standard deviation of the asset's excess return, as 10%. The risk-free return is constant. Then the Sharpe ratio (using the old definition) will be Example 2 Suppose that someone currently is invested in a portfolio with an expected return of 12% and a standard deviation of 10%. The risk-free rate of interest is 5%. What is the Sharpe ratio? The Sharpe ratio is: Strengths and weaknesses A negative Sharpe ratio means the portfolio has underperformed its benchmark. All other things being equal, an investor typically prefers a higher positive Sharpe ratio as it has either higher returns or lower volatility. However, a negative Sharpe ratio can be made higher by either increasing returns (a good thing) or increasing volatility (a bad thing). Thus, for negative values the Sharpe ratio does not correspond well to typical investor utility functions. The Sharpe ratio is convenient because it can be calculated purely from any observed series of returns without need for additional information surrounding the source of profitability. However, this makes it vulnerable to manipulation if opportunities exist for smoothing or discretionary pricing of illiquid assets. Statistics such as the bias ratio and first order autocorrelation are sometimes used to indicate the potential presence of these problems. While the Treynor ratio considers only the systematic risk of a portfolio, the Sharpe ratio considers both systematic and idiosyncratic risks. Which one is more relevant will depend on the portfolio context. The returns measured can be of any frequency (i.e. daily, weekly, monthly or annually), as long as they are normally distributed, as the returns can always be annualized. Herein lies the underlying weakness of the ratio - asset returns are not normally distributed. Abnormalities like kurtosis, fatter tails and higher peaks, or skewness on the distribution can be problematic for the ratio, as standard deviation doesn't have the same effectiveness when these problems exist. Because it is a dimensionless ratio, laypeople find it difficult to interpret Sharpe ratios of different investments. For example, how much better is an investment with a Sharpe ratio of 0.5 than one with a Sharpe ratio of -0.2? This weakness was well addressed by the development of the Modigliani risk-adjusted performance measure, which is in units of percent return – universally understandable by virtually all investors. In some settings, the Kelly criterion can be used to convert the Sharpe ratio into a rate of return. The Kelly criterion gives