Calculation of Sharpe Ratio, which method should I use

Recently, I deeply got involved in calculating the Sharpe Ratio for different portfolios, and sometimes the Sharpe Ratio is very high for (unknown) some reason. Then I went through some web page and try to figure out what’s the typical way to calculate the Sharpe ratio.

Start from this link:

http://quant.stackexchange.com/questions/10390/sharpe-ratio-annualized-monthly-returns-vs-annual-returns-vs-annual-rolling-ret

And, clearly, there is more than one way to do it and I would like to quote one of the popular answers, which says:

There are sufficiently different ways to calculate the Sharpe ratio that the best advice I can give is to do whatever your boss wants. Also, if it is for a paper or research document, just make clear you document your method.

My approach is usually to calculate the highest frequency Sharpe ratio I can based on the data. The higher frequency choice is to get a better estimate of the standard deviation. I might then put the annualized value in parentheses after it, mainly as others are more familiar with what a good annual Sharpe would be.

However, I almost always discuss the Sharpe ratio as relative to something else, i.e. the Sharpe of a portfolio strategy relative to some index or benchmark. It can be difficult to interpret these ratios by themselves.

For annualization, CAGRs are generally preferred to multiplying the return by the frequency, which really only holds if you assume a normal distribution for log returns. The CAGR is perhaps most common and can be thought of as the annualized return you would get if you invested in the portfolio over the relevant horizon. The only problem with CAGRs is that it’s not clear what the standard deviation should be that goes with it. Most people just multiply the standard deviation by the square root of 12. It’s probably not correct, but it’s what everybody does so you probably should too.

As Richard notes in the comments, what you calculate also depends on how you need the statistic to be interpreted. The most common way the Sharpe ratio is used is as an ex-post evaluation of portfolio performance. However, it is also possible to use the Sharpe ratio in portfolio optimization, which requires a forward-looking forecast of what the Sharpe ratio of a portfolio will be in the future. The relevant forward looking Sharpe ratio for optimization relies on the arithmetic returns and standard deviations since that is what is required to aggregate from security returns to portfolio returns. However, the ex post evaluation Sharpe ratio above was using CAGR, which is a geometric return. The goal in that case is to figure out what you actually returned on an annualized basis, rather than the distribution of the return as some point in the future.

I also want to include Andrew Lo’s paper http://edge-fund.com/Lo02.pdf for the reference.

 

 

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