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

A risk manager regresses daily P&L changes of a bond portfolio on daily P&L changes of a futures hedge and obtains an R-squared of 0.84. The unhedged portfolio has a daily P&L standard deviation of $200,000. What is the approximate standard deviation of the hedged position's daily P&L, assuming the minimum-variance hedge ratio is used?

The hedged standard deviation is about $80,000. With an R-squared of 0.84, 16% of variance remains, so the residual standard deviation is the unhedged $200,000 times the square root of 0.16, which is 0.4, giving $80,000.

  1. A$32,000
  2. B$80,000Correct
  3. C$168,000
  4. D$183,303

Explanation

Residual variance is (1 - R²) times the unhedged variance, so the standard deviation is 200,000 x sqrt(0.16) = 200,000 x 0.4 = $80,000. Multiplying the standard deviation by 0.16 or 0.84 mixes up variance and standard deviation; $183,303 is the hedged-away part, sqrt(0.84) x 200,000.

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