1. 1 Chapter 21 Removing Interest Rate Risk Portfolio Construction, Management, & Protection, 4e, Robert A. Strong Copyright ©2006 by South-Western, a division of Thomson Business & Economics. All rights reserved.

2. 2 Introduction u A portfolio has high interest rate sensitivity if its value declines in response to interest rate increases Especially pronounced: –For portfolios with income as their primary objective –For corporate and government bonds

3. 3 Treasury Bond Futures Contracts u U.S. Treasury bond futures: Call for the delivery of $100,000 face value of U.S. T-bonds that have a minimum of fifteen years until maturity (fifteen years of call protection for callable bonds) u Bonds that meet these criteria are deliverable bonds

4. 4 Treasury Bond Futures Contracts (cont’d) u A conversion factor is used to standardize deliverable bonds: The conversion is to bonds yielding 6 percent Published by the Chicago Board of Trade Is used to determine the invoice price

5. 5 Sample Conversion Factors

6. 6 Treasury Bond Futures Contracts (cont’d) u The invoice price is the amount that the deliverer of the bond receives when a particular bond is delivered against a futures contract:

7. 7 Treasury Bond Futures Contracts (cont’d) u Position day is the day the bondholder notifies the clearinghouse of an intent to delivery bonds against a futures position Two business days prior to the delivery date Delivery occurs by wire transfer between accounts

8. 8 Treasury Bond Futures Contracts (cont’d) u At any given time, several bonds may be eligible for delivery Only one bond is cheapest to delivery –Normally the eligible bond with the longest duration –The bond with the lowest ratio of the bond’s market price to the conversion factor is the cheapest to deliver

9. 9 Cheapest to Deliver Calculation

10. 10 Definition u Immunization means protecting a bond portfolio from damage due to fluctuations in market interest rates u It is rarely possible to eliminate interest rate risk completely

11. 11 Duration Matching u An Independent Portfolio u Bullet Immunization Example u Expectation of Changing Interest Rates u An Asset Portfolio with a Corresponding Liability Portfolio

12. 12 An Independent Portfolio u Bullet immunization is one method of reducing interest rate risk associated with an independent portfolio Seeks to ensure that a set sum of money will be available at a specific point in the future The effects of interest rate risk and reinvestment rate risk cancel each other out

13. 13 Bullet Immunization Example u Assume: You are required to invest $936 You are to ensure that the investment will grow at a 10 percent compound rate over the next 6 years –$936 × (1.10) 6 = $1,658.18 The funds are withdrawn after 6 years

14. 14 Bullet Immunization Example (cont’d) u If interest rates increase over the next 6 years: Reinvested coupons will earn more interest The value of any bonds we buy will decrease –Our portfolio may end up below the target value

15. 15 Bullet Immunization Example (cont’d) u Reduce the interest rate risk by investing in a bond with a duration of 6 years u One possibility is the 8.8 percent coupon bond shown on the next two slides: Interest is paid annually Market interest rates change only once, at the end of the third year

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18. 18 Expectation of Changing Interest Rates u The higher the duration, the higher the interest rate risk u To reduce interest rate risk, reduce the duration of the portfolio when interest rates are expected to increase Duration declines with shorter maturities and higher coupons

19. 19 An Asset Portfolio with a Liability Portfolio u A bank immunization case occurs when there are simultaneously interest-sensitive assets and interest-sensitive liabilities u A bank’s funds gap is its rate-sensitive assets (RSA) minus its rate-sensitive liabilities (RSL)

20. 20 An Asset Portfolio with a Liability Portfolio (cont’d) u A bank can immunize itself from interest rate fluctuations by restructuring its balance sheet so that:

21. 21 An Asset Portfolio with a Liability Portfolio (cont’d) u If the dollar-duration value of the asset side exceeds the dollar-duration of the liability side: The value of RSA will fall to a greater extent than the value of RSL The net worth of the bank will decline

22. 22 An Asset Portfolio with a Liability Portfolio (cont’d) u To immunize if RSA are more sensitive than RSL: Get rid of some RSA Reduce the duration of the RSA Issue more RSL Raise the duration of the RSL

23. 23 Immunizing with Interest Rate Futures u Financial institutions use futures to hedge interest rate risk u If interest rate are expected to rise, go short T-bond futures contracts

24. 24 Immunizing with Interest Rate Futures (cont’d) u To hedge, first calculate the hedge ratio:

25. 25 Immunizing with Interest Rate Futures (cont’d) u Next, calculate the number of contracts necessary given the hedge ratio:

26. 26 Immunizing with Interest Rate Futures (cont’d) Example A bank portfolio manager holds $20 million par value in government bonds that have a current market price of $18.9 million. The weighted average duration of this portfolio is 7 years. Cheapest-to-deliver bonds are 8.125s28 T-bonds with a duration of 10.92 years and a conversion factor of 1.2786. What is the hedge ratio? How many futures contracts does the bank manager have to short to immunize the bond portfolio, assuming the last settlement price of the futures contract was 94 15/32?

27. 27 Immunizing with Interest Rate Futures (cont’d) Example Solution: First calculate the hedge ratio:

28. 28 Immunizing with Interest Rate Futures (cont’d) Example Solution: Based on the hedge ratio, the bank manager needs to short 155 contracts to immunize the portfolio:

29. 29 Opportunity Cost of Being Wrong u With an incorrect forecast of interest rate movements, immunized portfolios can suffer an opportunity loss u For example, if a bank has more RSA than RSL, it would benefit from a decline in interest rates Immunizing would have reduced the benefit

30. 30 Lower Yield u The yield curve is usually upward sloping u Immunizing may reduce the duration of a portfolio and shift fund characteristics to the left on the yield curve

31. 31 Transaction Costs u Buying and selling bonds requires brokerage commissions Sales may also result in tax liabilities u Commissions with the futures market are lower The futures market is the method of choice for immunization strategies

32. 32 Immunization Is Instantaneous Only u A portfolio is theoretically only immunized for an instant With each day that passes, durations, yields to maturity, and market interest rates change u It is not practical for any but the largest portfolios to make daily adjustments to account for changing immunization needs u Smaller portfolios may be initially immunized and revised only after weeks have passed or when conditions have changed enough to make revision cost effective