and other

changes.

The system must be able to reflect that changes in prevailing interest rates affect difl‘erent assets and liabilities in different ways.

We also noted in Chapter 3 how income simulation meets those five requirements even though it fails to capture long-term IRR.

Economic value of equity sensitivity simulation can also meet those five requirements. And, in addition, EVE sensitivity simulation does a great job of capturing long-term IRR. However, it is important to remember that most applications of EVE sensitivity analysis are, as we have

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discussed, used in ways that fail to meet the fourth requirement and that only do a limited job of fulfilling the second and fifih requirements. In other words, unless you invest considerable time and resources to use a high-end EVE model, EVE sensitivity measures should really be considered to be supplements for good EAR simulations rather than substitutes for EAR simulations.

VaR meets the first test even better than EVE sensitivity measures by incorporating probabilistic information, but it does less well with some of the other requirements. And because it is both computationally intensive and subject to statistical problems that reduce its accuracy, VaR is a tool that should only be used by the most knowledgeable and wellsupported risk managers. Essential elements for best practice application of EVE and VaR:

∙

First, EVE sensitivity simulation and VaR are both potentially valuable risk measurement tools. Their main value lies in the fact that, when used appropriately, they do an excellent job of more capturing long-term IRR. These are complementary tools so than replacement or substitute tools — for good EAR simulations. Astute rate risk managers use both. In their joint policy statement on interest rate risk, the FDIC, the OCC, and the Fed said that “the agencies believe that a well-managed bank will consider both earnings and economic perspectives when assessing the full scope of its interest rate risk exposure."“

—

∙

Second, it is important to recognize that it is very easy to use EVE models and VaR poorly. A typical EAR model only looks at cash flows from assets or liabilities over a one- or two-year time period. An erroneous assumption regarding the rate or the change in volume for an asset or a liability in an EAR model therefore is far less likely to lead to as big an error in measured risk as the same incorrect assumption in an EVE model that incorporates cash flows from that asset or liability over its entire life. Furthermore, the accuracy of the EVE model depends on the accuracy of

11. Joint Agency Policy Statement: Interest Rate Risk, as published in Register, Vol. 61, No. 124, Jtme 26, 1996, page 33,171.

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the

Federal

Economic Value Simulation 8/09

∙

additional assumptions for things like discount rates and changes in the shape of the yield curve than an EAR model. VaR models, as we have discussed, are subject to some potentially fatal statistical flaws and must therefore be used with great care. VaR is usually the right tool for trading risk but the wrong tool for balance sheet risks. VaR, especially historical VaR, is commonly used as the primary risk measure in trading portfolios. This application is both sound and useful. VaR stress testing for trading portfolio risks is similarly beneficial. In both of those applications, problems faced by balance sheet risk managers - especially long time horizons and larger but less probable rate changes — have less impact on risk assessments. Using VaR to measure or stress test rate risk on the balance sheet appeals to risk managers with trading or math backgrounds but is suboptimal. Just because you have a perfectly good hammer doesn‘t mean that your problem is a nail. EVE and EAR are better tools for those tasks.

In short, EVE and VaR are powerful tools that can add significant value if, and only if, used carefully.

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5-64

Chapter 6 Measuring the Rate Risk of Indeterminate Maturity, Administered Rate, and Putable Deposits

So, How Important Is Deposit Rate Risk?............................................ 6-2 Exhibit 6.1: EAR Sensitivity to Indeterminate Maturity Deposit Repricing Assumption ..................................................... 6-4 Exhibit 6.2: EAR Sensitivity to Indeterminate Maturity Deposit Decay Assumption .......................................................... 6-5 Exhibit 6.3: EVE Sensitivity to Indeterminate Maturity Deposit Decay Assumption .......................................................... 6-6 A Summary: The Sensitivity of Measured IRR to Indeterminate Maturity Deposit Assumptions ......................................................... 6-7 Estimating the Maturity and/or Repricing of Indeterminate Maturity Deposits ................................................................................. 6-7 Maturity Assumptions Vary Hugely ................................................. 6-8 Exhibit 6.4: Illustrative Indeterminate Maturity Deposit Decay Rates and Average Lives ................................................... 6-9 An Overview of Quantitative Tools for Calculating Indeterminate Maturity Deposit Runoff Rates and Average Lives ....................... 6-10 Method One: Decay or Attrition Analysis ...................................... 6-12 Calculating Deposit Decay or Attrition ...................................... 6-12 Exhibit 6.5: Illustration of Simple Decay Analysis .................... 6-13 Exhibit 6.6: Example Attrition Measurements ........................... 6-14 Decay Analysis Limitations ....................................................... 6-14 The Influence of Changes in Prevailing Interest Rates on Changes in Deposit Volumes: A Digression ......................... 6-16 Exhibit 6.7: Indeterminate Maturity Deposit Volume Changes Transaction Accounts — Plus 200 vs. Minus 200...................... 6-19 Exhibit 6.8: Indeterminate Maturity Deposit Volume Changes Plus 200 vs. Minus 200 ......................... 6-19 Passbook Accounts Exhibit 6.9: Core Deposit Volume Changes Money Market Accounts — Plus 200 vs. Minus 200 ......................................... 6-20 Reasons Why Deposit Balances Are Not Always Rate Sensitive ............................................................................. 6-20

—

2/10

6-i

2/10 Interest Rate Risk Management

The Influence of the Exercise of Depositors’ Options on Changes in Deposit Volumes ................................................ 6-24 Segmented Volume and Replicating Portfolios.................................. 6-26 Method Two: Segmented Volume Analysis for Estimating Deposit Maturity ............................................................................. 6-27 Using Trend Analysis to Segment Stable and Volatile lndeterrninate Maturity Deposit Components — A Simple Application ................................................................. 6-29 Using Trend Analysis to Segment Stable and Volatile Indeterminate Maturity Deposit Components — A More Sophisticated Application ............................................. 6-29 Exhibit 6.10: Indeterminate Maturity Deposit Trend Analysis in Savings Account Balances ...................................... 6-30 Method Three: Simple Regression Analysis Finding a Floating Rate Bond with the Same Rate Sensitivity .................... 6-31 Exhibit 6.11: Coefficients for Modeling the Deposit Rate as a Function of l-Month LIBOR Rate ...................................... 6-31 Method Four: Replicating Portfolio Analysis for Estimating The Most Common Method .......................... 6-32 Deposit Maturity Exhibit 6.12: Illustration of Simple Portfolio Construction for Replicating Portfolio Analysis .............................................. 6-33 Combining Segmentation Analysis and Replicating Portfolios ..... 6-34 Method Five: Complex Replicating Portfolio Analysis ................. 6-35 Exhibit 6.13: Constant Deposit Balances with Complex Econometric Equations............................................................... 6-36 Method Six: Replicating Portfolio Analysis The Jacobs Method......................................................................... 6-37 Exhibit 6.14: Example Replicating Portfolio Using the Jacobs Method ...................................................................... 6-38 Moving Beyond Replicating Portfolios .......................................... 6-39 Method Seven: Structural Models of Aggregate Behavior............. 6-39 Method Eight: Option Adjusted Spread ......................................... 6-40 Exhibit 6.15: Example OAS Process .......................................... 6-41 Exhibit 6.16: Example OAS Cash Flows ................................... 6-42 A Summary ............................... 6-42 Estimating Deposit Maturities Exhibit 6.17: Comparing Methods for Quantifying Core Deposit Rate Sensitivity ............................................................. 6-43 Estimating Administered Rates for Checking and Savings Accounts ............................................................................................. 6-44

—

—

—

—

Measuring the Rate Risk of Indeterminate Maturity, Administered aniLmd Putable Deposits 2110

Five Administered-Rate Variables ................................................. Caps and Floors .......................................................................... Time Lags ................................................................................... Beta............................................................................................. Exhibit 6.18: Indeterminate Maturity Deposit Rate Correlation to Treasury Bill Rates Worksheet ........................... Exhibit 6.19: Indeterminate Maturity Deposit Rate Correlation to Prime Rate Worksheet ......................................... Administered Rate Sensitivity Summary ................................... Exhibit 6.20: Comparative Rate Volatility ................................. Asymmetrical Rate Changes ...................................................... Path Dependency of Administered Rates ................................... Dealing with Administered Rates ................................................... Certificates of Deposit ........................................................................

6-iii

6-45 6-45 6-45 6-46 6-47

6-47 6-47 6-48 6-50 6-51 6-51 6-53

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Interest Rate Risk Manggement

6-iv

Chapter 6 Measuring the Rate Risk of Indeterminate Maturity, Administered Rate, and Putable Deposits

∙

Checking accounts, passbook savings accounts, statement savings and similar liabilities are sometimes called “nonmaturity” or “indeterminate maturity" deposits. (In this chapter, all of these products are included in general references to “indeterminate maturity deposits” or to “checking and savings” deposits.) accounts,

Most banks hold substantial amounts of indeterminate maturity deposits. As of September 30, 2003, deposits with indeterminate maturities were equivalent to almost 59 percent of total assets. Undoubtedly, figures for savings banks and savings and loan associations would also show heavy dependence on these sources of ftmds. For all of these accounts, the interest rate risk analyst has two major problems.

∙

∙

2110

—

First, these liabilities are not perpetual they do have maturities. But the maturities are unknown and unknowable until the funds are removed. Depositors may add to the accounts or withdraw from the accounts on demand. In other words, these depositors own an infinite number of put and call options to change the notional amount of the accounts. Second, the interest rates that banks pay on these ftmds are either zero or some administered rate. As we shall see, even the zero rate funds still carry interest rate risk. The interest-bearing funds have IRR that is difficult to capture accurately because of implicit caps and floors in the administered rates. Lags between the time prevailing rates change and the time changes are made in the administered rates for indeterminate maturity fturds represent still another problem for the analyst attempting to capture IRR.

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Interest Rate Risk Management

—

These two issues the customer options to change the notional amount and the bank options to change the administered rates paid for the are discussed below. deposits

—

It is important to understand that the changes in indeterminate maturity deposit balances and the rates paid on these accounts are interconnected. We can consider a sequence of events that illusnates this interaction.

First, prevailing rates rise. Second, bankers evaluate the changes in prevailing rates, the changes made by competitors in the competitors’ administered-rate products, and the anticipated behavior of their own customers to changes in the administered rate paid on indeterminate maturity deposits. Third, some customers, by defrnition the rate-sensitive customers, make withdrawals or deposits to maximize their advantage from the difference between the new prevailing rates and the new bankadministered rates. (If prevailing rates rise, these customers will tend to withdraw funds from administered-rate deposit products in favor of higher yielding alternatives.) Fourth, the bank will have the benefit or expense of a new spread between the new level of prevailing rates and the new level of its administered rates. However, it will enjoy or suffer from that new spread only on the new level of deposit balances afier step three. In the next sections of this chapter, we discuss these issues separately. First, we consider estimated indeterminate maturity deposit maturities and how they are influenced by customer withdrawals and deposits. Then, we consider administered rates. These subjects are considered separately so that we can understand them more clearly. Readers should keep in mind that, as the four steps outlined above make clear, these seemingly separate topics are interdependent.

SO, HOW IMPORTANT IS DEPOSIT RATE RISK? The treatment of the IRR represented by indeterminate maturity deposits has a significant effect on any IRR assessment. In fact, a report published by the Board of Governors of the Federal Reserve System said that “the treatment of deposits without specific maturity or repricing dates may be

6-2

Measuring the Rate Risk of Indeterminate Maturity, Administered Rate, and Putable Deposits 2/10

the single most complex element in an institution‘s measured level of

IR exposure.”l

We can easily calculate how sensitive our measured amount of IR might be to a change in the indeterminate maturity deposit assumptions. First, let’s take a look at an earnings at risk (EAR) risk measure. Exhibit 6.1 shows one view of earnings at risk for an actual bank. This is an $840 million bank using an income simulation model to measure EAR. The particular rate scenario reported in Exhibit 6.1 is a 100 basis point decrease in prevailing interest rates. The bank has a complete model of its assets and liabilities. According to its model, if prevailing rates fall by 100 basis points and if it lowers the rate that it pays on indeterminate maturity deposits by the same amount, its net income for the next 12 months will be 4.47 percent more than the base case net income. We can see this on the top line of the table. The bottom line of the table shows that if prevailing rates fall by 100 basis points, but the bank makes no change in the rates paid for its core deposits, its net income for the next 12 months will fall by 2.26 percent. In other words, this bank's measured amount of earnings at risk, for a 100 bp decline in prevailing rates, may swing by as much as 6.73 percentage points, depending upon the indeterminate maturity deposit repricing assumption.

1.

Board of Governors of the Federal Reserve System, “Notice of Proposed Rulemaldng“, kirk-Based Capital Standards. March 26, 1993. page 29.

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Exhibit 6.1 EAR Sensitivity to Indeterminate Maturity Deposit Repricing Assumption CHANGE IN NET INCOME If prevailing rates fall by 100 basis points for a 12-monl.h period for an actual $840

million bank.

3.». CHANGE IN THE RATE

PAio FOR ADMINrerrtED RATE DEPOSITS 100 90 80 70 60 50 40

RESULTINGCHANGE IN NET INCOME (0005) 1,860

1,580 1,300

L020 740 460

180

30 20

(100)

10 0

(660) (940)

(380)

PERCENTAGE CHANGE IN NET lNCOME FROM BASE CASE 4.47% 3.80% 3.13%

7.45% 1.78% l. 11% 0.43% -0.24% -0.91% 4.59% —2.26%

A different view of EAR is shown in Exhibit 6.2. In this analysis, the bank is examining the sensitivity of its earnings at risk to differences in the assumed life of its indeterminate maturity deposits. As we will discuss later in this chapter, one way of looking at the life of a core deposit is to estimate the percentage of runoff each period. This is called the decay rate. Exhibit 6.2 shows how the projected changes in net income for nine different rate scenarios can change using three different decay rates. For example, look at the line labeled “-100.” (That is, the fourth line up fiom the bottom of the table.) The data on this line indicate that if prevailing rates fall by 100 basis points, and if indeterminate maturity deposits have a 25 percent annual decay rate, the bank’s net income will decrease by 9 percent. However, if prevailing rates fall by 100 basis points and indeterminate maturity deposits have a 50 percent annual decay rate, net income will fall by just 8 percent (the right-hand box on that line).

Measuring the Rate Risk of Indeterminate Maturity, Administered Rate, and Putable Deposits 2/10

Exhibit 6.2 EAR Sensitivity to Indeterminate Maturity Deposit Decay Assumption From the Base Case Net Income De

RATE CHANGE +400 +300

it Decay Rate

25%

33%

50%

1 8% 1 5%

l6%

12%

13%

10%

+200

12%

l 1%

9%

+100

7%

7%

6%

0

0

0

BASE

—100

—9%

-9%

—8%

-200

—20%

—l 9%

—17%

-300

—3 1%

—30%

—27%

—400

—44%

~42%

—39%

Source: Community Institution Services, IPS Sendero.

In Exhibit 6.1, we saw that EAR is quite sensitive to our repricing assumption for indeterminate maturity deposits. However, Exhibit 6.2 reveals that EAR is not too sensitive to decay rate assumptions. The low

sensitivity of EAR to indeterminate maturity deposit runoff is simply a reflection of the fact that EAR only looks at short-term rate risk. For Exhibits 6.1 and 6.2, we only examined the sensitivity of 12-month earnings at risk.

EVE is, as we have discussed at length, a long-term measure of rate risk. Not surprisingly, EVE measures of rate risk exposure are much more sensitive to the indeterminate maturity deposit maturity or runoff assumption. This is illustrated in Exhibit 6.3.

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Interest Rate Risk Management

Exhibit 6.3

EVE Sensitivity to Indeterminate Maturity Deposit Decay Assumption

From the Base Case Economic Value of Equity De Rate Chang

+400

sit Decay Rate

25% —15%

33%

50%

—29%

—45%

+300

—9%

—20%

—32%

+200

—3%

—10%

-l9%

+100

2%

—2%

—6%

BASE

0

0

0

—l00

—8%

—4%

1%

—200

—24%

-l 5%

-6%

—300

—39%

—26%

—1 l%

—400

—46%

—30%

—l 3%

Source: Community Institution Services, IPS Sendero.

Like Exhibits 6.1 and 6.2, a complete model of a bank’s IR is used for Exhibit 6.3. In Exhibit 6.3, we merely focus on the impact of a change in the decay rate assumption on the measured rate sensitivity for the bank. In this case, we can see that if prevailing rates fall by 100 basis points, and we assume a 25 percent decay rate, EVE will fall by 8 percent. However, if prevailing rates fall by 100 basis points and we assume a 50 percent indeterminate maturity deposit decay rate, EVE will rise by 1 percent. Notice that EVE is not merely highly sensitive to the indeterminate maturity deposit decay assumption. In addition to a change in the amount of rate risk exposure, the direction of the rate risk exposure changes too! For the bank shown in Exhibit 6.3, the same directional change occurs if rates rise by 100 basis points. In that case, EVE increases by 2 percent if deposits decay at a 25 percent rate, but EVE declines by 6 percent if deposits decay at a 50 percent rate.

Measuring the Rate Risk of Indeterminate Maturity. Administered Rate, and Putable Deposits 2/10

A Summary: The Sensitivity of Measured IRR to Indeterminate Maturity Deposit Assumptions

Three conclusions are very important for understanding the IR measurement:

∙

∙ ∙

acetu'acy

of

Banks of all sizes hold large volumes of liabilities with indeterminate maturities and administered rates. The amount of these holdings is equivalent to 35 percent to 44 percent of total assets.

Measures of earnings at risk from changes in interest rates are highly sensitive to the assumptions for changes in administered rates but not too sensitive to the assumptions for changes in the maturity of these funds. Measures of economic value at risk from changes in interest rates are highly sensitive to the assumptions for changes in the maturity of these ftmds.

ESTIMATING THE MATURITY AND/OR REPRICING OF

INDETERMINATE MATURITY DEPOSITS

The biggest problem faced by IRR analysts using gap analysis, duration analysis, or EVE sensitivity simulation is identifying the maturity of indeterminate maturity deposits. If you use simple gap analysis. you need to know the maturity of these deposits before you can allocate indeterminate maturity deposits into the appropriate maturity buckets. If you use either a duration approach to measuring IRR or an EVE sensitivity simulation, you need to know two types of information. First, you need to know how long the interest expense cash flows will persist at their present levels following a change in prevailing interest rates. Second, you need to know how much the principal is changed by new deposits or withdrawals in response to the rate change to enable you to calculate the present value of these cash flows. In addition, a more accurate application of duration analysis or EVE sensitivity simulation uses separate discount rates for cash flows attributable to different points in time on the yield curve rather than a single discount rate for all cash

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Interest Rate Risk Management

flows. This also requires an estimate of when the principal and interest expense cash flows are expected. The solution is to identify “efi‘ective” maturity dates for the indeterminate maturity deposits. No matter which of the above methods we use to measure interest rate risk, we must use fairly accurate assumptions for the estimated maturity of indeterminate maturity deposits. As we saw earlier in this chapter, a change ofjust six months in the estimated average life for the checking and savings accounts in our Typical Bank example led to a 4—percentage point shift in the measured amount of economic value at risk. And, as we see in Exhibit 6.3, a change from a 25 percent decay rate to a 50 percent decay rate not only resulted in a large change in the measured rate risk for the example bank, it also changed the direction of the measured risk.

Maturity Assumptions Vary Hugely The table shown as Exhibit 6.4 shows decay rates and average lives for indeterminate maturity deposits.

Illustrative data, such as the information shown in Exhibit 6.4, show very material differences in assumptions. Average lives for savings accounts, for example, range from 2.6 years to 6.6 years. In addition, the assumptions used to model the distribution of the runoff vary hugely. Notice, for example, that the 1998 survey shows 9 percent of demand deposits rtmning off in the first year but 20 percent of money market deposits rtmning off in that same year. In contrast, the OTS model assumes that 18 percent of demand deposits and 32 percent of the money market deposits are lost in the first year. (Note that, with some exceptions, the Office of Thrift Supervision (OTS) only requires thrifls with under $1 billion in assets to use their standard model. Other thrifts may use internal models that presumably include internally derived assumptions for the lives of their indeterminate maturity deposits.) The averages used in different sources vary immensely.

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Measuring the Rate Risk of Indeterminate Maturity. Administered Rate, and Putable Deposits 2/10

Exhibit 6.4 Illustrative Indeterminate Maturity Deposit Decay Rates and Average Lives

Decay Rates

Average

Indeterminate

Data Source OTS Model

FDICIA

∙

(.-

∙

305

never

5-10

Lll'e (yrs)

0-1

1-3

J-S

DDA

18%

21%

18%

23%

14%

NOW

31%

36%

17%

13%

2%

1.9

Savir_rgs

14%

23%

17%

25%

22%

4.5

MMDA

32% -

37%

17%

12%

2%

18

DDA

25%

45%

20%

10%

0%

20

Maturity Deposit Tyre

>10

3.5

NOW

0%

60%

20%

20%

0%

2.6

Savings

0%

60%

20%

20%

0%

7.6

MMDA

50%

50%

0%

0%

0%

1.0

DDA

9%

14%

12%

47%

19%

5.3

NOW financial institutions with average assets of Saving!

18%

32%

16%

20%

14%

4.1

16%

29%

12%

16%

28I%

6.6

MMDA

9620

37%

15%

16%

12%

*0

Averages (as of 12198) for 8

about $2 billion

Averaga (as of 12/94) for 10 of the largest U.S. finandal

Savings

2.9

MMDA

2.1

imtitutions

Sam-u The OTS data can: Eon-r tin Ofliee ctThn'll Suprvirion‘a standard model. The FDICIA 305 ml data come from a bank regulatory proponl {or inure-I rate risk Ihl Ins developedin the early 1990: bra met adopted. The 1998 semi: thin are token from arr-trey. For Ill lire-e, true duh are reprinIed hem "An Overview eI‘Corc Depuits.‘ Fred Pocrrmrr. BarkAur/LrabuIIj-mem, Dunbar 19.09, page 7. T1: I991 sample data are taken Iran a confidential survey conducted by the National Asset Liability Marlgarrmt Association, Spring 1995.

Actually, the average data obscure even larger variances. For example, the 1994 survey, as shown in Exhibit 6.4, found that the average life for savings deposits at the 10 banks was 35 months. However, one of those 10 banks was using a 60-month assumption while another used an 8month assumption. Similarly, the 6.6-year average life for savings

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Interest Rate Risk Management

accounts in the 1998 survey included one bank that used a 1.3-year assumption and three using a 12.5-year assumption. The average bank the range of individual bank data has a very high standard deviation data within the average is quite large.

—

An Overview of Quantitative Tools for Calculating Indeterminate Maturity Deposit Runoff Rates and Average Lives

Obviously, no two banks are alike. Differences between banks unquestionably justify major differences in the runofi~ rates and average lives of indeterminate maturity deposits. For example, a bank that maintains high indeterminate maturity deposit rates compared to its competitors and that changes its indeterminate maturity deposit rates promptly when prevailing rates rise, is likely to have a much higher percentage of rate-sensitive deposits in its total indeterminate maturity deposit holdings. Such a bank will consequently have much shorter average lives for its deposits than a bank that holds very low levels of rate-sensitive funds in products with indeterminate maturities. But differences in the business practices of banks do not explain all of the variations in runoff rates and average lives. It is important to note that the assumptions shown in Exhibit 6.4 do not vary because different banks made different subjective estimates. Each of the banks included in the 1994 and 1998 surveys used quantitative methods — not subjective estimates as the basis for their assumptions. Large differences result from the choice of measurement methodologies.

—

So, how do we get accurate assumptions? The task is not easy, but there are tools to help us calculate reasonable estimates. Quite a few methods are available and the most commonly used fall into the frrst three of the four groups summarized below. In the following subsections, we take a more detailed look at these main approaches and many of their

variations.

1. Decay or attrition analysis. Perhaps the oldest (and least valuable) tool for estimating maturities of indeterminate maturity deposits is attrition or decay analysis. This tool has been imported into IRR from the techniques used to value bank branches and branch deposits that are purchased and sold. It is described in the next

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Measuring the Rate Risk of Indeterminate Maturity. Administered Rate, and Putable Deposits 2/10

subsection mainly to illustrate decay concepts that are generally applicable to developing assumptions using other tools. 2. Segmented volume analysis. A second set of tools for estimating the rate sensitivity of indeterminate maturity deposits applies various statistical methods to identify distinct segments of the deposit balances. This technique has many variations. Several are discussed in detail later in this chapter because it is the best tool for rate risk managers who lack access to complex mathematical tools. Indeterminate maturity deposit assumptions derived using this method can be readily calculated using widely available spreadsheet software. A step-by-step process is described later in this chapter. 3. Replicating portfolios. These are statistical methods for matching portfolios with indeterminate maturities to portfolios with known maturities. This approach also has many variations. Several are discussed in detail because this is the most common approach.

4. Highly quantitative modeling. This is a catchall description for a wide range of mathematically based models. Some of these models are deterministic while others are stochastic. All of them can be described as “black boxes" in the sense that the user generally does not understand how the model produces the results it outputs. These tools generally ofi‘er at least two significant advantages. First, by incorporating the impact of a range of internal and external variables such as seasonal variations, changes in prevailing rate levels, the path rates took to get to their etu'rent levels, etc. — they can provide more accurate estimates of indeterminate maturity deposit behavior. Second, these techniques provide separate indeterminate maturity deposit maturity assumptions for different rate environments. At the same time, however, these advanced modeling techniques are not cheap. They require knowledgeable specialists to use and interpret the data as well as a high level of resources to acquire and maintain the models. Accordingly, we will largely ignore these tools.

—

These are not completely incompatible approaches. As we will see, they can be used together.

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2/10 Interest

Rate Risk Management

Method One: Decay or Attrition Analysis

Effective maturity dates can be estimated based on the pace of deposit withdrawals and account closures. Volatility studies have been used by banks for many years to determine effective maturity assumptions. These assumptions are then used in present value analysis to calculate indeterminate maturity deposit values for' deposit purchases, branch acquisitions, and bank acquisitions. Buyers of branches or branch deposits recognize that even though these deposits are liabilities, they have value that arises from the fact that they are liabilities that sometimes have below-market interest costs. Decay analysis is used to determine how long that value persists for the purchased deposits. Decay analysis is simply the statistical analysis of the rate at which deposit volumes fall from attrition. Attrition may be caused by the withdrawal of funds from still-existing accounts or from the closure of accounts. In other words, decay analysis establishes a terminal value for these purchased liabilities.

Decay analysis calculates a percentage that represents the measured attrition rate. For example, a decay analysis might show an annual decay rate of 20 percent for savings accounts. In that case, 20 percent of the bank’s savings account deposits could be assumed to “mature” each year. (Note that this does not mean the entire volume of savings accounts will leave in five years.) Decay rates are always applied to the remaining, undecayed balance. So, in the second year of this example, 20 percent of the remaining balance would decay. This equates tojust 16 percent of the original balance. Analysis of indeterminate maturity deposit attrition has been used by regulators to evaluate the apparent maturity or decay of indeterminate maturity deposits. In Exhibit 6.4, we saw attrition or decay rates developed by banking regulators in the early 19905 and more current rates used by the Office of Thrift Supervision. Calculating Deposit Decay or Attrition

To calculate decay, you must first select a sample of accounts. A statistical tool called a stratified random sample can be used for this purpose. Decay analysis looks at each account individually. Therefore, historical balance data for every account in the sample must be obtained for the entire time period. Ideally, monthly balances are used. Even

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Measuring the Rate Risk of Indeterminate Maturity, Administered Rate. and Putable Deposits 2/ 10

though average monthly balances might be a bit more accurate, these can easily be the balance at the beginning of the month or the end of the month. Exhibit 6.5 illustrates the process for a very simple decay analysis. Exhibit 6.5 Illustration of Simple Decay Analysis

1 Sample of Accounts Percent of Orlglonal Balance Still Retained Afier 12 months 24 months 36 months 48 menu 60 months Openned

i

.

June 2003 June 2004 June 2005 June 2006 June 2007 June 2003 Average

57% 52%

61% 77% 93% 79% 89%

91% 85%

16% 21% 17% 19%

519/. 43%

66%

’

56%

’

18%

5% 4%

7% 6% 3%

7

6%

'

5%

The time period for the attrition study needs to be considered carefully. If the period is too long, historical behavior will affect the data, even if the data are no longer relevant. On the other hand, if the period is too short, it may not be indicative of both rising and falling rate environments. The best idea may be to select a time period that captures the most recent complete cycle — the period from the most recent rate high through the most recent rate low, or vice versa. Once the data are obtained, the rate of decline in the sample account balances can be quickly calculated. This is expressed as an annual percentage of change. However, the rate of change is not the same in every month. The function is not linear. It is curvilinear. In other words, the rate of decrease is much larger in the earlier months and much smaller in the later months. Consequently, we can most clearly see decay rates over time when they are graphed. An example of a decay rate graph is shown in Exhibit 6.6. This is a graphical depiction of the actual but old attrition measurement from the OTS (Accordingly, these are numbers derived from deposits at savings and loan associations.). As you can see, for MMDAS, it shows the deposit balances declining from 100 percent at the beginning of the first month to zero or near zero by the 169th month. This indicates that these

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2/10 Interest Rate Risk

Management

deposits are completely withdrawn in about 14 years. Notice, however, that those money market balances are about 50 percent withdrawn injust about two years. The Exhibit 6.6 curves for transaction and passbook savings accounts depict slightly longer lives for those deposits. The attrition illustrated in Exhibit 6.6 is consistent with the OTS and Federal Reserve numbers mentioned above. Exhibit 6.6 Example Attrition Measurements assess: in

to O 70 I I

I

D In

a I

∙∙

D

− − ∙ raauururumummanmammu m

Decay Analysis Limitations Decay analysis has four inherent characteristics that can, and ofien do, reduce its value for interest rate risk analysis. The first, and perhaps least important, problem is the difficulty in calculating an acctn'ate decay rate. Some calculation problems arise from inconsistent or unavailable historical data. During the time period used in the sample, the bank’s data processing system may have been altered; deposits may have been affected by nonrecuning changes in product features or by the introduction of new products; and nonrecuning events such as mergers, deposit purchases, or changes in competition may have affected deposits. Other calculation inaccuracies result from problems inherent in comparisons of old and new data. The volatility of deposits 5 or 10 years

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Measuring the Rate Risk of Indetemtinate Maturity, Administered Rate. and Putable Deposits 2/10

ago may have been very different from the volatility of deposits in more recent years. And, of course, just because a correlation existed in the past doesn‘t mean that it will accurately predict the future.

A second, and much more significant, problem with decay analysis is that it does not include new activity. While old accounts may experience net withdrawals and eventually be closed, the bank is acquiring new accounts. In other words, decay analysis fails to treat the bank as an ongoing business. This is a key point to keep in mind. By ignoring this concept of ongoing business. decay analysis is essentially producing a “liquidation value” rather than a “going-concem_ value" for these deposits. Representatives of the OTS, which has been relying on decay analysis since the early 19905, explain that decay analysis is appropriate because it captures the indeterminate maturity deposit conditions at a point in time. This analytical approach has some merit for a regulator attempting to measure risk to a deposit insurance fund from the liquidation or forced sale of a troubled financial institution, for example. It is far more difficult to justify for a rate risk analyst attempting to measure an institution’s risk exposure to future interest rate changes. If rates can change in the future, so can new account activity.

The failure to consider new business is significant because, as discussed above, the changes in indeterminate maturity deposit volumes are used in decay analysis to determine effective maturities for the indeterminate maturity deposits. Those effective maturities are, in turn, used to evaluate the IRR of these products — especially in gap, duration, and economic value simulation approaches to assessing IRR. If the effective maturity is determined on the basis of a volume rtmoff that is significantly overstated because it does not reflect new activity, then overall interest rate risk may be significantly misstated. For a liability-sensitive bank, overstatement of deposit runoff will overstate the bank’s rate risk. For an asset-sensitive bank, overstatement of deposit runoff will understate the bank’s rate risk exposure. In other words, if funds in current savings passbook accounts run off in an average of 24, 36, or 48 months but are replaced by new fimds at the same rate, how significant is the average life for the rate risk analysis? We can, in fact, make an incomplete and 2.

David G. Berwick. “Non-Maturity Deposits — Where Do They Fit?" Bank Asset/Liability Management. Vol. 11, No. 7, July 1995. page 2.

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Interest Rate Risk Managegmnt

imperfect argument that for rate risk management purposes, most indeterminate maturity deposits never run off. Actually, neither concept is accurate enough to be usefiil. A reconciliation of these contradictory concepts is presented later in this chapter. A third characteristic of decay analysis is that it is simply inappropriate for floating-rate deposits. In the case of floating-rate assets and liabilities, the rate risk analyst is not concerned with the maturity of the cash flow. It is the time until the next repricing date that is important.

Finally, a fourth problem with decay analysis is that it captures all deposit withdrawals without regard for the cause of those withdrawals. Not all deposit withdrawals are prompted by changes in interest rates. As we discuss later in this chapter, competition, convenience, and other variables have a very large impact on indeterminate maturity deposit voltu‘nes and on changes in those volumes. That fact, by itself, does not reduce the value of decay analysis as a tool for measuring the estimated life of indeterminate maturity deposit balances. Alter all, we need to know the life to calculate the present value, but we can calculate present values without any need to know why the life changes. The problem arises when we also want to calculate the sensitivity of those values to changes in interest rates. For example, we don’t just want to know the economic or market value of savings accounts; we want to know how that value changes as rates rise or fall. For this purpose, it is important to know how much the decay rate and replacement rate are influenced by changes in prevailing rates. We may want to improve the accuracy of our measures of duration or economic value at risk by using a slightly shorter estimated life in a rising rate scenario and a slightly longer estimated life in a falling rate scenario. Furthermore, as we discuss below, we can obtain a more accurate estimate of depositor behavior if we can isolate the customers’ exercise of their put and call options (to make deposits or withdrawals) from the bank’s options to apply rate caps or to adjust how administered rates are changed.

The Influence of Changes in Prevailing Interest Rates on Changes in Deposit Volumes: A Digression IRR analysts should keep in mind that deposit volatility is caused by many factors: interest rates are only one of these factors. Even if

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Measuring the Rate Risk of Indeterminate Maturity, Administered Rate, and Putable Deposits 2/10

historical decay rates are indicative of future runoff, it does not necessarily follow that runofi‘ is caused by changes in interest rates. Runoff results from a variety of causes. Many of those causes have no correlation to changes in prevailing rates.

At first, it may seem counterintuitive to suggest that indeterminate maturity deposit volumes are not closely related to changes in interest rates. Many experts would have us believe that checking and savings account deposits are highly influenced by prevailing interest rates. For example, one knowledgeable commentator wrote that “indeterminate maturity deposit attrition rates are closely tied to the level of interest rates.”3 That conclusion considerably overstates the case, as shown below. In fact, interest rates do influence the volume of core deposits, especially when prevailing market rates of interest rise to exceed the implied caps on indeterminate maturity deposit rates. However, many other variables have equal or greater influence.

In fact, indeterminate maturity deposit volume changes do not always correlate closely with changes in interest rates. This can be seen in Exhibits 6.7, 6.8, and 6.9. These three exhibits are derived from the three curved lines in Exhibit 6.6. In Exhibit 6.7, the attrition rate for checking accounts is modified to show the anticipated efl‘ects of a 200 basis point increase in interest rates and a 200 basis point decrease in interest rates. The same projected rate changes are applied to passbook savings accounts in Exhibit 6.8 and to money market deposit accounts in Exhibit 6.9. Notice that in all three graphs, the changes resulting from those 200 basis point rate changes are relatively insignificant. In fact, they are so insignificant that they are almost impossible to see except in the middle portions of each curve. Deposit volumes have a low correlation to changes in prevailing interest rates alone. That assertion is supported by both a number of logical arguments and empirical evidence like the graphs shown in Exhibits 6.7, 6.8, and 6.9. The simple truth is that significant quantifies of what one might call “interest-sensitive” money are not generally kept in bank indeterminate maturity deposit products. Other higher yielding 3.

Donald G. Simonson, “Back to Gap Basics," United States Banker, November 1991, pages 57-58.

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Interest Rate Risk Management

investment alternatives have previously captured a great deal of these funds. The money kept in bank indeterminate maturity deposit products tends to be maintained in these accounts as a result of depositors‘ preferences for liquidity, safety, or convenience, or to compensate the bank for bank services. The opportunity cost of interest forgone because funds were kept in a comparatively low-rate indeterminate maturity deposit instead of a more interest-sensitive investment does play a role. However, interest rates are only one of a number of factors that affect indeterminate maturity deposit volumes. As one expert observed: Consumers frequently use the financial institution as a safekeeping agent rather than as a conservator of purchasing power. Typically, a bank is chosen as the depository more because of relationship or convenience than because of the interest rate offered on the indeterminate maturity deposit accounts. Therefore, the relationship of the offered rate to the market rate is more tenuous and the resulting estimates of duration much less precise than with liabilities that display a strong relationship to market rate movements.4

A number of these issues are discussed in the next section.

4.

David G. Bemick, “Non-Maturity Deposits — Where Do They Fit?” Bank

Asset/Liability Management, Vol. 11, No.7, July 1995, page 1.

6-18

Measuring the Rate Risk of Indeterminate Maturity, Administered Rate. and Putable Deposits 2110

Exhibit 6.7 Indeterminate Maturity Deposit Volume Changes Plus 200 vs. Minus 200 Transaction Accounts

—

−−

I

II

5

I

I!

U

W

t.

I.

I‘ll

m

an a:

114

all

N

h

Exhibit 6.8 Indeterminate Maturity Deposit Volume Changes Passbook Accounts — Plus 200 vs. Minus 200

I l

'r I O

u

I.

m ‘-

∙ I III

m

6-19

w

8

an m

u

II.

In

2/10

Interest Rate Risk Management

Exhibit 6.9 Core Deposit Volume Changes Money Market Accounts — Plus 200 vs. Minus 200

I.

∙ ∙ ∙∙

∙ ∙∙ I

L

name

∙∙∙ 4

fl

Reasons Why Deposit Balances Are Not Always Rate Sensitive

It is worthwhile to digress from our discussion of estimating indeterminate maturity deposit maturities to consider why these balances are not always sensitive to changes in prevailing rates. We can identify several reasons for this behavior:

factor. Depositors‘ preference for security is an important variable that weakens the correlation between indeterminate maturity deposit volumes and changes in prevailing rates. During the 19805, major banks experiencing credit problems had some reductions in their indeterminate maturity deposit volumes after each ratings downgrade. Clearly, some depositors are concerned about safety. Some banks have found that by segregating savings accounts into passbook and statement savings account groups, they can establish a base of passbook savings that shows little or no change in volume in response to decreases in rate. In fact, empirical evidence shows that a large quantity of deposits in passbook savings can be maintained, and even The safety

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Measuring the Rate Risk of lndetenninate Maturity, Administered Rate, and Putable Deposits 2/10

marginally increased, in spite of rates that are substantially less than prevailing rates for other deposit alternatives. The convenience factor. Depositors’ preference for convenience is evident in other variables that weaken the correlation between indeterminate maturity deposit volumes and prevailing interest rates. Depositors may find it physically convenient to keep their money in a particular bank. Variables influencing physical convenience include the number of bank branches, the location of bank branches, and the hours during which the bank is open for business. Customer service also plays a large role. Branch staffmg levels sufficient to avoid long waits in line and friendly branch staffers who know customers by name are examples. Small community banks have clearly demonstrated an ability to compete that, at least in part, centers on personal relationships with customers. Still another reason customers might keep deposits for convenience rather than interest rates might be package account products that offer additional services to attract and retain deposits. Local market conditions. Local market conditions, especially the degree of market competitiveness, create still other important variables that weaken the correlation between indeterminate maturity deposit volumes and prevailing interest rates. For example, one $150 million bank experienced more than a 30 percent increase in indeterminate maturity deposits over a 12month period during which indeterminate maturity deposit interest rates decreased an average of 18 percent. The obvious reason for this negative correlation is the fact that other financial institutions in the same markets lowered rates by even larger amounts. While this example of a negative correlation between indeterminate maturity deposit volumes and prevailing interest rates is extreme, it highlights the significant influence of local market conditions on volume changes.

Local market competition. The issue of local market competition is probably a key point. Earlier we noted that indeterminate maturity deposit volumes do not have a strong correlation with changes in prevailing interest rates. It may be much more accurate to say that

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Interest Rate Risk Management

indeterminate maturity deposit volumes are sensitive to changes in the relative differences between the rates paid by one bank and the rates paid by its local competitors. In other words, if Bank A pays 4 percent for passbook savings accounts, it may not lose any savings deposits if short-term U.S. Treasury rates move from 5 percent to 6 percent. At the same time, Bank A may lose significant savings deposits if it is paying 4 percent while the bank across the street raises its passbook savings rate from 4 percent to 5 percent. CI

Regulatory restrictions. Regulatory restrictions also afl‘ect indeterminate maturity deposit volumes. Regulations governing transaction accounts limit the alternatives available to depositors who are unwilling or unable to use nonbank financial accounts. As a result, demand, NOW, and MMDA account volumes are less likely to decline as a result of ftmds transferred to higher paying alternatives in high or rising rate environments. Customer relationships. In many small and medium-sized banks, substantial portions of total commercial demand deposits are composed of deposits held by commercial loan customers. Some studies suggest that 8 percent to 12 percent of all bank demand deposits in small and medium-sized banks are held by commercial loan customers. Some of these deposits are maintained with the banks as part of formal compensating balance arrangements to compensate the bank for loans or other services. However, the majority of these deposits are maintained as part of banking relationships that imply, but do not explicitly require, customers to maintain significant deposit balances. The connection between relationship banking and indeterminate maturity deposit stability is evident in the stability or indeterminate maturity deposit levels at a large number of banks that experienced major funding problems in the 19805. It is reasonable to conclude that the same banking ties explain some of the similar indeterminate maturity deposit stability that has been observed during rapidly rising rate environments. Indeterminate maturity deposits may be maintained in the bank by depositors to directly compensate for the use of bank services or just to give business to the bank that lends to the depositor. In either case, the relationship can have a significant

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Measuring the Rate Risk of Indeterminate Maturity, Administered Rate. and Putable Deposits 2/10

stabilizing influence on indeterminate maturity deposit volume —— one that insulates the bank from fluctuations caused by changes in interest rates. Other influences. Some indeterminate maturity deposit fluctuations are caused by seasonal changes. This is especially the case in markets such as agricultural communities. Changes in local market economic conditions, changes in consumer and business confidence, changes in savings or consumption rates, recessions, and recoveries are all additional examples of other variables that have only indirect correlations with changes in prevailing interest rates. Commercial transaction account balances, in particular, can be subject to changes that correlate with business cycles. Even the length of time that an account has been open can correlate with changes in balances. For example, older accounts are sometimes more stable than newer accounts. E]

Absolute level of interest rates. Yet another issue that weakens the correlation between changes in prevailing interest rates and changes in indeterminate maturity deposit volumes is the absolute level of interest rates. Not all changes in prevailing interest rates have the same effect on indeterminate maturity deposit volumes. Consider a series of examples. First, if prevailing rates are below the strike price of the embedded option, a change in prevailing interest rates is unlikely to lead to a change in indeterminate maturity deposit volumes. In other words, if savings accounts have an implied cap of 6 percent, an increase in rates for alternative investments from 4 percent to 5 percent may not induce many rate-sensitive depositors to move their funds as long as the savings rate is similarly increased, perhaps from 3.5 percent to 4.5 percent. Second, if prevailing interest rates are only slightly above the strike price, the difference may not be sufficient to induce many rate-sensitive depositors to move their ftmds. In other words, if rates available on alternative investments rise from 5 percent to 5.5 percent while savings account rates remain at an implied cap of 5 percent, the relatively small 0.5 percent difference may not motivate many customers to move their deposits. Third, if rates available on alternative investments move from near the strike price to a significantly higher level, indeterminate maturity deposit

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Management

volumes are likely to decline. In other words, if rates available on alternative investments rise from 5.5 percent to 7 percent while savings accounts continue to earn 5 percent, many rate-sensitive depositors may be motivated to switch. Finally, if rates on altemative investments rise from a point already well above the rate paid on savings accormts, the additional increase may not stimulate much additional deterioration in indeterminate maturity deposit volumes. In other words, if savings accounts are paying 5 percent while rates available on alternative investments rise from 9 percent to 11 percent, indeterminate maturity deposit volumes might be largely unafl‘ected, since the bulk of the rate-sensitive depositors may have already moved their deposits. All of the above examples illustrate that core deposit volumes may be closely correlated with changes in prevailing interest rates at some rate levels. At the same time, changes in indeterminate maturity deposit volumes may not be closely correlated with changes in prevailing interest rates at other rate levels. The absolute level of rates may make an important difference. The Influence ofthe Exercise of Depositors 'Options on Changes in Deposit Volumes Earlier in this chapter, we discussed how embedded options in bank products work just like exchange-traded options. If we examine how the various options in a single product interact, we can gain more insight into how to estimate the maturity of these products. In the case of checking and savings accounts, bankers give the floor option, which is valuable to the depositor, away for free. However, that option does not have much value, since the floors are quite low. We get the cap option for free from the depositor. This option can be valuable in low but rising rate environments (as it gets close to being “in the money"), in high rate environments (when it is in the money), and in times of volatile rates (when an out-of-the-money option has a better probability of eventually becoming in the money). However, not all depositors permit the bank to benefit from the “free” cap. That single fact may be the key to understanding how to analyze these deposits.

Rate-sensitive customers will use their put option to prevent the bank from benefiting from the free cap on the rate paid when the cap is in the

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Measuring the Rate Risk of Indeterminate Maturity. Administered Rate, and Putable Deposits 2/10

money. In other words, when the bank stops raising savings rates as market rates continue to rise, rate-sensitive customers simply withdraw their ftmds. They buy other, more rate-sensitive bank products — such as certificates of deposit (CDs) or they take their funds out of the bank and purchase alternative investments. When that happens, the bank must replace the lost funding with other, presumably now higher priced, liabilities. On the other hand, customers who are not rate sensitive will not exercise their put option when it is in the money and the bank will, therefore, benefit from that option. It will enjoy low-cost funding from those depositors.

—

The above discussion of savings and checking account options illustrates two points. First, bank products with embedded options have rate sensitivity that must be captured by the rate risk analyst. Second, as the previous example illustrates, not all options are exercised the same way in the same products. As we just saw, in a high-rate environment, one segment of depositors will exercise their put option (the rate-sensitive segment) while another segment will permit the bank to use its cap option. This second point is extremely important. In efl‘ect, a bank has a fixed-rate savings account product (because of the cap) for the non-ratesensitive customers and a floating-rate product with a put for the ratesensitive customers. This is a key insight. One logical conclusion is that we can benefit from evaluating indeterminate maturity deposit portfolios as if they were comprised of different groups or segments rather than considering them as a single portfolio.

So what are the dynamics of checking and savings account balances? What durations or average lives should we use for our rate risk analysis? Is it accurate to rely on the short estimated life projections that result from decay or attrition analysis? Is it accurate to rely on the long estimated lives that result from implicit rate caps? At first glance, it would appear that the regulators prefer the short lives predicted by decay analysis. This is, alter all, the methodology employed by the OTS rate risk model. Furthermore, as we noted in Exhibit 6.4, early proposals for interest rate risk adjustments to risk-based capital requirements included a supervisory model with strict limits, derived fi-om decay analysis, for the lives of indeterminate maturity deposits. The final rule only required internal bank models and did not include a

6-25

2/10 Interest Rate Risk Management

supervisory rate risk model. Nevertheless, those earlier proposals, as well as other published comments from the banking regulators, make it clear that the regulators equate “conservative” rate risk assessments with assumptions for rapid decay of indeterminate maturity deposit balances. Yet it is equally clear that the bank regulators recognize the complexity of estimating indeterminate maturity deposit maturities. The Office of the Comptroller of the Currency (OCC) specifically addressed the fact that static analysis of deposit balance runoff or decay was incomplete. In fact, the OCC lists six specific variables that each bank should consider to estimate the rate sensitivity of these deposits. Those six are:

∙

The bank’s need for funds and its ability to use alternative funding

∙ ∙ ∙

∙ ∙

sources.

The bank’s pricing structure and customer base. The bank’s marketing and strategic plans for its products. The number and type of competitors within the bank’s market.

The general level and trends of market interest rates. Product development and changes

regulation.5

in fmancial

institution

In short, three banking regulators are clearly saying that bankers need to assess a wide number of factors, not just the historical rate of withdrawals, to determine the appropriate assumptions for the maturity of deposits without contractual maturities. SEGIVIENTED VOLUNIE AND REPLICATING PORTFOLIOS

As we are about to explore, risk managers can choose between a variety of segmented volume and replicating portfolio methods. Some of these require only a few, simple statistical tools. Others are far more complex.

5.

Comptroller of the Currency of National Banks. “Interest Rate Risk” booklet in the Comptroller ’s Handbook, June 1997, pages 103-104.

6-26

Measuring the Rate Risk of Indeterminate Maturity, Administered Rate. and Putable Deposits 2/10

In reality, segmented volume analysis is little more than a set of simple ways to understand and apply replicating portfolio analysis. Most banks use one more variations of these approaches. As a general rule, we can say that banks that only want this information for rate risk modeling usually prefer the least complex methods. On the other hand, banks that want to incorporate this information into FTP and performance measurements require more accurate information. These banks oflen employ the most complex replicating portfolio methods. Not surprisingly, banks that calculate estimates of maturities for hedging indeterminate maturity deposits seek highly accurate information. These banks oflen avoid all replicating portfolio approaches and tend to prefer option-based methods.

No matter how complex your replicating portfolio model, never forget that all of these approaches are applying historical data and historical correlations to future risk. As they cliche goes: past performance does not predict future performance. Method Two: Segmented Volume Analysis for Estimating Deposit Maturity

Both the understanding of how bank and customer options are exercised as well as actual studies of deposit account balance changes support the idea of treating indeterminate maturity deposits in separate segments. As we just observed, the application of option concepts to the behavior of checking and savings accounts leads us to conclude that one workable idea is to evaluate indeterminate maturity deposits in separate groups or segments. In general, we might say that the group of nonrate-sensitive customers is those who place frmds with the bank or withdraw funds from the bank for many reasons that have little or nothing to do with the prevailing level of interest rates. These customers are the people and businesses that may choose to keep deposits with a bank based on convenience, relationships, or any one of the factors discussed in the previous section. To the extent that customers in this group withdraw funds or close accounts, the funds are replaced by new deposits and new accounts. The net growth or decrease in the bank’s holdings of these ftmds is mainly a function of variables such as changes in the population near the bank‘s location, changes in competition, advertising, etc. The

6-27

2/10 Interest

Rate Risk Management

first key attribute for this segment of the indeterminate maturity deposit base is that new dollars in these stable segments replace some or all departing dollars. And the second key insight is that regardless of whether the amount of new dollars equal or exceed the amount of departing dollars, for this segment of the indeterminate maturity deposit base, neither the volume trend nor its resulting volatility can be attributed to changes in prevailing interest rates.

Similarly, we might say that, in general, a separate group of rate-. sensitive customers will tend to remove their deposits from the bank when prevailing rates exceed the rates paid by the bank for checking and savings accounts. They will tend to increase deposits to the bank when prevailing rates are not high enough above savings rates to justify the lower return. (Many of these depositors are willing to accept slightly lower rates in exchange for the liquidity, safety, or convenience of checking and savings accounts. They are simply unwilling to accept more than a small reduction in their interest yield in exchange for those benefits.) When the bank wants to retain these funds, it must raise rates when prevailing rates rise. However, since raising rates increases the cost of retaining both the interest-sensitive and the noninterest-sensitive deposits, banks are rarely willing to raise checking or savings rates to retain the interest-sensitive balances. (The rate paid for new deposits is the same as the mean rate paid for all deposits.) Hence, the interestsensitive balances are volatile. The maturity of the interest-sensitive accounts is long in low- and falling-rate environments and short in rising-rate environments.

Treating segments of deposit balances with indeterminate maturities as if they had different maturities is a fairly common technique for IR analysts. Banks using gap analysis simply allocate a portion of their checking and savings deposits as stable, nonrate-sensitive deposits in a very long-term bucket. The other volatile segment of these deposits is slotted into a very short-term bucket. The same idea works well in duration and EVE sensitivity simulation approaches to measuring IRR. In those applications, the nonrate-sensitive component is assumed to have a long duration.

6-28

Measuring the Rate Risk of Indeterminate Maturity. Administered Rate. and Putable Deposits 2110

Using Trend Analysis to Segment Stable and Volatile Indeterminate Maturity Deposit Components — A Simple Application We can apply a statistical tool called regression analysis to split noncontractual deposit balances into stable and rate-sensitive segments. The level of indeterminate maturity deposits over time can be compared to a trend line. This is depicted in Exhibit 6.10. Core deposit volumes above the trend line are considered to be volatile and can be treated as if they were rate sensitive. The levels of deposits below the trend line can be treated as if they were not rate sensitive. As of December 31, 2007, the savings balances for the bank illustrated in Exhibit 6.10 were $119 million. The regression line level on that date was almost $153 million. Therefore, on that date, we might say that the size of the volatile or rate-sensitive segment was $34 million. But since the actual balance is even less, it appears that this is a poor way to define volatile and stable segments. While experience suggests that the stable component should be larger, this apparent relationship seems too large. At best, it seems to lack any margin for error.

Using Trend Analysis to Segment Stable and Volatile Indeterminate Maturity Deposit Components A More SophisticatedApplication

—

We can improve upon the method described as alternative four in the next section by introducing a “margin of error” using a simple statistical tool. This method measures the distribution of indeterminate maturity deposit volumes over time. The concept is that the levels of indeterminate maturity deposit volume that are within one or two standard deviations of the mean volume are stable deposits. Those amounts of indeterminate maturity deposit volumes that exceed the one or two standard deviation threshold are then deemed to be volatile. For example, using the savings account volumes shown in Exhibit 6.10, we can calculate a level that the average or mean volume of savings account deposits for the 12-year period is $113 million. We can also calculate that the volume of savings account balances that is two standard deviations below the mean is $54.3 million. We can then say that roughly 96 percent of the time, this bank’s savings account balances total at least $54.3 million.

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2/10 Interest Rate Risk Management

Exhibit 6.10 Indeterminate Maturity Deposit Trend Analysis in Savings Account Balances In,“

−

mono

mom

∙∙

∙∙

-

Mn

Even though we have now found a way to define stable and volatile with statistical precisions, the result remains unsatisfactory. The amount equal to two standard deviations below the median savings deposit level for the bank in our example is $54.3 million. That is the stable amount of savings deposits when considering 49 quarters of data. But take another look at the graph in Exhibit 6.10. The quarterly levels of savings account deposits are not random. More often than not, the total balance for each quarter is at least slightly higher than the quarter before. This has a huge impact on the analysis. If, for example, we only look at the most recent 10 quarters, then the level equal to two standard deviations below the mean is just over $117 million. In other words, the exact same methodology applied to 49 quarters of data or 10 quarters of data indicates that the “stable” component of savings accounts at this bank is either $54.3 million or $117 million. This is a huge difference and not very useful for IRR analysts.

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Measuring the Rate Risk of Indeterminate Maturity. Administered Rate, and Putable Deposits 2/10

Method Three: Simple Regression Analysis Rate Bond with the Same Rate Sensitivity“

—

Finding a Floating

Regression tools can be applied in more than just the simple trend analysis described above. For example, we can use “Constant Deposit Balances with Simple Econometric Rate Equation” to identify characteristics of deposit balance repricing similar to repricing for a floating rate bond. Consider the analyst who has used the regression capability in third-party sofiware to come up with these coefficients for modeling the deposit rate as a ftmction of the one-month LIBOR rate: Exhibit 6.11 Coefficients for Modeling the Deposit Rate as a Function of l-Month LIBOR Rate Rrgmnmsmm'cs 0951643185 Muliplell 0911078163 115qu Adjrnterlll 091559162 Squire StandadE-m omnssa mentions 58 I

ANOVA

if "_, Retrial Total

|

56 57

Corflidmtr lntnupt lMcth

0011508917

1mm 0041346245

6.

5

2.17505 2145116 1519405

HS 2.17505 383508

F

v

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F

619.13“

HIE-32

Starter-i Enur Nut 72155 4.17267

P-l’rh 4023-11

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0.010“

am

new

outrun

5.84552

0.00515

0.061157

0.043535

0.051157

14.18647

Upper Land“

9.7%

Lam 95.0%

Um: 9.1%

The author wishes to thank Mr. Ardi ‘l'avakol and Dr. Dennis Uyemura for the examples shown in this chapter for methods 3. 5 and 6.

6-31

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Interest Rate Risk Management

Using the data from the table, we would then model the savings portfolio as if it were a long-term floating rate bond. The term can be 20 years or more. The coupon rate on this hypothetical bond will adjust by 4.7 basis points for each 100 basis point change in one-month LIBOR. Note: To add non-interest expenses, add to the intercept and make it more positive. This will give a larger fixed rate component to the instrument. Method Four: Replicating Portfolio Analysis for Estimating Deposit Maturity -— The Most Common Method

The procedure described in the prior paragraphs for finding a floating rate bond with the same rate sensitivity as a savings account portfolio an example of what is known as “replicating portfolio analysis.” Our third method defined a floating rate bond that replicated the rate sensitivity of our selected deposit portfolio. Instead of looking for a single floating rate bond, a much better solution is to find a portfolio of bonds. A more statistically rigorous way to segment deposit balances into stable and volatile components is to find a combination of standard fmancial instruments with known cash flow amounts of interest and principal paid on known dates that behaves like the indeterminate maturity deposit balances. Specifically, this technique fmds a combination of standard financial instruments with rate changes that closely correlate with the rate changes in the selected indeterminate maturity deposits.

This application of replicating portfolio analysis has four steps.

1. Develop historical time series data for each portfolio of indeterminate maturity deposits (NOW, savings, etc.) and for various market rates, such as Treasury note rates. 2. Develop some trial divisions of each deposit portfolio into indeterminate maturity and stable segments. 3. Calculate some blended rates for the sample segments.

4. Use linear regression analysis to identify a securities portfolio that most closely replicates the deposit rate. (Optimization) You need to find a portfolio of market instruments, as illustrated in Exhibit

6-32

Measuring the Rate Risk of Indeterminate Maturity. Administered Rate, and Putable Deposits 2/10

6.12, for which the rate changes correlate with the rate changes in your indeterminate maturity deposit portfolio. From the portfolios with coefficients equal to 1.00, select the one with the highest R2. Exhibit 6.12 Illustration of Simple Portfolio Construction for Replicating Portfolio Analysis

Rate Canstant

SHORT RATE WEIGHT 30 day rate 0 10% 30 day rate 30 day rate 20% 30 day rate 30% 40% 30 day rate 30 day rate 50% 30 day [ale60% 30 day rate 70% 30 day rate 80% 90% 30 day rate 30 day rate 100%,

LONG RATE WEIGHT 100%

3 yea 4 year Syear 6 year 7 var 11year 9 year 10 year 15 year

We‘ hts and I

50%

40%

Rates

Vary

30% 20% 10% 0%

In the Exhibit 6.12 example, we use 11 different long rates and 11 different portfolio weights. This gives us 121 potential portfolios. Short rates are held constant in all 121.

For example, one bank found that a portfolio that consisted of 67.7 percent in 48-month Treasury obligations and 32.3 percent in 3-month CDs experienced the same rate changes as its money market deposit account balances. The behavior of the replicating portfolio mimics the behavior of the indeterminate maturity deposits. An iterative, or repetitive, trial-and-error process is required to find a replicating portfolio that has the necessary high correlation with the indeterminate maturity balances. To keep the correlation high as the indeterminate deposit balances change over time, growth or decay rates must be incorporated. For example, the stable component of the balances may be

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Interest Rate Risk Management

67.7 percent of the portfolio in the first month, but may decrease by 4 percent per year. Combining Segmentation Analysis and Replicating Portfolios Banking literature on estimating indeterminate maturity deposit maturities tends to describe replicating portfolio analysis and segmentation analysis as separate methodologies. This, for example, is true of the “Interest Rate Risk” booklet in the Comptroller’s Handbook.7 However, the first two or three steps in the four-step replicating portfolio method are simply descriptions of the segmentation process described earlier. The replicating portfolio methodology is little more than the application of statistical tools to assign maturities to the identified segments.

The two sets of procedures might be combined in several different variations. One workable set of combined procedures is:

∙ ∙

∙

7.

First, the bank develops historical time series data for each portfolio of indeterminate maturity deposits (NOW, savings, etc.). Both the rates paid and the volume for each portfolio should be included in the time series. It is also necessary to obtain historical time series information for various market rates, such as Treasury note rates, for the same time periods. Second, use regression analysis to find a trend line for the time series of volume changes for each indeterminate maturity deposit portfolio. This can be done without too much trouble, using widely available spreadsheet software. Third, assume that, for each indeterminate maturity deposit portfolio, the volume above the regression line is the volatile component of the portfolio. Assume that the volume below the regression line is the indeterminate maturity segment. (Alternatively, as we discussed earlier in this chapter, you might determine this split using the amount that is one or two standard deviations below the mean.) The end result of this process is the

Comptroller 's Handbook, 1997, pages 107-108.

6-34

Measuring the Rate Risk of Indeterminate Maturity. Administered Rate, and Putable Deposits 2/10

—

indeterminate creation of two sets of volume time series data for each indeterminate maturity deposit maturity and volatile

∙ ∙

type.

—

Fourth, compare the changes in time series of indeterminate maturity deposit volumes to the rate changes for each time series rate changes for market instruments. You can use the correlation tool in standard software for this purpose.

Fifih, select the market instruments, such as Treasury notes of a particular term, for which the rate changes correlate perfectly with the rate changes in your indeterminate maturity deposit portfolio. From the portfolios with coefficients equal to 1.00, select the one with the highest R2.

For example, in the third step, you might determine that 85 percent of your MMDA portfolio was volatile and 15 percent was “indeterminate maturity” or “stable.” Then in the filth step, you might determine that the changes in the volatile portion of your MMDA portfolio most closely correlate with the changes in 3-month Treasury bill rates. At the same time, you might f'md that changes in the stable component most closely correlate with changes in 10-year Treasury note rates. Based on that analysis, you can then use a 3-month maturity for 85 percent of your MMDA portfolio and a lO-year maturity for 15 percent of your MMDA portfolio.

Method Five: Complex Replicating Portfolio Analysis

Replicating portfolio analysis is typically applied to find a mix of proxy instruments rather than a single proxy instrument. To do this, we use “Constant Deposit Balances with Complex Econometric Equations.” What if the analyst had derived the following complex econometric function for the deposit rate?

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Interest Rate Risk Management

Exhibit 6.13 Constant Deposit Balances with Complex Econometric Equations

we!

Given the results shown in Exhibit 6.13, the savings portfolio could be modeled as a long-term, floating rate security. For the floating rate index, specify the regression coefl'icients, capturing the moving average definitions accordingly. Replicating Portfolio: Assuming this rate relationship is true, this instrument has the same cash flow characteristics as the sum of five floating rate bonds with these floating rate indexes:

∙ ∙ ∙ ∙ ∙

The moving average of the 5 year rate

The 2 year rate (a basis swap) The moving average of the 10 year rate

The 1 year rate (a basis swap) The moving average of the 1 year rate

The deposit rate will go to about 8.57 basis points when rates are zero.

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Measuring the Rate Risk of Indeterminate Maturity. Administered Rate, and Putable Deposits 2/10

Method Six: Replicating Portfolio Analysis

—

The Jacobs Method

Many analysts like to restrict the econometric specifications used to a subset of the explanatory variables in Method Four. By restricting the explanatory variables to moving averages, the approach used by Rod Jacobs [1984] can be applied. This approach models the interest rate on the deposit as moving averages because (when balances are constant) it produces an investment strategy that can be implemented without the need for the basis swaps needed in Method Four. With two investment maturities, the Jacobs approach solves for the weights b and c such that:

Estimated Deposit Rate = a + b1 (Moving Average Rate 1) + b2 (Moving Average Rate 2), where bi + b2=1

This approach has some implications that are different from approaches A and B:

∙ ∙

∙ ∙ ∙

If steady state moving average rate 1 and moving average rate 2 are less than -a, then the deposit rate will be negative. The steady state spread between the deposit rate and the weighted average moving average rates will always be equal to a, for all levels of rates (constant absolute spread assumption). The deposit spread to market rates is the same when rates are 20 percent as it is when rates are 2 percent. The full adjustment of the deposit rate to changes in market conditions takes as long as the longest maturity of rate 1 and rate 2.

If rate 1 and rate 2 are swap rates, then the implicit assumption is that the credit risk of the institution does not affect the deposit rate.

The estimated duration of the deposit category can never be negative if both b1 and b2 are positive.

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Interest Rate Risk Management

If both the Jacobs weights are not required to be positive, the following combinations of maturities with the 3-month moving average can be derived using regression analysis in any third party statistical tool exactly as Rod Jacobs did in 1984. Exhibit 6.14 Example Replicating Portfolio Using the Jacobs Method

l-a+b Short Portfolio

+c

whueb+c-lsol-a

Long

Short Portfolio

Portfolio

143%

15% -9% .4

47%

Given the results shown in Exhibit 6.14, the savings portfolio could be modeled as a long term, floating rate security. For the floating rate index, specify the regression coeflicients, capturing the moving average definitions accordingly. Replicating Portfolio: Assuming this rate relationship is true, this instrument has the same cash flow characteristics as the sum of five floating rate bonds with these floating rate indexes:

∙ ∙ ∙

The moving average of the 5 year rate

The moving average of the 3 month rate A bond with the same coupon as the negative 5.807% spread between the replicating portfolio and the deposit rate. The present value of this bond is the present value benefit of the below market rate.

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Measuring the Rate Risk of indeterminate Maturity. Administered Rate. and Putable Deposits 2/10

The deposit rate will go to negative 5.807% when the replicating interest rates are zero. This is a potential area of concern when modeling.

Moving Beyond Replicating Portfolios Earlier in this discussion, we noted that risk managers seeking to hedge indeterminate maturity deposits tend to use option-based approaches rather than replicating portfolio methods. In that discussion, we pointed out that replicating portfolio approaches, in one way or another, all apply historical data to forecast future risk.

Other errors result from deposit product changes. For example, a new indeterminate maturity deposit has no history and therefore can't be assessed with replicating portfolio analysis. Perhaps even more significant is the statistical “noise” of historical changes in deposit volume that were unrelated to changes in market rates. An example is the cannibalization that occurs when customers move funds from one deposit product to a similar deposit product to take advantage of a bank marketing incentive. Method Seven: Structural Models of Aggregate Behavior

Rate risk managers can now take advantage of reduced form/econometric models to evaluate the interest rate and deposit balance sensitivity of depositors. Statistical analysis of historical data is used to divine how depositors have reacted (or not reacted) to changes in financial influences such as rates and rate spreads over time. Both the variables used in the equations and the functional form of the equations are selected from this statistical discovery process. Typical variables identified include rates paid on deposits, spreads between deposit rates and market rates, trend .variables, seasonal factors, and general and local economic data. Some of those models incorporate time lags between changes in market rates and changes in indeterminate maturity deposit rates. Some evaluate the effect of the path that rates took to get to their current levels. For example, the fifih decline in prevailing market rates may have less impact than the first decline. Some models also attempt to incorporate implied caps and floors in indeterminate maturity deposit rate changes.

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2/ 10 Interest Rate Risk

Management

Method Eight: Option Adjusted Spread

Option-adjusted spread methodology can be used to estimate the duration of indeterminate maturity deposit portfolios. These models find a spread or premium between the rates paid by the bank prevailing market rates. Then they combine that information with a term structure model to calculate the rate sensitivity of that premium. A typical OAS process is depicted in Exhibit 6.15 and a typical output is shown in Exhibit 6.16.

It is not too much of an overgeneralimtion to say that only a handful of banks have interest rate risk analysts who can perform these kinds of calculations on their own. For the most part, banks that use such tools have them available as features that are embedded in high-end interest rate risk models. Accordingly, these models really do fit the definition of a black box. Banks with high-end models simply input the historical data and apply the resulting output. Risk managers looking for more information about option modeling for indeterminate maturities may wish to consult the following resources:

∙ ∙

∙

Selvaggio, R. “Using the OAS Methodology to Value and Hedge Commercial Bank Retail Demand Deposit Premiums.” In: Faboui, F., Konishi, A. (Eds), The Handbook of Asset/Liability Management, 1996.

Rigsbee, S. R., Ayaydin, S. S. and Richard, C. A. (1996): Implementing “Value at Risk" in Balance Sheet Management Using the Option-Adjusted Spread Model, in: Fabozzi, F. and Konishi, A. (Eds), The Handbook of Asset/Liability Management, 1996, Chicago.

—

Jarrow, RA. and van Deventer, D. R. (1998): The Arbitrage-free Valuation and Hedging of Demand Deposits and Credit Card Loans, Journal of Banking and Finance, 22, p. 249-272; In a subsequent paper the model has been slightly extended and discussed empirically. Cf. Janosi, T., Jarrow, R. A. and Zullo, F. (1999): An Empirical Analysis of the Jarrow-van Deventer Model for Valuing Non-Maturity Demand Deposits, The Journal of Derivatives, Fall 1999, p. 8-30.

∙ ∙ ∙

Measuring the Rate Risk of Indeterminate Maturity, Administered Rate. and Putable Deposits 2/10

The JvD model is adjusted for sticky rates: O’Brian, James M., “Estimating the Value and Interest Rate Risk of Interest-Bearing Transaction Accounts,” Board of Govemors of the Federal Reserve System, Washington DC, November 2000. The JvD is extended to the general case with simulation in Kalkbrener, M. and Willing, J. (2004): Risk Management of NonMaturing Liabilities, Journal of Banking and Finance, 28, p. 15471568. Marije Elkenbracht and Bert-Jan Nauta apply hedging concepts to modify the JvD model in “Managing Interest Rate Risk for NonMaturity Deposits,” risk.net, November 1, 2007. Exhibit 6.15 Example OAS Process

∙ ∙∙

[Tern Structure

Model

-i[

Rate Model

I

I

+

Value: Model

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Source: Martin M. Bardenhewer, Liquidity Risk Measurement and Management. page 240.

2/10

Interest Rate Risk Management

Exhibit 6.16 Example OAS Cash Flows

I

II

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ll

41

u

1|

M.

M511

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119"

Source: Martin M. Bardenhewer, Liquidity Risk Measurement and Management, page 250.

Estimating Deposit Maturities — A Summary Rate risk managers need to avoid being seduced by a false sense of and not entirely precision. Exhibit 6.17 shows a highly simplified view of the costs versus the benefits for the estimated accurate methods described above. It can be described as “not entirely accurate” because it presumes that accuracy increases with computational complexity. Consider the reliance on historical data as well as how many assumptions are required in some of these methods. Clearly a large error band has to surround the forecasted cash flows. Then consider that the output from OAS models, including the example results shown in Exhibit 6.16, are typically quite similar to the estimates from less mathematically intense methods.

—

—

One of the replicating portfolio methods may be optimal for your bank. The way the tool is used quite often makes a bigger impact than the complexity of the tool.

Measuring the Rate Risk of Indeterminate Maturity. Administered Rate, and Putable Deposits 2/l0

Exhibit 6.17 Comparing Methods for Quantifying Core Deposit Rate Sensitivity Hr

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The various techniques mentioned in the previous subsections are, at best, only fair for approximating the behavior of indeterminate maturity deposits. Among other weaknesses, these methods do not easily account for deposit changes caused by extraneous factors such as new branches or new competitors. In addition, all of these methodologies suffer from the usual weaknesses that result from trying to predict future behavior on the basis of an analysis of historical behavior. Just because a relationship existed in the past does not mean that it will continue. Nevertheless, in spite of their weaknesses, all of these methods lend at least some quantitative support to the obvious conclusion that not all indeterminate maturity deposits are rate sensitive. They can be viewed as workable methods that enable us to model indeterminate maturity deposit behavior with acceptable accuracy. So, what is a reasonable average life for indeterminate maturity deposit products? The answer depends entirely on two issues. One is the unique characteristics of your bank’s situation. This includes competition,

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Interest Rate Risk Manageinent

pricing strategies, customer demographics, and product features. The other determining issue is the methodology that your bank feels is most appropriate for estimating the average life. (In theory, methodology shouldn't be an issue, since all valid methodologies should provide the “correct” answer. However, since all of the tools are estimation processes more than measurement processes, without the hindsight available from checking old forecasts against subsequent changes, we cannot be sure what the correct answer is.) The 1mique combination of those two factors for each financial institution produces a distinctly difl'erent answer for each.

ESTIMATING ADMH‘JISTERED RATES FOR CHECKING AND SAVINGS ACCOUNTS

Estimating the future interest rates for indeterminate maturity deposits is just as difficult as estimating their maturity —— and just as important. In fact, for rate risk analysts using income simulations to measure earnings at risk, estimating rates for administered-rate products is the biggest problem associated with indeterminate maturity deposit balances. Less obviously, indeterminate maturity deposit rates are a major issue for users of duration analysis and economic value simulation. (This is true because measures of economic value at risk include the present value of the interest expense cash flow streams. Of course, this is not as material as the estimates of the duration or life of those deposits.) The rates that the bank expects to pay for indeterminate maturity deposit balances in the future, under all of the rate scenarios examined, affect both earnings at risk and economic value at risk. It is essential to understand that administered-rate deposits are neither fixed-rate nor floating-rate products. If administered rates behaved like floating rates, we could ignore the entire question of estimated lives for indeterminate maturity deposits. We would not care about the lives in that case. We would only care about the time until the first repricing. On the other hand, if administered rates behaved like fixed rates, we would only care about the estimated lives and the current rates. Obviously, neither case is completely accurate. Administered-rate products have both fixed- and floating-rate characteristics. Thus, we need to know more facts than just the current rate and the estimated life.

Measuring the Rate Risk of Indeterminate Maturity, Administered Rate, and Putable Deposits 2/10

Five Administered-Rate Variables To understand and therefore estimate the behavior of administered rates, we need to understand five different variables. These are the caps and floors on administered rates, the time lags, the relative volatilities (called betas), the asymmetrical behavior of the rates, and the path-dependent behavior of the rates. We must use fairly accurate assumptions for all the variables. Each of these five variables is considered in the following paragraphs.

Caps and Floors We have already observed that checking and savings accounts include bank options to cap the rates paid for these funds. Historical experience has indicated that even though rates available from other financial instruments may rise to levels well above 10 percent, the rates paid for checking and savings accounts rarely rise above 5 percent and almost never exceed 7 percent. An AL manager for one of the largest U.S. banks commented that he viewed savings accounts as floating-rate liabilities with a 5 percent cap. His assumed cap reflects how bank managers have exercised their noncontractual option since regulatory limits on these rates were eliminated. While these implied caps may not persist in future rate cycles, they have unquestionably existed in the past.

For some banks, explicit caps or floors must also be reflected. Occasionally, indeterminate maturity deposit products have explicit rate caps or floors. For example, one bank offers floating-rate MMDA deposits with a guaranteed floor. Since rates paid for funds are never going to be negative, a floor of zero is also relevant in IR simulation models.

Contractual as well as noncontractual options affect the sensitivity of the interest rates paid on administered-rate indeterminate maturity deposit products. Time Lag:

Time lags are known to exist between changes in prevailing interest rates and changes in the rates offered on bank indeterminate maturity deposit products. Almost all banks are able to employ pricing strategies for

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Interest Rate Risk Management

indeterminate maturity deposits that economists refer to as “sticky.” Banks are able to change the rates paid on their administered-rate deposit products afier rates for money market instruments have already changed. This behavior reduces the rate sensitivity of core deposit liabilities. Beta

One of the most distinctive characteristics of administered rates paid on indeterminate maturity deposit balances is that they are not as sensitive to changes as rates paid on money market financial instruments. In other words, administered rates may be rate sensitive, but they are relatively less rate sensitive than other rates. The changes are muted. Technically, or low beta we describe this by saying that they have low betas coefficients. This concept can be seen in Exhibits 6.18 and 6.19. For the analysis shown in Exhibit 6.19, the three-month U.S. Treasury bill rate represents prevailing interest rates. Changes in other administered-rate instruments are measured against the selected proxy for “prevailing” rates. Money market rates, for example, changed only 31 percent as much as the benchmark for prevailing rates in that analysis. Similarly, the author of the analysis shown in Exhibit 6.20 used the prime rate as the benchmark proxy for prevailing rates. In that analysis, changes in NOW and savings account rates were only 25 and 50 percent, respectively, of the changes in the benchmark rate. Both Exhibits 6.19 and 6.20 are sensitivity analyses. Both show that indeterminate maturity deposit interest rates have low betas. They are not very sensitive to changes in prevailing interest rates. Notice, however, that core deposits are more sensitive to falling rates (Exhibit 6.20) than to rising rates (Exhibit 6.19).

—

Measuring the Rate Risk of Indeterminate Maturity. Administered Rate. and Putable Deposits 2/10

Exhibit 6.18 Indeterminate Maturity Deposit Rate Correlation to Treasury Bill Rates Worksheet (Illustrated for a Year in Which Prevailing Rates Rose)

RATE Three-month T-bill NOW accounts SavingLaccormls Fixed-rate [RM

MMDAs

As or 6!Int I

As or 513 1IX2

CHANGE

6.49% 5.25% 5.50% 7.50% 5.40%

3.40%

+191 0 0 +50 +60

5.25% 5.50% 8.00% 6.00%

(hp)

∙ ∙CHANGE vs. T-BILL

100.00% 0.00% 0.00% 26.18% 31.41%

Exhibit 6.19 Indeterminate Maturity Deposit Rate Correlation to Prime Rate Worksheet

(Illustrated for a Year in Which Prevailing Rates Fell) CHANGE (hp)

.fit CHANGE VS. Parr":

6!] W1

AS OF

AS OF are/v2

Prime

8.50%

7.75%

-100

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NOW acacia-its

250%

7.25%

—25

25%

Passbook savings

4.00%

3.50%

—50

50%

Statement saving

4.50%

4.00%

-50

‘35

MMDA:

5.75%

4.75%

.100

∞∙∙∕∙

RATE

Administered Rate Sensitivity Summary

Exhibit 6.20 provides a slightly difl‘erent view of the same issues discussed in the prior paragraphs. This graph shows the 15-year trend for three series of interest rates. Two of the series, 6-month LIBOR and 2year constant maturity Treasuries, are market rates. The third series, the Ilth District Cost of Funds (COFI) index is a reflection of average deposit rates paid by thrift institutions on the West coast of the United States. (Note that the COFI index includes CDs and is therefore not

2/10

Interest Rate Risk Management

entirely consistent with some of the indeterminate maturity product examples discussed elsewhere in this chapter.) Exhibit 6.20 Comparative Rate Volatility more“ Ram

Comparative Rota Volatility

it

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∏∙

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fis‘fs’sfa‘ffw‘ffw‘ffa’fflfiffi-é’cfs’ Notice how the deposit index shown in Exhibit 6.20 rises and fall less titan the changes in the market rates. The trend in the Ilth district COFI is muted. When market rates fell in 1992 and 1993, deposit rates fell by less. When market rates rose in 1994, deposit rates rose by much less. Deposit rates have been less sensitive over the entire l7-year period and particularly insensitive for the most recent five years. The deposit rate index clearly has a lower beta coefficient than the two market indexes. Also notice that the changes in deposit index shown in Exhibit 6.20 clearly lag the changes in the both the 6-month and 2-year market indices. This is most clearly seen in the portion of the graph showing market rate increases in 1987, 1994, and 1999.

Measuring the Rate Risk of Indeterminate Manuity, Administered Rate, and Putable Deposits 2/10

From the examples shown above, it is clear that even if a change in prevailing interest rates led to an immediate change in the rates paid for indeterminate maturity deposits, the amount of the two groups of changes (the change in prevailing market rates and the changes in indeterminate maturity deposit rates) will almost certainly be materially different. This conclusion is supported by more sophisticated studies. For example, one analysis of money market deposit accounts from 1986 to 1989 showed that the rates paid on those accounts had only a 0.32 coefficient of correlation with rates paid on six-month certificates of deposit during the same period.a In this analysis, the interest rates paid on six-month certificates of deposit serve as the proxy for prevailing interest rates. The 0.32 coefi‘rcient of correlation found for money market deposits means that less than one-third of the changes in MMDA rates during the period covered by that study could be attributable to changes in prevailing rates. The other two-thirds of the changes in money market rates during that three-year period were caused by other factors. It is theorized that growth in the economic region from which the deposits are drawn probably explains more of the changes in deposit volumes than changes in rates paid to attract or retain those deposits. In any case, quite a bit of evidence, including the studies shown in Exhibits 6.18 and 6.19 as well as the MMDA study just described, indicates that indeterminate maturity deposit rates are far less volatile than prevailing rates for money market instruments such as Treasury bills. The low rate sensitivity of indeterminate maturity deposits may reflect the implied caps and the time lags discussed earlier. In addition, the low volatility of administered rates almost certainly reflects a phenomenon called “dampening.” This means that administered rates are deliberately managed to be less volatile. Dampening is evident in both rising and falling rate environments. Reports from various banks, such as the bank used for Exhibits 6.18 and 6.19, also indicate that the rates paid on bank indeterminate maturity deposits have become even less rate sensitive in recent years.

8.

Frank J. Fabbozzi and Atsuo Konishi, Asset/Liabilioz Management (Chicago. Probus Publishing Co., 1991), page 140.

2/10 Interest Rate Risk Management

Obviously, rate relationships vary from bank to bank and over time. Just as obviously, when prevailing interest rates change, indeterminate maturity deposit rates only change by a fraction of the amount of change in the prevailing rates if they change at all. Regardless of what interest rate risk management system is used, the magnitude of interest rate risk cannot be accurately assessed unless the low sensitivity of indeterminate maturity deposit rates to changes in prevailing money market rates is captured. As a practical matter, this is easy to do in income simulation models. Most gap analysis completely fails to capture these relationships; however, it can be done by using beta-adjusted gap analysis. Duration or economic value of equity sensitivity simulations can be manipulated to reflect betas. One practitioner reports adjusting the durations of assets and liabilities to reflect betas. He does this by multiplying the duration by the reciprocal of the beta — 1 divided by the beta.9 As we saw in Chapter 3, betas can also be incorporated in gap analysis by using betaadjusted gap analysis. Other gap approaches do not capture this important variable.

—

Asymmetrical Rate Changes

The relative rate sensitivities shown in Exhibits 6.18 and 6.19 are not equal in both rising and falling interest rate environments. In reality, administered rates for indeterminate maturity deposits often are more sensitive in falling rate environments and less sensitive in rising rate environments. For example, savings account rates may fall by amounts equal to 60 percent of the declines in Treasury rates but may only rise by 30 percent of the increases in Treasury rates. It is not just the size of rate changes that is asymmetrical. The time lags are not symmetrical either. Instead, in declining rate environments, the timing of indeterminate maturity deposit rate reductions has tended to closely follow the timing of decreases in the prime rate, even when the magnitude of the changes has been much less. Conversely, in rising rate environments, the timing of indeterminate maturity deposit rate increases has tended to lag behind the timing of increases in the prime rate. Lags in

9.

J. Kimball Hobbs, in correspondence with the author, September 6, I995.

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Measuring the Rate Risk of lndetemrinate Maturity. Administered Rate, and Putable Deposits 2/10

deposit rates are short when rates are falling and long when rates are rising.

Path Dependency ofAdministered Rates Administered rates paid on indeterminate maturity deposits are not just slow to change and do not simply change by some fraction of the change in market rates. The changes in administered rates are also pathdependent. This means that the change also depends on previous changes. While this may sound obtuse, it really is simple. Consider a real example. In 1994, the Federal Reserve raised short-term interest rates on six occasions. During that year, most banks did not increase the rates paid on savings passbooks at all. (This behavior probably reflects lags, low betas, and asymmetrical changes.) This no-change-in-rates path of savings rates during a period when prevailing money market rates increased six times means that savings rates were more likely to go up when prevailing rates rose the next time. (Actually, the seventh Federal Reserve change in that series was a decrease in rates, so the example is not perfect.) On the other hand, if savings rates have recently been increased, they will probably be less sensitive to the next change in prevailing rates. Dealing with Administered Rates

Not all rate risk managers are willing or able to reflect all of the above variables affecting administered rates. Sometimes, data are simply not available. More often, it is not cost-effective to estimate the impact of those variables. The time and effort necessary to estimate lags or betas may, for example, not be worth a marginal increase in the accuracy of the measured rate risk exposure. The institution‘s choice of rate risk measurement methods also has a bearing on how it estimates changes in administered rates. Gap analysis, for example, cannot be used to reflect rate caps unless a separate gap report is used for each rate scenario. In that case, deposit balances may be shown in a long bucket for an analysis prepared when prevailing rates are expected to equal or exceed the cap. On the other hand, deposit balances would be shown in a short gap bucket for an analysis prepared when prevailing rates are below the implied cap. The lags in administered rate changes might be reflected in whether rate-sensitive 6-51

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Interest Rate Risk Management

balances are shown as immediately repriceable or repriceable in a slightly longer bucket. Relatively low rate sensitivity can, as discussed in Chapter 3, be reflected if the bank uses beta-adjusted gap analysis.

Implied caps, lags, asymmetrical changes, betas, and path-dependent rate changes can all be incorporated into income simulations. They may be reflected in a number of separate assumptions for each administered-rate product. More ofien, however, banks just use a single rate change assumption for each group of balances modeled. In that case, the single rate assumption for each balance category can be tailored to include the impact of one or more of these five administered rate variables. For example, the lags and the betas may be reflected in an assumption that savings rates will rise from 3 percent to 3.5 percent one month after short-term CD rates rise from 4 percent to 6 percent. Even though income simulations can incorporate the impact of those five variables on administered rate changes, the time horizons make the effort especially hard to justify. Most income simulations, as discussed in Chapter 4, use a one-year time horizon. The measured amount of income at risk in a one-year period is probably not much different if we assume symmetrical changes in administered rates or asymmetrical changes. The other four-administered rate variables also have arguably small impacts on the measured quantity of income at risk. If that is the case, the time and effort required to quantify these effects is simply not worth the trouble. For this reason, most banks, especially small and medium-sized banks, rely on very rough estimates of the caps, lags, and other variables, like the CD assumption used as an example in the previous paragraph. Duration and economic value of equity sensitivity simulations can reflect caps by treating a stable segment of the deposit balances as if it had a different maturity than a rate-sensitive segment of those balances. (This was discussed earlier in the chapter.) Present value calculations can also be adjusted to incorporate smaller interest rate change assumptions than any given assumed change in prevailing interest rates to reflect lower betas for these rates. However, that type of detailed account-specific adjustment to discount rates or product coupon rates is seldom made.

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Measuring the Rate Risk of Indeterminate Maturity, Administered Rate, and Putable Deposits 2/10

CERTIFICATES 0F DEPOSIT At first glance, certificates of deposit would appear to be problem-free balances for rate risk analysis. They have defined rates and defined maturities. Indeed, they are far easier to evaluate than checking and savings accounts. However, CDs do present rate risk managers with one problem that merits discussion. Rate risk analysts must be careful not to underestimate the tendency of indeterminate maturity deposit customers to make changes in existing deposits in response to changes in prevailing interest rates. When rates rise significantly, depositors redeem CD5 prior to maturity. Often these funds are simply reinvested in new CDs at higher rates. As we discussed in Chapter 2, customers’ options to redeem CDs are a form of put option that the bank sells or gives away with the CD. Banks usually do impose a penalty for the early redemption of CDs. The problem is that the penalty is too small. Consider an example. Suppose that the interest rate for two-year CDs is 4 percent today but will be 4.60 percent in three months. Further assume that the bank charges a penalty for early redemption that is equal to three months' interest earnings. Depositor A invests $10,000 in a two-year CD that pays 4 percent and holds that CD for the full two-year term. The rate compounds monthly. Over the 24-month period of that investment, depositor A earns $831.42. At the same time, depositor B also invests $10,000 in a two-year 4 percent CD. However, depositor B redeems her 4 percent CD after three months and reinvests the $10,000 in a new two-year CD with a 4.60 percent rate. For the first three months, depositor B earns no interest at all, since she elected to incur the prepayment penalty for early redemption of her 4 percent CD. For the next 21 months, depositor B earns $836.62 on her 4.60 percent CD. Thus over the original two-year period, depositor A earns $831.42 while depositor B earns $836.62, even after incurring the penalty for early redemption. The 60 basis point increase in rates in this example more than ofl‘sets the penalty for early

redemption.

When rates fall or do not increase very much, as was the case in the late 19803 and early 19905, bank IRR managers tend to focus on loan prepayments. They pay far less attention to CD redemptions. However,

6-53

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Interest Rate Risk MarEgement

when rates rise, especially when they rise rapidly, the unpredictable cash flows from CD redemptions can also require attention.

Like checking accounts, savings accounts, and loans, early withdrawals of CDs are prompted by many different reasons. One study listed the following five:

∙ ∙

∙

∙ ∙

Death of the account holder Perceived superior investment alternatives (equities, purchase business)

of

Payment of medical bills for prolonged illness

Unplanned expenses (weddings, return to college) Increase in interest rates on new CDs10

The obvious question is how much of CD balance attrition the IRR analyst can attribute to early withdrawals by depositors seeking to reinvest their CD balances in higher yield investments. (From a rate risk point of view, we don’t care whether the depositor reinvests in a new CD at our bank or in an instrument not issued by our bank. In either case, a new bank liability, at the currently prevailing rates for the time of withdrawal, has to be incurred to replace the funds withdrawn from the CD.) Rate risk analysts can estimate the interest rate sensitivity of CD balances by comparing early withdrawals to rate changes. Early withdrawals can be quantified by reviewing balance changes for similar groups of CDs. For example, we can look at the change in balance for all of the two-year CDs issued in June of a particular year. How much of those balances remain outstanding 3, 6, 12, 18, and 24 months later? One bank reported finding that balances for three-year CDs fell by 38 percent over their three-year term.ll Of course, the attrition rate that you measure 10. Alan Kolosna and Joel Rosenberg, “In Search of Historical Deposit Decay Rates,” Bank Asset/Liability Management Newsletter, October 1997, page 6. 11. Alan Kolosna and Joel Rosenberg, “In Search of Historical Deposit Decay Rates,“ Bank Asset/Liability Management Newsletter, October 1997. page 6.

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Meastn'ing the Rate Risk of Indeterminate Maturity. Administered Rate, and Putable Deposits 2/10

for a period when prevailing rates rise will be quite different from the rate you measure for a previous period when rates fell or stayed relatively unchanged. When you evaluate the rate sensitivity of CD balances, keep in mind that you don’t want to compare the change in CD balances with the change in prevailing interest rates. Instead, focus on the change in the spread between CD rates and prevailing interest rates. For example, if we issued two-year CDs last June with an average rate of 5 percent, and if two-year Treasury rates last June averaged 5.25 percent, the initial spread was negative 25 basis points. If, six months later, Treasury rates rise to 5.75 percent, the spread changes to negative 75 basis points.

The study mentioned earlier in this discussion found that for every 100 basis point increase in prevailing interest rates, three-year CD balances would fall by 25 percent. While measures like this are helpful, rate risk analysts should consider three relevant issues that complicate the analysis: 1. In a decay analysis of CD balances, we compare the change in the balance to the change in spread as described above. The question is: What term or duration should we look at for determining the spread? For example, suppose we are looking at the decline in balances for two-year CDs six months afier they are issued. At that point, those CDs have remaining terms of 18 months. If prevailing rates have risen since the CDs were issued, some depositors may redeem their CDs to reinvest in a new instrument. That, of course, is the point of this analysis.

But should we assume that these depositors will always reinvest in a new two-year instrument? Or, should we assume that those depositors will reinvest in a new instrument with a duration similar to the remaining life of the CD that they redeem? Your choice of answers makes a big difference. If, for example, you assume that depositors wish to receive their money at or near the original maturity date, then you will be evaluating the spread between the CD rate and rates for money market instruments of decreasing term. For example, if two-year CD rates were 5.00 percent six months ago, we would compare that rate to the yield available from lS-month Treasury securities to determine today’s spread.

6— 49‘

− ∙− current coupon yield +12 months

3%

torwarfl

29. 13

s121824303642465‘60667278849096102109116120

Months

Unfortunately, the implied forwards are not accurate predictors of future interest rates. The yield curve ofien, but certainly not always, provides an accurate prediction of the long-term direction of interest rate changes. However, it is a notoriously inaccurate predictor of short-term interest rate trends.lo Moreover, it is a poor indicator of the amount and the timing of interest rate changes. Implied forward rates frequently overestimate the size of future rate increases. This is probably because many other factors besides the slope of the current yield curve influence future interest rates. On the other hand, implied forwards are a much more objective forecasting tool than the opinions of economists or bankers. Sometimes it is useful to use the forecasted rates from implied forwards in addition to other rate forecasts. In other words, this is a good way to determine an amount of expected interest rate change that can be used to measure the size of the bank‘s IRR exposure, as long as it is not the only approach used.

lO. Marcia L. Stigum and Rene 0. Branch, Managing Bank Assets and Liabilities: Strategies for Risk Control and Profit. (Homewood IL: Dow Jones-Irwin, 1983), page 265.

8-22

Rate Changes: Deterministic Scenarios and Stochastic Models 10/08

More importantly, in the context of this discussion of term structure models, implied forward rates provide only a single view or scenario of what rates may be in the future.

You don’t have to use VaR to employ historical rate volatility information as an objective source for forecasting future interest rate changes. We can use historical rate changes as a quick and easy tool for approximating reasonable projections for future rate changes. This can be done by examining the maximum rate movement fi'om recent cyclical rate peaks to recent cyclical rate lows. Since World 'War II, the U.S. economy has tended to have three-year to six-year economic cycles. Rates tend to peak near the end of recoveries and to trough near the end of recessions. Unfortunately, there tends to be considerable variation in both the size and the length of these cycles. Thus, simply examining the size of cyclical rate changes is not a very good way to estimate future rate changes. A more rigorous analysis of historical rate movements can, however, be quite useful. Statistical analysis of the interest rate changes during the defined period can be used to detennine how much that selected rate can be expected to move based on the rates' previous volatility. This analysis can also tell us something about the unusually large, and therefore extremely risky, rate changes that might occur.

To quantify the amount of volatility that occurred in the defined period, we want to look at a measure called the standard deviation. The standard deviation is a measure of how widely the observed data vary from the average. We know that a rate change that is equal to one standard deviation above and below the average will be equal to approximately 66 percent of the rate changes that occurred during the period. We also know that a rate change equal to two standard deviations above or below the average rate change will be equal to approximately 96 percent of the rate changes that occurred during the period. The Board of Governors of the Federal Reserve System published an analysis of historical interest rate volatility from March 1978 to December 1992. It used such a long period of time ∙−− nearly 15 years in its analysis to include several periods of increasing and decreasing rates. Using the average rate for constant maturity Treasury securities during the fourth quarter of 1992 to represent prevailing rates, it

—

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lO/08 Interest Rate Risk Management

determined that a 200 basis point change in rates would cover about two standard deviations of annual changes in market rates.11 In other words, if previous interest rate changes are representative of future changes, we could use an assumption of a 200 basis point change in interest rates per year in our IRR analysis. We could expect that that amount of rate change would equal or exceed 96 percent of the actual rate changes that occur. Not surprisingly, interest rates do not change as much in shorter time periods. A 100 basis point assumption would. capture 66 percent of the quarterly changes. Management could perform its own analysis of historical rate volatility or use a published analysis. Management could then decide to consider the effects of a one standard deviation change, a two standard deviation change, an even greater change, or more than one such change.

For example, a bank that decides to model the efi‘ects of a 100 basis point change is really deciding that it is concemed about the biggest rate

changes that occur about 66 percent of the time and not concerned about larger, less likely, rate changes. Similarly, a bank that decides to model the effects of a 200 basis point rate change is really deciding that it is concerned about the biggest rate changes that occur about 96 percent of the time and not concerned about larger, less likely, rate changes (as long as two standard deviations are roughly equivalent to a 200 basis point rate change). Clearly, the bank deciding to manage its exposure to changes as big as 200 basis points is far more conservative than the bank choosing to manage its exposure to 100 basis point changes. The first bank is protecting itself against about 96 percent of all changes, while the second is protecting itself against only about 66 percent of all changes. Exhibit 8.10 illustrates a distribution of rate changes. In this illustration, which has been oversimplified by smoothing the curve, by making it symmetrical, and by rounding 011‘ the standard deviation, there are an equal number of rate increases and rate decreases. The illustration shows that a change of plus or minus 75 basis points equals a change of plus or minus one standard deviation from the mean. A change of plus or minus 150 basis points equals a change of plus or minus two standard ll. Risk-Based Capital Standards: Interest Rate Risk. Notice of Proposed Rule Making, Joint Interagency Policy Statement, September 14, 1993, page 25.

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Rate Changes: Detemrinistic Scenarios and Stochastic Models lO/OB

deviations from the mean. Thus, the managers of this bank could elect to manage their exposure to adverse consequences from changes as big as 150 basis points, with the knowledge that such a decision would cover about 96 percent of all rate changes.

Exhibit 8.10

Distribution of Rate Changes by Size (period of low volatility) Nunosrot Rae Chews

\

16

14 12 -

_

1O 8

6

_

4

∙

2 O

−

−

+1

+2 -3)3

-230

∙ ∞

↓

0

919 at Rae Cranes

100

\ 2CD

3(1)

400

Unfortunately, it is extremely important for IRR analysts to use this approach with caution. We could use the most probable rate change to determine the amount of our exposure to that change in prevailing interest rates. However, this approach has two significant problems. First, the size of future changes in interest rates will probably not be the same as past changes in interest rates. They may not even be similar. Furthermore, not only the magnitude, but the frequency of rate changes varies over time. For example, during one five-year period, the annual rate changes may all be small, may all be large, or may be a mix of small and large changes. Similarly, one five-year period may see many rate changes, while another may see only a few. Both the size and the distribution of rate changes for any prior period are unlikely to be the same as the size and distribution of future rate changes. Interest rate

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volatility in prior periods is such a poor predictor of future rate changes that traders do not rely on this type of analysis.

In this context, bank IRR analysts need to be concerned that historical volatilities for one time period may be smaller than current or funn'e rate volatility. For example, for One period of time, the Federal Reserve study cited above found that a 200 basis point change in rates was roughly equivalent to a change of two standard deviations. That relationship may be materially different in the future. This problem can be seen in Exhibit 8.11. (Both curves in this exhibit have been smoothed and made symmetrical for purposes of illustration.) Exhibit 8.11 Normal and Fat-Tailed Distributions of Rate Changes Nunbor olnato Chmoos

I8

∙ 12'

400

400

.200

∙ ∞

Size ol Rue Chains

—— Distribution ot Rate Change: with Low Volafillty - - - - Distribution 01 Rate Changes with Higher Volatlllty

The taller curve in Exhibit 8.11 illustrates a hypothetical distribution of rate changes that has fewer very large increases and decreases in rates. It has a smaller number of rate changes greater than plus 150 basis points or minus 150 basis points. On the other hand, it has a larger number of rate changes that fall between minus 125 basis points and plus 125 basis points. The opposite is true for the shorter curve shown in Exhibit 8.11. Both curves illustrate exactly the same number of rate changes.

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Rate Changes: Deterministic Scenarios and Stochastic Models 10/08

However, the rate changes for the period illustrated by the shorter curve include more very large increases and decreases. It is these extremes that should be the focus of our attention. The shorter curve in this exhibit is what is called a “fat-tailed” distribution. It has more events at both tail ends of the curve. The following example may help clarify this issue. Suppose that a bank analyzes historical rate volatility and finds a pattern similar to the one illustrated by the taller curve in Exhibit 8.11. As noted above, this financial institution’s senior management has decided to manage its exposure to changes in rates of plus or minus 150 basis points. It made that decision because those changes are plus and minus two standard deviations fi'om the mean and therefore encompass 96 percent of all rate changes. Obviously, only 4 percent of all rate changes can be expected to be larger. Then suppose that during subsequent years, rates become more volatile, as depicted by the shorter curve in Exhibit 8.11. In that case, two standard deviations are closer to a change of plus or minus 200 basis points. (For both distributions, the standard deviations have been rounded to the nearest 50 basis points for purposes of illustration.) Thus, if the bank manages its exposure to changes of plus or minus 150 basis points, it will actually have much more risk than it expects. It will be exposed to the fatter tails in the more volatile rate environment and will therefore be exposed to rate changes larger than its 150 basis point threshold much more ofien than the 4 percent it expected from its analysis of the historical volatility. Second, the analysis assumes that all rates move by the same amounts. (If interest rates for all maturities change by the same amounts, we call that a “parallel shift in the yield curve”) A change in prevailing interest rates that is instantaneous and that also afl‘ects all maturities by equal amounts is doubly improbable. This is a highly improbable assumption and is discussed in more detail below. (The principal components tool, discussed later in this chapter, is an application of statistical analysis to historical rate changes that captures non-parallel rate changes.)

In spite of the obvious deficiencies in using historical analysis of interest rate volatility to predict future rate changes, this approach is not a complete waste of time. It offers the advantage of providing an objective

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measure of how much rate change should be used to calculate a change in the target measrn'ement of IR exposure.

Introduction to Stochastic Term Structure Models12

Instead of making assumptions about future rates, we can use stochastic models to analyze a specific financial instrument, a portfolio, or the whole bank by making an assumption about the process by which rates will move in the future. In effect, a large number of different, hypothetical future rates are selected mathematically. This is the premise behind Monte Carlo simulations and many of the advanced term structure models discussed in the following sections. (Stochastic simulation is ofien called Monte Carlo but this is not completely accurate. As we will discuss, Monte Carlo simulation is just one type of stochastic simulation.) These methods can model the effects of hundreds, even thousands, of different future interest rates. Once we have made an assumption about the random stochastic process by which rates move, we can then derive the probability distribution of interest rates at any point in the future. Without this kind of assumption, we can’t analyze interest rate risk effectively. The process is depicted in Exhibit 8.12. Exhibit 8.12 Steps for Stochastic Evaluation Fowvard Market Interest Rates Yield, Discount, and Forward Curve

Smoothing

Interest Rate

FOI'Wflfd Market Dynamics

Interest Rate Term Structure Models

Position Valuation

PositionSpecific Valuation

Models

12. Major portions of this section have been adapted from Kcuji lmai and Donald R. van Deventer, Financial Risk Mathematics: Applications to Banking, Investment Management and Insurance, Chapter 12, “American Fixed Income Options," May

20. 1996.

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Rate Changes: Deterministic Scenarios and Stochastic Models 10/08

More accurate term structure models provide a systematic way to assume the random movement of the interest rates along the yield curve. However, it is important to understand that, for the most part, these are not perfectly random. Instead, the models constrain the range of movement of the rates, and the corresponding probabilities. In other words, either the model or the model users limit or exclude some possible future rate conditions. The constraints are imposed to make the models both:

∙ ∙

lntemally consistent; that is, there is no risk-free profitable arbitrage

Externally consistent; that is, the values of certain securities implied from the model agree with the market values.

In the following sections, we will examine a wide range of stochastic term structure models. These models all use mathematical techniques to develop multiple future rate paths in order to simulate uncertain and random rate movements. Then, we will discuss the principal constraints, or parameters, used to limit or exclude some possible rate conditions. Over the past 30 years, many different stochastic, term structure models have been developed. Mathematical approaches used in these models are single-factor, multi-factor, affine, and quadradic. Users tend to refer to these techniques by the name of the model’s developers. So as an aid to the reader, Exhibit 8.13 lists the most well-known developers and the year the models were first introduced.

TYPES OF TERM STRUCTURE MODELS The stochastic term structure models listed in Exhibit 8.13, as well as many other not included in that list, can be best understood by grouping them based upon the type of modeling technique employed. Financial market participants generally use one of six approaches:

l. Analytical solutions

2. Monte Carlo simulation 3. Bushy trees

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Interest Rate Risk Management

4. Finite difference methods

5. Binomial lattices 6. Trinomial lattices Exhibit 8.13 Selected Term Structure Models

1977

Vasicek

1979

Brennan and Schwartz

1985

Cox, Ingersoll and Ross

1986

Ho and Lee / Extended Merton

1990

Hull and White / Extended Vasicek

1990

Heath Jarrow and Morton

1992

Longstaff and Schwartz

1993

Shimko, Tejima, and van Deventer

I999

Jarrow

1999

Duffie and Singleton

2002

Ahn, Dittrnar, and Gallant

Analytical Solutions

Analytical solutions are formulae and are sometimes referred to as “closed form solutions.” The four best known examples of analytical term structure models are the Merton Model, the Extended Merton Model/Ho and Lee, the Vasicek Model, and the Extended Vasicek/Hull and White Model. Those four are listed in order reflecting increasingly realistic assumptions about the random movement of interest rates.

Both the Merton model and its extended counterpart the Ho and Lee model are based on an assumption about random interest rate movements that imply that, for any positive interest rate volatility, zero coupon bond yields will be negative at every single instant in time for long maturities beyond a critical maturity. The extended version of the Merton model,

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Rate Changes: Detemrinistic Scenarios and Stochastic Models 10/08

the Ho and Lee model, offsets the negative yields with an “extension” factor that must grow larger and larger as maturities lengthen. Vasicek proposed a model that avoids the certainty of negative yields and eliminates the need for a potentially infinitely large “extension” factor. Vasicek accomplishes this by assuming that the short-rate r has a constant volatility sigma like the models above, with an important twist: the short-rate exhibits “mean reversion.” (Mean reversion is a key term structure model concept and is discussed later in this chapter.)

Hull and White bridged the gap between the observable yield curve and the theoretical yield curve implied by the Vasicek model by “extending” or stretching the theoretical yield curve to fit the actual market data. In essence, Hull and White “extended” the Vasicek model to make it more accurate by inserting a plug to balance the theoretical calculations to the observed market rates. A theoretical yield curve that is identical to observable market data is absolutely essential in practical application, since a model that does not fit actual data will propagate errors resulting from this lack of fit into hedge ratio calculations and valuation estimates for more complex securities. No sophisticated user would be willing to place large bets on the valuation of a bond option by a model that cannot fit observable bond prices. Of all the models in this group, only the Extended Vasicek model is adjustable to reflect the actual sensitivity of the long end of the yield curve to movements in shorter term interest rates. This allows a precise adjustment of hedges to fit market conditions unique to the submarket or the country being considered. In short, the Extended Vasicek model is the best analytical model for most users.

From Analytical to Numerical Solutions Analytical solutions are preferable for financial instruments with known cash flows (i.e., instruments without options) as well as for instruments with European style options. (A European-style option is an option that can be exercised only at one date. An American-style option, on the other hand, is exercisable at any time between the option date and the maturity date.) Instruments without options or with European-style options generally have explicit analytical solutions in the Vasicek family of models. They offer a rich array of closed form solutions that allow for

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Interest Rate Risk Management

greater precision in parameter fitting. Accordingly, more complicated and computationally intensive numerical term structure models are neither necessary nor desirable for those instruments.

Keep in mind, however, that the real rate risk measurement challenges arise from embedded options. Deposits and loans, as we discussed in Chapters 2, 6, and 7, ofien have lots of American-style options. The essence of the problem is simple. As we have repeatedly observed, for all financial instruments, the value of future cash flows varies with interest rate levels. But for instruments with options, the volume and timing of future cash flows, in addition to their value, also depends on future rate levels. The risk created by most options simply cannot be evaluated without a robust, stochastic, term structure model. Accordingly, richer term structure models like the Heath Jarrow and Morton model, discussed later in this chapter, are much more suited to the needs of most rate risk analysts. In the case of American-style fixed-income options, we generally have no alternative but to turn to a numerical technique. Nevertheless, it is important to remember that numerical techniques are not problem-free. They are normally more calculation-intensive, which reduces the speed of the model. Almost all steps taken to improve model speed by reducing the complexity of the numerical calculation introduce an error that can often be significant. Monte Carlo Simulation

Monte Carlo modeling is the granddaddy of stochastic models. Monte Carlo simulation avoids the necessity of picking a single forecast or running several single forecasts to make comparisons. Instead, Monte Carlo simulation uses random numbers to sample many thousands of different interest rate paths. Because a very large number of similar paths are generated, the simulation can create a normal distribution of the possibilities. The value of the bank or the bank’s portfolios or individual fmancial instruments is then evaluated for each of the possible interest rate paths, yielding a range of possible values or outcomes. In its simplest form, Monte Carlo simulation is simply the use of stochastic simulation to generate interest rate projections. However, as we will discuss later in this chapter, some key parameters, such as mean reversion and elimination of rate paths pemritting arbitrage, can be controlled to eliminate unrealistic or undesirable rate paths.

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Rate Changes: Deterministic Scenarios and Stochastic Models 10/08

Monte Carlo simulation has a number of advantages that should not be overlooked:

It is sometimes the only alternative where the cash flow is path dependent, as imprecise as it might be in that case. (Path dependency is discussed in Chapter 7.) It has speed advantages for problems with a large number of variables. Generally, these apply for three or more variables. It is relatively simple to implement. However, Monte Carlo simulation has a number of limitations. The two most important are:

Monte Carlo models are not ideal for valuing American-style options. Monte Carlo simulation is a forward-looking technique that projects from today into the fiiture. To correctly value an American option, one measures value by working backwards from maturity to calculate value, assuming at each decision point that the option holder does the rational thing. Monte Carlo works by projecting one interest rate path at a time, so there is not enough information at any point on that path to correctly analyze whether or not an American-style option holder should exercise the option. For this reason, Monte Carlo simulation almost always requires the user to specify a decision rule regarding what the holder of the option should do in any given interest rate scenario, often in the form of a prepayment table or prepayment function in the case of a prepayment option. This is putting the cart before the horse since the user has to guess how the option will be exercised before the user knows what the option is worth. Rather than going through this error-filled exercise, we think most users would get better results by just estimating the value of the option directly. Monte Carlo users inevitably must make an unhappy compromise. In practice, Monte Carlo simulation does not use all possible rate scenarios for valuation. There are an infinite number of interest rate scenarios, and Monte Carlo simulation, due to its speed problems, inevitably requires the user to use too few “scenarios” in the interests of time. As a result, Monte Carlo simulations have

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Interest Rate Risk Management

sampling error, which results from “throwing the dice” too few times. Many users of Monte Carlo simulation are under the mistaken impression that the beautiful probability distribution that is displayed on their computer screen reflects the true uncertainty about the value of a security as measured by Monte Carlo. Nothing could be farther from the truth. If you call a major securities firm to get a bid on a mortgage security, you get a bid in the form of one number, not a probability distribution. The beautiful probability distribution reflects the inaccuracy or sampling error of the technique itself, thus this kind of graph reflects a weakness of Monte Carlo, not a strength. This kind of sampling error can lead to very serious problems when calculating hedge amounts. For example, to value a cap with 99 percent accuracy, Monte Carlo simulation requires 25,000 simulations. To reduce sampling error to a meaningful level, a very large number of simulations are normally required to get stable answer and a sampling error small enough to allow decision-making to be based on the Monte Carlo

results.”

Monte Carlo simulation is justifiably popular in financial markets, but it must be used with great care. In general, Monte Carlo simulation is slow and a rough approximation that is best restricted to problems that cannot be solved by any other method (e.g., analytical methods, lattice approaches, or finite difference methods). Finite Difi‘erence Methods

Finite difference methods are more complex but more general solution methods commonly used in engineering applications. Finite difference methods provide a direct general solution of the partial differential equation (that defines the price of a callable security), unlike lattice 13. In discussions with sophisticated institutions vrith many years experience with Monte Carlo simulation, Bank of America executives stated that 2000 to 10000 iterations were necesary for a stable answer, while Tokyo Mitsubishi Bank argued that 5000 to 10000 runs were essential. A risk management expert at a very large New York bank expressed extreme concern that some line units in his bank were basing management actions on as few as 100 iterations per Monte Carlo calculation.

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Rate Changes: Deterministic Scenarios and Stochastic Models 10/08

methods, which model the evolution of the random variables. Finite difference methods fall into two main groups, explicit and implicit. The explicit finite difference methods are equivalent to the trinomial lattice methods. (Trinomial lattices are discussed later in this chapter.) Implicit methods are more robust in the types of problems that they can handle, but implicit methods are computationally more difficult. Both methods usually use a grid-based calculation method, rather than the lattice approach, to arrive at numerical solutions. Finite diflerence methods can be used to solve a wide range of valuation problems for instruments with embedded options. Furthermore, they are not restricted to a small number of stochastic processes (i.e., normal or lognormal) that describe how the random variable moves. These methods can be used to value both American- and European-style options. Like lattice methods, the valuation by finite difference methods is performed by stepping backwards through time. This is a one-stage process. Under the finite difference method; there is no need to model the evolution of the random variable before the valuation can be performed.

finite difference method, in its grid rather than a lattice implementation, should be an essential rate risk management for most institutions with significant holdings of instruments with American-style options.

The

Binomial Lattices

Another stochastic approach is to use lattices for rate paths instead of using randomly generated rates. Lattices, or decision trees, are simple, easy to understand applications of stochastic, term structure models. Lattices generate fewer rate paths than pure Monte Carlo simulations and therefore require fewer calculations. Lattices can realistically reflect yield curves and can be used to simulate large numbers of interest rate scenarios. Binomial lattices are simple ways of defining rate paths based on the starting assumption that, at any single moment in time, rates can either go up or they can go down. A simple binomial lattice for four time periods is shown in Exhibit 8.14.

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10/08 Interest Rate Risk Management

Exhibit 8.14 A Simple Binomial Lattice Blnomlal Lattlce

The time intervals are called nodes. The lines representing the possible rate movements fi'om each node are called “branches." The whole lattice is sometimes called a decision tree since the rate movements are shown as branching and rebranching fi'om node to node.

Notice that even a simple binomial lattice, such as the one shown in Exhibit 8.14, reveals a fairly large number of possible rate paths. For example, rates may start at 8 percent at period 0, go up to 8.12 percent in period 1, back down to 8 percent in period 2, down to 7.88 percent in period 3, and then down to 7.76 percent in period 4. That is just one possible rate path.

Lattices can be constructed with nodes for any desired time interval, e.g., daily, weekly, or monthly. And we can use as many nodes as we wish to extend the lattice to any desired future time horizon. In addition, lattices can employ any size rate change. In fact, since short-term rates tend to be more volatile than long-term rates, some computer lattice models can incorporate larger possible rate change amounts for shorter term nodes and smaller changes for longer term nodes. A binomial lattice (sometimes called a binomial tree) is a discrete time model for describing the movement of a random variable whose movements at each node on the tree can be reduced to an up or down movement with a known probability. The model is usually specified so that an upward movement followed by a downward movement gives the same value as a downward movement followed by an upward movement.

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Rate Changes: Deterministic Scenarios and Stochastic Models 10/08

Valuation with the binomial tree requires two passes through the lattice: On the first pass, which is forward from time zero, the values of the interest rate at each node are calculated; on the second pass, which is backwards, the values of the derivative security at each node are calculated. The evolution of the random variable in the first pass through the lattice is detennined by the parameters of the stochastic process and the size of the discrete time step. Unlike the Monte Carlo method, subsequent forward passes will always produce the same values. The binomial lattice can be used to value American-style options as well as European-style options. However, interest rate derivative securities often assume a more complicated stochastic process for interest rates, for which the trinomial tree method presents some advantages. Bushy Trees

Lattice techniques are computationally efficient because the lattices “recombine”: An interest rate increase followed by a decrease leads to the same interest rate as a decrease followed by an increase. For some stochastic processes, this recombination does not occur, particularly in the context of attractive assumptions about forward rate movements under the Heath, Jarrow and Morton model. In this case, that lattice takes on the structure of a “busy tree,“ where branches split over and over but never recombine with other branches. The result is a very efficient process for approximating the assumed stochastic process for interest rates and the ability to value complex securities that are path-dependent or which involve American options. The technique offers many of the advantages, but few of the disadvantages of Monte Carlo simulation. Trinomial Lattices

Binomial decision trees tend to overestimate cap values and underestimate floor values. Trinomial decision trees are more accurate. A trinomial decision tree is a discrete time interval model for describing the movement of a random variable. In this case, the random variable is interest rates. The trinomial lattice allows for three possible movements of interest rates at each time interval in a series of time movements. Instead of just saying that rates may go up or down at any one point in time, a trinomial lattice pemiits us to say that rates may go up, stay the same, or go down. As a result, trinomial lattices are much more realistic

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Interest Rate Risk Management

than binomial lattices. The model is specified so that an upward movement followed by a downward movement and a downward movement followed by an upward movement give the same value as two movements where no change occurs. A simple illustration of a trinomial lattice is shown in Exhibit 8.15.

Exhibit 8.15 A Simple Trinomial Lattice

Trlnomlal Lattlce

A very large number of rate scenarios, rate paths, can be generated using binomial lattices and an even larger number can be generated using trinomial lattices. In a trinomial lattice with just 4 time periods, 16 separate rate paths are defined. Generating thousands of rate paths is, of course, is both an advantage and a problem. It is helpful because examining a large number of potential rate paths will provide more useful insights into the rate risk exposure. The additional outcome at each node provides an additional degree of freedom which enhances the power of the model. Consequently, trinomial lattices can be used to model almost any Markov stochastic process, including ones in which the parameters are functions of time and the random variable itself. In modeling interest rate-related derivatives, it allows rates to be modeled so that the current term structure of interest rates and term structure of rate volatility are matched exactly by the modeling process. This offsets the more complicated calculations of the values at the ends of each branch. The trinomial lattice can be used to value American- and European-style options.

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Rate Changes: Deterministic Scenarios and Stochastic Models

10/08

On the other hand, the additional rate paths permitted by trinomial lattices can be a problem because simulating thousands of rate paths is computationally intensive. Some risk analysts deal with this problem by applying a tool called linear path space to reduce the number of paths that they examine. Linear path space applies probabilistic sampling to techniques to the lattice. Other risk analysts simply choose an alternative term structure model methodology.

Still, trinomial lattices are the preferred tool for most “power users” not withstanding the computationally intensive nature of this technique. The trinomial lattice valuation technique which has quickly established itself as the standard valuation method, not only for the Vasicek model and its extended version (the Hull and White model), but also for a number of other single factor term structure models that are Markov in nature.

PARAMETERS FOR TERM STRUCTURE MODEL

Users need to specify important variables or parameters before running virtually all types of stochastic term structure models. Some term structure models only need one or two parameters. Others need as more. In this section, we examine four key parameters: volatility, drift, mean reversion, and no free arbitrage. In almost every term structure model, the speed of mean reversion and the volatility of interest rates will play a key role in determining the value of securities that either are interest options or have interest rate options embedded in them. Volatility

Volatility, often referred to as sigma, is a critical variable. The simple lattice depicted in Exhibit 8.15 does not capture the term structure model concept completely. In addition to saying that rates may go up or down, we must also define the size of the change. We need a volatility assumption. We might, for example, say that at each change, rates may rise or fall by 1.5 percent. In other words, if the current rate is 8 percent, and volatility is 1.5 percent, then each rate change will be 12 bps (8.00) (0.015). This, more complete example of a binomial lattice is depicted in Exhibit 8.16.

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10108 Interest Rate Risk Management

Exhibit 8.16 A Simple Binomial Lattice with 1.5 Percent Volatility

We can set this interest rate volatility scale factor to any level we want, although normally it would be set to levels which most realistically reflect the movements of interest rates. We can calculate this implied interest rate volatility from the prices of observable securities like interest rate caps, interest rate floors, or callable bonds. Valuations of different types of instruments should use different volatilities. Later in this discussion of stochastic term structure models, we will discuss model calibration. For now, we just need to note that volatility varies over time. Drift

If we use a perfectly stochastic term structure model, change in the random variable, in this case interest rates, is a random walk. In other words, it is a stochastic process where the random variable drifis randomly with no trend. As time passes, ultimately rates will rise to infinity or fall to negative infinity. This isn’t a very realistic assumption about interest rates, which usually move in cycles of three to five years.

How can we introduce interest rate cycles to our model? We need to introduce some form of drift in interest rates over time. One form of drift is to assume that interest rates change by some formula as time passes. This form of drift is employed in the Ho and Lee and in the Heath, Jarrow and Morton models. Both of these models make it easy to fit actual yield curve data exactly with a simple assumption about how interest rates move.

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Rate Changes: Deterministic Scenarios and Stochastic Models 10/08

Mean Reversion Speed Using a drift assumption to modify the random changes in a purely stochastic model helps make the model more accurate. However, a drifi formula alone merely constrains the ups and downs in rate paths to make them conform more closely to real, cyclical peaks and troughs. The best way to build the interest rate cycle into the random movement of interest rates is to assume that the interest rate drifts back to some long run level, except for the random shocks. The process of drifting back to some long run level is called “reversion to the mean.”

Reversion to the mean makes sense for interest rate term structure models. The three- to five-year cycles of actual interest rates tend to oscillate around longer term trends. But mean reversion has to be described a bit more specifically. In order for a term structure model to accurately mimic real-world rate changes, we must define how quickly the rate paths revert to the mean. This is called the “speed to mean reversion."

Speed to mean reversion is always assumed to be a positive number. The larger it is, the faster rates drift back toward long run mean and the shorter and more violent interest rate cycles will be. The Vasicek model incorporates a speed to mean reversion assumption.

Speed to mean reversion controls duration. A faster speed to mean duration produces shorter durations. The durations produced from the model need to match actual durations as closely as possible. The Ho and Lee and the Heath Jarrow Morton constant volatility term structure models assume that mean reversion is equal to zero. That assumption is inconsistent with the no-arbitrage condition unless the yield curves are quadratic. In contrast, the Extended Vasicek and the Heath Jarrow Morton (exponentially) declining volatility term structure models assume mean reversion to be non-zero. These models fit best when the volatility term structure is declining (i.e., volatility values decrease for longer term along the yield curve). If, for example, the short-rate volatility was smaller than the one-year volatility, then the term structure model parameters could not be fitted to perfectly fit the observed yield curve.

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Arbitrage

One of the key problems with stochastic term structure models is the issue of arbitrage possibilities. Accurate term structure models must be internally consistent, that is, they must exclude risk-free profitable arbitrage. Arbitrage is a transaction in which one profits from the risk free, simultaneous purchase and sale of anything. The classic example is the purchase of gold on the London market at one price and the simultaneous sale of the same amount of gold on the New York market at a higher price. (The term is more commonly used to describe less perfect, not quite risk-free transactions, but that is another story.) For term structure models, the issue of arbitrage arises from difl‘erences between rates predicted by the model and actual market rates. All of these models begin with the current yield curve. They are called “no arbitrage” because they exclude all possible future rate paths that would enable investors to profit from rate changes. In a “no arbitrage” model, no two instruments with identical cash flows can have different values. There can’t be a difference between the theoretical price or yield and the actual price or yield. Understanding Term Structure Model Parameters

Notice that mean reversion speed and drift are not really separate concepts. Mean reversion speed merely describes an attribute of drift. The relationship between these two concepts illustrates a key point: the four parameters discussed in this section are somewhat arbitrarily defined. We could just as easily describe a different number of parameters or different definitions for parameters. Calibrating ParametersM

All term structure models require calibration to reflect the parameters. The problem is that many discussions of the use of term structure models in risk management overlook the very real difficulties of estimating the

l4. Adapted from Donald van Deventer, Kenji Irnai and Mark Mesler, “Estimating the Parameters of Term Structure Models,” Advanced Financial Risk Management (Wiley Finance. 2005) pages 241-252.

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Rate Changes: Deterministic Scenarios and Stochastic Models l0/08

parameters for use in such models. Values for model parameters can come from:

∙ ∙ ∙ ∙

Estimations using historical volatility Advanced volatility curve analysis

Implied parameters from an observable yield curve

Fitting parameters to volatility-sensitive instruments

All four, as well as parameter estimation for multi-factor models, are summarized in the following subsections. Term structure model users need to decide whether changes in the yield curve are random changes or more permanent, structural shifis. For structural shifis, you will have to recalibrate the term structure parameters. You should then try to recalibrate the term structure parameters as frequently as possible using one of the three approaches summarized in the following paragraphs.

Historical Volatility Curve Approach Historical volatility can be estimated from observable market data. “Implied volatility" is the value of volatility in the Black-Scholes model, which makes the theoretical price equal to the observable market price. This approach is familiar to traders, thanks to the popularity of the Black-Scholes option pricing model and the accepted market practice of estimating volatility for use in the model from market option prices. Many market participants use parameter estimates that are consistent with the historical relative degree of volatility of longer term yields in relationship to the short rate.

Rate risk managers can calculate observable variances for bond yields” and then choose values of sigma and alpha that best fit historical

15. Market participants often take the short cut of approximating zero coupon yields by the par bond coupon levels at each maturity, the same approach we take here in the interest of brevity. This simplification leads to some error and we recommend the precise calculation of zero yields via yield curve smoothing.

8-43

Interest Rate Risk Managemmt

10/08

volatility. The most precise method for doing this is to use advanced yield curve smoothing techniques to calculate zero coupon continuous yields at all of the key maturities for all of the observation dates. (Smoothing is discussed in Chapter 6.) The method chosen for yield curve smoothing does have an effect on the term structure model parameters estimated, so yield curve smoothing has an importance above and beyond the yield curve itself.

Consider an illustration using Canadian data. Here we take a shortcut and illustrate the process by using par bond coupon rates as proxies for zero coupon bond yields. We take the following approach:

1. Collect yield volatilities for various maturities. For Canada, these maturities are 1 month, 2 months, 3 months, and 6 months, and then 1, 2, 3, 4, 5, 7, 10, and 25 years. 2. Estimate initial values for the speed of mean reversion and interest rate volatility. Typical guesses would be 0.10 for alpha and 0.01 (which is 1 percent) for interest rate volatility. 3. Use enterprise risk management software or a spreadsheet to calculate by iteration the best-fitting values for alpha and sigma given the yield volatilities and initial guesses of parameter values.

The results of this analysis for Canada are summarized in the table in Exhibit 8.17. Exhibit 8.17 Variance in Canadian Government Interest Rates VuhnhMGnn-nll-Imm ∙ ∙ ∙ ∙ ∙ ∙∙ ∏∙

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1.9

Rate Changes: Deterministic Scenarios and Stochastic Models

10/08

The best fitting alpha value was 0.305. This is a fairly large speed of mean reversion and reflects the relatively large variation in short-term Canadian rates, relative to long rates, over the sample period. Interest rate volatility was also high at .0285. At the current low levels of Canadian interest rates, this volatility level would clearly be too high. Comparable figures for the United States swap market, based on a fit to 54 swaptions prices, which we discuss in a later section, were a speed of mean reversion of 0.05379 and an interest rate volatility of 0.01369. With the prevalence of low interest rates around the world in recent years, the values of both the speed of mean reversion and interest rate volatility continue to drop. Advanced Volatility Curve Approach In the previous section, we derived parameters for a single-factor term structure model. A more flexible approach takes the linear relationship between the short rate and zero coupon bond yields that would be consistent with a one-factor model, but we actually test whether the single-factor model is in fact “true.” For the Canadian market, we performed a regression of par bond coupon yields (as proxies for zero coupon bond yields) on the one-month Canadian government bill rate. The results of these regressions area higher implied mean reversion speed at shorter maturities, as Exhibit 8.18 shows.

8-45

10/08 Interest Rate Risk Management

Exhibit 8.18 Implied Mean Reversion Speed Implied Speed of Mean Reversion By Historical Sensitivity to Movements in the Canadian Treasury Bill Rate 1987-1996

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The best-fitting alpha at three years was a very high 1.00921. At 25 years, the alpha at 0.296 is much more consistent with the historical variances reported in Exhibit 8.17. This chart provides a strong clue that a multi-factor model would add value (assuming away other problems, like parameter estimation and the valuation of American options, which are strong disadvantages of multi-factor models) in the Canadian market. This is true of most markets where recent interest rate fluctuations have been large and where current rate levels are near historical lows.

Implied Parametersfrom an Observable Yield Curve Most market participants feel more comfortable basing analysis on parameter values implied from observable securities prices than on historical data when observable prices are sufficient for this task. For example, if the only observable data is the yield curve itself, we can still try to fit the actual data to the theory by maximizing the goodness of fit from the theoretical model.

We want the model we estimate to have the maximum goodness of fit, which means that we want to minimize the “extension” in the extended Vasicek model; this is consistent with our stress on the underlying

8-46

Rate Changes: Deterministic Scenarios and Stochastic Models 10/08

economic logic of the factors we could select in the multi-factor term structure model. We do thisby creating the best-fitting Vasicek yield curve. We have four unknowns in the Vasicek model. To maximize goodness of fit, we can pull a large number of zero coupon bond prices from the observable yield curve and try to find the parameters that fit the observable yield curve as well as possible. This can be done with spreadsheet sofiware; however, the lack of power in spreadsheet nonlinear equation solving is reflected in the low or zero values for interest rate volatility and illustrates the need for other data (caps, floors, swaptions, bond options prices, etc.) and more powerful techniques for obtaining these parameters. Fitting Parameters to Volatility-Sensitive Instruments The best approach is to use parameters estimated from observable caps, floors, and swaptions data (or other option-related securities prices”) to the extent they are available. These are the market instruments most sensitive to interest rate volatility. Using these instruments is also consistent with the equity market practice of implying stock price volatility from observable prices on options on common stock.

Swaptions provide a very rich data set with very good convergence properties that allow market participants to use even common spreadsheet sofiware to obtain high-quality term structure parameter estimates. In addition, the accuracy of the extended Vasicek model, using only two parameters held constant, is far superior to that of the Black commodity futures model in predicting actual market prices.

Moreover, if we allow interest rate volatility to vary by swaption quote, we get results that match the market perfectly while varying by less than implied volatilities using the Black commodity model. In estimating term structure parameters, the lesson is clear. A rich data set of current prices 16. In the U.S. market, there are a fairly large number of callable U.S. Treasury securities whose prices provide some guide to interest rate volatility. When rates are infinitely high, the value of the call option is zero; therefore the power to extract parameter estimates is greatest when bond prices trade roughly in the range between 95 and par value. Also in the U.S. market there are more than 400 callable U.S. agency securities which may actually provide the richest source of information on term structure model parameters for a nearly risk-free yield curve.

10/08

Interest Rate Risk Management

of securities with significant optionality is necessary to provide an easyto-locate global optimum for almost any popular term structure model. Parameter Estimationfor Multi-Factor Models

While we have focused on parameter estimation for single-factor models in this discussion, the same procedures apply equally well to multi-factor models. Market participants often add principal components analysis to their list of parameter estimation options (with factors including things like the short rate, the long-rate/short-rate spread, and a measure of the “bend” in the yield curve). This approach is practical and popular but comes at a cost: Since there is no economic rationale for factors like “bend,” there is even less assurance than usual that the future will be like the past. This means simulations based on this kind of popular but ad hoc model have to be taken with more than the usual dose of salt. CHOOSING A TERM STRUCTURE MODEL Three broad conditions should determine which term structure model you should use:

1. Are you evaluating rate risk in instruments with known cashflows or European-style options? Earlier in this chapter, we observed that analytical models (closed form solutions) are preferable for valuing instruments with certain cash flows or for instruments with embedded, European-style options. As we mentioned, analytical solutions value these instruments accurately while avoiding the computational problems associated with numerical solutions. Of the analytical solutions discussed, the Extended Vasicek or Hull and White model is the most accurate.

2. Are you evaluating rate risk in instruments with American-style options? If so, are the options strongly path dependent? Numerical solutions are necessary for valuing instruments with Americanstyle options. For these applications, a number of subsidiary questions become important. One is the degree of path dependency. Path dependency is the name we use to describe how much (or how little) influence the history of rate changes has on the exercise of options. For example, the holder of an 8 percent

8-48

Rate ChanEs: Deterministic Scenarios and Stochastic Models 10/08

mortgage has an option to refinance the loan and use the proceeds to pay off (prepay) the loan. The first time prevailing rates fall from 8 percent to 6 percent, there is a high probability that the holder will exercise the option and prepay is high. The third or fifth time that rates fall from 8 percent to 6 percent, the probability

that option will be exercised is low. That is because any option holder that did not exercise his option the fust two times it is in the money is not too likely to exercise it on subsequent occasions when it is in the money. (Options and path dependency are discussed in more detail in Chapter 7.)

Some financial instruments, such as callable bonds are weakly path dependent. Some, like mortgages, are strongly path dependent. Binomial trees work well for weakly path dependent instruments. The Ho and Lee and the Heath, Jarrow Morton models are good choices for weakly path dependent, Americanstyle options. Monte Carlo is better for strongly path dependent instruments. Monte Carlo is most appropriately used for problems that involve path dependence or three or more random variables.17 3. Finally, practitioners need models that are easy to run. Computational time is an issue. The extra value of the best analytics may be needed to value options but may not make much difference for valuations of bank assets and liabilities without embedded options. The nature of your risk exposures, therefore, should strongly influence your choice of term structure model. If, for example, you can‘t run many thousands (10,000 to 25,000 minimum) Monte Carlo runs, an alternative model will be more likely to produce accurate results.

Most importantly, keep in mind that all term structure models are approximations. Their use should always be tempered with judgment and experience. While these can be powerful tools, they still require rate risk analysts to make assumptions for parameters such as volatility. And they still require accurate prepayment or other option behavior assumptions in

17. Even in the case of path dependence, however. the use of Monte Carlo simulation is technically incorrect. as noted by Hull. For more on this point. see John C. l-Iull. Options. Futures and Other Derivatives, 2nd ed. (Englewood Cliffs, New Jersey: Prentice-Hall, 1993), pages 329—334.

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10/08 Interest Rate Risk

Management

your model. The rate changes that you choose to model and the number of those changes are merely some of the ingredients needed to bake an accurate risk measurement cake. Don’t be misled by the fact that these are rare, nuanced, or complex ingredients. Those attributes may or may not help you get the quality of cake you seek.

8-50

Chapter 9 Selecting and Installing AL Models

Modeling Process ................................................................................. 9-2 Exhibit 9.1: Model Process Flow Chart ....................................... 9-3 Ten Key Features of Asset/Liability Models ........................................ 9-3 1. Extent of Aggregation of Information Concerning the Bank’s Current Position ................................................................... 9-4 2. Manual vs. Automated Input of Information Conceming the Bank’s Current Position ................................................................... 9-5 Transferring Accounting Data into the Simulation Model∙∙∙∙∙∙∙∙∙∙∙ 9-6 Bank Needs and Simulation Model Sophistication ...................... 9-6 3. Ability to Capture Product Option and Basis Risk ....................... 9-7 Simulating the Exercise of Embedded Options ............................ 9-8 Criteria for Selecting Product Options Capabilities ................... 9-10 Basis Risk ................................................................................... 9-11 4. Number and Choice of Rate Scenarios ....................................... 9-12 5. Features for Facilitating Realism of Rate Scenarios ................... 9-13 6. Level of Output Detail Provided ................................................ 9—16 Detail Reports ............................................................................. 9-16 Comparative Reports .................................................................. 9-17 Management Reports .................................................................. 9-18 Deviations from Bank Policy ..................................................... 9-18 7. Risk Measurement Methodologies ............................................. 9-18 8. Regulatory Compliance Issues for Interest Rate Risk Models ............................................................................................ 9-1 8 Thrift Institutions ........................................................................ 9-19 Commercial Banks ..................................................................... 9-20 Bank Examiner Guidelines ......................................................... 9-22 9. Easy “What-If” Modeling........................................................... 9-26 10. Applicability to Other Management Goals ............................... 9-27 Budgeting ................................................................................... 9-27 Investment Portfolio Management ............................................. 9-28 Required Financial Disclosures .................................................. 9-28 Product Pricing ........................................................................... 9-29 Using Data fi'om Call Reports .................................................... 9-29

10/08

9-i

10/08

Interest Rate Risk Management

Option-Adjusted Spreads, Monte Carlo, and Other Advanced Modeling Features .............................................................................. Rate Scenarios: Stochastic and Term Structure Modeling Capabilities ..................................................................................... Capability to Model Prepayments and Other Embedded Options ........................................................................................... Option Adjusted Spreads ............................................................ Prepayment Models .................................................................... Advanced Modeling Summary ....................................................... Integrating Model Techniques ............................................................ Selecting a Rate Risk Model .............................................................. Identifying Your Rate Risk Model Requirements .......................... Evaluating Interest Rate Risk Models ................................................ Installing Interest Rate Risk Models .............................................. Appendix 9A: A Guide to ALM Software ......................................... Appendix 9B: ALM Outsourcing and Consulting Vendors ............... Appendix 9C: Required Model Features, Functions, and

9-30 9-31 9-34 9-34 9-35 9-36. 9-36 9-38 9-38 9-40 9-46 9-49 9-53

Characteristics .................................................................................... 9-57

Chapter 9 Selecting and Installing AL Models

Interest rate risk (IRR) measurement models may be purchased from a variety of software vendors or developed by the bank in-house. Both choices offer advantages and disadvantages. Many of the models available from vendors are particularly strong in some areas, but weak in others, causing some banks, especially the largest ones, to prefer customdesigned models. In practice, some larger banks use sophisticated models purchased from vendors, but then supplement those models with input from custom-designed models for portions of their business that the main models don’t seem to handle well. While it is possible for a bank to design a customized model comparable to the best models available from vendors, few do so. Most in-house models are simple PC-based spreadsheets. Few of these models can readily handle the detailed information needed to reflect basis risk and convexity. They often require time-consuming manual data entry. And, they may need to be rerun for every different rate and business scenario that the bank wants to model. Furthermore, all custom built models, no matter how sophisticated, suffer from some common problems. For one, the bank must rely on its own resources for model updates and revisions. They are also expensive to program. Additionally, there can be problems modifying them after the original programmers are gone.

More than a dozen different vendors now sell PC-based asset/liability management (ALM) models. (See the list of models in Appendix 9A. Also see the list of ALM outsourcing and consulting vendors in Appendix 93.) Early versions of these software packages performed only static gap analysis. Second-generation models, still in widespread use, allow users to apply income or economic value sensitivity simulation techniques under a variety of different rate scenarios. Today, rate risk managers can choose from software packages with a host of advanced features. Some models now extract data directly from a user's transaction

9.1

10/08 Interest Rate Risk Management

database for loans and deposits to simulate future cash flows in detail. Some models employ complex statistical tools to consider thousands of future alternative interest rates.

MODELING PROCESS Simulation models have different features, different levels of complexity, and different strengths. But the basic modeling process always involves variations of the three steps described in following paragraphs. These steps are shown graphically in Exhibit 9.1. 1. Data has to be marshaled and input into the model. Some data will be automatically linked into the model from your general ledger and various subsystems for investments, loans, and deposits. Some banks have enterprise-wide data warehouses that enable them to draw required data fiom a single source. invariably, some data must be input manually. The modelingprocess itself is not simple. For example, take a look at the bottom left portion of the “Modeling Section” in Exhibit 9.1.

Behavioral assumptions for loan prepayments, deposit withdrawals, and other option-driven volume changes are required inputs for the model. The exhibit shows that these volume changes can be developed and put in tables that are then read by the model. Or, these volume changes can be calculated by subordinate model processes that calculate prepayments and deposit losses. The advantage of using subordinate model processes to calculate the volume changes is that separate sets of volume changes can be calculated for each rate scenario being modeled. The model must be capable of producing the fit” panoply of required reports. Sometimes the model generates all of the reports. Sometimes the model exports data to a database from which it is automatically applied to populate custom designed reports. Sometimes the model generates both types of reports. Various requirements for output reports will be discussed later in this chapter.

9-2

Selecting and Installing AL Models lO/08

Exhibit 9.1 Model Process Flow Chart mDATA

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We can identify many details that influence the selection and use of models. A general discussion of key features of interest rate risk (IRR) models is presented in the following section. More specific discussions of steps involved in selecting models, model features, and control procedures are presented in subsequent sections. TEN KEY FEATURES OF ASSET/LIABILITY MODELS Selecting the right rate risk measurement software is a subjective process. Software packages are “feature rich.” They can do many things or produce lots of different reports. The difficulty lies in matching the resources, capabilities, and needs of your bank to the features of the software. Next, we consider 10 specific issues relevant to these choices. Each of these issues deserves careful consideration if you are planning to acquire IRR modeling software.

9-3

10/08 Interest Rate Risk Management

1. Extent of Aggregation of Information Concerning the Bank’s Current Position

Most simulation models require the user to establish a customized chart of accounts. It can consist of very brief balance sheets and income statements with highly consolidated accounts. In such cases, the data from the bank’s loan, deposit, and other transaction reporting systems are aggregated into the consolidated chart of accounts. For example, all residential mortgage loans may be treated as a single group, even though some are fixed-rate, some are floating-rate, some have 30-year amortizations, some have lS-year amortizations, some are new loans, and some are very seasoned loans. Alternatively, banks can use a very detailed chart of accounts in their models. (In part, this requires the user to choose a model that permits lots of asset and liability categories. Usually, however, the user only needs to take advantage of the model’s full capability.) In the previous paragraph, we mentioned a bank that combined all its residential mortgage loans into a single group. A bank that wants to model in more detail, and with more accuracy, might use six categories for those loans. An even more detailed model might break all those loans down further on the basis of their interest rates. For example, it might have a line on the chart of accounts for all 7 percent fixed-rate 30-year mortgages, one for all 8 percent fixed-rate 30-year mortgages, one for all 9 percent fixed-rate 30year mortgages, and so on. The most advanced programs model each instrument individually. For each transaction, these models look at all of the terms, such as required principal payments, the interest rate, the maturity date, repricing terms, prepayment options, etc., and then calculate all of the expected cash flows. This capability enables the program to project different quantities or prepayments, interest income for variable-rate instruments, and other option-based cash flow for every rate scenario modeled. Even though these models require a voluminous amount of input detail and produce a huge number of calculations, the end result is far more accurate.

Caps, floors, and other embedded options in bank products cannot be accurately modeled with any lower level of detail. Instrument level modeling is particularly valuable for EVE simulation and VaR measurement.

9-4

Selecting and lnstallingil. Models

l0/08

For most banks, it is simply too costly to model each of the institution’s investments, loans, and deposits individually. Thus, the vast majority of banks aggregate data for instruments with similar characteristics. That aggregation unavoidably creates estimation errors. Accordingly, the decisions made about how to aggregate data into groups are among the most important decisions that must be made for simulation modeling.

Accurate modeling results require separate measurement of balance sheet accounts or groups of accounts that have unique repricing or cash flow characteristics. Consider residential mortgage loans. The prepayments for a 10 percent 30-year mortgage loan will be very different from the prepayments on a 12 percent 30-year mortgage loan if prevailing interest rates rise from 8 percent to 10 percent. In that situation, the increase in rates to 10 percent will dramatically reduce the incentive for the holder of a 10 percent mortgage to prepay. It is a much smaller reduction in the incentive for the holder of the 12 percent mortgage to prepay. Similarly, a 12 percent 30-year mortgage that is 15 years old will almost certainly prepay differently than a 12 percent 30-year mortgage that is 4 years old. A simulation model that uses separate forecasts for 8 percent and 10 percent mortgage loans is likely to be more accurate than one that treats all mortgages identically. Similarly, a simulation model that uses separate forecasts for old mortgages and new mortgages is likely to be more accurate than one that treats all mortgages identically. Disaggregation may be time-consuming and expensive, but it offers the opportunity for greater simulation realism.

Of course, aggregation is not always as critical an issue as it is for mortgage loans. Certificates of deposit, for example, tend to have dollarweighted average remaining maturities of about one year. Thus, for most banks, a decision to model all certificates of deposit in a single group with one total balance, weighted average coupon rate, and weighted average remaining maturity will be unlikely to create any significant estiman'on errors.

2. Manual vs. Automated Input of Information Concerning the Bank’s Current Position

Despite the necessity for huge amounts of information, the simulation model is not a duplicate bank accounting system. The model’s charts of

9-5

10/08 Interest Rate Risk Management

accounts should never approach the level of detail used in the bank’s deposit, loan, investment, and general ledger accounting systems. It must be far less detailed, or it will be too expensive and much too cumbersome to use. Most banks solve this problem by using computer programs to extract the required data fi'om their accounting records and electronically enter the data in their models.

Transferring Accounting Data into the Simulation Model

Simulation models can be set up to capture data from the bank’s loan and deposit systems automatically at various levels of detail. For example, all residential mortgage loans can be treated alike, each loan can be modeled separately, or the loans can be aggregated into groups that are modeled at the group level. In part, the issue is the work involved in setting up the simulation model when it is first put into service. Automated extracts or downloads from the bank’s nansactional databases usually require the creation of “mapping” programs that direct the flow of information from the accounting systems into the simulation program. Once a mapping program is established, it only requires updating as account types or the bank’s chart of accounts is changed. A far more serious problem with many simulation models is the amount of detail about the transactions automatically transferred from the accounting systems into the simulation program. For example, interest rate caps and floors for floating-rate loans may not be put into the model automatically. Off-balance sheet hedge positions are another example of information that some models do not automatically extract from the bank's accounting records. In these cases, rate risk analysts may have to input manually or ignore material information. Bank Needs and Simulation Model Sophistication

The issue of manual vs. automated input deserves special attention when evaluating new simulation software. It is common for sofiware vendors whatever “it" may be. to assure buyers that “the model can do it" True, the model probably can do “it." But can it do it without the interest rate risk analysts entering required data manually? If manual input is required, are the data readily available? If manual input is required, do the time and expense of gathering and entering the data justify the benefit

—

9.6

Selecting and Installing AL Models 10/08

derived? If manual input is required, does the input have to be changed for every rate scenario modeled? The last question refers to assumptions that are different in each rate scenario simulated. Often, this is a particularly important issue. Many vendors correctly claim that their models can handle loan prepayment options. However, in a lot of cases, those models only reflect the variable rate sensitivity of those loans if the prepayment speed assumptions are put in manually for each loan or group of loans. It would be a tedious job if it had to be done only once. Consider, however, that prepayment speeds increase as rates fall or decrease as rates rise. Different prepayment assumptions are required for each interest rate scenario that is modeled. In value at risk models, the changes in prepayment speeds materially alter the maturity of those assets. In income simulation models, the changes in prepayment speeds change the outstanding volumes and thus the income earned from those assets. The work involved in obtaining and manually entering different prepayment speeds for each scenario can be daunting.

Of course, the extent to which the simulation software automatically captures product terms must be evaluated in perspective. It is not an important concern for banks with negligible holdings of products that have features or options not automatically put into the model. It is very significant for banks with material holdings of products that have features or options not automatically put into the model. For example, banks with material holdings of floating-rate loans that have rate floors or ceilings should use software that automatically receives information on those floors and caps from the transaction accounting records. Banks with large holdings of mortgage-backed bonds should consider models that can automatically transfer so-called “dealer” or “street" consensus prepayment assumptions for each individual bond from investment services or databases. 3. Ability to Capture Product Option and Basis Risk A great deal of future activity arises from the options embedded in current and new loan and deposit products. Future activity includes customer decisions to exercise put options such as withdrawals from savings accounts or drawdowns under loan commitments. It also includes customer decisions to exercise call options like deposits to savings

10/08 Interest Rate Risk Management accounts and prepayments of fixed-rate loans. Other product options, like rate ceilings and floors, are exercised simply by a change in interest rates. (Product optionality is discussed in chapters 2, 6, and 7.)

Simulation models must incorporate product optionality. Embedded options risk may comprise as much as 25 percent of total IRR exposure. Models that do not facilitate the simulation of option exercise will, therefore, fail to measure a significant portion of the bank’s overall IRR exposure. Data on options, such as rate caps and floors, must be obtained from bank transaction accounting databases, and put into simulation models. In addition, assumptions about customer exercise of embedded options must be put into the models. The issue of future loan prepayment rates, discussed above, is just one example of data regarding the bank’s future position that must also be incorporated into simulation models. Certificate of deposit (CD) volumes are another example. Historical trends in certificate of deposit rollover rates can be used to forecast CD early withdrawals and renewals. As with loan prepayments, the trends in CD early withdrawals and renewals will vary as interest rates change. More CDs are renewed when rates are high. Core deposit products like checking and savings accounts are particularly difficult to model. As discussed in Chapter 6, many variables influence the volumes of these liabilities. Changes in interest rates are not the most important influence on their volumes. The ability of both income and economic value of equity (EVE) sensitivity model software to reflect rate-driven changes in core deposit volumes can make a material difference in rate risk measurement. For banks that use one model for both income and EVE sensitivity measurement, the flexibility to use one set of assumptions for core deposit “lives” in the EVE model and a different set in the income model may be another important feature. Simulating the Exercise of Embedded Options When banks hold material amounts of products with embedded options, they must include assumptions about the exercise of those options for accurate simulation. Even though most simulation models can accept a tremendous amount of input and produce a dazzling quantity of output, they are not very good at simulating the way in which loan prepayments, deposit withdrawals, and other embedded options are influenced by

Selecting and Installing AL Models 10/08

changes in interest rates. In fact, the analytical treatment of embedded options in some of these models can best be described as crude. Many of these models handle all embedded options in that the sofiware does have the capacity to permit the analyst to model the effects of different prepayment assumptions in different rate environments. However, they are crude in the sense that the user must determine the changes in volume that result from changes in interest rates and then manually put into the model separate sets of assumptions for each rate scenario.

It is simply wrong, not to mention misleading and inaccurate, to assume that loan prepayments or the exercise of other options will occur to the same extent in high interest rate environments as they do in low rate environments. When such changes are meaningful, the simulation model should not only include them but should also allow for these assumptions to be varied easily for each rate scenario simulated. As noted above, automated input of different prepayment assumptions for different rate environments can be critical for some banks.

Simulation software can incorporate even more complex features for simulating the exercise of embedded options. Some interest rate risk software vendors are now promoting models with highly sophisticated analytical techniques to capture the rate risk created by embedded options. Monte Carlo analysis, discussed later in this chapter, is one of the more popular new approaches. A major feature of some of the models with the most sophisticated analytics is the ability to simulate the way in which the exercise of embedded options depends on previous rate levels, not just currently prevailing rates. As discussed, rate levels are a significant factor. The path of all the historical rate changes since any given asset or liability was created can materially influence the probability of the customer exercising an option embedded in that product. (Path dependency is discussed in Chapters 7 and 8.) The potentially material influence of rate paths can be seen in the following example, taken from Chapter 7. As interest rates have risen and declined in cycles over the past decades, three different groups of Government National Mortgage Association (GNMA) 9 percent coupon pass-through pools were issued. Investors purchased GNMA 95 issued in 1979, in 1986—1987, and in

9-9

10/08 Interest Rate Risk Manggement

1990. When prevailing mortgage rates fell from 9 percent in 1990 to less than 7 percent in late 1993, prepayments on all mortgage-backed securities increased substantially. Nevertheless, older GNMA 95 did not prepay as quickly as the newer pools. This is because borrowers with older mortgages who wanted to take advantage of lower rates by refinancing their loans had previous opportunities to do so, whereas borrowers with newer loans who wanted to take advantage of lower rates to refinance their loans had their first opportunity to do so in 1992 and

1993.

In reality, the age of the asset or liability with an embedded option, together with the path followed by rates since that product was issued, has a strong influence on whether the customer will exercise the option. The actual level of rates is not the only influence. As a result, some rate risk managers want their simulation software to reflect those age and path effects. This is especially true for large banks with major holdings of residential mortgage loans, mortgage-backed bonds, savings accounts, and negotiable order of withdrawal (NOW) accounts. Criteriafor Selecting Product Options Capabilities At the same time that we emphasize the ability of simulation software to facilitate the accurate modeling of embedded options, we must also keep a second consideration in mind. The effort to model the exercise of product options accurately must be proportional to the bank's situation. It is not worth the efl‘ort for banks with negligible holdings of products with options. On the other hand, it is clearly significant for banks with material holdings of products with options that are not automatically put into the model. The obvious example is banks with material holdings of residential mortgage loans or mortgage-backed securities.

Some banks with either large holdings of hard-to-analyze assets and liabilities or a need for more precise IRR measurements may want a model with sophisticated analytics. Other banks, especially community banks, may not need such software and may even find it counterproductive. Models capable of calculating hundreds of different rate paths or option-adjusted spreads are another appropriate tool for rate risk managers in a few sophisticated banks. However, most community banks probably don't need them and would find them almost impossible to cost justify. The same is true for models incorporating calculation

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techniques like mathematical theories of uncertainty, including the use of chaos theory, neural networks, and fuzzy logic.1 Basis Risk

The model should be able to reflect difi‘erent amounts of change in different interest rates. The need for rate risk managers to evaluate basis risk is particularly acute for banks with large portfolios of prime-rate loans. Since these loans usually reprice on the day that the prime changes or shortly thereafier, prime-rate loans are correctly viewed as assets with very little yield curve or mismatch risk. Prime-rate loans do, however, have considerable basis risk. During a recent two-year period, the spread between the prime rate and rates for three-month certificates of deposits (CDs) ranged from a low of 190 basis points to a high of 290 basis points. This fluctuation led to a 10 to 20 percent improvement in the net interest margins of regional U.S. banks during that period.

Basis risk is not static. It can change considerably over time. Consider the spread that banks can earn by making prime-based loans that are funded by overnight federal funds. Such transactions create very little mismatch risk since the interest rates for most prime-based loans change whenever the prime rate changes. Nevertheless, they create quite a bit of basis risk. In 1986, a bank that followed this strategy would have earned an average spread of 177 basis points between the rates paid for the ovemight federal funds and the rates received from the prime-based loans. In 1994, a bank that followed this strategy would have earned an a 72 percent fatter margin. The average spread of 305 basis points reduction in profits that could result from a change from a 305 basis point spread back to a more typical prime/federal funds spread — in other words, the basis risk —— is material even though the mismatch between the repricing date of prime-rate loans and the repricing date of ovemight federal funds is not. (The only mismatch risk in this case results from the time lags.)

—

I.

Peter J. Brennan, “Banks Are firming to Software to Manage Mortgage Risk," Bank Management, October 1993, page 20.

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4. Number and Choice of Rate Scenarios The number of rate scenarios that can be modeled is important. As discussed in Chapter 8, large rate changes are important for some analyses, while smaller rate changes may be more realistic. Consider the arguments for measuring the impact of large changes in interest rates. We can identify two principal arguments. First, if we model 50 or 100 basis point rate changes, our simulations will not reflect the true extent of our rate risk. Take an adjustable-rate mortgage loan with a current coupon rate of 9.5 percent and a lifetime rate cap of 11 percent. If we simulate the effects of an increase in prevailing rates from 9.5 percent to 10.5 percent, the cap will still be out of the money. The asset will still appear to convey no adverse consequences from the increase in rates. Alternatively, if we choose to simulate the effects of a 200 basis point rate increase, the adjustable-rate loan will suddenly appear as an asset conveying significant adverse consequences from the increase in rates. A second argument can also be made to support the evaluation of the effects of large rate changes. The thought is that any adverse consequences from small changes in prevailing rates will tend to be less material than adverse consequences from large changes in prevailing rates. If a 100 basis point rate change causes an 8 percent decline in net income or a 0.50 percent net income, changes of this magnitude are too inconsequential to require major amounts of management time and effort. But if a 300 basis point change in rates can produce a 50 percent decrease in net income or a 10 percent reduction in equity, the risk requires management’s time and effort. On the other hand, one can argue that small rate changes should be simulated. The case for examining the consequences of small rate changes is based on the argument that big rate movements are less common than small rate changes. Furthermore, even when rates do change by 200, 300, or 400 basis points, they do so in smaller increments spread out over months or years. It is more realistic to simulate the effects of small rate changes because that is what we are more likely to experience.

In truth, IRR analysts should be considering the effects of both small and large rate changes. Accordingly, simulation software needs to be able to accommodate multiple scenarios. In Chapter 4, we saw examples using 9-12

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four scenarios: a rising-rate scenario, a falling-rate scenario, a mostprobable rate change scenario, and a no-change scenario. In Chapter 5, we saw a sample EVE sensitivity report that reflected nine difi‘erent rate scenarios: up 200, up 150, up 100, up 50, no change, down 50, down 100, down 150, and down 200. The need to simulate the consequences of both large and small rate changes is not the only criterion for determining the number of scenarios. Some managers may want to run simulations using an anticipated “most likely” rate environment. The most likely rate case may be obtained from internal analysis, such as the histograms discussed in Chapter 9. Alternatively, it may come from external forecasts or from implied forward yield curves. The most likely rate case scenario may be the same rate forecast used in the bank’s budget. In fact, banks using income simulation models for budgeting will require a most likely rate scenario.

For most banks, models that permit analysis of 4 to 10 different rate scenarios are all that is necessary. Four are fine; 10 are more than adequate. Large, sophisticated banks may use stochastic mathematical tools such as Monte Carlo analysis to model hundreds or even thousands of different rate scenarios. (Monte Carlo analysis is discussed later in this chapter.)

If you are running deterministic scenarios, the size of the rate change is not the only variable to consider. You should also evaluate non-parallel yield changes. This will enable you to capture the yield curve twist component of IR. 5. Features for Facilitating Realism of Rate Scenarios

At least some rate risk analysis requires the capability to model realistic changes. (Modeling likely and improbable rate changes is discussed in Chapter 12.) The obvious elements for realistic scenarios are non-parallel and non-instantaneous rate changes. Less obvious elements include correlau'ons between changes in variables. Consider the following model functions: El

Instantaneous vs. phased-in rate changes. More realistic rate change modeling may include scenarios in which rate changes are phased in over a number of months instead of being implemented 9-13

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instantaneously as assumed by rate shocks. Rates, as we have let alone seen, rarely change in one jump by 100 basis points 150 or 200 basis points. Instead, they tend to increase or decrease in a series of smaller changes. If interest rates rise by 365 basis points tomorrow and then stay the same for 364 days, rates will be 3.65 percent higher a year from now than they are today. Alternatively, if rates rise by I basis point a day every day for the next 365 days, rates will still be 3.65 percent higher a year from now than they are today. Although the rate change in both cases is the same by the end of the year, the prevailing rates during the two hypothetical years were obviously different. Consequently, the

—

interest income and expense for a bank would be different for each scenario. A realistic simulation might model rate changes from a starting yield curve to a horizon date yield curve. Rising vs. falling rates. More realistic rate change modeling may reflect rising rate scenarios with different rate relationships than are reflected in falling rate scenarios. For example, in Chapter 7, we noted that a study of changes in the prime rate found that after an increase in money market rates, the prime rate reflected 60 percent of the change in the first month, 10 percent of the change in the second month, and 20 percent of the change in the third month. In contrast, after a decrease in money market rates, the prime rate reflected 30 percent of the change in the first month, 30 percent in the second month, and 15 percent in the third month after the change.

Not surprisingly, banks are quicker to raise the prime than to lower it. Similar asymmetrical movements can be found in other administered rates, such as rates paid on savings and NOW accounts. Economic value of equity sensitivity models must employ separate discount rates for each product group as well as for falling and rising rate scenarios to reflect the timing differences in the rate changes for administered-rate products. Short-term vs. long-term rates. More realistic rate change modeling may reflect scenarios in which short-term and long-term rates do not change by equal amounts whenever prevailing rates change (nonparallel). In other words, it is important to be able to simulate yield curve, or yield curve twist, risk. Short-term rates are

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usually more volatile than long-term rates. This issue of nonparallel changes in rates is discussed in more detail in Chapter 8.

Variations in efl'ect on assets and liabilities. By far the most important, more realistic rate change modeling may reflect scenarios in which rate changes are larger for some assets and liabilities than for others. This variation is far more realistic than the implied assumption in rate shock scenarios that all rates change by identical amounts. Yield curves for different instruments change by different amounts. For example, an asset or liability tied to the 90-day London interbank offered rate (LIBOR) may change by 20 basis points on the same day that an asset or liability tied to the three-month U.S. Treasury bill rate changes by only 10 basis points.

It is important to be able to simulate basis risk. As noted in Chapter 1, basis risk may comprise as much as 60 percent of total interest rate risk. A model that cannot easily simulate rate change scenarios in which some rates change by difl'erent amounts than others will miss a major aspect of overall IRR.

Irregular rate paths. Some rate risk managers, especially those in large banks with material portfolios of retail products with embedded options, want to simulate irregular paths for future rate changes. As noted, interest rate changes follow irregular paths. Both the amount and the timing of rate changes are irregular. It is even possible to experience years that see both increases and decreases in prevailing rates. Advanced modeling techniques like Monte Carlo analysis, discussed later in this chapter, may calculate and analyze hundreds of different rate paths for each rate change scenario. A typical example is a regional bank that considers 200 alternative rate paths for each of eight different rate scenarios.

Models may also incorporate statistical tools that effectively

emphasize more probable rate paths and de-emphasize improbable rate paths. For example, it is reasonable to include assumptions for “mean reversion.” It is improbable to assume that rate changes will continue in one direction (rising or falling) for long periods of

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time. Experience shows that short-term increases or decreases in prevailing interest rates do not continue indefinitely. Instead, over time, changes tend to switch back toward long-term trends or average levels. If yield curves are flatter or steeper than usual, the bank may want to forecast a reversion to more normal relationships between long- and short-term rates. If spread relationships between rates for different instruments are wider or narrower than usual, the bank may want to forecast changes that bring them more in line with experienced spreads.

6. Level of Output Detail Provided

The output reports generated by income and EVE sensitivity models can be voluminous. Some models produce an almost overwhelming amount of data in dozens of reports. Nevertheless, the essential issue is the usefulness —— not the volume — of reported information. Data are not necessarily the same thing as information. We can consider a number of report features that can be useful to rate risk managers. Detail Reports Detail reports from income simulation model output typically consist of future balance sheet and income statements for each different interest rate scenario forecasted. Obviously, separate sets of financial reports are generated for each interest rate scenario modeled. EVE sensitivity simulation models produce future balance sheets for each difl'erent interest rate scenario forecast.

In most cases, only the analysts read the detail reports. It is important for these reports to be sufficiently encompassing, adequately organized, and clear enough for rate risk analysts to be able to isolate and examine individual influences on the measured rate risk exposure. Good output reports give analysts the ability to “drill down” through the data. For example, if the model shows an unacceptably large amount of rate risk, the detail reports should clearly show the products or changes that most significantly contribute to that risk. If the detail reports provide the needed information in a clear and well-organized manner, the analysts can find and link the causes with the effects. In addition, good data output from the model helps analysts locate errors. The clear and organized presentation of the appropriate amount of detailed information

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also enables analysts and auditors to track how forecasted behaviors for individual components in the model, like individual bank products, compare with the actual changes in those products subsequently observed.

Comparative Reports Simulation models should also produce comparative reports. Comparative reports provide a wealth of detail that IRR analysts can use to pinpoint the balance sheet sources of rate risk. Comparative reports can also be used to monitor the accuracy of simulations. Since the simulation depends so heavily on the assumptions for the variables described above, some quality control is a good idea before the model’s output is presented to bank management. Line-by-line comparisons of the yields and costs (for income simulations) or of economic values (for EVE sensitivity simulations) can highlight errors in the projections so you can ensure that the component assumptions and forecasts are

internally consistent.

For example, an assumption of rapidly declining mortgage loan volumes resulting from a fast rate of mortgage loan repayments is probably not consistent with a forecast of sharply higher interest rates. Consumers are less likely to refinance loans when interest rates are higher. Similarly, a scenario that forecasts a 200 basis point increase in prevailing interest rates might show a 200 basis point increase in the cost of short-term borrowings, but it should not show a 200 basis point increase in the interest expense for CDs. That is because only some CDs mature and are then renewed or replaced with new CDs at the projected higher rates. Other CDs will not reprice when prevailing rates rise 200 basis points, because they don‘t mature until later. Some CDs might not reprice for one or more years. As discussed in Chapter 10, such comparisons are a necessary part of the control and benchmarking needed to ensure that future simulations are reliable.

Additional management reports, such as reports listing assumptions currently employed by the simulation and reports logging the history of assumption revisions, are also a necessary part of the control and benchmarking. Model controls are discussed in Chapter 10.

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Management Reports Unlike rate risk analysts, rate risk managers do not need detailed reports. In fact, asset/liability committee (ALCO) meetings can easily bog down with too much review of reported data and not enough consideration of the implications of the reported data. For this reason, the simulation software should produce clear and concise management reports. The more succinct, the better. In many cases, the best management reports consist of tables or graphs. Exhibit 3.4 in Chapter 3 has one of the best formats for presenting the analysis from income simulation models. Exhibit 5.2 in Chapter 5 has one of the best formats for presenting the analysis from EVE sensitivity simulation. These data can be supplemented with graphs like the ones shown in Exhibits 3.7 and 5.3.

Deviationsfrom Bank Policy Last, but certainly not least, the management reports should indicate clearly deviations from rate risk exposure limits set forth in approved bank policies.

7. Risk Measurement Methodologies

The software model’s approach to measuring rate risk exposure is one of its most important attributes. Gap models, particularly static gap models, are simply inadequate. The vast majority of banks must choose income simulation, EVE sensitivity simulation, or software that does both. Some software excels at income simulation modeling; other software is better for EVE sensitivity simulation modeling. Some software incorporates advanced modeling techniques like Monte Carlo simulation. The bank must match the strengths of the software it selects with the primary objectives and philosophies of its approaches to rate risk assessment. Be sure that the software provides the type of analysis that meets your

requirements.

8. Regulatory Compliance Issues for Interest Rate Risk Models

No list of model features could be complete without consideration of those features needed to meet regulatory requirements. Specific

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requirements for thrift institutions are included in the Thrift Bulletin 13 (TB-133) directive for thrift institutions. For commercial banks, regulatory compliance requirements for interest rate risk management come from a variety of sources. These include the Joint Agency Final Rule Amending Risk-Based Capital Standards to Include Exposure to Interest Rate Risk issued in 1995 to implement Federal Deposit Insurance Corporation Improvement Act (FDICIA) section 305, the Joint Agency Policy Statement on Interest Rate Risk issued in 1996 as a supplement to the FDICIA 305 rule, and published guidelines for bank examinations. Federally regulated banks, thrifis, and credit unions must also comply with the 1998 Federal Financial Institutions Examination Council (FFIEC) Supervisory Policy Statement on Investment Securities and End-User Derivatives Activities. While this policy statement obviously focuses on investment activities, it also includes a paragraph discussing institution-wide measurement of interest rate (market) risk. That paragraph notes: “Institutions employing internal models should have adequate procedures to validate the models and to periodically review all elements of the modeling process.” Model validation is discussed in Chapter 10.

Thrill Institutions Thrift institutions follow Office of Thrift Supervision (OTS) procedures for measuring interest rate risk. These are set fourth in Thrift Bulletin 13a. (TB-13a replaced TB 13, l3-l, 13-2, 52, 52-1, and 65 in December 1998.) Due to the long-term and option-laden nature of many thrift assets, the OTS regulation of IR tends to be more structured than the requirements of the banking regulators. The OTS requires thrifts to measure the sensitivity of their economic value of equity to an immediate, parallel yield curve shift of plus or minus 100, 200, and 300 basis points. The OTS uses the term net portfolio value or NPV instead of EVE. With some exceptions, thrift institutions with total assets of less than $1 billion are required to use a standard OTS model. Other thrifts must use internal models acceptable to the OTS. Thrifis are encouraged, but not required, to supplement their NPV sensitivity analysis with measures of earnings at risk (EAR).

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Interest Rate Risk Management

Commercial Banks

Commercial banks do not have a required risk management methodology. However, FDICIA 305 required the banking agencies to revise their risk-based capital standards to ensure that those standards take adequate account of interest rate risk. In 1995, the Office of the Comptroller of the Currency (OCC), the Federal Reserve, and the Federal Deposit Insurance Corporation (FDIC) issued a final rule to implement that requirement. The 1995 final rule does not codify a. measurement framework for assessing the level of a bank’s interest rate risk exposure. Instead, it states that the regulators will evaluate the bank’s exposure to declines in the economic value of its capital due to changes in interest rates. As a result of that evaluation, the final supervisory judgment of a bank’s capital adequacy may differ from the conclusion drawn solely from the calculation of its risk-based capital ratio using the (credit risk-based) formula for that ratio that is currently in effect. Because the final rule issued by the bank regulators to implement FDICIA 305 did not establish a specific interest rate risk measurement system, the bank regulators supplemented that rule in 1996 with their Joint Agency Policy Statement on Interest Rate Risk. That policy statement includes a number of general descriptions that effectively constitute standards or requirements for internal bank rate risk measurement systems. In particular, thejoint agency policy statement states the following:2 The measurement system should include all material interest rate positions of the bank. CI

The measurement system should consider all relevant repricing and maturity data, including:

∙

2.

The current balance and the contractual rate of interest associated with the instruments and portfolios

Joint Agency Policy Statement: Interest Rate Risk, as published in the Federal Register. Vol. 61, No. 124, June 26, 1996. p886 33,171 and 33,172.

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∙ ∙ CI

The principal payments, interest rate reset dates, and maturities The rate index used for repricing and contractual interest rate ceilings or floors for adjustable-rate items

The measurement system assumptions and techniques.

should

have

well-documented

The measurement system should measure rate risk over a probable range of potential interest rate changes, including meaningful stress situations. The scenarios used should incorporate a sufficiently wide change in market interest rates (e.g., i200 basis points over a one-year horizon) and include immediate or gradual changes in market interest rates as well as changes in the shape of the yield curve in order to capture the material effects of any explicit or embedded options.

Assumptions about customer behavior and new business activity should be reasonable and consistent with each rate scenario evaluated.

Reports reflecting the bank’s interest rate risk profile should be provided to the bank’s senior management and its board or a board committee at least quarterly. More frequent reporting may be appropriate. Reports should provide sufficient information to allow senior management and the board to do the following:

∙ ∙ ∙ ∙

Evaluate the level and trends of the bank’s aggregate interest rate risk exposure. Evaluate the sensitivity assumptions.

and reasonableness of key

Verify compliance with the board‘s established risk tolerance levels and limits, and identify any policy

exceptions.

Determine whether the bank holds sufficient capital for the level of its interest rate risk exposure.

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Independent internal controls for the bank’s risk measurement system must be appropriate, given the nature, scope, and complexity of its activities. They must periodically verify and validate the accuracy and completeness of data entered in the bank’s risk management system, the reasonableness and validity of scenarios used in the rate risk management system, and the validity of the risk measurement calculations. (See the discussion of model risk, in Chapter 10, for more information on model controls and on regulatory expectations for model controls.) Bank Examiner Guidelines Bank examiner guidelines comprise an additional group of regulatory requirements. These are essentially the minimum IRR measurement standards set by the examiners in publications issued to both bankers and bank examiners.3 All of the major requirements that apply to simulation modeling in the examination guidelines are included in the above discussions of model features. A summary of the OCC, Federal Reserve, and FDIC requirements is given in the following paragraphs. Model risk management requirements are discussed in Chapter 10. El

OCC. The OCC, the regulator of national banks, provides some guidelines for model requirements. These include:

∙ ∙ ∙

∙

3.

Above all, management should consider the ability of bank personnel to understand and update the model. A bank’s model should be able to handle every type of financial instrument (on— and ofi-balance-sheet) that the bank uses. The reports generated by the model should be easy to prepare and interpret.

If the bank uses the model for budgeting or planning, the model should be able to track and compare actual results with projections.

See Comptroller's Handbook for National Bank Examiners; FDIC, Division of Supervision. document FIL-60-94, August 26, 1994.

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Will the model expend so much computer time that the production of other computer-generated reports will be compromised?

If the bank uses an outside model vendor, does the vendor supply initial and ongoing support, updates, and model validation? A model that can flag inconsistent data facilitates the early discovery of errors.

Comprehensive documentation of the model‘s operation should help track errors. Can the model accommodate a number of accounts and products sufficient to meet the bank’s current and projected

needs?

Can the bank, not just the vendor, add or modify accounts analyzed by the model?

Is the model capable of running the number of rate scenarios desired by the bank? Can the bank define rate scenarios, or are they limited to generic scenarios built into the model?

Does the process by which data is input into the model preserve the data’s accuracy and integrity?

Is the model capable of producing the types of analysis (e.g., gap, duration, net income simulation, economic value sensitivity simulation, VaR) that the bank requires? 4

FDIC. The FDIC has published a memorandum on the assessment of interest rate risk. It contains a summary of requirements for measurement systems. (The memorandum also includes other requirements, many of which address controls for simulation a topic covered in more detail in Chapter 10.) The modeling requirements are as follows:

—

Comptroller of the Currency, “Interest Rate Risk“ booklet in the Comptroller’s

Handbook. June 1997. pages 99-101.

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Interest Rate Risk Management

∙ ∙ ∙ ∙

∙ ∙ ∙ ∙

∙ ∙ ∙

Institutions with significant holdings of instruments with embedded options or institutions that are exposed to basis risk should use interest rate risk measurement systems that are capable of measuring these risks. Simulation model input must be reconciled to financial statements.

Simulation model input must employ appropriate data

aggregation.

Simulation model input must include adequate account data.

Assumptions for customer/account behavior must be specific to each rate scenario and should vary by type of instrument, geographic location, and customer base.

Assumptions should be supported by documented analysis or studies. Assumptions should have been reviewed and approved by the bank’s internal rate risk management committee or the board of directors. The institution should have adequate documentation with respect to the equations, assumptions, and methodologies used in the measurement system. The methodologies employed in the rate risk measurement system should be appropriate and adequate for the bank’s on- and off-balance sheet positions.

The

institution should review actual performance vs. forecasted performance.

The system must measure significant risks, including overall asset/liability mismatches, basis risk, embedded option risk, and risks resulting from nonparallel yield curve shifts.

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∙ III

The results from the measurement system should reveal deviations from rate risk exposure limits established by bank policy.5

The Federal Reserve. The Federal Reserve’s Commercial Bank Examination Manual makes two important general observations about risk measurement and monitoring systems. First, the sophistication and complexity of this process should be appropriate to the size, complexity, nature, and mix of both an institution’s business lines and its IRR characteristics. Second, well-managed banks have IRR measurement systems that measure the effect of rate changes on both earnings and economic value.

Beyond those general observations, the Fed identifies three main requirements for IRR measurement systems. It states that measurement systems should:

∙

∙

∙

Assess all material IRR associated with an institution’s assets, liabilities, and off-balance sheet positions. Material sources of IR include mismatch, basis, and option risk exposures.

Use generally accepted financial concepts and risk measurement techniques. Have well-documented assumptions and parameters.

D The Commercial Bank Examination Manual goes on to discuss some more specific requirements. Rate risk measurement techniques and associated models should be sufficiently robust to adequately measure the risk profile of the institution’s holdings. Depending on the size and sophistication of the institution and its activities, as well as the nature of its holdings, its IRR measurement system should:

∙

Be capable of reflecting uncertain principal amortization and prepayments.

“Assessment of Interest Rate Risk," FDIC Memorandum 6230 (IXS). August 12. 1994, page: 6-14.

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∙

∙ ∙ ∙ ∙

Be capable of reflecting caps and floors on loans and securities, where material. Be capable of reflecting the characteristics of both basic and complex off-balance sheet instruments held by the institution. Be capable of reflecting changing spread relationships necessary to capture basis risk.

Provide clear reports that identify major assumptions. Provide reports that allow management to evaluate the reasonableness of and internal consistency among key

assumptions.6

9. Easy “What-Ii” Modeling

Still another model feature that is important to many rate risk managers is the capability for doing “what-it" modeling quickly and easily. The modeling sofiware should allow users to investigate the consequences of just one or two changes. For example, suppose that the bank’s simulation model indicates the bank’s net EVE will decline by 23 percent in the event of a 200 basis point rate increase. The bank’s ALCO proposes to reduce this exposure by attracting $10 million in new five-year CDs at a rate of 5 percent. The funds will be used for a $10 million investment in a floating-rate security, tied to LIBOR. The floating-rate security has a current coupon of 6.475 percent and a cap of 10 percent. Will these changes reduce the bank’s liability sensitivity? A few fast entries in the model quickly produce a report that shows a revised exposure to a 19 percent decline in equity resulting from a 200 basis point increase in rates. In this case, the ALCO’s proposed changes can be expected to reduce the bank's liability sensitivity by 4 percent of capital. The ALCO can then decide whether the 4 percent improvement is sufficient to justify the changes that it wants to make.

6.

“Interest Rate Risk Management,” Section 4090.1, Commercial Bank Examination Manual, Federal Reserve Board of Governors, November I996. pages 6-8.

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The same type of what-if analysis can be used whenever rate risk managers want to model the effects of proposed changes planned by loan, deposit, or investment managers. The capability of easy, rapid, on-screen what-if modeling can also create a subtler benefit. Often, the bank executives responsible for managing IRR are not familiar with the actual operation of the simulation software (even though they are quite knowledgeable in the analysis and application of the model’s output). When this is the case, managers may be reluctant to make frequent or spur-of-the-moment requests to the analysts to rerun the simulation with a few changes. If these managers can, instead, access an easy-to-use what-if model, they may make more use of the simulation software. A closer examination of more alternative strategies should contribute to better decision making. 10. Applicability to Other Management Goals

Interest rate risk measurement sofiware must be evaluated on the basis of its effectiveness in the measurement of IR. Nevertheless, some measurement models also offer other bank management benefits that enhance their utility. The most common uses of interest rate risk sofiware for other management tasks include budgeting, investment portfolio management, required financial disclosures, and product pricing. These applications are discussed below. Budgeting Banks that use income simulation models for IR measurement can benefit by using the same software for budgeting. Budgeting, after all, requires many of the same assumptions for rates and volumes. In fact, banks that include a most likely rate scenario as one of the rate scenarios used in their simulation model will find it hard to justify using any rate or volume assumptions in that scenario that vary from the rate and volume assumptions used in their budgets. If budgeting is important for your bank, be sure that the software can generate the budget output your bank requires. Budget reports, for example, should be able to compare the budget with the actual results subsequently realized.

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Interest Rate Risk Management

Investment Portfolio Management Economic value of equity sensitivity simulation software can help investment portfolio managers comply with Statement of Financial Accounting Standards No. 115 (FAS 115). As noted in Chapter 5, the Financial Accounting Standards Board (FASB) issued FAS 115,

Accounting for Certain Investments in Debt and Equity Securities, in 1993. The rule creates three separate categories for investment securities and establishes distinctly separate accounting treatments for securities in each category. The three categories are trading, available for sale, and held to maturity. For most banks, the main decision FAS 115 requires pertains to the assignment of investment securities as either available for sale (AFS) or held to maturity (HTM). Changes in the market value of AFS investments must be reflected in reported capital. As a result, managers need to manage AFS holdings to keep market value changes within acceptable boundaries. Economic value of equity sensitivity simulation can provide managers with the data necessary to achieve that goal. Specifically, EVE sensitivity simulation can provide managers with forecasts of market or economic values under a number of different rate scenarios. (Bond calculators can do this too, but they do it one bond and one rate scenario at a time.)

Required Financial Disclosures

EVE sensitivity simulation software can produce disclosures required for compliance with FAS 107, Disclosures About Fair Value of Financial Instruments. The FASB issued FAS 107 in 1991. The rule requires financial institutions to disclose, to the extent practicable, the market

value of financial assets. Clearly, most investment securities have actively traded markets with readily available market prices. Just as clearly, most bank assets and almost all bank liabilities do not have actively traded markets with readily available market prices. When market prices are not available, FAS 107 suggests calculating “the present value of estimated future cash flows using a discount rate commensurate with the risks involved.” EVE sensitivity simulations have all of the required data necessary for these disclosures. In effect, the disclosures required by FAS 107 are nothing more than the economic values of the assets and liabilities in the no-change-in-rates scenario.

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Product Pricing Another benefit of EVE sensitivity simulation sofiware is that market or economic value sensitivities of individual asset and liability types can be used to make pricing and marketing decisions. The market or economic values for individual groups of assets and liabilities must be calculated as intermediate steps in the process of calculating EVE. Data entered in the EVE sensitivity simulation are aggregated in groups selected by the users. For example, loans may be aggregated as closed-end consumer loans, open-end consumer loans, closed-end business loans, open-end business loans, and mortgage loans. Economic value sensitivities for each asset and liability aggregation group in the simulation can be examined and compared. Bank products can even be ranked by their economic value sensitivity.

One important application of these data can be in product pricing. For example, the rates charged for loans should include a charge for the interest rate risk. A short-term fixed-rate loan requires only a small rate risk premium. A long-term fixed-rate loan clearly requires a larger rate risk premium. The same data can also be used to make marketing decisions. For example, a bank exposed to declining EVE in rising rate environments can reduce that exposure by focusing on increasing liability products with the largest rate sensitivity or reducing assets that have the largest rate sensitivity. This type of management activity can be an example of natural hedging, a concept discussed in Chapter 15.

Using Datafrom Call Reports Sometimes small banks are tempted to use low-cost modeling solutions provided by third-party vendors who use call report data to construct risk exposure measurements. This is a bad idea.

Three points are particularly relevant. First, in schedule RC-B, fixed-rate mortgage-related securities are reported based upon their contractual maturity. Second, in schedule RC-C, fixed-rate loans are reported based on their contractual maturity. As a result, auto loans, as well as mortgage loans, will be seriously overstated. Third, the call report does not request information about the bank’s estimates for the repricing of characteristics

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of checking, savings, NOW, and MMDA deposits. Therefore, anyone attempting to assess rate risk using call report data must make some heroic assumptions about core deposits.

In addition to those three major data problems, there are two other limitations. First, call report data on bank debt does not distinguish between floating-rate and fixed-rate debt. Since few banks have much debt, that is not a serious problem. Second, call report data on offbalance sheet positions only provide a bit of data on hedges. Any bank using swaps or other derivatives hedges probably has less risk than is apparent from an analysis of call report data. Notwithstanding those five data problems, we can use call report data to construct gap reports for banks. But gap reports are woefully inadequate measures of rate risk. We cannot use call report data to measure earnings at risk unless we also make the heroic assumption that all runoff is replaced by identical volumes of new business at some new level of rates. And, we cannot use call report data to measure economic value of equity at risk unless we also make some very over-simplified assumptions about both discount rates and timing of principal cash flows. The end result is that any interest rate risk analysis created from call report data is simply too inaccurate to use for rate risk management.

OPTION-ADJUSTED SPREADS, MONTE CARLO, AND OTHER ADVANCED MODELING FEATURES

A number of long-term trends are pushing IRR managers towards more sophisticated income and economic value simulation models. Retail products include more embedded options than previously. Investment bankers design more complicated security structures, such as ABS, CMO, and CLO instruments, complicating analysis of risk in bank investment holdings. Advances in computer hardware and software technology permit more computational intensive modeling. And last but not least, regulators are more insistent that each bank’s risk measurement tools are capable of capturing the risks that the bank is exposed to from the assets, liabilities, and off-balance sheet commitments it chooses to hold.

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So what are “more sophisticated” income and economic value models? No clear bright line separates “sophisticated" and “unsophisticated.” Instead, there is a continuum. Models at the high end are characterized by two features:

∙ ∙

High-end models do not require aggregation. As we discussed above, positions are modeled at the instrument level. Cash flows are calculated for each instrument.

High-end models employ probability-based decision-making tools. The nature and application of these tools are described in the following paragraphs.

At many points in our tour of rate risk measurement techniques up to this point, we have talked about rate risk measurement problems. A common element for most of those problems is customer or bank options in loan and deposit products. In the Chapter 3 discussion of earnings at risk, we emphasized how customer and business behaviors had to be incorporated into the assumptions for each rate scenario modeled. For example, if we want to project the impact of a worst case rising rate scenario, we might define the size of the rate increase to be examined, but we must also define the changes in loan prepayments, deposit withdrawals, etc. that can be expected to occur if rates rise by that amount. This is a form of simple scenario analysis. In the Chapter 5 discussion of economic value of equity sensitivity, we used sample output reports for a handful of rate shock scenarios. More issues pertaining to option-laden bank loan and deposit products were then considered in Chapter 6.

Rate Scenarios: Stochastic and Term Structure Modeling Capabilities Now we can focus on the fact that all of the rate risk measurement techniques discussed in Chapters 3 through 6 relied on a small number of defined scenarios. At most, we might examine a dozen possible rate change scenarios using those techniques. Some of them don’t incorporate any rate-related changes in customer or bank behavior. At best, we might have a dozen different sets of assumptions reflecting option-driven variances in the amount or timing of cash flows.

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Notice that we haven’t merely limited the number of scenarios that we examine when we use those simple techniques. In addition, we have also “tied” a defined change in the timing or amount of cash flows to each projected rate change. All such approaches are “detemrinistic” because the possible interest rate paths and the associated changes in option exercise are predetermined by the model user. Although deterministic models are valuable, the accuracy of their outcomes depends on the accuracy of the interest rate scenarios. If actual interest rates or option exercise differs from assumptions, the risk to the bank may be substantially different from the measured risk. The truth is that static cash flow calculations, such as duration, and limited scenario analysis, such as the simple EAR and EVE models discussed so far, are fine for evaluating the rate risk inherent in everything except products with contingent cash flows, i.e., products with options. For any instrument with options, every time we consider a different interest rate scenario, both the applicable discount rate and the expected cash flows change. Neither the cash flow amounts nor the timing of the cash flows is static. There is no “closed form” solution. This is why mortgage loans, core deposits, and other bank products with options are so hard to model. Deterministic approaches are not very effective in situations were there are complex relationships among multiple variables. Instead of relying on deterministic scenarios, many banks prefer to use models that offer more complex statistical modeling methods to measure the probable outcomes of events, such as a movement in interest rates, that have a random element. Advanced rate risk models address those issues in a variety of ways. In Chapter 8 we considered a whole range of stochastic, term structure rate models including Monte Carlo models and trinomial lattices. Banks with significant holdings or core deposits and consumer loans should seriously consider models with stochastic rate

modeling capabilities.

Stochastic simulations are popular tools for rate risk managers and strategic planners. They provide a more complete simulation in the sense that they consider far more possible changes and outcomes. And they can provide more accurate measures of risk exposures for banks with material holdings of option-laden products. And there is an undeniable

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appeal to models that incorporate advanced math just because almost all of us have a natural tendency to associate sophisticated tools with better measurement.

Stochastic simulations, like deterministic modeling, are based on assumptions about future changes. The stochastic approach merely allows us to simulate a range of probable changes instead of a small number of selected changes. Even though the model sofiware handles complex calculations, rate risk analysts must nevertheless understand how the concepts work. As we discussed in Chapter 8, a number of key variables or critical input decisions can have a huge impact on the model’s output. For example, just for generating rate paths, critical assumptions involve rate volatility, mean reversion, and other rules for limiting rate scenarios. OAS calculations also require selection of riskfree yield curves. Prepayment models, whether standalone or not, require assumptions about bank and customer behaviors. Stochastic simulations, like all interest rate risk measurement systems, are only as good as the data and assumptions underlying the calculations. As the OCC notes: “... certain properties are usually built into this process to ensure that the mean (average) interest rate generated is consistent with the current structure of interest rates and that the dispersion (distribution) of possible interest rates is consistent with observed volatility. These properties are important to ensure that the model does not introduce the possibility of “risk-free” arbitrage.”7 In addition, the simulation requires assumptions about how the amount and the timing of each instrument’s cash flows will vary with changes in rates. In other words, the cash flow patterns change for each rate path. For mortgage loans, this, of course, is more familiarly known as the prepayment assumptions. Obviously, a model that uses different prepayment assumptions for new and seasoned mortgage loans will be more accurate than one which does not. The reliability of the measured output is heavily dependent upon these input variables. All of these topics are beyond the scope of this overview but should be understood by bankers electing to use models with Monte Carlo features. Just because the model employs whiz-bang math doesn’t necessarily mean that the 7.

“Interest Rate Risk" booklet in the Comptroller's Handbook, Oflice of the Comptroller of the Currency, June 1997, page 95.

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results are always more accurate. The OCC observes that: “To correctly derive and apply this modeling process, a bank must have staff members with considerable expertise in financial and statistical theory.”a

Capability to Model Prepayments and Other Embedded Options Of course the need for a model that captures the riskiness of embedded options is not only a matter of supporting appropriate rate scenarios. Banks with significant holdings of products with embedded options need the capability to model how and when options get exercised.

For many banks, particularly small banks, the potential exercise of embedded options merely requires careful construction of assumptions for deposit withdrawals, loan prepayments, etc. For each product type, the bank needs sets of assumptions. Within each set, there should be an assumption for each rate scenario. For example, in a rising rate scenario, the bank might assume that more customers will exercise their options to redeem CDs prior to maturity. However, you may want to select a simulation model that enables some or all of the option related assumptions to be created analytically. Two specific features, OAS and prepayment models, are discussed in the following subsections:

Option Adjusted Spreads Banks employing EVE simulation may want to have models that include option adjusted spread (OAS). In a nutshell, OAS measures the average difference between the yield available from an instrument with optionality and the yield available fi'om risk-free alternatives in a number of alternative rate scenarios. The average difference, or spread, is the value of the option feature. In order to calculate OAS, investors or rate risk analysts need to know three sets of information:

1. Interest rate generation. What future paths might interest rates take?

8.

“Interest Rate Risk" booklet in the Complroller's Handbook, Office of the Comptroller of the Currency. June 1997, page 97.

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2.

Volatility estimates. How much will interest rates change? What is the dispersion of rate changes in each possible rate path?

3. Prepayment models. How much will the amount and the timing of cash flows tied to options vary for each rate path, each volatility estimate, and each time period?

Of course, unlike investors, rate risk analysts are not primarily interested in finding the option-adjusted spread. Instead, rate risk analysts want to know about the rate sensitivity of cash flows with optionality. So, the important point is not whether or not your model can calculate optionadjusted spreads. Instead, the important point is whether your model can use OAS methods.

Prepayment Models As we noted near the beginning of this section, modeling the rate risk of options requires more thanjust a large number of possible rate paths. We also need some reasonable idea of how changes in the exercise of options changes in the amount and timing of option-related cash flows, — connect to each rate path. We have already seen how many Monte Carlo models combine stochastic rate generations with prepayment models.

—

Prepayment models are simply software programs that analyze a group of variables to predict how options will be exercised. Consider a simple example. Suppose you have a 9 percent, fixed rate mortgage loan. If rates fall fi'om 11 percent to 10 percent, the loan is not much more likely to be prepaid. If rates fall from 9 percent to 8 percent, the loan is very much more likely to be prepaid than it was. If rates fall from 6 percent to 5 percent, the loan is not much more likely to be prepaid. In each of these examples we have considered a 1 percentage point change in rates and three different rate paths. A more complete model considers rate levels, rate paths, and rate volatility. In addition, more complete models consider burnout, seasoning, and seasonality. You may acquire a high-end rate risk model that includes a prepayment model. Both models with Monte Carlo and lattice rate generation capabilities may incorporate a prepayment model. Alternatively, you may simply use the output from a standalone prepayment model as another set of inputs in your rate risk model.

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Advanced Modeling Summary

Some rate risk managers make a serious mistake. They overlook the fact that just because they have a more powerful model does not mean that they are measuring their rate risk exposure more accurately. On the contrary. Using a more powerful model creates more opportunities for data errors, assumption errors, and model operational errors. Furthermore, there can easily be gaps between theoretical risk evaluations and observable risk in the real world. The well-known risk expert, Dr. Robert Merton, summarized this problem beautifully in his Nobel Prize acceptance lecture.

At times we can lose sight of the ultimate purpose of the models when their mathematics become too interesting. The mathematics of financial models can be applied precisely, but the models are not at all precise in their application to the complex real world. Their accuracy as a useful approximation to that world varies significantly across time and place. The models should be applied in practice only tentatively, with careful assessment of their limitations in each application.”

INTEGRATING MODEL TECHNIQUES

In the discussion of model features earlier in this chapter, we considered an example of a bank that was exposed to a 23 percent decline in its EVE because of a 200 basis point rate increase. In that example, the bank’s ALCO proposed to reduce the bank‘s exposure by making two changes. The EVE sensitivity simulation model indicated that the result of those two changes would be a 4 percent reduction in the bank’s liability sensitivity. In that example, the exposure of the bank’s EVE in the event of a 200 basis point increase in interest rates fell to 19 percent of the net economic value of equity. An ALCO that considered its IRR exposure only in terms of EVE at risk might then be satisfied to consider whether the 4 percent reduction in its

9.

Nobel Lecture by Dr. Robert Merton, December 9, 1997.

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rate risk was sufficient to justify the contemplated changes. However, a more complete analysis might shed more light on the subject. An ALCO that considered its IRR exposure in terms of income at risk might model the effects of the exact same proposed changes. In this case, the same proposed changes applied to the same bank at the same time indicate the following change: A 200 basis point increase in rates would cause a 6 percent decrease in net income before the two changes but less than a 1 percent change in net income after the two proposed changes. That is, in this case, the proposed changes reduce both income and EVE volatility in a rising rate environment.

In other situations, a proposed change might reduce interest rate risk when measured by income simulation but increase the risk when measured by EVE sensitivity simulation. The opposite is also true. Such cases arise due to timing differences. Recall that income simulations capture only interest rate exposure between a starting date and a horizon date — usually a year. EVE sensitivity simulation is capturing interest rate risk over all time periods. Thus, a change that affects time periods difl‘erently can have opposite effects on the two measures of risk. For example, if a bank buys a five-year fixed-rate investment at a yield of 10 percent and funds that asset with a one-year fixed-rate CD with a cost of 8 percent, the transaction will benefit net income for the next year, regardless of any changes in interest rates. However, since the oneyear CD must be renewed or replaced at rates prevailing a year later, the EVE benefits from that transaction only if rates subsequently decline. If rates rise, the transaction that increased income will decrease EVE.

This is another instance of the interest rate “time bomb” weakness in income simulation modeling that we considered in Chapter 3. As this example shows, income simulation modeling and EVE sensitivity simulation modeling can complement each other, because EVE sensitivity simulation captures risk that income simulation does not. The benefits of using both approaches are even greater. Recall that, in Chapter 5, we considered an example of how EVE sensitivity simulation overstates short-term interest rate risk. Thus, another reason income

simulation modeling and EVE sensitivity simulation modeling complement each other is that income simulation is a more accurate way of measuring short—term risk. 9-37

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TB-13 requires thrifi institutions to establish tolerance levels for both changes in net income over one year and changes in EVE (called “net portfolio value” by the OTS). Not all commercial banks do the same. The FDIC probably overstates the case when it notes that “banks often use a combination of all of these systems in their interest rate risk measurement process.”'° Even so, most banks should.

As one observer noted, managing IRR from net income simulation is like driving a car and looking at nothing but the speedometer. You have upto-date information on the current situation but almost no information about the long-term consequences of your speed. Managing IRR from EVE sensitivity simulation is like driving a car and looking at nothing but the oil pressure, temperature, and fuel gauges. You have a great view of potential long-term problems but not much information about the current situation. Looking at all the instruments gives you all the information you need to drive successfully.n

SELECTING A RATE RISK MODEL Taken together, the general descriptions of model features described so far in this chapter comprise an education in modeling concepts. They are essential background knowledge for bankers using models or contemplating the purchase of models. However, they are not detailed enough to guide a banker through the process of evaluating, purchasing, and installing a new model. These issues are described in the following sections.

Identifying Your Rate Risk Model Requirements At the beginning of this chapter, we made general observations about models that bear repeating. One of the most fundamental of these is that each bank must select modeling software with features that best meet the specific needs of that bank. This requires two steps:

10. “Assessment of Interest Rate Risk," FDIC Memorandum 6230 (0(8), Augmt 12, 1994, page 12. 11. Robert C. Colvin, president, Risk Analytics, Inc., Denver, Colorado, in an interview with the author, November 2, 1994.

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First, before you can select a model to purchase, the needs of the bank must be clearly identified. The result of this process may be a list that includes 30 to 50 items. It should be as complete as possible. But more importantly, it should be customized to meet the specific needs of your bank. Resist the temptation simply to use the checklist in Exhibit 9.1 or a checklist obtained from another bank. If the bank wants to improve productivity, make sure that the checklist of desired features includes questions about run times and automatic downloading of data. Ifthe bank wants to improve the accuracy of its rate risk measurement by capturing more of the effects of customer options, make sure that the checklist includes plenty of questions about the software’s capacity to both capture data and model installment loan prepayments, mortgage loan prepayments, caps and floors on loan or deposit rates, changes in core deposit volumes, and the like. The rate risk measurement system must be appropriate for the nature of the risks posed by your bank‘s assets, liabilities, and off-balance sheet positions. E]

Second, the features and characteristics that your bank wants in an interest rate risk model must also be prioritized. Clearly, some capabilities are essential requirements while others are merely “nice to have.” Again, resist the temptation to use priorities from other banks or from this manual. The best model for your bank is the one with the strongest features that match the highest priorities of your bank’s rate risk managers, senior management, and directors.

A list of model features and characteristics is shown in Appendix 9C. Even though this list may omit some model features that are important to your bank, your list will almost certainly be shorter for two reasons. First, of necessity, the list in Appendix 9C has to be generic. Many items on the list simply won’t be considered options desired by your bank. Second, a number of the potential requirements are simply not costjustifiable for the vast majority of banks. Many features that are theoretically nice to have do not provide much practical improvement in the accuracy of rate risk measurement for small banks. Do not try to buy more features than you need.

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EVALUATING INTEREST RATE RISK MODELS

A step-by-step process for evaluating models is provided in the following portions of this section. While these topics and details are essential, it is vital to first consider these two broad perspectives. First, each bank must select modeling software with features that best meet the specific needs of that bank. The needs of the bank must be identified clearly before it buys a software package. For example, if the bank wants to improve productivity, does the sofiware ofl‘er such features as automatic downloading of data from the bank’s main accounting systems? If the bank has material

holdings of retail products with embedded options, does the software automatically simulate different rates of withdrawals and prepayments in different rate environments? The rate risk measurement system must be appropriate for the nature of the risks posed by its assets, liabilities, and off-balance sheet positions. The best model for each bank is the one in which the strongest features of the model match the highest priorities of that bank’s rate risk managers. In each situation, some model features are less important than others.

Second, each bank must find the compromise between costs and benefits that best suits its situation. For example, some advanced models offer automated downloading of data for each cash flow from each loan and deposit. This feature allows each cash flow to be modeled in each interest rate scenario evaluated. It is also expensive. Simulation models that link to transaction databases can cost more than $100,000 a year. (That figure is based on a purchase price of more than $250,000 amortized over five years plus maintenance costs of more than $50,000 a year.) Simple models, on the other hand, are available for less than $30,000 a year. How valuable are the extra benefits provided by highly sophisticated models? The answer must be determined separately for every bank.

For both custom-designed models and purchased software programs, compromises are almost unavoidable. One of the primary goals of this chapter is to explain the issues that must be understood to make appropriate compromises. We discuss in detail the major model features

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and also consider suggestions for evaluating models and some vital management procedures for controlling models.

Selecting a model available from one of the interest rate risk model software vendors can be time-consuming and even frustrating. Sometimes vendors will say their models “can do it" when the function in question can really only be done with lots of hard-to-justify extra effort. Sometimes features described in marketing literature are unavailable until a future software upgrade is released. Even when all the facts about each package are known and understood, the differences between packages often make comparisons difficult. Nevertheless, investing time and effort to research carefully and analyze thoroughly alternative sofiware packages can be extremely beneficial. The key is to invest that time and efion in a well-planned, well-executed search and review process.

Such a process can involve as many as 16 different steps, as outlined below: CI

ldentrfi/ your rate risk model requirements as described in the previous section. Develop a draft version ofa requestfor proposal (RFP).

El Develop a preliminary list of vendors. Look for rate risk sofiware vendors whose products seem likely to fit at least most of your key IRR measurement requirements. El

Finalize both your RFP and your initial vendor list. Send your RFP to each of the vendors on your initial list. Review and reformat the RFP responses. When the RFPs are returned, review the responses and, to the extent necessary, reformat the responses so that each vendor's responses can be compared with other vendors’ responses. It is generally wise to be careful to make sure that you understand exactly what is included in the scope of each answer. You may need to call one or more vendors and request clarification of some of the written responses to your RFP. If follow-up calls are made, be sure that all vendors

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—

are treated fairly others are not given.

none should have an opportunity that the

Analyze how well the software capabilities seem to meet the needs identified as the highest priority IRR measurement requirements for your bank. Even though your highest priority requirements

were identified in step one, your RFP will almost certainly have included a great many other requirements. At this stage in the review process, you just want to identify those vendors whose. models meet most of your highest priorities. You may, for example, establish a numerical threshold such as a requirement that the models meet at least 75 percent of your highest priorities.

Finalize your list of qualified vendors. The models that do not meet solutions of your highest priority functions need to be dropped from consideration. Also eliminate the models that are too far out of your price range. Since you will be spending quite a bit of time evaluating the vendors on this list, try to keep it short. You will probably want no more than four to six vendors on the semifinalist list. Send a letter to all of the vendors who took the time to complete your RFP but who nevertheless did not make your short list of semifinalists. El

of questions and issues that you want to address during sofi‘ware demonstrations. Vendors will usually follow their own presentation formats; however, those presentations may not cover all of the questions or concerns that you have about their models. For that reason, you should have a written checklist or question list. Consider sending a copy of your written checklist or question list to each vendor before the demonstration. If you provide copies of your list to the vendors in advance of the demonstration, the salespeople who will make the demonstration can get answers to technical questions from people in their organizations, such as programmers and technical support personnel. It is usually a good idea not to tell the vendors which model features are your highest priorities. This way, the vendor’s sales staff will not be tempted to overstate the model's capabilities.

Prepare a checklist

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Be particularly careful to include questions that will, in the next step, require the vendor to demonstrate every model function that is important to your bank. Bankers tell ‘fiuar stories” of vendors who showed them slides of mocked-up model screens that did not actually exist in the model. Schedule and participate in demonstrations for each model on your qualified list. The demonstrations will usually be held in your bank; however, there is nothing wrong with on-site visits to the vendors’ offices to view demonstrations. Make sure that the version of the model used in the demonstration is the same software available for installation in your bank. Ask enough follow-up questions to be sure you understand exactly how the vendors’ models do or do not meet your needs. Do not assume that you understand all of the implications of a broad or general answer. Simple mismderstandings at this stage can lead to major disappointments afier you have installed a model.

Keep in mind that every vendor has salespeople who have wellpracticed demo routines. These are rapid, smooth, and managed to highlight the software favorably. Watching this demo and asking some questions is fine. But don’t stop there. You also want to see the model do non-choreographed operations for the functions must important to you. At a minimum, spend time asking the salespeople to demonstrate variations of functions. Also keep in mind that some otherwise reputable model vendors like to devote part of their presentation to highlighting deficiencies in their competitor’s models. Here again, bankers tell “war stories" of vendors who materially misrepresented the facts about their competitors’ models. Be particularly careful about accepting such statements flour a vendor who presents after the vendor he or she is criticizing. In those cases, you may need to go back to the vendor who presenter earlier for clarification before you accept the statement made by the competitor. Evaluate the expertise of the vendor '3 key stafi Do not focus on the sales people who are your main contacts at this point in the selection process. You may never talk to them again afier installing their model. Instead, either talk to or research individuals who will provide customer support and who you may

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turn to when you have thomy questions. You want to know: Are

these people familiar with the risks I take and the markets I serve? And, does the vendor employ individuals who can supplement the bank's in-house expertise. Sometimes, you can do a search for published articles to identify experts. Sometimes you may have to add this to the list of questions you ask the vendor’s references.

Cl

Eliminate vendors on the qualified list whose models seem least capable of meeting your needs. Narrow your list of potential vendors down to two or three finalists. Send thank-you letters to each vendor who made a demonstration but was eliminated from further consideration. Talk to clients fi'om each vendor on your list. Try to find banks that have a similar mix of business to yours.

[1

Visit or interview other banks already using the models on your

final list. Ask the vendors for a list of banks that might permit such

phone interviews or visits. Try to find banks that have a similar mix of business to yom's. For example, if your bank does a large amount of indirect installment lending and obtains most of its funding from core deposits with indeterminate maturities, try to find similar-sized banks that also have large holdings of indirect installment loans and indeterminate maturity core deposits. Don't restrict your questions to model ftmctions. In addition to questions about functions, ask about:

∙∙∙ ∙

∙∙∙

Training provided by the vendor

Ease of installation

Unexpected problems encountered during installation Any discrepancies between model ftmctions described in the sales process and what the model actually does (vapor ware) Any promises the vendor failed to honor in full

Customer support The timelines of enhancements

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∙

The vendor’s willingness to incorporate client requests in future software versions

Most importantly, never forget that buying and installing a model can take months but using a model continues for years. Ongoing support from the vendor is more important than installation glitches. [fyou have time, it is a good idea to ask the vendor to run a sample set of your bank '3 positions. You can then compare the output from their model to your current risk assessment for those positions. The model vendors will almost always agree to run' the analysis for a limited number of test transactions at no cost to you. Larger'pilot tests are sometimes requested by banks who really want to verify functionality and are usually done on a paid basis.

Prepare and review a cost/benefit analysis. This analysis should include the costs of model software, ongoing support or maintenance costs, the costs of hardware such as personal

computers, the cost of software that may be needed to transfer data from your application programs to the model, and installation costs, including training. The least expensive model is not necessarily going to be your first choice if it doesn’t meet enough of the highest priority requirements that you identified in step one. On the other hand, higher cost models that offer more features are not necessarily better choices if those additional features are not among your highest priority requirements. Each bank must find

the compromise between costs and benefits that best suits its situation.

Select your first-choice vendor and begin contract negotiations. It is a good idea not to inform the remaining finalists that they are not your first choice. Delaying that notification gives you more leverage in your contract negotiations with your first-choice vendor. Do not simply negotiate the price. Make sure that any promises made to your bank by the vendor are written into the contract. If the vendor has made a promise to perform work, such as a promise to include a feature that you want in the next model software update, try to negotiate penalties that the vendor must pay if the promise is not fulfilled on time. Make sure that adequate

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training will be provided by the vendor for your staff. You may want to include some training in advance of the installation —— not just a fast tour through the program menus and the software documentation after the model is installed. El Sign the model contract and notify the losing bidders.

Installing Interest Rate Risk Models

Even the best model installations are usually time-consuming. Installations often take longer and involve more problems than either bankers or vendors initially estimate. While nothing can be done to ensure a trouble-free installation, good planning and organization go a long way toward smoothing the process. The following steps can help you plan and organize the installation: [1

Build a schedule and assign tasks. Make a timetable or schedule of the tasks that need to be completed, the individuals responsible for completing those tasks, and the estimated completion dates or deadlines for those tasks. Be realistic. Allow time for resolving unforeseen problems. Some bankers recommend scheduling installation of the quickest and easiest deliverables first. This tactic enables your implementation team to gain familiarity with all of the requirements while working on a comparatively easy task. It also enables ALCO to report some quick progress. Arrange to have all of the hardware and software that you need to run your model. Don‘t forget any sofiware that may be needed to transfer information from application systems to the model and all the hardware components. Set a realistic timetable for delivery.

[3

Arrange training. If you have negotiated training at the vendor’s location, arrange to send the members of your staff who will be trained. Even if your vendor has not agreed to provide any advance training, you should arrange to have your staff become familiar with key model operations especially data input

—

requirements.

El

Planfor manually imported data. If you plan to use any bank data in the model that will not be automatically downloaded fi'om 9-46

Selecting and Installing AL Models lO/OB

existing loan, deposit, and investment accounting application programs, determine how this information will be fed into the model and who will do the work. Develop written procedures to ensure that manual entries to the model are accurate and complete. Arrange to cross-train personnel so that the model can be run even if the person responsible for manual entry is unavailable. Planfor third-party data. If you plan to use data such as mortgage prepayment speed forecasts from third-party vendors, finalize the arrangements to receive the data. Develop the procedures and controls to get the data into the model.

Scrub (audit) your application databases for source information. A great deal of information that may be important for the operation of your rate risk analysis is relatively unimportant to product managers and accountants. This includes information on the original dates of loans, caps, or floors on floating-rate loans and other customer options. Sometimes, data such as dates and options that cannot be reconciled to accounting records have not been audited and, therefore, include the accumulated mistakes from years of data input errors. Install the model software on the hardware and make sure that it runs. You can use either test data from your bank or dummy data from the vendor, but be sure that the model operates on the hardware before you put a lot of time and effort into the first attempt to measure your bank’s IRR exposure. Enter bank data in the model and produce test runs. Make sure that all of the data from all assets, liabilities, and ofl-balance sheet positions, if applicable, are being received by the model. If the new model is replacing an old model, you should compare the difi‘erences between the measured rate risk fi'om each. The measured outputs from your old system and your new system will be different. After all, if the new model didn’t measure risk any differently than the old one, you almost certainly would not have purchased the new model. Nevertheless, you should be able to explain the differences well enough to satisfy yourself that the new model seems to be doing what you want it to do.

9-47

lO/08 Interest Rate Risk Management

satisfied with the model 's performance with live datafrom your bank before you sign of with the vendor. The model’s performance, including availability of features, run time, and output reports, should not be materially different from the performance you saw during the vendor’s demonstration when the model was being evaluated.

El Make sure that you are

El

Finalize written procedures for the operation of your model. Be sure to include control procedures such as those described later in Chapter 10.

9-48

Selecting and Installing AL Models

lO/OB

Appendix 9A A Guide to ALM Software

This chart, provided by Mary Brookhart, Southeast Consulting, Inc., presents profiles of the most widely used, commercially available asset/liability management software. The software is organized by price in three categories: under $10,000, from $10,000-$50,000, and more complex software models priced over $50,000. The models exhibited provide tools for identifying specific interest rate risk characteristics, transfer pricing solutions, auditing controls, budget developments, credit risks, and more.

Although the charts do not list every available ALM software vendor, they provide the A/L manager or ALCO executive with a sampling of the more popular sofiware vendors currently offering ALM models. Vendors The Baker Group Inc. Okalahoma City, OK Valle L. McGinnis (800) 832-0630

Plansmt'th Corporation Schaumburg, 11. Bill Smith (800) 323-328]

Bank Reporting Scierwes Columbia, MD Michael Fasone

Darling Consulting Group, Inc. Newburyport, MA Michael Guglielmo (978) 463-0400

ProfitSIars, a Jack Henry Company Omaha, NE

Olson ResearchAssociates. Inc.

COR-F8, Inc.

F[MACSolutions LLC

IPS-Sendero Norcmss, GA Kurt Guenther/ LaChrisha Dourisseau (800) 321-6899 x3326 (770) 409-0047 Int‘l

Martin Webster (800) 356-9099 (402) 431-8800

Margy E. Kern (303) 680-8444

[email protected]

mfasone@

bankreportingsciencescom

Columbia. MD

Brad Olson/Susan Regan (888) 657-6630

Denver, CO Bob Davidson

rdavidson@

fimacsolutionseom

10/08 Interest Rate Risk Management

Appendix 9A A Guide to ALM Software (cont.) Kannakura Corporation Honolulu, HA Warren A. Sherman, President (724) 654-9775

SunGard BaneWare Boston, MA Kristen Sylva (617) 542-2800 x723

Quantitative Risk Management, Inc. (QRM) Chicago, IL Charles Richard (312) 782-2855

Note: FIMAC Solutions LLC ofl‘ers an outside ALM Model for Consumer and Commercial Loss Modeling Base/Multiple Systems. None of the models includes Counterparty Risk Management Base of Multiple Systems. All models listed include online help. QRM online help includes oper. guide. All models listed offer gap analysis. All models over $10,000 ofi‘er unlimited AIL categories and rmlimited interest categories. QRM offers flexible account hierarchies. All models under $10,000 ofi‘er gap analysis and unlimited A/L categories. RiskExpert ofl‘ers advanced duration prepayment A/L categories. Profitstar offers standard chart of account interest categories. All other models under $10,000 ofi‘er unlimited categories

9-50

Selecting and Installing AL Models 10/08

Appendix 9A A Guide to ALM Software (cont.)

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Interest Rate Risk Manggement

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Selecting and InstaIIinLAL Models 10/08

Appendix 93 ALM Outsourcing and Consulting Vendors This appendix presents a survey of the ALM outsourcing and consulting vendors most commonly used by the U.S. financial services industry. This listing, prepared by Mary Brookhart of Southeast Consulting, Inc. of Charlotte, NC, profiles ALM outsourcing vendors and their contact information. Information on other vendor characteristics may be obtained by contacting the software vendor directly.

Although this appendix does not list every available ALM outsourcing vendor, it does provide the AL manager or ALCO executive with a sampling of the more popular vendors currently offering ALM outsourcing services.

Vendor ALM Advisory

Service (Sunlmst) Atlanta, Ga 30302 (800) 24 l-0901 (X66800)

Bancware Inc.

Boston. MA 02110 (617) 542-2800

ALM Services

Vendor Contact Jon Koliowski, ALM Modeling Director

lon.kozlowslu'@

ALM consulting ∙

ALM reporting

suntrusteom

Courtney Rand, Stephen Rooney

[email protected]

ALM modeling

_

_

Burt: and regulatory reporting Customized reports

The Bankers Bank Atlanta. GA 30339

Jeanne Mauney. Asst. Vice president jmaurrey@ bankersbankeom

ALM modeling

BN'K Advisory Group Bethlehem, PA 18017 (800) 780-8362

Michael Van Zandl.

ALM mung/assessment! . / l .

(X 3713)

bnkadvisorygroupeom

(800) 277-2265

Manager

_

ALM consulting

”m“ "a “m“

Seminars for board, management. trade coups

∙

Bank Birmingham, AL 35233 (800) 239-6669

Policy review development

ALM modeling and validation

Cindy Watson, Vice President

muon@

ALM consulting and training for

compassbnlreom

board/ALCO

Review/analysis of policies

9-53

10/08 interest Rate Risk Management

Appendix 93 ALM Outsourcing and Consulting Vendors (cont.) Vendor

ALM Services

Vendor Contact

Darling CmsulIins Group Inc. Newburyport. MA

Frank L Fame. Managing Director

01950 (978) 463-0400

darlingconsultingcom

DDI Myers, Lid. Phoenix, AZ 85008 (602) 840-9595

Deedee Myers, Plesidcnt and CEO

Leadership developmem

FIMAC Solutions. LLC Denver, co 30209 (303) 320-1900 (x729)

Bob Davidson, Vice President

Risk analyticsO ALM model and ba1 sh

fimaceolutionseom

Comprehensive IRR analysis and

ALM consulting, education, and

fl'arone@

software ALM process reviews and model validation

Investment analytics service Core deposit analysis

-" ‘Mum rdavidson@

an“

°°

reponins Leading light budgeting model

Web-based solutions

mam

Financial Institution Maria email es Corp.

Greg Dorrer, President fica .com don er@ P g

Denver, CO 80209 (877) 789-5905

Risk audits and balance sheet . management consulting

Multi-ALM vendor models reporting and “FPO“

Non-maturity deposit studies I-TN Financial Memphis.TN 38117 (800) 456-5460

Chbd McKeithen, Vice

President. ALM chadmckeithm@

ALM reporting/consulting and PM al'da'

"

flcmcom

W"

Strategy development

Board, sr. magenrem, ALCO

education seminars

IPS-Sendero Corporation

Kurt Gueuthe‘r

(800) 879-1996 or (770) 409-0047

ips-sendero.com Chuck Rowland (non-us)

All. and profitability management -

ips-sendero.oom

Comprehmsive IRR analysis and

Auanta. GA 30092

ALM modeling/minaret

(US/Canada)

.

kurLgumther@

chuck.row1and@

.

..

”ms/”mm”?

“mm“

reporting Budgeting and planning] corp. performance mgr.

9-54

Selecting and Installing AL Models 10/08

Appendix 93 ALM Outsourcing and Consulting Vendors (cont.) Vendor Jameson Associates

Scottsviile, NY 14546

(585) 889-8090

Jamey Montgomery Scott, LLC Ardmore, PA 190102415 (800) 211-2663 The Kamalrura

Corporation Honolulu, r-n 96822 (808) 539-3830

ALM Services

Vendor Contact Michael Jameson, Principal [email protected]

Brian A. Velligan. Vice President

bvelligan@

jmscniine.com

Leonard Matz. Senior Vice President

lmatz@

lramalturacocom

ALM consulting and training (Wd‘m‘i‘m‘o Review/analysis of ALM process.

policies. and reports ALM modeling, validation. and consultin

3 ALM reporting Liquidity risk .

.

.

.

CM" “5“ ”‘d “P ”W ”“9" “d

development

ALM training. modeling. and

installation Kawailer & Company, LLC Brooklyn, NY 11202 (718) 694-6270 Olson Research Asociatee Inc. Columbia, MD 21046 (410) 290-6999 (x262) (888) 657-6680

Plansrnith Corporation Schaumburg, IL 60173 (800) 323-3281

lra Kawaller, Preaidurt

Derivatives valuation and modeling

Irawallercom

FAS 133 accounting treatment prqnaration review - risk management

Rose Valerie, Accotmt Erecutive

ALM reporting. modeling

kawaller@

inf0@

olsoru‘searchcom

Validation. SFAS 107 um measurement/shock analysis (web-

bmed curriculum)

Lew Caliento. Vice President

[email protected]

Simulation training Comprehensive ALM call reporting service Customized ALM modding

ALM consulting, training

ProfitSlars, a Jack Harry Company Omaha. NE 68137 (800) 356-9099

Bob Goedlren, President and CEO

[email protected]

ALM consulting/modeling (custom -

-

"mm”

ALM cur-site and clamoom training Regional client conferarces

Profitability accounting Consulting/modeling (custom

installation)

9-55

10/08

Interest Rate Risk Management

Appendix 9B ALM Outsourcing and Consulting Vendors (cont.) Vendor Quantitative Risk Manage-It Inc. Chicago, 60602

∙

ALM Services

Vendor Contact Charles Richard, Sr. Vice Preaidart

inl'o@qrn1com

(312) 782-1880

ALM marker/forecasting .

.

.

.

FTP/profitabrlrty drstrrbuted

budgeting and forecasting

Credit risk management Sanders Morris Ham‘s Houston, TX 77002 (800) 733-5001

Peter W. Badger, President, Fixed Income peter’.hadger@ smhhoucom

Smith Breeden Associates inc. Grapel Hill. NC 27517 (919) 967-7221

Robert Perry, Principal

investmmt products and service

“”01“ “'5‘ ““8 Secondary market for loans/loan

servicing

merry@

ALM modeling, validation, and consulting

srnithhreedencom

Investment portfolio management and advisory services Budgeting and strategic planning

Southeast Consulting Inc. (SCI) Charlotte, NC 23247-

Peter Mihaltian, President

US Banking Alliance Atlanta, GA 30075 (300) 241-3139

Mitchell Epstein, Managing Partner

[email protected]

strategic ALM .

“ms AL“

Consulting ALM

0886 (704) 541-0489

.

Sofiware selection

Loan and deposit pricing models .

mepstein@

mwlimw-Wfll John Whetstcne, Senior Relationship Manager

.

.

N“ "1““ “'3” ”mm“ Strategies consulting on loan/deposit pricing strategies

jwhetstone@

usbankirmalliancecom

Vining-Sparks, IBG Memphis, TN 38119 (800) $294,321

Wade Oliver. Sr. Vice presid-t, ALM

woliver@

viningsparks.com

ALM modeling and consulting .

.

Comprehensrve IRR and investment reporting

ALM inveament data exports to all systems

9-56

Selectingand Installing AL Models 10/08

Appendix 9C Required Model Features, Functions, and Characteristics First State Bank of Cyberville

Checklist Prepared by:

Most Recent Revision Date:

Date of ALCO Approval: Priority

Requirement

Critical

Important

Hardware

1.

Runs on a mainframe Runs on a PC

3.

4.

Rims on a local area network (LAN) Rtms on hardware the bank already owns

5.

Runs under DOS“I

6.

Rtms under

7.

Runs under UNDC"M

8.

Other:

9.

Other:

Windows”

System

10. Detailedchart of accounts

ll. Allows at least X separate line items

12. User-defined chart of accounts

9-57

Optional

Comments

10/08 interest

Rate Risk Manageiient

Appendix 9C Required Model Features, Functions, and Characteristics (cont.) Priority Requirement

Critical

Important

13. Sofiware includes btrilt-in help features 14. Data input and report generation screens and menus easy to tmderstand

15. Data input and report generation procedures prompt users

16. Historical data storage for at least X months 17. The version of the sofiware evaluated by the bank is already installed and used by at least x other banks 18. Software is modular 19. Can probably be installed within X

months

20. Other:

21. Other:

Data Input 22. Automated extract of data from loan applicationsystems 23. Automated extract of data from investment application systems

9-58

Optional

Comments

Selecting and Installing AI. Models 10/08

Appendix 9C

Required Model Features, Functions, and Characteristics (cont.) Priority

Requirement

Critical

Important

24. Automated extract of data fiom deposit application systems

25. Automated extract of data from the bank‘s general

ledger

26. Other:

27. Other:

Capacity to Reflect

Embedded Options

28. Accepts manual input of loan prepayment assumptions

29. Accepts automated input of loan prepayment assumptions

30. Accepts manual input of investment prepayment assumptions

31. Accepts automated input of investment prepayment assmnptions 32. Accepts manual input of withdrawal/new

deposit assrnnptions for deposits with indeterminate maturities

9-59

Optional

Comments

10/08

Interest Rate Risk Management

Appendix 9C Required Model Features, Functions, and Characteristics (cont.) Priority

Requirement

Critical

Important

33. Accepts automated inptrt of withdrawal/new

deposit assumptions for deposits with

indeterminate maturities

34. Applies different loan prepayment

assumptions for each different scenario modeled 35. Applies different

deposit decay/new deposit/withdrawal assumptions for changes in each different rate scenario modeled

36. Allows separate quantities of rate changes for

administered-rate products vs. floating-

rate products

37. Allows separate timing (lags) for changes in administered rates vs.

floatingiales

38. Can automatically reflect difl‘erences in prepayments based on the age of the loan

9-60

Optional

Comments

Selecting and Installing AL Models lO/OB

Appendix 9C Required Model Features, Functions, and Characteristics (cont.) Priority

Requirement

Critical

Important

39. Can automatically reflect difierences in prepayments based on the path of rate changes since the origination of the loan

40. Can automatically capture caps and floors on floating-rate assets and liabilities from the application accounting systems

41. Can automatically reflect the impact of caps and floors on floating-rate assets and liabilities in each

different rate scenario

42. Can automatically capture call dates from callable and step-up securities

43. Can reflect the different exercise of all] options for bankowned securities in difl‘erart interest rate scenarios

incorporates OAS analysis 45. Allows users of OAS to reflect changes in volatility tmder different rate scenarios

Incorporates Monte Carlo simulations

9-61

Optional

Comments

10/08

Interest Rate Risk Management

Appendix 9C Required Model Features, Functions, and Characteristics (cont.) Priority Requirement

Critical

Important

47. Other: 48. Other:

Rates and Rate Scenarios

49. Accepts projections/forecasts

for at least X number of different interest rates for different

instruments

50. Accepts projections/forecasts for at least X ntnrnber of different rates for difl‘ererit maturities 51. Automatically interpolates rates for terms other than the terms entered

52. Capacity to download interest rate forecasts from third parties 53. Can reflect lags in rate changes

54. Can reflect asymmetrical lags

55. Can reflect nonparallel yield curve shifis

56. Can reflect changes in basis risk (different rate changes for difl‘erent instruments)

9—62

Optional

Comments

Selectiniand InstallingAL Models

10/03

Appendix 9C Required Model Features, Functions, and Characteristics (cont.) Priority Requirement

Critical

Important

57. Can reflect a sufficient number of difl‘erent scenarios

58. Can reflect userdefined rate change scenarios

59. Can include a base case or most likely scenario 60. Other:

61. Other: Business Scenarios

62. Allows the bank to project different assumptions for changes in the volume of new loans in each difi'erent rate scenario modeled

63. Allows the bank to project difl‘erent assumptions for changes in the volume of new deposits in each different rate scenario modeled

64. Allows the bank to project difl‘erent assumptions for changes in

administered rates paid for loans in each difl'erent rate scenario modeled

9-63

Optional

Comments

lO/OB

Interest Rate Risk Management

Appendix 9C Required Model Features, Functions, and Characteristics (cont.) Priority Requirement

Critical

Important

65. Allows the bank to project different assumptions for changes in administered rates paid for deposits in each difl‘erent rate scenario modeled

66. Allows alternative business strategies to be ranked or optimized

67. Other:

68. Other: Gap Analysis

69. Performs static gap analysis

70. Performs dynamic gap analysis

71. Performs betaadjtsted gap analysis

72. Performs liquidity

grimlysis 73. Can use at least X separate time periods

74. Captures ofi-balance sheet positions

75. Other:

76. Other. Duration Analysis

77. Calculates duration of equity 78. Uses modified duration

9-64

Optional

Comments

Selecting and Installing AI. Models 10/08

Appendix 9C Required Model Features, Functions, and Characteristics (cont.) Priority

Requirement

79. Reports the durations of each asset and liability smut: individually

80. Captrn'es off-balance sheet positions

81. Other:

82. Other: Income Simulation 83. Can simulate the impact of multiple rate scenarios on net income

84. Can simulate the impact of multiple

rate scenarios on the net interest margin

85. Reports yields or costs separately for

each category of assets and liabilities

86. Calculates net interest margin for earning assets

87. Output isolates basis risk

‘88. Output isolates yield curve twist risk

Output isolates options risk 90. Can easily reflect new business assumptions

Critical

Important

Optional

Comments

lO/08 Interest Rate Risk Management

Appendix 9C Required Model Features, Functions, and Characteristics (cont.) Priority Requirement

Critical

Important

91. Can separately

simulate income and income at risk for each month in the next 12 months

92. Can simulate income and income at risk for at least X years after the uncut year 93. Readily accepts extensions of forecasts to produce rolling 12-month simulations each month

Can combine discounted or weighted measures of eamings at risk in future years with the earnings at risk in the present year 95. Captures taxable or nontaxable status of income from assets

Can apply multiple

tax rates

97. Can apply both federal and state income taxes 98. Reports income both before and alter taxes

Captures off-balance sheet positions

9-66

Optional

Comments

Selecting and installing AL Models

10/08

Appendix 9C Required Model Features, Functions, and Characteristics (cont.) Priority Requirement

Critical

Important

100. Reflects rate sensitivity of noninterest income or noninterest expense

101. Can rim multiple

scenarios without additional manual intervention after each

102. Other

103. Other:

EVE Sensitivity Simulations

104. Calculates EVE equity under each difl'erurt rate scenario

105. Calculates the dollar amormt of change in EVE for each difl‘erent rate scenario

106. Calculates the percentage change in EVE for each different rate scenario

107. Calculates economic values for each individual group of assets and liabilities in the model

9-67

Optional

Comments

10/08

interest Rate Risk Management

Appendix 9C Required Model Features, Functions, and Characteristics (cont.) Priority

Requirement

Critical

Important

108. Applies difi‘erent

discount rates to assets and liabilities based on the remaining life of

eachjroup

109. Ranks each separate group of assets and liabilities based on rate sensitivity

110. For each difl‘erent rate scenario.

automatically applies different volume and remaining life assumptions to loans subject to prepayment

111. For each difl‘erent rate scenario.

automaticaily applies difl‘erent volume and remaining life assumptions to indeterminate maturity core dgiosits

112. Can download security pricing

information from third parties

113. Can download all applicable information necessary to value collateralized mortgage obligations _ under each difi‘erent rate scenario

9—68

Optional

Comments

Selecting and installing AL Models

10/08

Appendix 9C Required Model Features, Functions, and Characteristics (cont.) Priority

Requirement

Critical

Important

114. Output isolates basis risk

115. Output isolates yield curve twist risk 116. Can easily reflect new business assumptions ll7. Captrn'es offbalance sheet positions

118. Reflects rate sensitivity of noninterest income or noninterest expense

119. Reflects valuation changes in noninterest income and noninterest expense rmder each difl‘erent rate scenario 120. Can run multiple scenarios without additional manual intervention atter each

121. Other: l22. Other: Output

123. Provides sufl'rcient management

information to meet management requirements

9-69

Optional

Comments

10/08 interest Rate Risk Managem-t

Appendix 9C Required Model Features, Functions, and Characteristics (cont.) Priority

Requirement

Critical

Important

124. Provides sufficient management information to meet bank regulatory

requirements

125. User-defined report formats

126. Adequate graphics

carJLbilities

127. Can automatically transfer data to separate report writer software

128. Projected results can be viewed on screen prior to printing

fePOflS 129. Other: 130. Other:

Operations, Support.

and Controls

131. Computer-based training (on-line tutorials)

132. Training provided at vendor‘s location before installation 133. On-site training provided by vendor before installation 134. On-site training provided by vendor after installation

135. Comprehensive and readable docrunentation

9-70

Optional

Comments

SelectingLand installing AL Models 10/08

Appendix 9C Required Model Features, Functions, and Characteristics (cont.) Priority Requirement

Critical

Important

136. Help keys or help available in the sofiware

137. Run time is fast

“DESI!

138. Minor revisions (“tweaking the analysis") can be accomplished quickly and easily

139. Telephone line support available hour the vendor 140. Retains all assumptions in an easy-to-read. easyto-retrieve manner 141. Creates and retains records of changes in assumptions — who made them, what was changed. and when the change was made

142. Other:

143. Other: Additional Management Goals

144. Can produce FAS 107-required disclosru'es

145. Produces repricing data needed for call reports

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Optional

Comments

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Interest Rate Risk Management

Appendix 9C Required Model Features, Functions, and Characteristics (cont.) Priority

Requirement

Critical

Important

146. Can be used to prepare the bank's

budget

147. Can provide an

automated data download into the soflware progam used for the bmk‘s

budget

148. Calculates riskadjusted renu'ns on equity for each separate group of assets and liabilities 149. Calculates organizational profitability

150. Can reflect fimds transfer pricing 151. Calculates customer profitability

152. Calculates product profitability

153. Runs in multibank holding companies at both the bank and consolidated levels 154. Other:

155. Other:

Costa 156. Available for purchase

157. Purchase price

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Optional

Comments

Selecting and Installing AL Models 10/08

Appendix 9C Required Model Features, Functions, and Characteristics (cont.) Priority

Requirement

Critical

Important

158. Available for purchase in segments or modules

159. Available for lease

160. Annual or monthly lease cost 161. Periodic maintenance costs

162. Cost of updates if not included in maintenance costs

163. Cost of training if not included in other costs

164. Cost of customer support if not included in other

costs

165. Installation costs 166. Cost of obtaining or writing programs to get data fiorn bank application software into the interest rate risk model 167. Cost of any thirdparty programs 0" data services to obtain data used when running the

model

168. Hardware costs

169. Other: 170. Other:

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Optional

Comments

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Chapter 10 Using Models and Managing Model Risk

Managing Model Risk ........................................................................ lO-l Model Flaws, Model Errors, and Model Obsolescence .................. 10-2 Exhibit 10.1: Eight Sources of Model Risk ................................ 10-3 Data and Assumption Inputs 10-4 Data Describing the Bank’s Current Position................................. 10-4 Exhibit 10.2: Cash Flow Over Time ........................................... 10-5 The Impact of Data Aggregation .................................................... 10-6 Common Risk Characteristics .................................................... 10-6 10-7 Match to Bank‘s Risk Exposure Profile Information About Future Activity ................................................. 10-7 Incorporating Assumptions for Future Business: The Good, the Bad, and the Surprising ...................................... 10-8 What Is Best Practice Modeling Methodology? ........................... 10-10 What Is Best Practice Model Governance? .................................. 10-11 Exhibit 10.3: Best Practice Model Governance ....................... 10-12 Understanding the Accuracy of Model Output ................................. 10-12 Managing the Integrity of Simulation Models: Benchmarking, Backtesting, and Validation .............................................................. 10-13 Three Processes for Model Validation ......................................... 10-13 What Is Backtesting? .................................................................... 10-14 Controlling Data Quality .............................................................. 10-16 Controlling, Validating, and Backtesting Assumptions ............... 10-19 Exhibit 10.4: Percentage Change in EVE from the Base Case EVE∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 10-22 Limitations of Interest Rate Risk Models ......................................... 10-24 10—25 Limited or No Capture of External Variables Weak Links ................................................................................... 10-25 Overly Detailed Models................................................................ 10-26 Using Models to Maximize Risk Management Benefits .................. 10-27 Creating Logical Scenario Groupings .......................................... 10-27 The Inter-Related Components of Scenarios ............................ 10-28 Scenario Selection 10-28 Improving Model-Generated Management Reports ..................... 10-29

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What Is Needed? ...................................................................... What Is Not Needed? ............................................................... Improving Management Confidence in IRR Modeling................ Internal Control Checklist for IRR Models ......................................

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Chapter 10 Using Models and Managing Model Risk

MANAGING MODEL RISK Not surprisingly, using interest rate risk models involves more than simply pushing a button or two and watching the lights blink until a report prints out. You must have accurate and complete input. You must have sound assumptions. You must have prudent procedures, controls, and, to the extent possible, tests for assessing the accuracy of the model output. If you don’t, you are not likely to obtain accurate or even usable output.

In addition, you must have a sound understanding of the limits on the accuracy of the rate risk exposure measured by your model. Management decisions based on flawed or misunderstood information will be less likely to reduce rate risk and may even make it worse. The old saying “garbage in, garbage out” is as true for the most expensive, sophisticated models as it is for simple spreadsheet models. All models are imperfect because a model is, by definition, a simplification of reality. The OCC notes that: Model development is a complex and error-prone process. While many completed models work as planned, some models contain ftmdamental errors. Moreover, the internal logic of most models is usually very abstract and limiting, so it requires considerable judgment and expertise to apply model results outside of the narrow context under which they are derived. The OCC has observed several instances in which decision makers either relied on erroneous price or exposure estimates, or on an overly broad interpretation of model results, with serious consequences for their bank’s reputation and profitability. There are many more instances in which the incorrect use of models created potential

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for large losses, which were avoided only fortuitously. This problem is generally referred to as “model risk."l Don’t let the OCC warning in the prior paragraph lead you to conclude that errors in the way a model works are the sole source of model risk. Focusing only on the workings of the models misses the broader problem. In truth, model risk arises from as many as eight different elements in the modeling process. These are listed in Exhibit 10.]. Model Flaws, Model Errors, and Model Obsolescence

Casual observers, as well as some senior manager and auditors, view model risk as synonymous with logic or calculation errors in the model engine itself. That view is overly narrow at best and is ofien very misleading. Today most banks use models acquired from vendors. While the vendors all claim to test their models and upgrades before release, errors in the model engine are quite common in the period shortly following each release. But the large number of users for each vendor model detects the glitches and bugs quickly. This is not to say that model engines are error free. Merely, the other sources on the Exhibit 10.1 list are usually responsible for much larger risk management errors.

We can consider “model flaws,” the fifih risk source listed in Exhibit 10.1, as a broader subject than only errors in model logic or calculations. Even when all of the calculations are done exactly as the developers intended, the model may still be flawed from the point of view of the user.

Model design decisions can be suboptimal. Three design aspects are particularly important:

1. Does the model math employ short cuts? For example, if statistical analysis is used, does the model assume that distributions are normal?

2. Does the model include all risk factors in the measured risk exposure? For example, AIG’s model forecast a $6 billion

1.

“Risk Modeling," OCC Bulletin 2000-l6, May 30. 2000, page 2.

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