6.1

Interest Rate Futures

Chapter 6

Focus: Eurodollar futures and duration

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

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

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.

Long Eurodollar Futures

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

QQtrans

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

Qtrans

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.

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?

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

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).

6.11

Duration of a bond that provides cash flow ci at time ti is

where B is its price and y is its yield (continuously compounded)

This leads to

B

ect

iyti

n

ii

1

yDB

B

Duration

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”

my

yBDB

1

D

y m1