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FRM Part II · FRM Exam Part II · Private Markets Investing

A fund holds an appraisal-based real estate index with observed annual returns that follow R_obs,t = (1 - a) R_true,t + a R_obs,t-1, with a = 0.60. The true return volatility is 12%, and true returns are serially uncorrelated. Using the standard unsmoothing relation, what is the approximate observed volatility? (Use sigma_obs = sigma_true x sqrt((1-a)/(1+a)).)

Observed volatility is about 6.0%. With a = 0.60, the factor is the square root of 0.4/1.6, which equals 0.5, and multiplying true volatility of 12% by 0.5 gives 6.0%, showing how smoothing halves apparent risk.

  1. A4.8%
  2. B7.6%
  3. C6.0%Correct
  4. D9.5%

Explanation

(1-a)/(1+a) = 0.4/1.6 = 0.25; square root = 0.5. Observed volatility = 12% x 0.5 = 6.0%. Using 0.4 alone (4.8%) forgets the denominator; sqrt(0.4/1.6) is not 0.63, so 7.6% is wrong; 9.5% would come from sqrt(0.625).

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