# Compare ex-post Sharpe ratio of multiple portfolios?

Say I want to compare the Sharpe ratio of two portfolios, is it necessary to look at the excess return? Or can you just compare their average return divided by their standard deviation?

So basically, since in both cases you subtract the same proxy for risk-free rate (of course under the assumption that both were held over the exact same time horizon), can you just leave that proxy out?

Naturally, the value of the Sharpe ratio is different from the value obtained by this shortcut, but I am only interested in the relative position of the sharp ratios between each other.

I assume that if with this shortcut portfolio A will do better than portfolio B, then the Sharpe ratio of portfolio A is also always higher than portfolio B. Since if that would not be the case then theoretically you could pick a proxy for the risk-free rate that gets the desired result?

• $\frac{r_1}{\sigma_1} > \frac{r_2}{\sigma_2}$ does not imply that $\frac{r_1-r_f}{\sigma_1} > \frac{r_2-r_f}{\sigma_2}$, so $r_f$ does matter. – Alex C Apr 5 at 23:27