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A trader owns 60,000 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 $32 and the standard deviation of the change in this
price over the life of the hedge is estimated to be $0.80. The futures price of the related asset
is $50 and the standard deviation of the change in this over the life of the hedge is $1.43. The
coefficient of correlation between the spot price change and futures price change is 0.95.
What is the optimal hedge ratio?
How many contracts should she use?
Should the hedger take a long or short futures position?


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