I'm computing different metrics for mutual fund performance. I want to use classic Sharpe ratio, but I also got to know there is geometric Sharpe ratio. Unfortunately I didn't find enough info about it, could you please explain how to compute it?
Link to discussion in the other thread notwithstanding, calculating Sharpe ratio using arithmetic return is more 'classic' than using geometric return.
To start, Sharpe himself used arithmetic returns in ex-post calculation in his originating paper (JPM, 1964).
Most texts also use arithmetic return, among them Grinold and Kahn and Christopherson, Carino, Ferson.
Personally, I think using arithmetic returns, aside from the above, are a little easier to work with. There's a semantic argument to be made that geometric return is what you would actually end up with, but it's kind of weak and provided you use a single calc across portfolios it's not going to matter much in comparing portfolio performance. Trivially, the fact that 'geometric Sharpe ratio' is a term yet 'arithmetic Sharpe ratio' isn't should make the situation somewhat apparent.
The Geometric Sharpe ratio is the geometric average of compounded excess returns divided by the standard deviation of those compounded returns. This is equivalent to the arithmetic average and standard deviation of log(1+rt).
Geometric returns should be the preferred way of calculating returns over a time series.