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

A portfolio manager's hedge with a given futures contract has a correlation of 0.50 between spot and futures changes. If the manager switches to a different futures contract with a correlation of 0.90, with all volatilities unchanged, what happens to the optimal hedge ratio and to hedge effectiveness (R-squared)?

The hedge ratio increases by a factor of 1.8 and effectiveness rises from 0.25 to 0.81. The ratio is proportional to correlation when volatilities are unchanged (0.90/0.50), while hedge effectiveness is the squared correlation, giving 0.25 and 0.81.

  1. AThe hedge ratio rises by a factor of 1.8 and R-squared rises from 0.25 to 0.81Correct
  2. BThe hedge ratio rises by a factor of 1.8 and R-squared rises from 0.50 to 0.90
  3. CThe hedge ratio is unchanged and R-squared rises from 0.25 to 0.81
  4. DThe hedge ratio rises by a factor of 3.24 and R-squared rises from 0.25 to 0.81

Explanation

h* = rho x sigma_S/sigma_F, so with volatilities fixed it scales with rho: 0.90/0.50 = 1.8. Effectiveness is rho squared: 0.25 becomes 0.81. Treating effectiveness as rho gives 0.50 to 0.90, and 3.24 is the ratio of the squared correlations.

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