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Choosing a Target Return for the Sortino Ratio

Article Quant Q&A · Author: HappySad
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Summary

The document discusses a calculation problem that arises when an annual set of monthly strategy returns has no returns below the target level. In that case, downside deviation can be zero, leaving the Sortino ratio’s denominator at zero and the ratio undefined under that calculation. The response suggests revisiting the target return rather than treating the resulting division-by-zero error as a usable performance value.

Possible alternatives named are a sample-based return measure, such as the average, median, or mode, or a benchmark index return. The chosen target should be applied consistently across the years being compared. These suggestions are not a universal rule: the target should reflect the investor’s objective, and changing it can materially change the ratio. The document does not specify a downside-deviation convention, a target annualization method, or a preferred alternative, and it provides no comparative calculation.

Key ideas

  • The Sortino ratio is undefined when downside deviation is zero under the chosen target return.
  • A target return can be reconsidered using a sample return measure or a benchmark return.
  • The target should be applied consistently across the periods being compared.
  • The ratio’s interpretation depends on the target-return choice and downside-deviation convention.

Tags

Risk managementBacktestingStatistics
Full text
# Sortino Ratio calculation


# Sortino Ratio calculation












I've been using an Excel template to calculate the Sortino ratio for my automated trading strategies. http://investexcel.net/calculate-the-sortino-ratio-with-excel

Basically I input my monthly returns in the return column. That's 12 months of returns for each year from 2006 to 2014.

However, for one of the strategies, let's call it strat A, it had one exceptional year, which had no negative monthly returns. So when the template tries to calculate the Sortino ratio by dividing the returns by the downside risk etc it can't do the calculation because there was no downside risk. So it's dividing by 0 which messes up the calculation.

So I'm wondering what to do in such a scenario?

## Answer by Quantopik (score 2, accepted)

https://quant.stackexchange.com/a/17415

Firstly, I suggest you to use more recognized source to study and compute quantitative finance model or indicators; in such case, for instance, you could take as example the following paper as reference.

Precisely there, the authors describe some common errors that one can do in computing the Sortino ratio; although surely you did not do any of them, anyway it could be a good source.

As regards your question, the fact that you rightly get an error is mainly due to the way you set the target return; I suggest you to replace that value with average (median, mode, ...) return in the data sample or the benchmark index return and try to solve the issue in this way; of course, you should replace the target return with for all years.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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