A trader owns 55,000 units of a particular asset and decides to hedge the value of her position with futures contracts on another related asset. Each futures contract is on 5,000 units. The spot price of the asset that is owned is $28 and the standard deviation of the change in this price over the life of the hedge is estimated to be $0.43. The futures price of the related asset is $27 and the standard deviation of the change in this over the life of the hedge is $0.40. The coefficient of correlation between the spot price change and futures price change is 0.95.

a) What is the minimum variance hedge ratio?
b) Should the hedger take a long or short futures position?
c) What is the optimal number of futures contracts with no tailing of the hedge?
d) What is the optimal number of futures contracts with tailing of the hedge?

a) 1.02125

b) Short position

c) 11

d) 12

Explanation:

A) Calculate the minimum variance hedge ratio:

Formula:

Minimum variance hedge ratio h = correlation coefficient *  std. deviation of asset/Std. deviation of related asset.

Putting values=  ×

B) Since there are the expectation that it will rise in future, decision should be the short position.

C) What is the optimal number of futures contracts with no tailing of the hedge?

Formula:

Number of contracts N = Minimum variance hedge ratio * N(quantity) / N(future quantity)

Putting values into the formula:

D) What is the optimal number of futures contracts with tailing of the hedge?

Formula:

Number of contracts N = Minimum variance hedge ratio * N(quantity) * Spot price / N(future quantity) * future price.

Putting values in the formula we get:

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