1. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

2. Chapter 7 7 Asset-Liability Management: The Concept of Duration and Managing a Bank’s Duration Gap This chapter introduces us to yet another way to measure a bank’s exposure to loss from changes in interest rates – the concept of duration. We also see how bankers use duration analysis as a management weapon, offsetting the potentially damaging effects of rising or falling market interest rates.

3. Copyright © 2002 by 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

4. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. To Calculate Duration

5. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Price Sensitivity of a Security

6. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Convexity The Rate of Change in an Asset’s Price or Value Varies with the Level of Interest Rates or Yields

7. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 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

8. Copyright © 2002 by 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

9. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Duration Gap

10. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Change in the Value of a Bank’s Net Worth

11. Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Impact of Changing Interest Rates on a Bank’s Net Worth Positive RiseDecrease Gap FallIncrease Negative RiseIncrease Gap FallDecrease Zero RiseNo Change Gap FallNo Change

12. Copyright © 2002 by 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