How to Compare Strategies with Negative Sharpe Ratios

Summary

The note explains why ranking strategies by Sharpe ratio alone can be misleading when both ratios are negative. It compares two cases: strategies with equal negative excess returns but different volatility, and strategies with equal volatility but different negative excess returns. In each example, the strategy with the less negative Sharpe ratio ranks higher, even though the preferred choice depends on whether the difference comes from lower risk or a better return.

The examples show that the usual ordering of Sharpe ratios does not by itself capture every practical comparison between losing strategies. A trader should also inspect return and volatility separately and consider which tradeoff matters for the decision. The discussion is conceptual and relies on two illustrative scenarios; it does not offer a general ranking rule, account for other risk measures, or discuss uncertainty in estimated returns and volatility.

Key ideas

• With negative Sharpe ratios, the numerically higher ratio does not always identify the more attractive risk-return tradeoff.
• At equal excess returns, lower volatility can make a strategy preferable.
• At equal volatility, a smaller loss can make a strategy preferable.
• Inspect the underlying return and volatility alongside the Sharpe ratio.

Tags

# Comparing Negative Sharpe Ratio


# Comparing Negative Sharpe Ratio












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 $SR_A < SR_B$.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.