1. 6.1 Interest Rate Futures Chapter 6 Focus: Eurodollar futures and duration

2. 6.2 Eurodollar Futures Quote Q% Q% = 100% - R% R% = 3-month Eurodollar forward interest rate (LIBOR), compounded quarterly, pertaining to contract maturity date E.G. Q% = 96 or R% = 4 Notional principal on 1 futures contract is $1,000,000

3. 6.3 A change of one basis point or 0.01% in a Eurodollar futures quote corresponds to a contract price change of $25 If long, Gain/contract = $25 x Qbps If short, Gain/contract = - $25 x Qbps Why $25? If R changes by 1 bp (likewise Q in opposite direction), interest earned changes by $1,000,000x.25x.0001 = $25 Eurodollar Futures

4. 6.4 Eurodollar Futures continued A Eurodollar futures contract is settled in cash When it expires (on the third Wednesday of the delivery month) Q is set equal to 100 minus the 90 day Eurodollar interest rate and all contracts are closed out 4 delivery months: Mar., Jun., Sept., Dec.

5. Long Eurodollar Futures Hedge a future 3-month investment (anticipatory rule): worried about drop in R; hedge compensates when Q rises or R drops Q Q trans

6. Short Eurodollar Futures Hedge a future 3-month disinvestment or financing (anticipatory rule): worried about rise in R; hedge compensates when Q drops or R rises Q Q trans

7. Euro$ Futures vs. FRAs Hedge future debt issuance or interest payment : short Euro$ futures or buy FRA. Hedge future deposit or interest receipt: long Euro$ futures or sell FRA. Why contrasting positions? Interest rates (R) and bond prices (Q) move inversely. X-axes: FRA is R; Euro$ futures is Q.

8. 6.8 Using Eurodollar Futures It is Jan 8. An investor wants to lock in the interest rate for 3 months starting June 20 on $5 million The investor buys (goes long) 5 June Eurodollar futures contracts at 94.79. On June 20 the final settlement price is 96 What interest rate has the investor locked in?

9. Solution Futures contract gain = 5x25x(9600-9479) = $15,125 Jan 8 R% = 100% - 94.79 = 5.21 June 20 R% = 100% - 96 = 4 Opportunity loss = $15,125 = $5,000,000x.25x(5.21%-4%) Ergo on Jan 8, investor locked-in R% = 5.21

10. 6.10 Eurodollar Futures vs. FRAs Eurodollar futures are settled daily; FRAs are not The payoff from Eurodollar futures is at the beginning of the period covered by the underlying interest rate; the payoff from FRAs is at the end of this period (but settlement occurs at start of FRA period).

11. 6.11 Duration of a bond that provides cash flow c i at time t i is where B is its price and y is its yield (continuously compounded) This leads to Duration

12. 6.12 Modified Duration When the yield y is expressed with compounding m times per year The expression is referred to as the “modified duration”