Chapter 6
Interest Rate Futures (part2)
Geng Niu
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Measure interest rate risk
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“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.
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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, noncoupon bearing instruments, i.e., money
market instruments such as Eurodollars,
Treasury bills, Certificates of Deposit (CDs),
etc.
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Basis point value (BPV)
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Recall: day count convention for money
market instruments is actual/360
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BPV=FaceValue*(Days to maturity/360)*0.01%
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E.g., a $10 million 180-day money market
instrument carries a BPV = $500.
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BPV=10,000,000*(180/360)*0.01%=$500
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Eurodollar deposit (ED)
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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
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6
Eurodollar Futures (Page 136-141)
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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.
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Eurodollar Futures continued
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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).
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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
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Formula for Contract Value (page 137)
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If Q is the quoted price of a Eurodollar futures
contract, the value of one contract is 10,000[1000.25(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*(100-0.25*(100-Q))
This corresponds to the $25 per basis point rule
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Example
Date
Nov 1
Quote
97.12
Nov 2
97.23
Nov 3
96.98
…….
……
Dec 21
97.42
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Eurodollar futures
For the long:
Profit Day1-Day2: (97.23-97.12)*100*25
Profit Day2-Day3: (96.98-97.23)*100*25
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Hedging with Eurodollar futures
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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?
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Hedging with Eurodollar futures
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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.
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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)-(100R2)]*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.
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Extending the LIBOR Zero Curve
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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
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Example (page 141-142)
so that
R2T2  R1T1
F
T2  T1
F (T2  T1 )  R1T1
R2 
T2
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.
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Example
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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).
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Example
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The 491-day zero rate is
(0.053*91+0.048*400)/491=0.04893
The 589-day rate is
(0.055*98+0.04893*491)/589=0.04994
We are assuming that the second futures rate
applies to 98 days rather than the usual 91
days.
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Duration Matching
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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
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Duration-Based Hedge Ratio
PDP
VF DF
VF
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
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Example
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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 93-02 or 93.0625 and the duration of the
cheapest to deliver bond is 9.2 years
The number of contracts that should be shorted is
10,000,000 6.80
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93,062.50 9.20
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Limitations of Duration-Based Hedging
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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
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