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# Asset-Liability Management 1

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### Asset-Liability Management 1

1. 1. Asset-Liability Management <ul><li>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 </li></ul>
2. 2. Yield to Maturity (YTM)
3. 3. Bank Discount Rate (DR) Where: FV equals Face Value
4. 4. Conversion of DR into YTM <ul><li>YTM equivalent yield = </li></ul><ul><ul><li>(100 – purchase price)/Purchase Price * (365/days to maturity) </li></ul></ul><ul><li>Note that the DR ant the conversion to YTM equivalent yields are approximations that are popular with banks. </li></ul>
5. 5. Example <ul><li>Suppose that we purchase a money market security for \$96. The security will mature in 90 days and its face value is \$100. </li></ul><ul><ul><li>What is the DR, the YTM equivalent yield, and the actual YTM? </li></ul></ul>
6. 6. Example <ul><li>DR = (100 – 96)/100 * 360/90 = 0.16 </li></ul><ul><li>Equivalent YTM = (100 – 96)/96 *365/90 = 0.1690 </li></ul><ul><li>Actual YTM = </li></ul><ul><ul><li>PV = -96, FV = 100, N = 90/365, I = ? </li></ul></ul><ul><ul><ul><li>I = 18% </li></ul></ul></ul>
7. 7. Interest Rate Risk : GAP & Earnings Sensitivity <ul><li>When a bank’s assets and liabilities do not reprice at the same time, the result is a change in net interest income. </li></ul><ul><ul><li>The change in the value of assets and the change in the value of liabilities will also differ, causing a change in the value of stockholder’s equity </li></ul></ul>
8. 8. Interest Rate Risk <ul><li>Banks typically focus on either: </li></ul><ul><ul><li>Net interest income or </li></ul></ul><ul><ul><li>The market value of stockholders' equity </li></ul></ul><ul><li>GAP Analysis </li></ul><ul><ul><li>A static measure of risk that is commonly associated with net interest income (margin) targeting </li></ul></ul><ul><li>Earnings Sensitivity Analysis </li></ul><ul><ul><li>Earnings sensitivity analysis extends GAP analysis by focusing on changes in bank earnings due to changes in interest rates and balance sheet composition </li></ul></ul>
9. 9. Interest Rate Risk <ul><li>Price Risk </li></ul><ul><ul><li>When Interest Rates Rise, the Market Value of the Bond or Asset Falls </li></ul></ul><ul><li>Reinvestment Risk </li></ul><ul><ul><li>When Interest Rates Fall, the Coupon Payments on the Bond are Reinvested at Lower Rates </li></ul></ul>
10. 10. Interest Rate Risk: Reinvestment Rate Risk <ul><li>If interest rates change, the bank will have to reinvest the cash flows from assets or refinance rolled-over liabilities at a different interest rate in the future. </li></ul><ul><ul><li>An increase in rates, ceteris paribus, increases a bank’s interest income but also increases the bank’s interest expense. </li></ul></ul><ul><li>Static GAP Analysis considers the impact of changing rates on the bank’s net interest income. </li></ul>
11. 11. Interest Rate Risk: Price Risk <ul><li>If interest rates change, the market values of assets and liabilities also change. </li></ul><ul><ul><li>The longer is duration, the larger is the change in value for a given change in interest rates. </li></ul></ul><ul><li>Duration GAP considers the impact of changing rates on the market value of equity. </li></ul>
12. 12. Measuring Interest Rate Risk with GAP <ul><li>Traditional Static GAP Analysis GAP t = RSA t -RSL t </li></ul><ul><ul><li>RSA t </li></ul></ul><ul><ul><ul><li>Rate Sensitive Assets </li></ul></ul></ul><ul><ul><ul><ul><li>Those assets that will mature or reprice in a given time period (t) </li></ul></ul></ul></ul><ul><ul><li>RSL t </li></ul></ul><ul><ul><ul><li>Rate Sensitive Liabilities </li></ul></ul></ul><ul><ul><ul><ul><li>Those liabilities that will mature or reprice in a given time period (t) </li></ul></ul></ul></ul>
13. 13. What Determines Rate Sensitivity? <ul><li>An asset or liability is considered rate sensitivity if during the time interval: </li></ul><ul><ul><li>It matures </li></ul></ul><ul><ul><li>It represents and interim, or partial, principal payment </li></ul></ul><ul><ul><li>It can be repriced </li></ul></ul><ul><ul><ul><li>The interest rate applied to the outstanding principal changes contractually during the interval </li></ul></ul></ul><ul><ul><ul><li>The outstanding principal can be repriced when some base rate of index changes and management expects the base rate / index to change during the interval </li></ul></ul></ul>
14. 14. Interest-Sensitive Assets <ul><li>Short-Term Securities Issued by the Government and Private Borrowers </li></ul><ul><li>Short-Term Loans Made by the Bank to Borrowing Customers </li></ul><ul><li>Variable-Rate Loans Made by the Bank to Borrowing Customers </li></ul>
15. 15. Interest-Sensitive Liabilities <ul><li>Borrowings from Money Markets </li></ul><ul><li>Short-Term Savings Accounts </li></ul><ul><li>Money-Market Deposits </li></ul><ul><li>Variable-Rate Deposits </li></ul>
16. 16. Example <ul><ul><li>A bank makes a \$10,000 four-year car loan to a customer at fixed rate of 8.5%. The bank initially funds the car loan with a one-year \$10,000 CD at a cost of 4.5%. The bank’s initial spread is 4%. </li></ul></ul><ul><ul><li>What is the bank’s one year gap? </li></ul></ul>
17. 17. Example <ul><li>Traditional Static GAP Analysis </li></ul><ul><ul><li>What is the bank’s 1-year GAP with the auto loan? </li></ul></ul><ul><ul><ul><li>RSA 1yr = \$0 </li></ul></ul></ul><ul><ul><ul><li>RSL 1yr = \$10,000 </li></ul></ul></ul><ul><ul><ul><li>GAP 1yr = \$0 - \$10,000 = -\$10,000 </li></ul></ul></ul><ul><ul><ul><ul><li>The bank’s one year funding GAP is -10,000 </li></ul></ul></ul></ul><ul><ul><ul><ul><li>If interest rates rise (fall) in 1 year, the bank’s margin will fall (rise) </li></ul></ul></ul></ul>
18. 18. Measuring Interest Rate Risk with GAP <ul><li>Traditional Static GAP Analysis </li></ul><ul><ul><li>Funding GAP </li></ul></ul><ul><ul><ul><li>Focuses on managing net interest income in the short-run </li></ul></ul></ul><ul><ul><ul><li>Assumes a ‘parallel shift in the yield curve,’ or that all rates change at the same time, in the same direction and by the same amount. </li></ul></ul></ul>
19. 19. Other Gap Measurements Relative Interest-Sensitive Gap Interest Sensitivity Ratio
20. 20. Asset-Sensitive Bank Has: <ul><li>Positive Dollar Interest-Sensitive Gap </li></ul><ul><li>Positive Relative Interest-Sensitive Gap </li></ul><ul><li>Interest Sensitivity Ratio Greater Than One </li></ul>
21. 21. Liability Sensitive Bank Has: <ul><li>Negative Dollar Interest-Sensitive Gap </li></ul><ul><li>Negative Relative Interest-Sensitive Gap </li></ul><ul><li>Interest Sensitivity Ratio Less Than One </li></ul>
22. 22. Net Interest Margin
23. 23. Factors Affecting Net Interest Income <ul><li>Changes in the level of interest rates </li></ul><ul><li>Changes in the composition of assets and liabilities </li></ul><ul><li>Changes in the volume of earning assets and interest-bearing liabilities outstanding </li></ul><ul><li>Changes in the relationship between the yields on earning assets and rates paid on interest-bearing liabilities </li></ul>
24. 24. Example <ul><li>Consider the following balance sheet: </li></ul>
25. 25. Examine the impact of the following changes <ul><li>A 1% increase in the level of all short-term rates? </li></ul><ul><li>A 1% decrease in the spread between assets yields and interest costs such that the rate on RSAs increases to 8.5% and the rate on RSLs increase to 5.5%? </li></ul><ul><li>Changes in the relationship between short-term asset yields and liability costs </li></ul><ul><li>A proportionate doubling in size of the bank? </li></ul>
26. 26. 1% increase in short-term rates With a negative GAP, more liabilities than assets reprice higher; hence NII and NIM fall
27. 27. 1% decrease in the spread NII and NIM fall (rise) with a decrease (increase) in the spread. Why the larger change?
28. 28. Changes in the Slope of the Yield Curve <ul><li>If liabilities are short-term and assets are long-term, the spread will </li></ul><ul><ul><li>widen as the yield curve increases in slope </li></ul></ul><ul><ul><li>narrow when the yield curve decreases in slope and/or inverts </li></ul></ul>
29. 29. Proportionate doubling in size NII and GAP double, but NIM stays the same. What has happened to risk?
30. 30. Changes in the Volume of Earning Assets and Interest-Bearing Liabilities <ul><li>Net interest income varies directly with changes in the volume of earning assets and interest-bearing liabilities, regardless of the level of interest rates </li></ul>
31. 31. RSAs increase to \$540 while fixed-rate assets decrease to \$310 and RSLs decrease to \$560 while fixed-rate liabilities increase to \$260 Although the bank’s GAP (and hence risk) is lower, NII is also lower.
32. 32. Changes in Portfolio Composition and Risk <ul><li>To reduce risk, a bank with a negative GAP would try to increase RSAs (variable rate loans or shorter maturities on loans and investments) and decrease RSLs (issue relatively more longer-term CDs and fewer fed funds purchased) </li></ul><ul><li>Changes in portfolio composition also raise or lower interest income and expense based on the type of change </li></ul>
33. 33. Changes in Net Interest Income are directly proportional to the size of the GAP <ul><li>If there is a parallel shift in the yield curve: </li></ul><ul><li>It is rare, however, when the yield curve shifts parallel </li></ul><ul><ul><li>If rates do not change by the same amount and at the same time, then net interest income may change by more or less. </li></ul></ul>
34. 34. Summary of GAP and the Change in NII
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