McGraw-Hill/Irwin ©2008 The McGraw-Hill Companies, All Rights Reserved Chapter Seven Asset-Liability Management: Determining and Measuring Interest Rates and Controlling Interest-Sensitive and Duration Gaps

7-2 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Goals of This Chapter The purpose of this chapter is to explore the options bankers have today for dealing with risk – especially the risk of loss due to changing interest rates – and to see how a bank’s management can coordinate the management of its assets with the management of its liabilities in order to achieve the institution’s goals.

7-3 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Key Topics in This Chapter 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

7-4 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. RMB, millions/ % Asset/Liability Average AmountInterest income/expensesAverage Rate(revenue/cost) Assets Loans5,318,554277, Security Investment3,183,56296, Deposits in PBC1,519,05523, Deposits in other financial institutions 837,6739, Total Earning Assets 10,858, , Nonearning Assets438,991 Assets Prepared for Loss145,858 Total Assets 11,151,977 Liabilities Deposits from Customers9,103,898145, Borrowings from Other Financial Institutions 1,002,53413, Subordinate Debentures53,0871, Total Interest-payment Liabilities 10,159, , Noninterest-payment Liabilities350,840 Total Liability10,510,359 Net Interest Income 245,821 Net Interest Margin 2.16

7-5 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

7-6 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Asset-Liability Management Historical View of Asset-Liability Management: Asset Management Strategy Liability Management Strategy Funds Management Strategy

7-7 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest Rate Risk The Measurement of Interest Rate: 1. YTM (Yield to Maturity)

7-8 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Measurement of Interest Rate Example 7-1: A government bond is currently selling for $900 and pays $80 per year in interest for nine years when it matures. If the redemption value of this bond is $1,000, what is its yield to maturity if purchased today for $900? The yield to maturity equation for this bond would be: Using a financial calculator the YTM = 9.72%

7-9 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Measurement of Interest Rate 2. HPR (Holding Period Rate of Return) Example 7-2: Suppose the government bond described in example 1 above is held for three years and then the thrift institution acquiring the bond decides to sell it at a price of $950. Can you figure out the average annual yield? Using a financial calculator, the HPY is 10.56%

7-10 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest Rate Risk Kinds of 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

7-11 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. The Component of Interest Rates Function of: Risk-Free Real Rate of Interest Various Risk Premiums –Default Risk –Inflation Risk –Liquidity Risk –Maturity Risk

7-12 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. The Goals of Interest-Rate Hedging The Net Interest Margin (NIM): to freeze the spread between asset revenues and liability expenditures The equity: to insulate the equity (net worth) from the damaging effects of interest rate changes

7-13 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest Rate Sensitive Gap Management 1. Interest-Sensitive Assets 2. Interest-Sensitive Liabilities 3. Interest-Sensitive Gap Measurements Dollar Interest-Sensitive Gap Interest Sensitivity Ratio 4. Gap Positions and the Effect of Interest Rate Changes 5. Strategies in Gap Management

7-14 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest-Sensitive Assets Short-Term Securities Issued by the Government and Private Borrowers Short-Term Loans Made by the Bank to Borrowing Customers Variable-Rate Loans Made by the Bank to Borrowing Customers

7-15 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest-Sensitive Liabilities Borrowings from Money Markets Short-Term Savings Accounts Money-Market Deposits Variable-Rate Deposits

7-16 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest-Sensitive Gap Measurements Dollar Interest- Sensitive Gap Interest-Sensitive Assets – Interest Sensitive Liabilities = Interest Sensitivity Ratio

7-17 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Gap Positions and the Effect of Interest Rate Changes on the Bank Asset-Sensitive Bank –Interest Rates Rise NIM Rises –Interest Rates Fall NIM Falls Liability-Sensitive Bank –Interest Rates Rise NIM Falls –Interest Rates Fall NIM Rises

7-18 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Zero Interest-Sensitive Gap Dollar Interest-Sensitive Gap is Zero Interest Sensitivity Ratio is One –When Interest Rates Change in Either Direction - NIM is Protected and Will Not Change

7-19 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Example of IS GAP Management Example 7-3: Coming Week Next 30 Days Next Days More Than 90 Days Loans$210$100$175$225 Securities Total IS Assets$240$120$205$250 Transaction Dep.$250$ --- Time Accts Money Mkt. Borr Total IS Liab.$386$104$196$100 GAP- $146+ $16+$9+ $150 IS Ratio62.18%115.38%104.59% 250%

7-20 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. NIM Influenced By: Changes in Interest Rates Up or Down The Spread Between Interest-Sensitive Assets and Liabilities Important Decision Regarding IS Gap: –Management Must Choose the Time Period Over Which NIM is to be Managed –Reallocate Assets and Liabilities to change the Spread –Develop Correct Interest Rate Forecast

7-21 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Aggressive Interest-Sensitive Gap Management Expected Change in Interest Rates Best Interest- Sensitive Gap Position Aggressive Management’s Likely Action Rising Market Interest Rates Positive IS GapIncrease in IS Assets Decrease in IS Liabilities Falling Market Interest Rates Negative IS GapDecrease in IS Assets Increase in IS Liabilities

7-22 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Limits of Interest-Sensitive Gap Management Interest-Sensitive Gap Does Not Consider the Impact of Changing Interest Rates on Equity Position It’s difficult to make sure the amount of interest-sensitive assets and the amount of interest-sensitive liabilities. Correct interest forecasting is very important.

7-23 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration Gap Management The Conception of Duration Using Duration to Hedge Against Interest-Rate Risk

7-24 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration Gap Management The Conception of Duration –Definition of Duration –Calculation of Duration –Price Risk and Duration

7-25 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration Gap Management Using Duration to Hedge Against Interest- Rate Risk A.Duration Gap Dollar Weighted Duration of Assets Dollar Weighted Duration of Liabilities Positive Duration Gap Negative Duration Gap B.Change in the Bank’s Net Worth

7-26 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. The Concept of Duration Duration is the Weighted Average Maturity of a Promised Stream of Future Cash Flows.

7-27 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. To Calculate Duration

7-28 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration and the Price of Bond The pricing formula of bonds: The pricing formula of bonds: First derivative ：

7-29 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration and the Price of Bond The relationship between the price change of a bond and duration, YTM is as follows:The relationship between the price change of a bond and duration, YTM is as follows: Price Sensitivity of a Security

7-30 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration Gap Management Duration of an Asset portfolio: Where: w i = the dollar amount of the ith asset divided by total assets D Ai = the duration of the ith asset in the portfolio

7-31 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration of a Liability Portfolio Where: w i = the dollar amount of the ith liability divided by total liabilities D Li = the duration of the ith liability in the portfolio

7-32 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration Gap

7-33 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Change in the Value of a Bank’s Net Worth

7-34 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Example of Duration Management Examples 7-4: New Phase National Bank holds assets and liabilities whose average duration and dollar amount are as shown in this table: What is the weighted average duration of New Phase’s asset portfolio and liability portfolio. What is the leverage-adjusted duration gap? Asset and Liability ItemsDuration$ Amount Investment Grade Bonds10$50 Commercial Loans4$400 Consumer Loans7$250 Deposits1.1$600 Nondeposit Borrowings0.1$20

7-35 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Example of Duration Management

7-36 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Impact of Changing Interest Rates on a Bank’s Net Worth PositiveInterest Rate RiseNW Decrease GapInterest Rate FallNW Increase NegativeInterest Rate RiseNW Increase GapInterest Rate FallNW Decrease ZeroInterest Rate RiseNo Change GapInterest Rate FallNo Change

7-37 McGraw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 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