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I was asked whether Sharpe Ratio was a better measure than Cumulative Returns, in the context of hedge funds.

To me, personally, Sharpe Ratio is a more important measure. By definition, it tells us how much reward we are getting for each unit or risk we are taking. A portfolio that returns 10% that is extremely volatile, indicating a bigger standard deviation of daily returns, is not as favorable as a portfolio that returns 8% with low volatility (however this is purely an opinion). Cumulative returns just tell us how much the portfolio has improved over time, there is no context with regard to volatility. If you had to invest in a portfolio and you could only receive one measure of the portfolio, namely Sharpe Ratio or Cumulative returns, which would you choose as the more important metric and why?

I was just wondering the community's thoughts before I respond back to this person.

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Your opinion is correct. There is simply more information about risk-reward encoded in the Sharpe ratio than cumulative returns.

The other thing that's important to know is that whatever ratio you choose is simply a social construct or conventional benchmark that people use to compare between each other. The ratio is only useful insofar as other people are using the ratio in a standardized way.

To that note, it's difficult to compare cumulative returns also partly because somehow people have more nonstandard ways of computing these. Are you talking about over the entire horizon of a portfolio's existence or arithmetically annualized? Is this a cumulative return on each 1M invested up to 500M or up to 1B? Is this over a 10 year period or a 3 month period?

Another corollary of this is that there's fancier ratios (Sortino, Omega, Calmar etc.) - to which your client may ask, why aren't you using those? Well, these ratios are simply less often used by other trading participants, which make it difficult for you to make an apples-to-apples comparison. I could just as easily come up with an arbitrary Madilyn ratio that encodes more statistics than Sharpe but it would be useless because no one else uses it. "I have a great strategy with a Madilyn ratio of 10830.28."

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