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FRM Part II · FRM Exam Part II · The Rise and Risks of Private Credit

A fund reports annual returns with true volatility of 10% but its reported returns follow a smoothing process: reported return = 0.6 × current true return + 0.4 × prior reported return, with true returns independent. Reported variance equals true variance times a factor of 0.6²/(1−0.4²). What is the approximate reported volatility?

Reported volatility is about 6.5%. The smoothing factor is 0.36 divided by 0.84, which is 0.4286 for variance. Its square root is about 0.655, times the true 10% volatility. Smoothing therefore understates risk by roughly a third.

  1. A6.0%
  2. B6.5%Correct
  3. C7.3%
  4. D10.0%

Explanation

Reported variance factor = 0.36/(1−0.16) = 0.36/0.84 = 0.42857. Reported volatility = 10% × sqrt(0.42857) = 10% × 0.6547 ≈ 6.5%. Choosing 6.0% uses the weight alone and ignores the autoregressive term; 10% ignores smoothing.

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