FRM Part II · FRM Exam Part II · Illiquid Assets
A fund of hedge funds observes that reported monthly returns of an illiquid strategy follow R_obs = 0.6 R_true(t) + 0.4 R_true(t-1), where true returns are independent with monthly volatility of 5%. What is the approximate monthly volatility of the observed returns?
The observed volatility is about 3.6% per month. With independent true returns, the variance equals the sum of squared weights, 0.36 plus 0.16, times 25, giving 13, and its square root is roughly 3.6%. Smoothing therefore cuts measured volatility by about 28% compared with the true 5%.
- A5.0%
- B3.0%
- C3.6%Correct
- D4.0%
Explanation
Variance of observed = (0.6^2 + 0.4^2) x 5%^2 = (0.36 + 0.16) x 25 = 13.0 (%^2). The square root is about 3.6%. The 5.0% option ignores smoothing, and 3.0% takes only the current weight 0.6 x 5%. The 4.0% option takes 0.4 x 5% ... wrongly or sums weights incorrectly.
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