© 2004 South-Western Publishing 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( T r ), your cost of carry is zero Solving for C in the futures pricing equation yields the implied repo rate R p (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) Maturity Coupon LowerHigher LowerAmbiguousDuration Lower HigherDuration Higher Ambiguous

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 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?

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

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 25