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FRM Part II · FRM Exam Part II · Illiquid Assets

A risk manager unsmooths a hedge fund-of-illiquid-loans return series and then computes beta against an equity index. Compared with the beta from the raw smoothed series regressed contemporaneously, what is the most likely outcome, and why?

Beta typically rises after unsmoothing. Smoothing spreads market moves over later periods, so contemporaneous covariance with the index is understated and raw beta is biased downward. Unsmoothing restores the timely response, revealing higher true market exposure.

  1. ABeta rises, because smoothing spreads the market's effect across several periods so contemporaneous co-movement is understatedCorrect
  2. BBeta falls, because unsmoothing adds idiosyncratic noise that is uncorrelated with the index
  3. CBeta is unchanged, because unsmoothing rescales both covariance and variance equally
  4. DBeta falls, because unsmoothed returns have lower volatility than smoothed returns

Explanation

Smoothing lags the market impact, so same-period covariance with the index is understated and beta is biased downward. Unsmoothing restores the contemporaneous response, raising beta. Unsmoothed volatility is higher, not lower, and the transformation does not scale covariance and variance equally.

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