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

A portfolio manager hedges a USD 20 million jet fuel exposure using heating oil futures. The standard deviation of changes in jet fuel price is 0.040 and of heating oil futures price is 0.050 per period, with correlation 0.90. One futures contract covers USD 100,000 of exposure at current prices. Using the minimum-variance hedge ratio, how many contracts should be shorted... assuming the exposure is a long physical position?

Short 144 contracts. The minimum-variance hedge ratio is 0.90 × 0.040 / 0.050 = 0.72, so the hedged notional is 0.72 × USD 20 million = USD 14.4 million, which divided by USD 100,000 per contract gives 144 contracts.

  1. A144Correct
  2. B180
  3. C200
  4. D225

Explanation

h* = rho x sigma_S / sigma_F = 0.90 x 0.040 / 0.050 = 0.72. Hedge notional = 0.72 x 20,000,000 = 14,400,000. Contracts = 14,400,000 / 100,000 = 144. 180 uses 0.90 as the ratio (ignores volatility ratio); 200 ignores correlation (0.8 ratio gives 160... not applied) and 225 inverts the volatility ratio.

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