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FRM Part II · FRM Exam Part II · Illiquid Assets

A fund holds a private equity position whose appraisal-based returns show annual volatility of 8%. Analysts believe true economic volatility is 14% because of return smoothing. The fund's reported correlation with listed equities is 0.30 and listed equity volatility is 16%. Which conclusion about the position's reported beta to listed equities is correct?

Reported beta equals 0.30 times 8% divided by 16%, which is 0.15. Because appraisal smoothing depresses measured volatility and correlation with listed markets, this figure understates the position's true market exposure, so unsmoothing would be needed before using it in portfolio risk.

  1. AReported beta is 0.15, which understates the true exposure because smoothing lowers measured volatility and correlationCorrect
  2. BReported beta is 0.60, which overstates the true exposure
  3. CReported beta is 0.15, which overstates risk because smoothing raises volatility
  4. DReported beta is 0.26, which is unaffected by smoothing

Explanation

Beta = correlation × asset vol / market vol = 0.30 × 8% / 16% = 0.15. Smoothing dampens measured volatility and correlation with markets, so reported beta is biased downward relative to true exposure. Option with 0.60 inverts the volatility ratio.

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