Lecture 12
Topic:
Futures
I.
Definition of Futures
II.
Trading Interest Rate Futures
III.
Risk of Trading Interest Rate Futures
I. Definition of Futures
~ Definition
Futures contract is a legal agreement between a buyer and a seller,
in which:
1) The buyer agrees to take delivery of something at a specified price on a
specified future date (settlement date).
2) The seller agrees to make delivery of something at a specified price on
a specified future date (settlement date).
Buyer
Specified price
Deliver on settlement date
Seller
~ Futures versus Forward contracts:
Futures
Yes
Forward
No
Organized exchange
(CME)
5%~20% or above
OTC
None
Marked to market
Yes
No
Credit risk
No
Yes
Standardized contract
Clearing house
Margin requirement
1
|
Example:
a) U.S. Treasury Bills 13 week (CME:TB)
Exchange: CME
Face value: $1,000,000
Index price=100-(T-bill discount × 100)
b) U.S. Treasury Bond (CBOT:US)
Exchange: CME
Face value: $100,000
Index price: calculated based on a hypothetical 20-year, 6% coupon bond.
Profit
as i ↑
as i ↓
Short
Long
Market value of
future contract
Loss
2
II. Trading interest rate futures
~ 1) Speculating:
Example 1:
If short-term interest rates are expected to decrease 
Buy T-bill futures contract
Profit
as i ↓
Long
$98.0000
$98.2800
as i ↑
Loss
Loss: $2,800
(98.0000-98.2800)×$1,000,000/100
3
Profit: $2,200
(98.500-98.2800)×$1,000,000/100
$98.5000
Example 2:
If long-term interest rates are expected to increase 
Profit
Sell T-bill futures contract
Profit: $1,062.5
(108 5/32 -107 3/32)×$100,000/100
as i ↑
Short
107 3/32
Loss
108 5/32
Loss: $1,062.5
(108 5/32-109 7/32)×$100,000/100
4
109 7/32
as i ↓
~ 2) Hedging:
Short hedging:
for investors who long bond positions.  as i ↑, lose $$$
as i ↓(profit)
Profit
as i ↑ (profit)
Short
Long
Future contract
as i ↑ (Loss)
as i ↓(profit)
Example:
Prudential insurance longs $500 million of 30-year bonds with 8% coupon rate.
It plans to “fully” hedge the long positions by using T-bond futures contracts with 1-year
of maturity. What would happen if interest rate increases from 5% to 7%? What would
happen if interest rate decreases from 5% to 7%?
Current price of 30-year bonds: $146.36
(FV=100, N=60, CP=4%, i=2.5%)
Fully hedge: sell 5,000 contracts of T-bill futures at $112.55
(FV=100, N=40, CP=3%,i=2.5%)
i=7%
Bond value
Gain (loss)
Current price of 30-year bond
112.47
(33.89)
Value of the futures contract
89.32
23.23
5
i=3%
Bond value
Gain (loss)
198.45
52.09
144.87
(32.32)
as i ↓(profit)
Profit
as i ↑ (profit)
Short
Long
$52.09
$23.23
Bond price
$33.89
$32.32
as i ↑ (Loss)
as i ↓(profit)
Basis risk
∆holding position ≠∆hedging position
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III. Risk of Trading Interest Futures Contracts
1) Market risk:
The change of interest rates
2) Basis risk:
∆holding position ≠∆hedging position
This inequality can be caused by
i)
Partially hedging
ii)
Cross hedging
3) Liquidity risk:
The difficulty to square (close-out) futures positions
4) Prepayment risk: The change that the loans (i.e., mortgage loans) to be hedged may
be prepaid. It will result in naked short futures contract positions.
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