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