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Chapter 12

Chapter 12. Futures Contracts and Portfolio Management. Outline. The concept of immunization Altering asset allocation with futures. The Concept of Immunization. Introduction Bond risks Duration matching Duration shifting Hedging with interest rate futures

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Chapter 12

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  1. Chapter 12 Futures Contracts and Portfolio Management

  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. Year 1 Year 2 Year 3 Year 4 Year 5 Year 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 $8,800 Interest $68,805 Bond $97,920 Total $165,817 Bullet Immunization (cont’d) Bullet Immunization Example (cont’d) Panel A: Interest Rates Remain Constant

  16. Year 1 Year 2 Year 3 Year 4 Year 5 Year 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 $8,800 Interest $66,568 Bond $99,650 Total $166,218 Bullet Immunization (cont’d) Bullet Immunization Example (cont’d) Panel B: Interest Rates Fall 1 Point in Year 3

  17. Year 1 Year 2 Year 3 Year 4 Year 5 Year 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 $8,800 Interest $69,247 Bond $96,230 Total $165,477 Bullet Immunization (cont’d) Bullet Immunization Example (cont’d) Panel C: Interest Rates Rise 1 Point in Year 3

  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)

  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 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?

  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 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.

  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 = 1020.00 Treasury Bond Futures • September settlement = 91.05 • Cheapest to deliver bond: • Price = 95% • Maturity = 18 years • Coupon = 9 % • Duration = 8.60 • Conversion factor = 1.3275

  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:

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