FRM Part I · FRM Exam Part I · Futures Markets
A firm hedges a position in an asset using futures on a related asset. The standard deviation of the spot price change is 0.30, the standard deviation of the futures price change is 0.40, and the correlation between them is 0.8. The firm's exposure is 1,000,000 units. What is the minimum-variance hedge ratio and the optimal number of futures units to short, respectively?
The minimum-variance hedge ratio is 0.60, so the firm should short 600,000 units of futures. It equals correlation 0.8 times the spot volatility 0.30 divided by the futures volatility 0.40, applied to the 1,000,000-unit exposure.
- A0.60; 600,000 unitsCorrect
- B1.07; 1,070,000 units
- C0.80; 800,000 units
- D0.60; 1,000,000 units
Explanation
h* = rho x sigma_S / sigma_F = 0.8 x 0.30 / 0.40 = 0.60. Units = 0.60 x 1,000,000 = 600,000. Using 0.8 ignores the volatility ratio, and 1.07 inverts the ratio (0.8 x 0.4/0.3).
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