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

A company holds 2,000,000 barrels of exposure to be hedged with a futures contract of 1,000 barrels. The hedge ratio is 0.75. Spot changes have standard deviation 0.06 and the correlation with futures changes is 0.90. What is the proportion of variance eliminated by the optimal hedge, and how many contracts are needed?

Hedge effectiveness is the squared correlation, 0.90 squared or 81%, so 81% of variance is eliminated. The number of contracts is the hedge ratio 0.75 times 2,000,000 barrels divided by 1,000 per contract, which equals 1,500 contracts.

  1. A81% of variance eliminated; 1,500 contractsCorrect
  2. B90% of variance eliminated; 1,500 contracts
  3. C81% of variance eliminated; 2,000 contracts
  4. D90% of variance eliminated; 2,000 contracts

Explanation

Hedge effectiveness equals rho squared = 0.81, so 81% of variance is removed. Contracts = 0.75 x 2,000,000 / 1,000 = 1,500. Using 0.90 as effectiveness confuses correlation with its square; 2,000 ignores the hedge ratio.

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