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FRM Part II · FRM Exam Part II · Illiquid Assets

An analyst observes that a private fund's reported quarterly returns have first-order autocorrelation of 0.50. Assuming a simple smoothing model in which reported return equals a weighted average of the current true return and the prior reported return, with the autocorrelation of reported returns equal to the weight on the prior reported value, which approach best corrects the risk estimate?

The analyst should unsmooth the returns, recovering the underlying series by removing the lagged component, then recompute volatility and correlations. Smoothing with positive autocorrelation understates risk, so adjustments must increase measured volatility. Multiplying or halving volatility would move the estimate the wrong way.

  1. AUnsmooth the returns to recover the underlying series, then recompute volatility and correlationsCorrect
  2. BMultiply the reported volatility by the autocorrelation of 0.50
  3. CReduce the reported volatility by half to reflect illiquidity
  4. DUse only the highest quarterly returns to estimate risk

Explanation

With smoothing, r_reported = (1-a)r_true + a r_reported(-1), so true r = (r_rep - a r_rep(-1))/(1-a). Unsmoothing raises the measured volatility, here by a factor of roughly (1+a)/(1-a) in variance terms under the model. Scaling by 0.50 or halving would go in the wrong direction.

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