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FRM Part I · FRM Exam Part I · How Do Firms Manage Financial Risk?

A corporate treasurer hedges a 10 million exposure and the hedge ratio estimated by regressing spot changes on futures changes has slope 0.85 and R-squared 0.60. Later the treasurer discovers that the futures volatility is 20 percent higher than in the estimation sample, while spot volatility and correlation are unchanged. Assuming the new relationship holds, which is the best revised hedge ratio?

The revised hedge ratio is about 0.71. The minimum-variance ratio is inversely proportional to futures volatility, so a 20 percent rise divides 0.85 by 1.2, giving 0.708. Correlation and spot volatility are unchanged, so only the futures volatility term alters the result.

  1. A0.71Correct
  2. B0.85
  3. C1.02
  4. D0.60

Explanation

The hedge ratio is rho x sigma_S / sigma_F. With sigma_F rising by 20 percent, the ratio falls by a factor of 1.2: 0.85 / 1.2 = 0.708, about 0.71. The 1.02 option multiplies instead of dividing, which is the wrong direction. Keeping 0.85 ignores the changed volatility, and 0.60 confuses R-squared with the ratio.

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