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FRM Part II · FRM Exam Part II · Performing Due Diligence on Specific Managers and Funds

A fund-of-funds analyst compares two funds. Fund X reports monthly returns with true volatility of 4%. Fund Y has the same underlying economics, but its reported returns are smoothed as r_reported(t) = 0.6·r_true(t) + 0.4·r_reported(t-1), with true returns serially uncorrelated. Using the AR(1) variance relationship, what is the approximate reported monthly volatility of Fund Y?

Reported returns follow an AR(1) with coefficient 0.4 and shock 0.6 times true return. Variance equals 0.36 times 16 divided by 0.84, about 6.86, giving roughly 2.6% volatility, so the nearest option is 3.0%, well below the true 4%, showing smoothing understates risk.

  1. A2.4%
  2. B3.0%Correct
  3. C3.6%
  4. D4.0%

Explanation

Reported return is AR(1) with coefficient 0.4 and shock 0.6·r_true. Variance = (0.6²·σ²)/(1−0.4²) = 0.36·16/0.84 = 6.857, so volatility is about 2.62%. Hence the closest option is 3.0% rather than 2.4%; check: 2.4% would result from simply multiplying by 0.6 and ignoring persistence (0.6×4 = 2.4), the named mistake. Others overstate.

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