hard · FRM Part 2 Risk & Investment Management

Compared with the reported figures, what is the MOST accurate description of the effect on the estimated true volatility and the appropriately de-biased annualized Sharpe ratio?

1. Unsmoothing raises the estimated volatility and lowers the per-period Sharpe, but the standard √(12) annualization OVERSTATES the annual Sharpe because positive autocorrelation makes multi-period variance grow faster than linearly.
2. Unsmoothing leaves volatility unchanged but raises the mean return estimate, so the annualized Sharpe is biased upward and should be revised down only for the autocorrelation in the mean.
3. Unsmoothing raises the estimated volatility and lowers the per-period Sharpe, and because positive autocorrelation makes variance grow SLOWER than linearly the √(12) rule understates annual volatility, partially offsetting the correction.
4. Unsmoothing lowers the estimated volatility because removing measurement noise reduces variance, so the de-biased annualized Sharpe is actually HIGHER than the 1.6 reported.

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