Sharpe ratio limitations

Text says that the Sharpe ratio has the following limitation with respect to hedge fund evaluation:

Assumes uncorrelated returns. Returns correlated across time will artificially lower the standard deviation. Correlation leads to lower standard deviation, so since we assume uncorrelated returns, isn’t this a good thing, since it means we have a higher standard deviation. That is, this is not a limitation?

The sharpe ratio is a return measure over total risk, i.e. systematic and unsystematic risk is both present. If returns are correlated with each other then that would reduce the unsystematic risk portion and reduce the STD and the sharpe ratio would increase.

The other thing is that the sharpe ratio assumes normal distribution of returns, but a hedge fund normally experiences some kurtosis or skewness.

I think I read in the text somewhere that given limitation of Sharpe ratio, comparing Sharpe ratio of hedge fund manager universe is valid.

text also mentioned some other risk measure like value added and rolling average I believe. I can’t remember correctly.

It is a limitation because it biases the sharpe ratio upward. Just because it makes it look better, doesn’t mean its a good thing…since it no longer accurately reflects the true risk-return tradeoff.

Pokhim is correct regarding using sharpe ratio for HFs, jmsp is incorrect.

I get that if returns are correlated with each other then that would reduce the Standard Deviation and the sharpe ratio would increase (it is biased upward and looks better). But the text says that we assume uncorrelated returns, hence we are not affected by this bias?

It’s just a principal of the sharpe ratio to assume returns are not correlated. If they were assumed correlated your sharpe ratio would biased.

I get that. So since the Sharpe ratio assumes returns are not correlated, this is not a limitation? The text says that assuming uncorrelated returns IS a limitation.

its a limitation of sharpe ratio because now you can use sharpe ratio effectively only for the investments whose returns are not serially correlated.

Yes, so we should only use Sharpe when returns are not serially correlated. And the text says we are assuming returns are not correlated. Hence it is not a limitation? What am i missing here?

Another limitation is the Sharpe Ratio can be gamed. By smoothing returns and/or minimizing the frequency of performance measurement, the Sharpe Ratio can be biased upward.

You are missing the fact that you must make unrealistic assumptions to use the sharpe ratio.


If the assumptions were actually true, then there would be no need for the assumptions and no limitations.

i don’t recall seeing that anywhere in the text, nor do i really understand what you mean by this. the fundamental use of the Sharpe ratio is assessing the avg (past) portfolio returns, not necessarily the expected returns (if that’s what you mean by assumptions).

the limitations of Sharpe Ratio are specified/discussed in the Alt Inv section, specifically relating to Hedge Funds. the “return assumptions,” while somewhat true when using it for “expected returns,” are not a very important component of the Sharpe’s limitations.

Sharpe is time dependent (using a longer time interval will help lower volatility), it is not appropriate to use when there is skewness (should only be used for normal distributions, as someone above stated previously), should not be used when there are illiquid holdings (because of smoothing of returns lowers standard deviation as i mentioned previously), and the ratio can be gamed (ie using OTM options in a portfolio bias the returns upward without factoring in risk).