what is the sharpe ratio 
the sharpe ratio compares the return of an investment with its risk it s a mathematical expression of the insight that excess returns over a period of time may signify more volatility and risk rather than investing skill economist william f sharpe proposed the sharpe ratio in 1966 as an outgrowth of his work on the capital asset pricing model capm calling it the reward to variability ratio 1 sharpe won the nobel prize in economics for his work on capm in 1990 2the sharpe ratio s numerator is the difference over time between realized or expected returns and a benchmark such as the risk free rate of return or the performance of a particular investment category its denominator is the standard deviation of returns over the same period of time a measure of volatility and risk michela buttignolformula and calculation of the sharpe ratioin its simplest form sharpe ratio r p r f p where r p return of portfolio r f risk free rate p standard deviation of the portfolio s excess return begin aligned textit sharpe ratio frac r p r f sigma p textbf where r p text return of portfolio r f text risk free rate sigma p text standard deviation of the portfolio s excess return end aligned sharpe ratio p rp rf where rp return of portfoliorf risk free rate p standard deviation of the portfolio s excess return standard deviation is derived from the variability of returns for a series of time intervals adding up to the total performance sample under consideration the numerator s total return differential versus a benchmark rp rf is calculated as the average of the return differentials in each of the incremental time periods making up the total for example the numerator of a 10 year sharpe ratio might be the average of 120 monthly return differentials for a fund versus an industry benchmark the sharpe ratio s denominator in that example will be those monthly returns standard deviation calculated as follows 