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It is widely accepted that the higher the Sharpe Ratio, the better. But, how do we compare two strategy with negative Sharpe Ratio?

Suppose we have two trading strategy $A$ and $B$. Consider the following scenarios:

Scenario 1: Assume that strategy $A$ and $B$ have the same excess return of $-10\%$. But, the volatility of strategy $A$ is $5\%$ and strategy $B$ is $10\%$. Then, the Sharpe Ratios of $A$ and $B$ are $-2$ and $-1$, respectively.

Scenario 2: Assume that strategy $A$ and $B$ have the same volatility of $10\%$. But, the excess return of strategy $A$ is $-20\%$ and strategy $B$ is $-10\%$. Then, the Sharpe Ratios of $A$ and $B$ are $-2$ and $-1$, respectively.

In scenario 1, strategy $A$ is favorable since it has a lower risk while yielding the same return as strategy $B$ and $SR_A < SR_B$.

While in scenario 2, strategy $B$ is favorable since it has higher excess return for taking the same risk as strategy $A$. But, still $SR_A < SR_B$.

Ricky The Ising
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  • In scenario 2: $SR_A = -2$ and $SR_A = -1$ right? Then your last sentence is false. – Bob Jansen Jul 30 '21 at 11:51
  • @BobJansen oh yes, thank you for spotting. I have edited it – Ricky The Ising Jul 30 '21 at 12:08
  • Then the problem disappears right? – Bob Jansen Jul 30 '21 at 12:08
  • I don't think so. Since in scenario 1 $A$ is better but $SR_A < SR_B$. While in scenario 2 $B$ is better but $SR_A < SR_B$. Which means higher Sharpe Ratio doesn't mean better when the ratio is negative. Am I missing something? – Ricky The Ising Jul 30 '21 at 12:14
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    In the paper "Interpreting the Sharpe Ratio when excess returns are negative" the authors claim that sharpe ratio should be interpreted probabilistically and in that setting you should choose the fund with highest SR because such fund has the highest probability of beating the risk free rate. https://www.researchgate.net/publication/285365236_Interpreting_the_Sharpe_ratio_when_excess_returns_are_negative – emot Jul 30 '21 at 13:49
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    Also one of the advantages of the "M Squared" measure is that it can be interpreted even when the Sharpe Ratio is negative. – nbbo2 Jul 30 '21 at 17:29

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