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FRM Part II · FRM Exam Part II · Regression Hedging and Principal Component Analysis

A risk analyst estimates a regression hedge ratio of a position's price changes on a hedge instrument's price changes. The position's daily volatility is 2.0%, the hedge instrument's daily volatility is 1.6%, and their correlation is 0.80. What is the minimum-variance hedge ratio (hedge units per unit of position, in value terms)?

The minimum-variance hedge ratio is 1.00. It equals correlation times position volatility divided by hedge instrument volatility: 0.80 times 2.0% divided by 1.6%, which is 1.00. Using the volatility ratio alone gives 1.25, and using correlation alone gives 0.80, both of which are wrong.

  1. A1.00
  2. B0.64
  3. C1.25Correct
  4. D0.80

Explanation

Minimum-variance hedge ratio = rho x sigma_position / sigma_hedge = 0.80 x 2.0 / 1.6 = 1.00. Check: 0.8 x 1.25 = 1.0, so the answer is 1.00. Option 0.80 is the correlation alone, 0.64 is rho times sigma_hedge/sigma_position (0.8x0.8), and 1.25 is the ratio of volatilities without correlation.

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