Take the 2-minute tour ×  What are the advantages/disadvantages
of using the arithmetic Sharpe Ratio vs the geometric Sharpe
Ratio? Is one more correct? Or is one better in certain
circumstances?  share|improve this question add comment  4
Answers  In addition to John's answer and just to make things
clear:  The arithmetic mean is given by  $$\mu_a = \frac{1}{n}
\sum_{i=1}^n x_i$$  The geometric mean is given by  $$\mu_g =
\sqrt[n]{\prod_{i=1}^n (1+x_i)} -1$$  And we have that  $$\mu_g
\leq \mu_a$$  So not only would the geometric sharp ratio would
be taking into account the "actual" return of the portfolio, but
it is also a more conservative measure.  share|improve this
answer Where can I find a demonstration that $$\mu_g \leq
\mu_a$$ –  Marco Demaio Mar 4 at 20:50 add comment  I'm not sure
it makes sense to think of one as more correct than another.
However, they do have significant differences. It may help to
distinguish between ex-post evaluation of a strategy and ex-ante
prediction of what the strategy's