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FRM Part I · FRM Exam Part I · Modeling Non-Parallel Term Structure Shifts and Hedging

A portfolio's daily P&L has a standard deviation of $200,000. A hedge instrument's daily P&L has a standard deviation of $150,000, and the correlation between the two is 0.80. If the hedge is set at the minimum-variance ratio, what is the standard deviation of the hedged portfolio's daily P&L?

The hedged standard deviation is $120,000. With a minimum-variance hedge, residual risk equals the unhedged standard deviation times the square root of one minus the squared correlation: 200,000 × sqrt(0.36) = 200,000 × 0.6.

  1. A$160,000
  2. B$72,000
  3. C$120,000Correct
  4. D$80,000

Explanation

At the minimum-variance hedge, residual standard deviation is σ·sqrt(1 - ρ²) = 200,000 × sqrt(1 - 0.64) = 200,000 × 0.6 = $120,000. The $160,000 figure is σ·ρ, the hedged part, not the residual. The $72,000 figure applies 1 - ρ² without the square root.

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