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

A hedger has a spot exposure with variance of price changes 0.0400 and uses a futures contract with variance 0.0225. The correlation is 0.60. If the hedger uses the minimum variance hedge ratio, what is the variance of the hedged position per unit of exposure (variance of dS - h dF)?

The hedged variance is 0.0256. At the minimum variance ratio, residual variance equals spot variance times one minus correlation squared: 0.0400 times 0.64. The hedge removes 0.0144, which is the explained portion, and leaves the remainder.

  1. A0.0256Correct
  2. B0.0144
  3. C0.0400
  4. D0.0360

Explanation

Hedged variance = sigma_S^2 (1 - rho^2) = 0.0400 x (1 - 0.36) = 0.0400 x 0.64 = 0.0256. Check: h = 0.6 x 0.2/0.15 = 0.8; 0.04 + 0.64x0.0225 - 2x0.8x0.6x0.2x0.15 = 0.04+0.0144-0.0288 = 0.0256. The 0.0144 option is the variance removed? Actually removed is 0.0144, not remaining.

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