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

A portfolio manager holds an asset worth 12 million and hedges with futures. The hedge ratio is estimated from a regression of spot changes on futures changes: slope 0.90, R-squared 0.64. What percentage of the variance of the unhedged position is eliminated by the optimal hedge, and what is the optimal hedge ratio?

The optimal hedge ratio is 0.90, the regression slope, and the hedge removes 64% of the variance, which is the R-squared. The remaining 36% is residual basis risk that the futures cannot offset.

  1. AHedge ratio 0.90; variance reduction 64%Correct
  2. BHedge ratio 0.64; variance reduction 90%
  3. CHedge ratio 0.90; variance reduction 36%
  4. DHedge ratio 0.80; variance reduction 64%

Explanation

The optimal hedge ratio equals the regression slope, 0.90. Hedge effectiveness is the R-squared, 0.64, the share of spot variance eliminated. Option 3 confuses the remaining variance (36%) with the eliminated portion. Option 4 uses the square root of R-squared, 0.80, which is the correlation.

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