# (a) A trader owns 55,000 units

(a) 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.

(i) Find the minimum variance hedge ratio.

(ii) Decide whether the hedger should take a long or short futures position.

(iii) Estimate the optimal number of futures contracts with no tailing of the hedge.

(iv) Calculate the optimal number of futures contracts with tailing of the hedge.

(b) Suppose that the 9-month and 12-month LIBOR rates are 2% and 2.3%, respectively. Find the forward LIBOR rate for the period between 9 months and 12 months. Estimate the value of an FRA where 3% is received and LIBOR is paid on \$10 million for the period. Hint: All rates are quarterly compounded. Assume that LIBOR is used as the risk-free discount rate.

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