1. Chapter 6 Interest Rate Futures (part2)
Geng Niu

2. Eurodollar deposit (ED)
A Eurodollar is a dollar deposited in a bank outside the United States
The rates that apply to Eurodollar deposits in interbank transactions are LIBOR.
Eurodollar deposits market is the among the largest financial markets with many participating institutions.
Interest on ED is calculated on actual/360 basis
E.g. One million dollars is borrowed for 45 days in the Eurodollar time deposit market as a quoted rate of 5.25% (annualized). The interest due after 45d is $1,000,000*0.0525*(45/360)=$6562.5 2 2

4. Eurodollar Futures (Page 136-141)
A 3-month Eurodollar futures contract is a futures contract on the interest rate that will be paid (by someone who borrows at the Eurodollar interest, same as 3-month LIBOR rate) on $1 million for a future period of 3 months.
Maturities are in March, June, September, and December, for up to 10 years in the future.
The contract ends on the third Wednesday of the delivery month (settlement date).
The contract is settled daily until that day.
Most popular interest rate futures contract in the US.

5. Eurodollar Futures Eurodollar futures is quoted as Q=100-R
R (%) is a three month deposit rate, expressed with quarterly compounding .
R uses an actual/360 day count convention.
On settlement date, R (%) is the actual three month Eurodollar deposit rate (LIBOR). 5 5

6. Eurodollar Futures
A one-basis-point (=0.01) move in the futures quote corresponds to a gain or loss of $25 per contract.
When a quote increases by one basis point, a trader who is long one contract gains $25 and a trader who is short one contract loses $25.
A one-basis-point change in the futures quote correspondents to a 0.01% change in the futures interest rate, which leads to:
1,000,000×0.01%× =25

7. Example Date Quote Nov 1 97.12 Nov 2 97.23 Nov 3 96.98 ……. …… Dec 21
97.42

8. Eurodollar futures For the long:
Profit Day1-Day2: ( )*100*25
Profit Day2-Day3: ( )*100*25

9. Formula for Contract Value (page 137)
If Q is the quoted price of a Eurodollar futures contract, the contract price is defined as:
10,000[ (100-Q)]
Recall:
90 day interest:1,000,000*0.25*R%=10,000*0.25R
R=100-Q
Contract value: 1,000,000- interest
=10,000*( *(100-Q))
This corresponds to the $25 per basis point rule 9 9

10. Hedging with Eurodollar futures
It is Mar 1, 2015, an investor expects that he/she will deposit $100 million in ED market for 3 months beginning from Sep 19, 2012.
The Sep 2012 ED futures quote is
How to hedge the interest rate risk using ED futures?
What is the interest rate that can be locked in for a 3-month investment in ED market beginning from Sep 19, 2012?

11. Hedging with Eurodollar futures
For one-basis point decrease in 3-month ED rate in Sep, 2012, the loss for the 100 million investment is :
$100,000,000*0.01%*(90/360)= $
If the investor longs one ED futures contract, for one-basis point decrease in 3-month ED rate in Sep, 2012, the profit from the futures market is $ 25
Thus, should long 100 contracts for hedging.

12. Hedging with Eurodollar futures
Suppose the three-month ED rate turns to be R% on Sep 19, 2012.
The interest earned on the 3-month deposit beginning from Sep 2012 is:
$100,000,000*R%*(90/360)=$250,000R
The gain/loss from futures market is:
100*[(100-R)-96.5]*100*25=$(3.5-R)*250,000
Total gain: 250,000R+(3.5-R)*250,000=3.5*250,000
Net interest rate earned (locked in):
3.5×250, ,000,000 × =3.5% (forward rate)

13. Further adjustment Mismatch: futures is settled on Sep 19, 2012
interest payment on the deposit is three month after Sep 19, 2012.
Assume that three-month interest rate is 3.5% in Sep 19, 2012.
For each dollar gained from the futures market, its value after three months is :
1+3.5%*0.25
Therefore, %×0.25 = contracts can be longed for hedging.

14. Extending the LIBOR Zero Curve
LIBOR deposit rates define the LIBOR zero curve out to one year
Eurodollar futures can be used to determine forward rates and the forward rates can then be used to bootstrap the zero curve 14 14

15. Example (page )
so that 15 15

16. Example
A 400-day LIBOR zero rate has been calculated as 4.80% with continuous compounding and, from Eurodollar futures quote, it has been calculated that
(a) the forward rate for a 90-day period beginning in 400 days is 5.30% (cont. comp.),
(b) the forward rate for a 90-day period beginning in 491 days is 5.50% (cont. comp.),
(c) the forward rate for a 90-day period beginning in 589 days is 5.6% (cont. comp). 16 16

17. Example The 491-day zero rate is (0.053*91+0.048*400)/491=0.04893
The 589-day rate is
(0.055* *491)/589=
We are assuming that the second futures rate applies to 98 days rather than the usual 91 days.

18. Duration Matching
This involves hedging against interest rate risk by matching the durations of assets and liabilities
It provides protection against small parallel shifts in the zero curve 18 18

19. Duration-Based Hedge RatioVF
Contract price for interest rate futures DF
Duration of asset underlying futures at maturity P
Value of portfolio being hedged DP
Duration of portfolio at hedge maturity 19 19

20. Example
It is August. A fund manager has $10 million invested in a portfolio of government bonds with a duration of 6.80 years and wants to hedge against interest rate moves between August and December
The manager decides to use December T-bond futures. The futures price is or and the duration of the cheapest to deliver bond is 9.2 years
The number of contracts that should be shorted is 20 20

21. Limitations of Duration-Based Hedging
Assumes that only parallel shift in yield curve take place
Assumes that yield curve changes are small
When T-Bond futures is used assumes there will be no change in the cheapest-to-deliver bond 21 21