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

A hedger regresses changes in spot price (dependent variable) on changes in futures price and obtains a slope of 0.85 and an R-squared of 0.64. The hedger is exposed to 100,000 units of the asset, and each futures contract covers 5,000 units. How many futures contracts minimize variance, and what proportion of spot price variance is eliminated by the optimal hedge?

Short 17 contracts, and the hedge removes 64% of variance. The regression slope of 0.85 is the optimal hedge ratio, so 0.85 times 100,000/5,000 gives 17. Hedge effectiveness equals R-squared, 0.64, not the correlation of 0.80.

  1. A17 contracts; 64% eliminatedCorrect
  2. B20 contracts; 85% eliminated
  3. C17 contracts; 80% eliminated
  4. D20 contracts; 64% eliminated

Explanation

The regression slope is the minimum variance hedge ratio, 0.85. Contracts = 0.85 x 100,000 / 5,000 = 17. Hedge effectiveness equals R-squared, 0.64, so 64% of variance is removed. Using 80% confuses R with R-squared.

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