FRM Part II · FRM Exam Part II · Illiquid Assets
An analyst observes that reported returns of a private equity fund follow R_obs,t = 0.6 R_true,t + 0.4 R_obs,t-1, with true returns i.i.d. and true volatility of 20% annually. Ignoring the mean, the variance of observed returns equals 0.36 σ² / (1 − 0.16). What is the approximate observed volatility?
Observed volatility is about 13.1%. With an AR(1) coefficient of 0.4, variance equals 0.36 × 0.04 divided by 0.84, about 0.01714, whose square root is 13.1%, well below the true 20%, showing how smoothing understates risk.
- A12.0%
- B13.1%Correct
- C15.5%
- D20.0%
Explanation
Observed variance = 0.36 × 0.04 / (1 − 0.4²) = 0.0144 / 0.84 = 0.017143. Square root ≈ 0.1309, so about 13.1%. Using 0.6 × 20% = 12% ignores the autoregressive carry-over term.
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