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 The first mistake is usually the cheapest mistake. A trader adage

3. 3 Outline u Introduction u Interest Rate Futures Contracts u Concept of Immunization

4. 4 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

5. 5 Interest Rate Futures Contracts u Categories of Interest Rate Futures Contracts u U.S. Treasury Bills and Their Futures Contracts u Treasury Bonds and Their Futures Contracts

6. 6 Categories of Interest Rate Futures Contracts u Short-Term Contracts u Intermediate- and Long-Term Contracts

7. 7 Short-Term Contracts u The two principal short-term futures contracts are: Eurodollars –U.S. dollars on deposit in a bank outside the U.S. –The most popular form of short-term futures –Not subject to reserve requirements –Carry more risk than a domestic deposit U.S. Treasury bills

8. 8 Intermediate- and Long-Term Contracts u Futures contract on U.S. Treasury notes is the only intermediate-term contract u The principal long-term contract is the contract on U.S. Treasury bonds u Special-purpose contracts: Municipal bonds U.S. dollar index

9. 9 U.S. Treasury Bills and Their Futures Contracts u Characteristics of U.S. Treasury Bills u Treasury Bill Futures Contracts

10. 10 Characteristics of U.S. Treasury Bills u U.S. Treasury bills: Are sold at a discount from par value Are sold with 91-day and 182-day maturities at a weekly auction Are calculated following a standard convention and on a bond equivalent basis

11. 11 Characteristics of U.S. Treasury Bills (cont’d) u Standard convention:

12. 12 Characteristics of U.S. Treasury Bills (cont’d) u The T-bill yield on a bond equivalent basis adjusts for: The fact that there are 365 days in a year The fact that the discount price is the required investment, not the face value

13. 13 Characteristics of U.S. Treasury Bills (cont’d) u The T-bill yield on a bond equivalent basis:

14. 14 Characteristics of U.S. Treasury Bills (cont’d) Example A 182-day T-bill has an ask discount of 5.30 percent. The par value is $10,000. What is the price of the T-bill? What is the yield of this T- bill on a bond equivalent basis?

15. 15 Characteristics of U.S. Treasury Bills (cont’d) Example (cont’d) Solution: We must first compute the discount amount to determine the price of the T-bill:

16. 16 Characteristics of U.S. Treasury Bills (cont’d) Example (cont’d) Solution (cont’d): With a discount of $267.94, the price of this T-bill is:

17. 17 Characteristics of U.S. Treasury Bills (cont’d) Example (cont’d) Solution (cont’d): The bond equivalent yield is 5.52%:

18. 18 Treasury Bill Futures Contracts u T-bill futures contracts: Call for the delivery of $1 million par value of 90-day T-bills on the delivery date of the futures contract

19. 19 Treasury Bill Futures Contracts (cont’d) Example Listed below is information regarding a T-bill futures contract. What would you pay for this futures contract today? Discount OpenHighLowSettleChangeSettleChangeOpen Interest 92.4392.4992.4192.48–.017.52+.01250

20. 20 Treasury Bill Futures Contracts (cont’d) Example (cont’d) Solution: First, determine the yield for the life of the T- bill: 7.52% × 90/360 = 1.88% Next, discount the contract value by the yield: $1,000,000/(1.0188) = $981,546.92

21. 21 Treasury Bonds and Their Futures Contracts u Characteristics of U.S. Treasury Bonds u Treasury Bond Futures Contracts

22. 22 Characteristics of U.S. Treasury Bonds u U.S. Treasury bonds: Pay semiannual interest Have a maturity of up to 30 years Trade readily in the capital markets

23. 23 Characteristics of U.S. Treasury Bonds (cont’d) u U.S. Treasury bonds differ from U.S. Treasury notes: T-notes have a life of less than ten years T-bonds are callable fifteen years after they are issued

24. 24 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

25. 25 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

26. 26 Sample Conversion Factors

27. 27 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:

28. 28 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

29. 29 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

30. 30 Cheapest to Deliver Calculation

31. 31 Concept of Immunization u Definition u Duration Matching u Immunizing with Interest Rate Futures u Immunizing with Interest Rate Swaps u Disadvantages of Immunizing

32. 32 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

33. 33 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

34. 34 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

35. 35 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

36. 36 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

37. 37 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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40. 40 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

41. 41 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)

42. 42 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:

43. 43 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

44. 44 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

45. 45 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

46. 46 Immunizing with Interest Rate Futures (cont’d) u To hedge, first calculate the hedge ratio:

47. 47 Immunizing with Interest Rate Futures (cont’d) u Next, calculate the number of contracts necessary given the hedge ratio:

48. 48 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?

49. 49 Immunizing with Interest Rate Futures (cont’d) Example Solution: First calculate the hedge ratio:

50. 50 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:

51. 51 Immunizing with Interest Rate Swaps u Interest rate swaps are popular tools for managers who need to manage interest rate risk u A swap enables a manager to alter the level of risk without disrupting the underlying portfolio

52. 52 Immunizing with Interest Rate Swaps (cont’d) u A basic interest rate swap involves: A party receiving variable-rate payments –Believes interest rates will decrease A party receiving fixed-rate payments –Believes interest rates will rise u The two parties swap fixed-for-variable payments

53. 53 Immunizing with Interest Rate Swaps (cont’d) u The size of the swap is the notional amount The reference point for determining how much interest is paid u The price of the swap is the fixed rate to which the two parties agree

54. 54 Immunizing with Interest Rate Swaps (cont’d) u Interest rate swaps introduce counterparty risk: No institution guarantees the trade One party to the swap may not honor its agreement

55. 55 Disadvantages of Immunizing u Opportunity Cost of Being Wrong u Lower Yield u Transaction Costs u Immunization Is Instantaneous Only

56. 56 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

57. 57 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

58. 58 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

59. 59 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