1. © 2002 South-Western Publishing 1 Chapter 12 Futures Contracts and Portfolio Management

2. 2 The Concept of Immunization Introduction Bond risks Duration matching Bullet Immunization Bank immunization Duration shifting

3. 3 The Concept of Immunization (cont’d) Hedging with interest rate futures Increasing duration with futures Disadvantages of immunizing

4. 4 Introduction An immunized bond portfolio is largely protected from fluctuations in market interest rates – Seldom possible to eliminate interest rate risk completely – A portfolio’s immunization can wear out, requiring managerial action to reinstate the portfolio – Continually immunizing a fixed-income portfolio can be time-consuming and technical

5. 5 Bond Risks A fixed income investor faces three primary sources of risk: – Credit risk – Interest rate risk – Reinvestment rate risk

6. 6 Bond Risks (cont’d) Credit risk is the likelihood that a borrower will be unable or unwilling to repay a loan as agreed – Rating agencies measure this risk with bond ratings – Lower bond ratings mean higher expected returns but with more risk of default – Investors choose the level of credit risk that they wish to assume

7. 7 Bond Risks (cont’d) Interest rate risk is a consequence of the inverse relationship between bond prices and interest rates – Duration is the most widely used measure of a bond’s interest rate risk - a measure of the % change in the price of the security for a given change in the yield

8. 8 Bond Risks (cont’d) Reinvestment rate risk is the uncertainty associated with not knowing at what rate money can be put back to work after the receipt of an interest check – The reinvestment rate will be the prevailing interest rate at the time of reinvestment, not some rate determined in the past

9. 9 Duration Duration may be considered as the weighted average maturity for a bond or other fixed income security takes into consideration that some of the cash flows i.e the coupons are received before maturity – remember that the value of the a bond is the PV of its future cash flows - both the coupon payments and the face value of the bond at maturity at prevailing market interest rates.

10. 10 Duration Discount or zero coupon bonds maturity equals duration Coupon or interest bearing bonds duration differs from maturity becasue these interest payments are received prior to maturity

11. 11 Duration - Calculation N D 1 = E(t)(CF t )/(1+Y/2) t=1 P Where: t = time period until receipt of cash flow P = current price of the bond/security CFt = cash flow received at the end of period t Y = yield to maturity or discount rate N = number of discounting periods

12. 12 Duration - Calculation the cash flows are weighted by the time remaining until they are received the weighted cash flows are discounted at the bond’s current yield and the sum is divided by the current price of the bond

13. 13 Duration - Example Two year 8% coupon bond, paying interest semi- annually and selling at par....what is the duration

14. 14 Duration Matching (hedging) Introduction Bullet immunization Bank immunization

15. 15 Introduction Duration matching selects a level of duration that minimizes the combined effects of reinvestment rate and interest rate risk Two versions of duration matching: – Bullet immunization – Bank immunization

16. 16 Bullet Immunization Seeks to ensure that a predetermined sum of money is available at a specific time in the future regardless of interest rate movements

17. 17 Bullet Immunization (cont’d) Objective is to get the effects of interest rate and reinvestment rate risk to offset – If interest rates rise, coupon proceeds can be reinvested at a higher rate – If interest rates fall, proceeds can be reinvested at a lower rate

18. 18 Bullet Immunization (cont’d) Bullet Immunization Example A portfolio managers receives $93,600 to invest in bonds and needs to ensure that the money will grow at a 10% compound rate over the next 6 years (it should be worth $165,818 in 6 years).

19. 19 Bullet Immunization (cont’d) Bullet Immunization Example (cont’d) The portfolio manager buys $100,000 par value of a bond selling for 93.6% with a coupon of 8.8%, maturing in 8 years, and a yield to maturity of 10.00%.

20. 20 Bullet Immunization Example (cont’d) Panel A: Interest Rates Remain Constant Bullet Immunization (cont’d) Year 1Year 2Year 3Year 4Year 5Year 6 $8,800$9,680$10,648$11,713$12,884$14,172 $8,800$9,680$10,648$11,713$12,884 $8,800$9,680$10,648$11,713 $8,800$9,680$10,648 $8,800$9,680 Interest$67897 Bond Total$166,725 $8,800 $97,920

21. 21 Bullet Immunization (cont’d) Bullet Immunization Example (cont’d) Panel B: Interest Rates Fall 1 Point in Year 3 Year 1Year 2Year 3Year 4Year 5Year 6 $8,800$9,680$10,648$11,606$12,651$13,789 $8,800$9,680$10,551$11,501$12,536 $8,800$9,592$10,455$11,396 $8,800$9,592$10,455 $8,800$9,592 Interest$66,568 Bond Total$166,218 $8,800 $99,650

22. 22 Bullet Immunization (cont’d) Bullet Immunization Example (cont’d) Panel C: Interest Rates Rise 1 Point in Year 3 Year 1Year 2Year 3Year 4Year 5Year 6 $8,800$9,680$10,648$11,819$13,119$14,563 $8,800$9,680$10,745$11,927$13,239 $8,800$9,768$10,842$12,035 $8,800$9,768$10,842 $8,800$9,768 Interest$69,247 Bond Total$165,477 $8,800 $96,230

23. 23 Bullet Immunization (cont’d) Bullet Immunization Example (cont’d) The compound rates of return in the three scenarios are 10.10%, 10.04%, and 9.96%, respectively.

24. 24 Bank Immunization Addresses the problem that occurs if interest-sensitive liabilities are included in the portfolio – E.g., a bank’s portfolio manager is concerned with the entire balance sheet – A bank’s funds gap is the dollar value of its interest rate sensitive assets (RSA) minus its interest rate sensitive liabilities (RSL)

25. 25 Bank Immunization (cont’d) To immunize itself, a bank must reorganize its balance sheet such that:

26. 26 Bank Immunization (cont’d) A bank could have more interest-sensitive assets than liabilities: – Reduce RSA or increase RSL to immunize reduce $value or the duration A bank could have more interest-sensitive liabilities than assets: – Reduce RSL or increase RSA to immunize reduce the $value or the duration

27. 27 Duration Shifting - Cash Market The higher the duration, the higher the level of interest rate risk If interest rates are expected to rise, a bond portfolio manager may choose to continue to bear some interest rate risk but at reduced levels and will want to then shift the portfolio duration

28. 28 Duration Shifting (cont’d) The shorter the maturity, the lower the duration The higher the coupon rate, the lower the duration A portfolio’s duration can be reduced by including shorter maturity bonds or bonds with a higher coupon rate Duration shifting can lead to duration matching

29. 29 Duration Shifting (cont’d) Maturity Coupon LowerHigher LowerAmbiguousDuration Lower HigherDuration Higher Ambiguous

30. 30 Hedging with Interest Rate Futures Complex area – numerous approaches in determining the hedge ratio – we make a number of simplyfying assumptions that enable understanding at the introductory level

31. 31 Hedging With Interest Rate Futures A financial institution can use futures contracts to hedge interest rate risk Essentially achieving the same result as duration matching - now done with the application of futures and not in the ‘cash market’ as previously discussed. The hedge ratio using the Duration Model:

32. 32 Hedging With Interest Rate Futures (cont’d) The number of contracts necessary is given by:

33. 33 Hedging With Interest Rate Futures (cont’d) Futures Hedging Example A bank portfolio holds $10 million face value in government bonds with a market value of $9.7 million, and an average YTM of 7.8%. The weighted average duration of the portfolio is 9.0 years. The cheapest to deliver bond has a duration of 11.14 years, a YTM of 7.1%, and a CBOT correction factor of 1.1529. An available futures contract has a market price of 90 22/32 of par, or 0.906875. What is the hedge ratio? How many futures contracts are needed to hedge?

34. 34 Hedging With Interest Rate Futures (cont’d) Futures Hedging Example (cont’d) The hedge ratio is:

35. 35 Hedging With Interest Rate Futures (cont’d) Futures Hedging Example (cont’d) The number of contracts needed to hedge is:

36. 36 Increasing/Decreasing Duration With Futures Extending duration may be appropriate if active managers believe interest rates are going to fall – Adding long futures positions to a bond portfolio will increase duration Decreasing duration where the risk is with interest rates increasing – selling or creating a short futures position will decrease duration

37. 37 A Model for Effectively Changing Duration With Futures One method for achieving target duration has its origin in the basis point value (BPV) method – Gives the change in the price of a bond for a one basis point change in the yield to maturity of the bond – We can determine the number of futures contracts required to adjust the duration of the bond or portfolio using the following model

38. 38 PURE BPA MODEL BPV = $ change for a $100,000 face value security per.01 (basis point) change in yield Hedge Ratio = DVC c /DVC f * B B = relative yield change volatility DVCf = DVC cd /CF cd

39. 39 Effectively Changing Duration With Futures (cont’d) To effectively change the duration of a portfolio with the BPV method requires calculating three BPVs:

40. 40 Effectively Changing Duration With Futures (cont’d) The current and target BPVs are calculated as follows:

41. 41 Effectively Changing Duration With Futures (cont’d) The BPV of the cheapest to deliver bond is calculated as follows:

42. 42 Effectively Changing Duration With Futures (cont’d) BPV Method Example A portfolio has a market value of $10 million, an average yield to maturity of 8.5%, and duration of 4.85. A forecast of declining interest rates causes a bond manager to decide to double the portfolio’s duration. The cheapest to deliver Treasury bond sells for 98% of par, has a yield to maturity of 7.22%, duration of 9.7, and a conversion factor of 1.1223. Compute the relevant BPVs and determine the number of futures contracts needed to double the portfolio duration.

43. 43 Effectively Changing Duration With Futures (cont’d) BPV Method Example (cont’d)

44. 44 Effectively Changing Duration With Futures (cont’d) BPV Method Example (cont’d)

45. 45 Effectively Changing Duration With Futures (cont’d) BPV Method Example (cont’d) The number of contracts needed to double the portfolio duration is:

46. 46 Duration - Simplfying Assumptions We have made two simplfying assumptions to illustrate how duration can be applied to immunize a bond portfolio assumed parallell shifts of a flat yield curve assumed stable reinvestment rates......neither are realistic......perfect immunization is not likely but it can still be a very effective tool in managing interest rate risk!

47. 47 Duration - Summary We have seen that it is possible to reduce interest rate risk by matching the duration of a bond or portfolio - including the ability to shift the duration by replacing a bond with a different coupon and or maturity(cash market) OR by using futures

48. 48 Immunizing - Considerations Opportunity cost of being wrong - always a consideration of hedging Lower yield - comes with shorter duration(tradtional upward sloping curve) Transaction costs Immunization: instantaneous only - need for ongoing process

49. 49 Opportunity Cost of Being Wrong An incorrect forecast can lead to an opportunity cost/missed opportunity for immunized portfolios - always a consideration in hedging – need clarity on objectives of hedging

50. 50 Lower Yield Immunization usually results in a lower level of income generated by the funds under management – if the immunization results in a reduction of the the portfolio duration, the portfolio return will effectively shift to the left on the yield curve, resulting in a lower level of income

51. 51 Transaction Costs Costs include: – Trading fees – Brokerage commissions – Bid-ask spread – Tax liabilities.......a futures driven immunization will result in much lower transaction costs than one done in the cash market

52. 52 Immunization: Instantaneous Only Durations and yields to maturity change every day – A portfolio may be immunized only temporarily duration changes over time ytm’s change over time market interest rates change