When the Sortino Ratio Falls Below the Sharpe Ratio

Summary

The note compares two return-based performance measures. The Sharpe ratio scales mean excess return by overall volatility, while the Sortino ratio uses downside semideviation, which measures dispersion associated with negative returns. Because their denominators differ, the ratios can diverge when the return distribution is asymmetric.

For a roughly symmetric distribution, the measures are expected to be similar. If the Sortino ratio is lower, its downside-risk denominator is larger relative to total volatility, which is consistent with substantial downside variation and negative skew. The note observes that negative skewness can occur in individual-stock log returns, but gives no empirical sample or formal conditions proving the relationship. Interpretation also depends on the precise semideviation convention and whether both ratios use the same return and risk-free-rate inputs.

Key ideas

• The Sharpe ratio uses total volatility, while the Sortino ratio uses downside semideviation.
• Symmetric return distributions generally make the two ratios more similar.
• A lower Sortino ratio indicates greater downside semideviation relative to the Sharpe denominator.
• Negative skewness is one possible reason downside risk makes the Sortino ratio lower.

Tags

# Sortino ratio lower than sharpe ratio?


# Sortino ratio lower than sharpe ratio?












Under what circumstances is a sortino ratio lower than a sharpe ratio? What does it mean about the distribution?

## Answer by kurtosis (score 3, accepted)

https://quant.stackexchange.com/a/57998

Whereas the Sharpe ratio divides the risk premium (mean excess return) by the volatility, the Sortino ratio instead divides by semideviation: the standard deviation computed using only negative returns.

For perfectly symmetric return distributions, these should not differ much. However, if a return distribution has skewness, then the Sortino ratio may be very different. In this case, a smaller Sortino ratio means a larger semideviation -- so a negatively-skewed return distribution. When we look at log-returns for individual stocks, such negative skewness is not unusual for a number of economic reasons.

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