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FRM Part II · FRM Exam Part II · Illiquid Assets

An analyst observes an illiquid asset's reported returns follow r_reported(t) = 0.6 × r_true(t) + 0.4 × r_reported(t-1). True returns have annual volatility of 20% and are serially uncorrelated. Which statement about the reported series is correct?

The reported series has positive first-order autocorrelation of about 0.4 and volatility below 20%. The lagged-return term makes it an AR(1) process with variance 0.36σ²/(1−0.16), giving roughly 13% volatility, so smoothing understates true risk.

  1. AIts first-order autocorrelation is positive and its volatility is below 20%Correct
  2. BIts first-order autocorrelation is zero and its volatility equals 20%
  3. CIts first-order autocorrelation is negative and its volatility is above 20%
  4. DIts first-order autocorrelation is positive and its volatility is above 20%

Explanation

The reported series is an AR(1) process with coefficient 0.4, so autocorrelation is 0.4 (positive). Its variance is 0.36σ²/(1−0.16)=0.4286σ², so volatility is about 0.655×20% ≈ 13.1%, below 20%. Option with zero autocorrelation ignores the lag term.

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