Chapter 12

1. Chapter 12 Futures Contracts and Portfolio Management

2. Outline • Pricing of interest rate futures • Duration • The concept of immunization • Bank • bullet • Hedging with interest rate futures

3. Pricing Interest Rate Futures Contracts • Interest rate futures prices come from the implications of cost of carry:

4. Computation • Cost of carry is the net cost of carrying the commodity forward in time (the carry return minus the carry charges) • If you can borrow money at the same rate that a Treasury bond pays(Tr), your cost of carry is zero • Solving for C in the futures pricing equation yields the implied repo rateRp (implied financing rate)

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

6. 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

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

8. Bond Risks (cont’d) • Interest rate risk (price and reinvestment) is a consequence of the inverse relationship between bond prices and interest rates and the risk of reinvestment of coupons • Duration is the most widely used measure of a bond’s interest rate risk

9. Duration Matching • Duration matching selects a level of duration that minimizes the combined effects of reinvestment rate and interest rate risk • 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 • (skip details on the example) • Choose a bond with YTM=desired return and duration matching the time you will need the money from the investment

13. 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)

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

15. 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

16. 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)

17. 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

18. Duration Shifting (cont’d)

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

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

21. 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?

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

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

24. 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 • One method for achieving target duration is the basis point value (BPV) method (the convexity of Duration) skip BPV

25. Review: • Futures – 3 theories of pricing; differences between options&futures; futures&forwards. • Stock Index Futures –Pricing, Hedge ratio; # of contracts to increase or decrease market risk exposure. Beta is a linear function. • FX futures – Pricing PPP, IRP. • Interest rate futures – Pricing, discount vs. bond equiv. yield. Hedge ratio, # of contracts, duration, convexity of duration