Question

Anglo American Platinum Limited is a major worldwide producer of platinum. Platinum is widely used in the production of catalytic converter. It is now August 1. The company is committed to selling 250 ounces of platinum on September 14. To hedge the risk, the company is considering using October futures contracts to offset the risk exposure. The standard deviation of monthly changes in the spot price of platinum per ounce is 30 and the standard deviation of monthly changes in the futures price of wheat per bushel the closest contract is 35. The correlation between the futures price changes and the spot price changes is 80. Each contract is for the delivery of 50 ounces platinum.

(a) What is the optimal hedge ratio?

(sample answer: 25.30%)

(b) Should the hedger take a long or short futures position?

(sample answer: long; or short)

(c) What is the optimal number of futures contracts with the hedge?

(sample answer: 12; it should be a whole number)

Answer 1

•Hedge Ratio is defined as the size of the position taken in the futures contract to the size of the exposure in the spot market

•Optimal hedge ratio is the proportion of exposure that should be optimally hedged and is given by

i) Hedge Ratio= 0.8 * 30/35 = 68.57%

ii) The sign of the optimal hedge ratio is determined by the sign of the correlation ρ. If ρ > 0, the hedge ratio is positive, meaning that if the hedger has a long spot exposure, he must take a long futures position and vice-versa.

The Platinum producer have a Short position in Platinum, Since he want to sell it. The Platinum producer should therefore take a Short position in bushel Contract.

iii) Optimal number of futures contracts with the hedge: 250/50 * 68.57% = 3.42

3.42 is rounded off to 4 Contract to be optimally Hedged

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