Sortino vs. Sortino
Often in trading literature and trading software packages we have seen the Sortino ratio, and in particular the target downside deviation, calculated incorrectly. Most often, we see the target downside deviation calculated by “throwing away all the positive returns and taking the standard deviation of negative returns.” We hope that by reading this article, you can see how this is incorrect. Specifically:
In Step 1, the difference with respect to the target level is calculated, unlike the standard deviation calculation where the difference is calculated with respect to the mean of all data points. If every data point equals the mean, then the standard deviation is zero, no matter what the mean is. Consider the following return stream: [–10, –10, –10, –10]. The standard deviation is 0; while the target downside deviation is 10 (assuming target return is 0).
In Step 3, all above target returns are included in the averaging calculation. The above target returns set to 0% in Step 1 are not thrown away.
The Sortino ratio takes into account both the frequency of below-target returns as well as the magnitude of them. Throwing away the zero underperformance data points removes the ratio’s sensitivity to frequency of underperformance. Consider the following underperformance return streams: [0, 0, 0, –10] and [–10, –10, –10, –10]. Throwing away the zero underperformance data points results in the same target downside deviation for both return streams, but clearly the first return stream has much less downside risk than the second.
In this article we presented the definition of the Sortino ratio and the correct way to calculate it. While the Sortino ratio addresses and corrects some of the weaknesses of the Sharpe ratio, we feel there is one measure that is even better yet: The Omega Ratio. We look forward to tackling the Omega Ratio in our next article.
Tom Rollinger is director of new strategies development for Sunrise Capital Partners. Previously he was a portfolio manager for quantitative hedge fund legend Edward O. Thorp. Scott Hoffman is the founder of CTA Red Rock Capital Management.