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FRM Part I · FRM Exam Part I · Fund Management

A hedge fund's reported monthly returns show a low standard deviation and positive first-order autocorrelation of 0.40, because the fund holds illiquid securities that are marked using stale or smoothed prices. An investor uses the reported monthly volatility to compute an annualized Sharpe ratio by multiplying by the square root of 12. Which statement is correct?

Volatility is understated and the Sharpe ratio is overstated. Smoothed, stale prices dampen measured variation, and positive autocorrelation means the square-root-of-time rule underestimates annual risk even more, so the reported risk-adjusted performance looks better than it truly is.

  1. AVolatility is understated and the Sharpe ratio is overstated, and the square-root-of-time scaling is itself unreliable under positive autocorrelationCorrect
  2. BVolatility is overstated and the Sharpe ratio is understated, because smoothing adds noise
  3. CVolatility and Sharpe ratio are both unbiased because autocorrelation does not affect the mean
  4. DThe Sharpe ratio is understated because autocorrelation raises the mean return

Explanation

Smoothed prices dampen measured return variability, so monthly standard deviation is too low. With positive autocorrelation, true multi-period variance exceeds the independent-returns scaling, so annualizing by the square root of 12 understates risk further. Both effects inflate the Sharpe ratio.

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