What is the Sortino Ratio?
Sean P. Gilligan, CFA, CPA, CIPM
June 30, 2020
The Sortino Ratio is similar to the Sharpe Ratio as it is used to compare and rank managers with similar strategies. However, unlike Sharpe, the Sortino Ratio measures the incremental average strategy return over a minimum acceptable return per unit of downside risk rather than total risk.
Because of this difference, the Sortino Ratio may be more appropriate than the Sharpe Ratio when assessing strategies with non-normal return streams. For example, the Sharpe Ratio is appropriate when assessing a traditional equity manager, while the Sortino Ratio would be more appropriate for a hedge fund strategy that uses derivatives to seek asymmetrical, positive spikes in performance. The Sharpe Ratio, using total risk (measured by standard deviation), would penalize this hedge fund manager for these positive spikes in performance, while the Sortino Ratio, using downside risk (measured by downside deviation), would not.
Sortino Ratio Formula
Annualized Sortino Ratio
When calculating the Sortino Ratio using monthly data, the Sortino Ratio is annualized by multiplying the entire result by the square root of 12.
What is a Good Sortino Ratio?
The Sortino Ratio is a ranking device so a portfolio’s Sortino Ratio should be compared to that of other portfolios rather than evaluated independently. In general, investors prefer higher Sortino Ratios when comparing similarly managed portfolios.
Sortino Ratio vs. Sharpe Ratio Calculation Example
Suppose two similar strategies, Strategy A and Strategy B, had the following characteristics over one year. For this period, the minimum acceptable return is the risk-free rate, which is 0.10% (monthly average return).
Please note that the Sortino Ratio calculated in this example is based on monthly data and, therefore, must be annualized to get the final result. The following is a breakdown of the calculation:
For more details on how to calculate the Sharpe Ratio, check out What is the Sharpe Ratio.
Although the strategies have the same average monthly return over the one-year period, the Sortino Ratios differ significantly due to their differences in downside risk (i.e., downside deviation). Strategy A is preferred over Strategy B to an investor deciding between the two because it has a higher Sortino Ratio.
When using the Sharpe Ratio to evaluate the two strategies, the result is the opposite than it is when using the Sortino Ratio. How can this be?
If the Standard Deviation (i.e., total risk) is higher for Strategy A than Strategy B, but Downside Deviation (i.e., downside risk) is lower for Strategy A than Strategy B, we can infer that at least some of the volatility in Strategy A’s return stream is caused by positive spikes in performance. Standard Deviation treats all volatility (both positive and negative) equally, while Downside Deviation does not penalize the manager for positive volatility.
Sortino Ratio Interpretation
The Sortino Ratio is one of the best measures for return streams with non-normal distributions (such as hedge funds). This is because Sortino only penalizes for negative volatility and not positive spikes in performance.
If, for example, an investor is looking for a high reward strategy, then upside volatility can be a good thing.
Why is the Sortino Ratio Important?
The Sortino Ratio allows investors to evaluate portfolio performance for non-normal return distributions after adjusting for risk. Comparing returns without accounting for risk does not provide a complete picture of the strategy. Using total risk, as the Sharpe Ratio does, can make a strategy look riskier than it truly is if the volatility is skewed positively.
Sortino Ratio Calculation: Using Arithmetic Mean or Geometric Mean
Because the Sortino Ratio compares return to risk (through downside deviation), we use Arithmetic Mean to calculate the strategy return. Geometric Mean penalizes the return stream for taking on more risk. However, since the Sortino Ratio already accounts for risk in the denominator, using Geometric Mean in the numerator would account for risk twice. For more information on the use of arithmetic vs. geometric mean for performance appraisal measures, please check out Arithmetic vs Geometric Mean: Which to use in Performance Appraisal.