Question

A trader owns 55,000 units of a particular asset and wants to hedge the value of his position with futures contracts on another related asset. Each futures contract is on 5,000 units. The spot price of the owned asset is $28 and the standard deviation of its price change is $0.45. The futures price of the related asset is $27 and the standard deviation of price change is estimated to be $0.40. The correlation between the spot price of the owned asset and the futures price of the related asset is 0.94.

a) What is the optimal hedge ratio? b) Should the trader long or short the futures? How many futures contracts? c) If the spot price of the owned asset drops to $25 at the end of the hedge, is it possible for the trader to lose more than $165,000? Explain your answer.

Answer 1

a) optimal hedge ratio = correlation between the spot price of the owned asset and the futures price of the related asset*(standard deviation of owned asset/standard deviation of related asset)

optimal hedge ratio = 0.94*(0.45/0.40) = 0.94*1.125 = 1.0575

b) the trader should short the futures because he owns the asset and to hedge that long position, he needs to take a short position in futures.

No. of futures contracts = optimal hedge ratio*(no. of units of asset owned/no. of units of futures contract)

No. of futures contracts = 1.0575*(55,000/5,000) = 1.0575*11 = 11.6 or 12 contracts

c) If the spot price of the owned asset drops to $25 at the end of the hedge, it is not possible for the trader to lose more than $165,000. the actual loss will be less than $165,000.

loss on sale of owned asset if sold at $25 spot price = 55,000*($28 - $25) = 55,000*$3 = $165,000

Profit from futures position = 5,000*12*($27 - $25) = 5,000*12*$2 = $120,000

Futures price is $27 and spot price is $25 at the end of the hedge. so there is profit of $27 - $25 = $2.

Actual loss = $165,000 - $120,000 = $45,000