FRM Part II · FRM Exam Part II · Illiquid Assets
Observed returns follow R_obs,t = 0.6·R_true,t + 0.4·R_obs,t-1, where true returns are i.i.d. with monthly volatility of 3.0% and no autocorrelation. Using the stationary variance of the observed series, what is the approximate monthly volatility of observed returns?
Observed monthly volatility is about 1.97%. The AR(1) stationary variance equals shock variance 0.36×9 = 3.24 divided by 1 − 0.16 = 0.84, giving 3.857, whose square root is about 1.96–1.97%, well below the true 3.0% because of smoothing.
- A1.80%
- B1.97%Correct
- C2.25%
- D3.00%
Explanation
For an AR(1) with coefficient phi=0.4 and shock 0.6·R_true, variance = (0.6^2 × 3.0^2)/(1 − 0.4^2) = (0.36×9)/0.84 = 3.24/0.84 = 3.857, so volatility = 1.964%, about 1.97%. The 1.80% option is the shock volatility 0.6×3.0 without the autocorrelation feedback. The 3.00% option ignores smoothing altogether.
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