FRM Part I · FRM Exam Part I · Using Futures for Hedging
A fund manager holds a portfolio of corn and hedges with futures on a closely related grain. The correlation between changes in spot price and futures price is 0.80. The standard deviation of spot price changes is 0.30 per unit and that of futures price changes is 0.25 per unit. What is the minimum variance hedge ratio?
The minimum variance hedge ratio is 0.96. It equals the correlation multiplied by the ratio of spot volatility to futures volatility: 0.80 times 0.30 divided by 0.25. Inverting the volatility ratio gives 0.67, and ignoring correlation gives 1.20, both wrong.
- A0.67
- B0.96Correct
- C1.00
- D1.20
Explanation
h* = rho x (sigma_S / sigma_F) = 0.80 x (0.30/0.25) = 0.80 x 1.2 = 0.96. Using 0.67 results from inverting the volatility ratio (0.8 x 0.25/0.30). A ratio of 1.20 ignores the correlation.
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