# Interest Rate Futures

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1 Interest Rate Futures Chapter 6 6.1

2 Day Count Conventons n the U.S. (Page 129) Treasury Bonds: Corporate Bonds: Money Market Instruments: Actual/Actual (n perod) 30/360 Actual/360 The day count conventon s used to calculate the nterest earned between the two dates 6.2

3 Treasury Bond (>10yrs) Prce Quotes n the U.S. Cash prce (drty prce) = Quoted prce (clean prce) + Accrued Interest 6.3

4 Treasury Bond Futures Pages The short sde can delver any government bond has more than 15 years to maturty on the frst day of the delvery month and s not callable wth 15 years from that day 6.4

5 Treasury Bond Futures Pages Cash prce receved by party wth short poston = Most Recent Settlement Prce Converson factor + Accrued nterest 6.5

6 Example Quoted prce of bond futures = Converson factor = Accrued nterest on bond =3.00 Prce receved for bond s = \$ (per \$100 of prncpal) 6.6

7 Converson Factor The converson factor for a bond s approxmately equal to the value of the bond on the assumpton that the yeld curve s flat at 6% wth semannual compoundng 6.7

8 CBOT T-Bonds & T-Notes Factors that affect the futures prce: Delvery can be made any tme durng the delvery month Any of a range of elgble bonds can be delvered The wld card play Above statements descrbe the delvery opton n the Treasury bond futures contract 6.8

9 Eurodollar Futures (Page ) A Eurodollar s a dollar deposted n a bank outsde the Unted States The Eurodollar nterest rate s the rate of nterest earned on Eurodollars deposted by one bank wth another bank. It s essentally the same as LIBOR ntroduced before Eurodollar futures are futures locks the 3- month Eurodollar depost forward rate at the maturty date of the futures 6.9

10 Eurodollar Futures contnued One contract s on the rate earned on \$1 mllon If Z s the quoted prce of a Eurodollar futures contract, the value of one contract s 10,000[ (100-Z)] A change of one bass pont or 0.01 n a Eurodollar futures quote corresponds to a contract prce change of \$

11 Eurodollar Futures contnued A Eurodollar futures contract s settled n cash When t expres (on the thrd Wednesday of the delvery month) Z s set equal to 100 mnus the 90 day Eurodollar nterest rate (actual/360) and all contracts are closed out 6.11

12 Example Suppose you buy (take a long poston n) a contract on November 1 The contract expres on December 21 The prces are as shown How much do you gan or lose a) on the frst day, b) on the second day, c) over the whole tme untl expraton? 6.12

13 Example Date Nov 1 Nov 2 Nov 3. Dec 21 Quote

14 Example contnued If on Nov. 1 you know that you wll have \$1 mllon to nvest on for three months on Dec 21, the contract locks n a rate of = 2.88% In the example you earn = 2.58% on \$1 mllon for three months (=\$6,450) and make a gan day by day on the futures contract of 30 \$25 =\$

15 Forward Rates and Eurodollar Futures (Page ) Eurodollar futures contracts last as long as 10 years For Eurodollar futures lastng beyond two years we cannot assume that the forward rate equals the futures rate 6.15

16 Forward Rates and Eurodollar Futures contnued There are two reasons Futures s settled daly where forward s settled once Futures s settled at the begnnng of the underlyng three-month perod; forward s settled at the end of the underlyng threemonth perod The varable underlyng the Eurodollar futures contract s an nterest rate and tends to be hghly postvely correlated to other nterest rates => futures rate > forward rates 6.16

17 Forward Rates and Eurodollar Futures contnued A " convexty adjustment " 1 Forward rate = Futures rate σ 2 where t s the tme to maturty of per 1 futures contract, (90 days later standard devaton of year t (typcally 2 the rate underlyng the futures contract than s the maturty of t σ 1 ) and σ the short s about often made s 2 s the t t ) 2 the rate changes 6.17

18 Convexty Adjustment when σ=0.012 (Table 6.3, page 141) Maturty of Futures Convexty Adjustment (bps)

19 Extendng the LIBOR Zero Curve LIBOR depost rates defne the LIBOR zero curve out to one year Eurodollar futures can be used to determne forward rates and the forward rates can then be used to bootstrap the zero curve 6.19

20 6.20 Example so that If the 400 day LIBOR rate has been calculated as 4.80% and the forward rate for the perod between 400 and 491 days s 5.30 the 491 days rate s 4.893% T T R T T R F = ) ( = T R T T T F R

21 Duraton Matchng Ths nvolves hedgng aganst nterest rate rsk by matchng the duratons of assets and labltes It provdes protecton aganst small parallel shfts n the zero curve 6.21

22 Use of Eurodollar Futures One contract locks n an nterest rate on \$1 mllon for a future 3-month perod How many contracts are necessary to lock n an nterest rate for a future sx month perod? 6.22

23 Duraton-Based Hedge Rato PD F C P D F nterest rate futures wll be shorted for hedge F C D F P D P Contract prce for nterest rate futures Duraton of asset underlyng futures at maturty Value of portfolo beng hedged Duraton of portfolo at hedge maturty 6.23

24 Example It s August. A fund manager has \$10 mllon nvested n a portfolo of government bonds wth a duraton of 6.80 years and wants to hedge aganst nterest rate moves between August and December The manager decdes to use December T-bond futures. The futures prce s or and the duraton of the cheapest to delver bond s 9.2 years The number of contracts that should be shorted s 10,000,000 93, =

25 Lmtatons of Duraton-Based Hedgng Assumes that only parallel shft n yeld curve take place Assumes that yeld curve changes are small 6.25

26 GAP Management (Busness Snapshot 6.3) Ths s a more sophstcated approach used by banks to hedge nterest rate. It nvolves Bucketng the zero curve Hedgng exposure to stuaton where rates correspondng to one bucket change and all other rates stay the same. 6.26

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