FRM Part I · FRM Exam Part I · Using Futures for Hedging
A fund manager holds a USD 20 million equity portfolio and hedges with futures. The standard deviation of portfolio value changes is 4.5%, the standard deviation of futures price changes is 3.0%, and the correlation is 0.80. Each futures contract is worth USD 250,000 (futures price times multiplier). How many futures contracts should be shorted to minimize variance?
The manager should short 96 contracts. The hedge ratio is 0.80 times 4.5/3.0, which is 1.20. Multiplying by portfolio value divided by contract value (20 million / 250,000 = 80) gives 96 contracts. Ignoring correlation gives 120, and ignoring the ratio gives 80.
- A96Correct
- B80
- C120
- D64
Explanation
h* = 0.80 x 4.5/3.0 = 1.20. Number of contracts = h* x Q_A / Q_F = 1.20 x 20,000,000 / 250,000 = 1.20 x 80 = 96. Using 80 ignores the hedge ratio, and 120 misuses the ratio as 1.5 (4.5/3.0 without correlation).
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