1. Futures Contracts and Portfolio Management
Chapter 12
Futures Contracts and Portfolio Management
© 2004 South-Western Publishing

2. Outline The concept of immunization
Altering asset allocation with futures

3. The Concept of Immunization
Introduction
Bond risks
Duration matching
Duration shifting
Hedging with interest rate futures
Increasing duration with futures
Disadvantages of immunizing

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

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. 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

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. Duration Matching
Introduction
Bullet immunization
Bank immunization

10. 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

11. 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

12. 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

13. 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).

14. 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%.

15. Bullet Immunization (cont’d)
Bullet Immunization Example (cont’d)
Panel A: Interest Rates Remain Constant
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
$8,800
$9,680
$10,648
$11,713
$12,884
$14,172
Interest
$68,805
Bond
Total
$165,817
$97,920

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

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

18. 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.

19. 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)

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

21. Bank Immunization (cont’d)
A bank could have more interest-sensitive assets than liabilities:
Reduce RSA or increase RSL to immunize
A bank could have more interest-sensitive liabilities than assets:
Reduce RSL or increase RSA to immunize

22. Duration Shifting
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 bear some interest rate risk (duration shifting)

23. 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

24. Duration Shifting (cont’d)
Maturity
Coupon
Lower
Higher
Ambiguous
Duration Lower
Duration Higher

25. Hedging With Interest Rate Futures
A financial institution can use futures contracts to hedge interest rate risk
The hedge ratio is:

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

27. 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 years, a YTM of 7.1%, and a CBOT correction factor of
An available futures contract has a market price of 90 22/32 of par, or What is the hedge ratio? How many futures contracts are needed to hedge?

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

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

30. Increasing 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

31. Increasing Duration With Futures (cont’d)
One method for achieving target duration is 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

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

33. Increasing Duration With Futures (cont’d)
The current and target BPVs are calculated as follows:

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

35. Increasing 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 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 Compute the relevant BPVs and determine the number of futures contracts needed to double the portfolio duration.

36. Increasing Duration With Futures (cont’d)
BPV Method Example (cont’d)

37. Increasing Duration With Futures (cont’d)
BPV Method Example (cont’d)

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

39. Disadvantages of Immunizing
Opportunity cost of being wrong
Lower yield
Transaction costs
Immunization: instantaneous only

40. Opportunity Cost of Being Wrong
If the market is efficient, it is very difficult to forecast changes in interest rates
An incorrect forecast can lead to an opportunity cost of immunized portfolios

41. Lower Yield
Immunization usually results in a lower level of income generated by the funds under management
By reducing the portfolio duration, the portfolio return will shift to the left on the yield curve, resulting in a lower level of income

42. Transaction Costs Costs include: Trading fees Brokerage commissions
Bid-ask spread
Tax liabilities

43. Immunization: Instantaneous Only
Durations and yields to maturity change every day
A portfolio may be immunized only temporarily

44. Altering Asset Allocation With Futures
Tactical changes
Initial situation
Bond adjustment
Stock adjustment
Neutralizing cash

45. Tactical Changes
Investment policy statements may give the portfolio manager some latitude in how to split the portfolio between equities and fixed income securities
The portfolio manager can mix both T-bonds and S&P 500 futures into the portfolio to adjust asset allocation without disturbing existing portfolio components

46. Initial Situation Portfolio market value = $175 million
Invested 82% in stock (average beta = 1.10) and 18% in bonds (average duration = 8.7; average YTM = 8.00%)
The portfolio manager wants to reduce the equity exposure to 60% stock

47. Initial Situation (cont’d)

48. Initial Situation (cont’d)
Stock Index Futures 
September settlement =
Treasury Bond Futures
September settlement = 91.05
Cheapest to deliver bond:
Price = 95%
Maturity = 18 years
Coupon = 9 %
Duration = 8.60
Conversion factor =

49. Initial Situation (cont’d)
Determine:
How many contracts will remove 100% of each market and interest rate risk
What percentage of this 100% hedge matches the proportion of the risk we wish to retain

50. Bond Adjustment
Using the BPV technique:

51. Bond Adjustment (cont’d)
The number of contracts to completely hedge the bond portion of the portfolio is:
Thus, the manager should buy 410 T-bond futures

52. Stock Adjustment For this portfolio, the hedge ratio is:
Selling 619 stock index futures would turn the stock into a synthetic T-bill

53. Stock Adjustment (cont’d)
The current equity investment is $143,500,000
The desired equity investment is $105,000,000, which is 26.83% less than the current level

54. Stock Adjustment (cont’d)
We can use 26.83% of the stock index futures hedge ratio:

55. Stock Adjustment (cont’d)
The portfolio manager can change the asset allocation from 82% stock, 18% bonds to 60% stock, 40% bonds by
Buying 521 T-bond futures and
Selling 166 stock index futures

56. Neutralizing Cash
It is harder to “beat the market” with the downward bias in relative fund performance due to cash
Cash can be neutralized by offsetting it with long positions in stock index futures
Cash can be neutralized by offsetting it with long positions in interest rate futures