Chapter Seven Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques McGraw-Hill/Irwin Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.

Key Topics Asset, Liability, and Funds Management 7-2 Key Topics Asset, Liability, and Funds Management Market Rates and Interest-Rate Risk The Goals of Interest-Rate Hedging Interest-Sensitive Gap Management Duration Gap Management Limitations of Hedging Techniques

Asset-Liability Management 7-3 Asset-Liability Management The Purpose of Asset-Liability Management is to Control a Bank’s Sensitivity to Changes in Market Interest Rates and Limit its Losses in its Net Income or Equity

Historical View of Asset-Liability Management 7-4 Historical View of Asset-Liability Management Asset Management Strategy (control over assets, no control over liabilities) Liability Management Strategy (control over liabilities by changing rates and other terms) Funds Management Strategy (work with both strategies)

Interest Rate Risk Price Risk Reinvestment Risk 7-5 Interest Rate Risk Price Risk When Interest Rates Rise, the Market Value of the Bond or Asset Falls Reinvestment Risk When Interest Rates Fall, the Coupon Payments on the Bond are Reinvested at Lower Rates

Interest Rate Risk: One of the Main Challenges 7-6 Interest Rate Risk: One of the Main Challenges Forces Determining Interest Rates Loanable Funds Theory The Measurement of Interest Rates YTM Bank Discount Components of Interest Rates

Yield to Maturity (YTM) 7-7 Yield to Maturity (YTM)

Bank Discount Rate (DR) 7-8 Bank Discount Rate (DR) Where: FV equals Face Value of a Security, such as Treasury Bills

Market Interest Rates Function of: Risk-Free Real Rate of Interest 7-9 Market Interest Rates Function of: Risk-Free Real Rate of Interest Various Risk Premiums Default Risk Inflation Risk Liquidity Risk Call Risk Maturity Risk

7-10 Yield Curves Graphical Picture of Relationship Between Yields and Maturities on Securities Generally Created With Treasury Securities to Keep Default Risk Constant Shape of the Yield Curve Upward – Long-Term Rates Higher than Short- Term Rates Downward – Short-Term Rates Higher than Long- Term Rates Horizontal – Short-Term and Long-Term Rates the Same Shape of the Yield Curve and a Maturity Gap

7-11 Net Interest Margin

Goal of Interest Rate Hedging 7-12 Goal of Interest Rate Hedging One Important Goal of Interest Rate Hedging is to Insulate the Bank from the Damaging Effects of Fluctuating Interest Rates on Profits

Quick Quiz What forces cause interest rates to change? 7-13 Quick Quiz What forces cause interest rates to change? What makes it so difficult to correctly forecast interest rate changes? What is the yield curve, and why is it important to know about its shape and slope? What is the goal of hedging? First National Bank of Bannerville has posted interest revenues of $63 million and interest costs from all of its borrowings of $42 million. If this bank possesses $700 million in total earning assets, what is First National’s net interest margin? Suppose the bank’s interest revenues and interest costs double, while its earning assets increase by 50%. What will happen to its net interest margin?

Interest-Sensitive Gap Measurements 7-14 Interest-Sensitive Gap Measurements Dollar Interest-Sensitive Gap Interest-Sensitive Assets – Interest Sensitive Liabilities = Relative Interest-Sensitive Gap Interest Sensitivity Ratio

Examples of Repriceable (Interest Sensitive) Assets and Liabilities 7-15 Examples of Repriceable (Interest Sensitive) Assets and Liabilities

Asset-Sensitive Bank Has: 7-16 Asset-Sensitive Bank Has: Positive Dollar Interest-Sensitive Gap Positive Relative Interest-Sensitive Gap Interest Sensitivity Ratio Greater Than One

Liability Sensitive Bank Has: 7-17 Liability Sensitive Bank Has: Negative Dollar Interest-Sensitive Gap Negative Relative Interest-Sensitive Gap Interest Sensitivity Ratio Less Than One

Computer-Based Techniques and Maturity Buckets 7-18 Computer-Based Techniques and Maturity Buckets

Gap Positions and the Effect of Interest Rate Changes on the Bank 7-19 Gap Positions and the Effect of Interest Rate Changes on the Bank Liability- Sensitive Bank Interest Rates Rise NIM Falls Interest Rates Fall NIM Rises Asset-Sensitive Bank Interest Rates Rise NIM Rises Interest Rates Fall NIM Falls

Zero Interest-Sensitive Gap 7-20 Zero Interest-Sensitive Gap Dollar Interest-Sensitive Gap is Zero Relative Interest-Sensitive Gap is Zero Interest Sensitivity Ratio is One When Interest Rates Change in Either Direction - NIM is Protected and Will Not Change

Important Decision Regarding IS Gap 7-21 Important Decision Regarding IS Gap Management Must Choose the Time Period Over Which NIM is to be Managed Management Must Choose a Target NIM To Increase NIM Management Must Either: Develop Correct Interest Rate Forecast Reallocate Assets and Liabilities to Increase Spread Management Must Choose Volume of Interest-Sensitive Assets and Liabilities

NIM Influenced By: Changes in Interest Rates Up or Down 7-22 NIM Influenced By: Changes in Interest Rates Up or Down Changes in the Spread Between Assets and Liabilities Changes in the Volume of Interest-Sensitive Assets and Liabilities Changes in the Mix of Assets and Liabilities

7-23 Cumulative Gap The Total Difference in Dollars Between Those Bank Assets and Liabilities Which Can be Repriced over a Designated Time Period

Aggressive Interest-Sensitive Gap Management 7-24 Aggressive Interest-Sensitive Gap Management

Problems with Interest-Sensitive Gap Management 7-25 Problems with Interest-Sensitive Gap Management Interest Paid on Liabilities Tend to Move Faster than Interest Rates Earned on Assets Interest Rate Attached to Bank Assets and Liabilities Do Not Move at the Same Speed as Market Interest Rates Point at Which Some Assets and Liabilities are Repriced is Not Easy to Identify Interest-Sensitive Gap Does Not Consider the Impact of Changing Interest Rates on Equity Position

7-26 Quick Quiz Commerce National Bank reports interest-sensitive assets of $870 million and interest-sensitive liabilities of $625 million during the coming month. Is the bank asset sensitive or liability sensitive? What is likely to happen to the bank’s net interest margin if interest rates rise? If they fall? People’s Savings Bank , a thrift institutions, has a cumulative gap for the coming year of +$135 million, and interest rates are expected to fall by two and a half percentage points. Calculate the expected change in net interest income that this thrift institution might experience. What will occur in net interest income if interest rates rise by one and a quarter percentage points?

The Concept of Duration 7-27 The Concept of Duration Duration is the Weighted Average Maturity of a Promised Stream of Future Cash Flows

To Calculate the Instrument’s Duration 7-28 To Calculate the Instrument’s Duration

Price Sensitivity of a Security 7-29 Price Sensitivity of a Security

7-30 Convexity The Rate of Change in an Asset’s Price or Value Varies with the Level of Interest Rates or Yields

Dollar-Weighted Duration of Asset Portfolio 7-31 Dollar-Weighted Duration of Asset Portfolio Where: wi = the dollar amount of the ith asset divided by total assets DAi = the duration of the ith asset in the portfolio

Dollar-Weighted Duration of a Liability Portfolio 7-32 Dollar-Weighted Duration of a Liability Portfolio Where: wi = the dollar amount of the ith liability divided by total liabilities DLi = the duration of the ith liability in the portfolio

7-33 Duration Gap

Change in the Value of a Bank’s Net Worth 7-34 Change in the Value of a Bank’s Net Worth

Impact of Changing Interest Rates on a Bank’s Net Worth 7-35 Impact of Changing Interest Rates on a Bank’s Net Worth

Limitations of Duration Gap Management 7-36 Limitations of Duration Gap Management Finding Assets and Liabilities of the Same Duration Can be Difficult Some Assets and Liabilities May Have Patterns of Cash Flows that are Not Well Defined Customer Prepayments May Distort the Expected Cash Flows in Duration Customer Defaults May Distort the Expected Cash Flows in Duration Convexity Can Cause Problems

7-37 Quick Quiz What is duration? How is a financial institution’s duration gap determined? What are the advantages of using duration as opposed to interest-sensitive gap analysis? Suppose that a thrift institution has an average asset duration of 2.5 years and an average liability duration of 3.0 years. If the thrift holds total assets of $560 million and total liabilities of $467 million, does it have a significant leverage-adjusted duration gap? If interest rates rise, what will happen to the value of its net worth?