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FRM Part I · FRM Exam Part I · Using Futures for Hedging

A portfolio manager holds a diversified equity portfolio worth USD 50 million and hedges with futures contracts on a stock index. The estimated regression of portfolio returns on futures returns gives a slope of 0.90. The futures price is 2,000 and each contract has a multiplier of USD 250 (contract value USD 500,000). How many contracts should be sold to minimize variance, using the minimum variance hedge ratio?

The manager should sell 90 contracts. The minimum variance hedge ratio of 0.90 multiplies the exposure of USD 50 million, divided by the contract value of USD 500,000. That gives 0.90 times 100, or 90 contracts. Ignoring the ratio would give 100 contracts.

  1. A90Correct
  2. B100
  3. C111
  4. D80

Explanation

Optimal number of contracts N* = h* x Q_A / Q_F = 0.90 x 50,000,000 / 500,000 = 0.90 x 100 = 90. Selling 100 contracts ignores the hedge ratio, and 111 divides by the slope instead of multiplying (100/0.9).

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