FRM Part II · FRM Exam Part II · Illiquid Assets
An analyst uses a first-order smoothing model, r_reported(t) = (1 - α) r_true(t) + α r_reported(t-1), with α = 0.60. A private equity fund reports annualised volatility of 8.0%. Assuming the true returns are serially uncorrelated, what is the approximate unsmoothed (true) volatility, using the relationship σ_reported = σ_true × sqrt((1 - α)/(1 + α))?
True volatility is about 16.0%. With α of 0.60, the smoothing factor sqrt(0.40/1.60) equals 0.5, so reported volatility of 8.0% must be divided by 0.5 to recover the underlying risk.
- A16.0%
- B12.8%
- C20.0%Correct
- D5.0%
Explanation
(1 - α)/(1 + α) = 0.40/1.60 = 0.25, whose square root is 0.5. So σ_true = 8.0%/0.5 = 16.0%. Multiplying instead of dividing gives 4.0%. Using sqrt(1-α)=0.632 gives 12.6%, roughly 12.8%, a wrong formula.
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