Chapter 3
(all editions)

• Many investors in futures markets are hedgers (farmer and Kellogg’s)
• Perfect hedge eliminates all risk but is rare
• When is a short/long futures position appropriate?
• Which futures contract to use?
• What is the optimal contract size?
• Hedge and forget strategy: no attempt is made to adjust the hedge with the change in the price of the underlying asset

• A long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the price
• A short futures hedge is appropriate when you know you will sell an asset in the future & want to lock in the price

• Companies should focus on the main business they are in and take steps to minimize risks arising from interest rates, exchange rates, and other market variables

• Shareholders are usually well diversified and can make their own hedging decisions
• Explaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult, pg 52 (old text), pg 50 (new text)

• Hedging is not quite straightforward:
– Asset to be hedged may not be the same as the asset underlying the futures contract
– Hedger uncertain of exact date to buy/sell asset
– Futures contract may have to be closed before the delivery month
• Basis risk arises because of the uncertainty about the basis when the hedge is closed out
• If asset to be hedged and asset underlying futures contract are the same, basis is zero at expiration
• Basis is the difference between spot & futures
Basis = Spot price – Futures price

Spot Price
Futures
Price
Time
Futures
Price
Spot Price
Time
(b) (a)
If the asset to be hedged and the asset underlying the futures contract are the same , the basis should be zero at the expiration of the futures.

• Suppose that
F
1
: Initial Futures Price
F
2
: Final Futures Price
S
2
: Final Asset Price
• You hedge the future purchase of an asset by entering into a long futures contract
• Cost of Asset =
S
2
–(
F
2
–
F
1
) = F
1
+ Basis
• If the basis strengthens, the hedger’s position
_________.

• Suppose that
F
1
: Initial Futures Price
F
2
: Final Futures Price
S
2
: Final Asset Price
• You hedge the future sale of an asset by entering into a short futures contract
• Price Realized=
S
2
+ ( F
1
–F
2
) = F
1
+ Basis
• If the basis strengthens, the hedger’s position
_________.

• Key factor affecting basis risk is the choice of the futures contract and choice of delivery month
• Choose a delivery month that is as close as possible to, but later than, the end of the life of the hedge (futures price are erratic during the delivery month
• Cross hedging: occurs when asset underlying the futures contract is different from the asset to be hedged

Hedge ratio: ratio of the size of the position taken in futures contracts to the size of the exposure where h
*  r s
S s
F s
S is the standard deviation of the change in the spot price during the hedging period s
F is the standard deviation of the change in the futures price during the hedging period r is the coefficient of correlation between d
S and d
F .
• When cross hedging, choose a value for the hedge ratio that minimizes the variance of the value of the hedged position

N
*  h * N
A
Q
F
• Optimal number of contracts:
– N
A
– Q
F size of position being hedged size of one futures contract
– N* optimal number of futures contracts hedged
– Example on pg. 60 (old text), pg 59 (new text)

• Stock index futures can be used to hedge an equity portfolio
• To hedge the risk in a portfolio the number of contracts that should be shorted is
N *
 b
P
• where
P
A hedged, b is its beta, and A is the value of the assets underlying one futures contract, pg 64 (old); pg 62 (new)

• Desire to hold portfolio for a long time
(Hedging may be cheaper than selling the portfolio and buying it back.)
• Desire to hedge systematic risk
(Appropriate when you feel that you have picked stocks that will outperform the market.)

Questions (all editions): 3.1, 3.2, 3.6,
3.7, 3.10, 3.16, 3.18