Hedging Interest Rate R isk

1. Class 8, Chap 22 & 24 Hedging Interest Rate Risk

2. Duration & Convexity Review/Discussion • http://vimeo.com/31788176 • http://video.cnbc.com/gallery/?video=3000114010

3. Where would you put your money if you wanted the lowest interest rate risk exposure? • 5 year Greek bond • 10 year UK bond • 30 year US Government Treasury • 20 year German bond • Well diversified equity portfolio

4. Hedging interest rate risk Purpose: To understand how banks can use duration to hedge interest rate risk exposure on the balance sheet • Duration Gap • Calculate duration of assets and liabilities • Calculate equity duration • Immunize the equity capital to changes in interest rates

5. DURATION GAP IMMUNIZING THE ENTIRE BALANCE SHEET

6. Duration Gap • We know that matching durations can immunize an asset or a portfolio against changes in interest rates • We can now apply this logic to measure how exposed a bank is to interest rate risk • Question: what component of the balance sheet indicates how risky or safe a bank is? Equity capital: it is the buffer between assets and liabilities – if the bank looses too much equity capital the bank becomes insolvent We know: Rewrite: We want to know how equity will change with a change in interest rates:

7. Duration Gap • Question: If we had the duration for the portfolio of assets and liabilities on the balance sheet could we find ΔA and ΔL? Remember:

8. Duration Gap • The book has a slightly different form This expression which includes the duration gap tells us how equity will change when interest rates change k = leverage L/A Leverage adjusted duration gap

9. Leverage Adjusted Duration GAP • Tells us – on a leverage adjusted basis, how much more/less sensitive are assets than liabilities to a change in interest rates. • What does k do – why is it there? If the interest rate (on both assets and Liab.) increased from 3% to 7% would you expect equity capital to increase, decrease or stay the same? (think intuitively) • Both A & L have the same sensitivity to interest rates so the % change will be the same • What about the change in dollar value? It will be larger for Assets (the denominator is larger) ∆E = ∆A – ∆L so ∆E > 0

10. Leverage Adjusted Duration GAP • Tells us – on a leverage adjusted basis, how much more/less sensitive are assets than liabilities to a change in interest rates. • What does k do – why is it there? k – adjusts for the fact that healthy companies have more assets than liabilities therefore asset duration will have a larger impact on the change in equity k – In our example, the value of L ↑ by ½ as much as the value of A AND LEVERAGE = 50M/100M = 1/2

11. Leverage Adjusted Duration GAP • Tells us – on a leverage adjusted basis, how much more/less sensitive are assets than liabilities to a change in interest rates. • What does k do – why is it there? • Measured in years – but it is not a duration • The larger the gap, either positive or negative, the more exposed the bank is to interest rate risk • possibility that equity capital will increase/decrease with interest rate changes • Shows the degree of maturity mismatch at a bank Would you expect the leverage adjusted duration gap to be positive or negative?

12. Lev. Adj. Duration GAP Other factors that contribute to interest rate risk • FI Size: in terms of total assets “A”: The larger the bank is (more assets they hold) the larger the dollar gain or loss will be from a change in interest rates • Size of the rate change Dr/(1+r): The larger the shock to interest rates, the greater the gain or loss will be to the FI. These are external, and uncontrollable by the FI

13. Example: Suppose the duration of a financial institutions assets is 5 years and the duration of their liabilities is 3 years. Suppose the interest rate is currently 10%, and is expected to increase to 11% • Calculate the change in equity capital • Calculate the change in the equity capital ratio

14. Result • A 1% increase in interest rates would decrease the FIs equity capital ratio from: • Because of the effect on equity capital, the bank may want to immunize their balance sheet to changes in interest rates

15. Example: readjust the banks asset duration so that the firm’s balance sheet will not be effected by changes in interest rates. Repeat the exercise for the liability duration.

16. Result • To immunize the balance sheet to changes in the interest rate the bank must set its leverage adjusted duration gap to zero Key point about leverage: leverage affects the way that duration of assets and liabilities should be weighted to eliminate interest rate risk.

17. Calculating Durations To this point we have been given asset and liability durations. However, these can also be calculated from the durations of individual securities Asset Duration: it is simply a weighted average of individual asset durations Liability Duration: it is simply a weighted average of individual liability durations

18. Calculating Durations To this point we have been given asset and liability durations. However, these can also be calculated from the durations of individual securities Asset Duration: it is simply a weighted average of individual asset durations Liability Duration: it is simply a weighted average of individual liability durations

19. Calculating Durations To this point we have been given asset and liability durations. However, these can also be calculated from the durations of individual securities Equity Duration: Where does it come from?

20. D D Example: Use the following balance sheet to answer the questions below: • Calculate the banks equity duration • Adjust the banks equity duration to 25 years by Selling Mortgages for cash at 100% of their book value

21. Lecture Summary • Duration Gap • Can adjust the sensitivity of equity capital to interest rates • Immunization is the extreme case • Leverage adjusted duration gap • Measures sensitivity of equity capital to interest rate changes • Calculate: • Asset Duration • Liability Duration • Equity Duration

22. Duration Practice Problems

23. Isaac West Bank currently holds a bond portfolio with duration (Macaulay) of 5.3 years the current yield to maturity of the portfolio is 6.3% on average. Find the expected change in the value of the portfolio if the average YTM is expected to increase to 7%. The current market value of the portfolio is $2.8M, total face value of the portfolio is $142M and the 5 year treasury rate is currently 2.3%. • Calculate the change in value using Macaulay Duration • Calculate the change in value using Modified Duration • Calculate the change in value using Dollar Duration

24. Calculate the duration of a two year bond with $3,000 face value and 7% coupon paid semiannually if the YTM is currently 3%. • Suppose that the maximum loss you can afford to suffer on this bond is $1200. Find the approximate change in interest rate that will result in a $1200 loss on your position. • Do you believe your estimate of the change in interest rate is accurate, too large or too small? Explain your answer.