Sharpe Ratio for Measuring Return on Risk

The Sharpe ratio is also commonly expressed as:

$Sharpe \hspace{1 mm} Ratio = \frac{Return - Risk\hspace{1 mm} free\hspace{1 mm} Rate}{Standard\hspace{1 mm} Deviation\hspace{1 mm} of\hspace{1 mm} Returns}$

Both the return and the standard deviation are annualized. To annualize returns, you multiply linearly by time. For example, a monthly return of 1 % converts to an annualized return of 12%. Standard deviation of return is a measure of risk, or uncertainty, of returns. To annualize standard deviation, multiply by the square root of time.

For example, a monthly standard deviation of return of 1 % converts to annualized standard deviation of 1 %*sqrt(12)= 3.46%.

A higher Sharpe ratio indicates better portfolio performance. Sharpe ratios can be increased either by increasing returns or by decreasing risk.

As we know, a portfolio can achieve higher returns by taking on additional risks. Using the Sharpe Ratio one can determine the source of higher returns: better performance or from additional risks.

Historically, Sharpe ratios over long periods of time for most major asset classes have ranged from 0.3 to 2.