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

2. Measure interest rate risk
“You can’t manage what you can’t measure”
How to measure interest rate exposure?
1. Duration: expected percentage change in bond value given a 1% (100 basis point) change in yield
Popular risk measure for medium and long term coupon paying securities.

3. Basis point value (BPV)
Definition: the expected monetary change in the price of a security given a 1 basis point (0.01%) change in yield. Preferred risk measure for short-term, non-coupon bearing instruments, i.e., money market instruments such as Eurodollars, Treasury bills, Certificates of Deposit (CDs), etc.

4. Basis point value (BPV)
Recall: day count convention for money market instruments is actual/360
BPV=FaceValue*(Days to maturity/360)*0.01%
E.g., a $10 million 180-day money market instrument carries a BPV = $500.
BPV=10,000,000*(180/360)*0.01%=$500

5. 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 5 5

7. 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.
Hypothetically, the long (short) will receive (pay) interest in the future for $1 million 90-day ED according to a predetermined rate. (note: not happen in reality under the contract)
Maturities are in March, June, September, and December, for up to 10 years in the future.

8. Eurodollar Futures continued
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.
E.g. Interest earned for a 1 million 90-day Eurodollar deposit is 1,000,000*(90/360)*R%
On settlement date, R (%) is the actual three month Eurodollar deposit rate (LIBOR). 8 8

9. Eurodollar Futures
For a $1 million face value Eurodollar deposit, a basis point change (0.01%) in yield is associated with
1,000,000*(90/360)*0.01%=$25 fluctuation in interest received.
Correspondingly, a change of one basis point in a Eurodollar futures quote corresponds to a contract price change of $25
For long position trader, the monetary gain if futures quote changes from Q1 to Q2 is : $ (Q2-Q1) *100*25
For the short, it is $ (Q1-Q2) *100*25
A Eurodollar futures contract is settled in cash

10. Formula for Contract Value (page 137)
If Q is the quoted price of a Eurodollar futures contract, the value of one contract is 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 10 10

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

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

13. Hedging with Eurodollar futures
It is march 2015, a corporation anticipates it will require a $100 million loan for a 90-day period beginning in six months time that will be based on 3-month LIBOR rates plus some fixed premium.
What is the interest rate exposure for this loan measured as BPV?
How many Eurodollar futures contracts to hedge the exposure?

14. Hedging with Eurodollar futures
If rates rise before the loan is needed, higher interest will be paid.
BPV=100,000,000*(90/360)*0.01%=$2500
This measures the change in interest associated with a one basis point change in yield for the loan.
Thus, a basis point rise in yield will bring $2500 more cost
If one ED futures is sold, a basis point rise in yield is associated with a $25 gain
This exposure may be hedged by selling 2500/25=100 Eurodollar futures.

15. Hedging with Eurodollar futures
Suppose the quote for Sep-2015 ED futures is Q1.
This implies a predetermined rate: R1=100-Q1
The actual three-month Libor in Sep 2015 is R2(%).
Then settlement quote for ED futures: Q2=100-R
Cost for the 100 million loan:
100,000,000*(90/360)*R2%=250,000R2
Profit from selling 100 ED futures:100* [(100-R1)-(100-R2)]*100*25=250,000*(R2-R1)
Net cost is : 250,000R2-250,000(R2-R1)=250,000R1
Not matter how interest rate varies, the company can lock in an interest rate of 100-Q1 per annum for a 90-day loan beginning in the future, by using the Eurodollar futures contract. Interest rate implied in a Eurodollar futures is actually a forward rate.

16. 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 16 16

17. Example (page 141-142) so that
If the 400-day LIBOR zero rate has been calculated as 4.80% and the forward rate for the period between 400 and 491 days is 5.30 the 491 day rate is 4.893%
Forward rates can be inferred from Eurodollar futures quotes. 17 17

18. 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). 18 18

19. 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.

20. 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 20 20

21. 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 21 21

22. 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 22 22

23. 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 23 23