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

A hedger estimates that the standard deviation of the change in spot price is 0.06 and the standard deviation of the change in futures price is 0.04, with a correlation of 0.80. Using the optimal hedge ratio, what is the percentage of the variance of the unhedged position that is eliminated by hedging (hedge effectiveness)?

Hedge effectiveness equals the squared correlation between spot and futures price changes. With a correlation of 0.80, the squared value is 0.64, so 64% of the variance is eliminated. Using 80% mistakes correlation for variance reduction, and 36% is the residual variance left.

  1. A80%
  2. B64%Correct
  3. C36%
  4. D92%

Explanation

Hedge effectiveness is the R-squared of the regression of spot changes on futures changes, equal to rho squared = 0.80^2 = 0.64. So 64% of variance is removed. The 80% option uses the correlation instead of its square; 36% is the remaining variance, not the amount eliminated.

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