Sharpe Ratios are equal to the effective return divided by the standard deviation. Commonly, Sharpe Ratios on a daily, weekly or monthly basis are annualized by multiplying by the square root of the higher frequency time period. This is because
- The effective return is proportional to time.
- Assuming a Weiner process governs stock prices, variance is proportional to time. Hence standard deviation is proportional to the square root of time.
So you would scale a Sharpe Ratio by multiplying by t/√t = √t, where t is the frequency you are annualizing from. To summarize,
- Monthly Sharpe Ratios are annualized by multiplying by √12
- Daily Sharpe Ratios are annualized by multiplying by √252 (assuming 252 trading days in a year)
But (and this is a big but), a paper has demonstrated that this is misleading, and can often overestimate the actual Sharpe Ratio. The Sharpe Ratio is calculated from estimated quantities, and subject to errors. You have to take into account the specific properties of the returns distribution. For example, the Sharpe Ratio of hedge funds can be overestimated by 65% or more if you do not correctly model their serial autocorrelation.