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FRM Part II · FRM Exam Part II · Hedge Fund Investment Strategies

A hedge fund holds illiquid positions that are marked using stale prices, so its monthly returns show positive first-order autocorrelation. An analyst computes the Sharpe ratio from these reported monthly returns and annualizes by multiplying the monthly Sharpe ratio by the square root of 12. What is the most likely consequence?

The Sharpe ratio is overstated. Stale pricing smooths returns and lowers measured volatility, and positive autocorrelation means the square-root-of-12 scaling understates true annual volatility, so the annualized ratio looks better than the fund's real risk-adjusted performance.

  1. AThe Sharpe ratio is understated because smoothing raises measured volatility
  2. BThe Sharpe ratio is overstated because smoothing lowers measured volatility and the square-root-of-time rule ignores autocorrelationCorrect
  3. CThe Sharpe ratio is unaffected because the mean return is unchanged and volatility scales with time
  4. DThe Sharpe ratio is overstated because smoothing raises the mean return

Explanation

Return smoothing reduces measured monthly standard deviation. With positive autocorrelation, true annual volatility exceeds monthly volatility times the square root of 12. Both effects inflate the annualized Sharpe ratio. Option D is wrong because smoothing does not change the mean return in a meaningful way.

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