# Sharpe Ratio Calculation Best Practice

For Sharpe ratio formula : $SR(s) = \frac{(x_s - r)}{\sigma_s}$ where for the time period under evaluation :

$x_s$ represents the average return of the portfolio

$r$ represents average return of the risk-free rate

is there a particular reason why do we use average return ? Wouldn't a best practice be to use the cumulative return over the time period under valuation ?

• It is a standard practice in Statistics to compare the average of a variable to the standard deviation of that variable, and that is what is going on here. (It wouldn't make sense to have one thing in the numerator and the standard deviation of a different thing in the denominator, unless you adjusted for that somehow). – Alex C Apr 12 '18 at 17:02
• But in this case you can potentially have a situation that fund that have a negative cumulative return show positive SR and vice and versa. Don't seen to me a fair risk adjusted performance indicator. – RiskTech Apr 12 '18 at 17:30
• OK, I see your point. Maybe you should clarify in your question what your concern is. (That the compound return could be of a different sign than the average return (or the sum of returns)). – Alex C Apr 12 '18 at 17:42