# Sortino Ratio: Are you calculating it wrong?

We read the recent whitepaper: “Sortino: A Sharper Ratio” by Red Rock Capital with great interest.  You see, as we’ve discussed before, the Sharpe ratio is both one of the most accepted and at the same time most critiqued forms of performance measurement in the managed futures world. The better ratio for many, including us – is the Sortino ratio, which doesn’t penalize programs for outlier gains as the Sharpe ratio does.

Here’s a little recap on the two… Sharpe measures Return divided by (upside and downside) volatility, while the Sortino measures Return divided by (downside) volatility only.

Graph Courtesy: Red Rock Capital

The general way we’ve seen the Sharpe and Sortino ratios calculated is as follows, with the Sharpe’s denominator the standard deviation of all returns, and the Sortino’s the standard deviation of all negative returns. Seems simple enough:

“Sharpe = (Compound ROR – risk free ROR) / (Standard Deviation of Returns)”

“Sortino = (Compound ROR – risk free ROR) / (Standard Deviation of Negative Returns)”

But is the industry as a whole using the Sortino ratio correctly? Our friends at Red Rock Capital don’t think so, saying in their recent paper:

“We believe the Sortino ratio improves on the Sharpe ratio in a few areas. [But] the purpose of this article…is not necessarily to extol the virtues of the Sortino ratio, but rather to review its definition and present how to properly calculate it since we have often seen its calculation done incorrectly.”

Red Rock states the real definition of the Sortino ratio uses not the standard deviation of negative returns, but instead the ‘target downside deviation’, which is the deviations of the realized return’s underperformance from the target return.  What does that mean to the normal person who has trouble reading math equations? Well, it means the usual method of throwing away all the positive returns and taking the standard deviation of negative returns isn’t technically correct, as it ignores the fact that you’re supposed to be looking at just the below target return deviations. As Red Rock puts it:

“Standard deviation is a measure of dispersion of data around its mean, both above and below. Target Downside Deviation is a measure of dis­persion of data below some user selectable target return with all above target returns treated as underperformance of zero. Big difference.

The [correct] Sortino ratio takes into account both the frequency of below target returns as well as the magnitude of below target returns. [The normal way of] 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.”

Which method is correct? We will take Red Rock’s word for it that this is how the equation was originally written up – but we also know that the other method is quite widely used (our own website, for example).  Surely there is value in the widely used method, but Red Rock makes some excellent points on the issues therein. So, we looked at a few programs (the 10 largest CTAs as of June 2013 plus Red Rock) to see what differences were there between the widely used Sortino method and Red Rock’s “correct” method.

(Disclaimer: Past performance is not necessarily indicative to futures results)
Above stats from Sept. ’03 through Jul. ’13, excepting the following:
Two Sigma from Jan. ’05, Cantab from March ’08, Harness from April ’09

You can see the value of the Sortino rose in each program on our list by using the calculation outlined by Red Rock, but we know that Sortino values don’t really mean all that much. The measure is better used as a way to compare the risk adjusted performance of programs with differing risk and return profiles. Any risk adjusted ratio is really trying to just normalize the risk across programs, and then see which has the higher return per that normalized unit of risk.

So, when considering not the value of the ratio when changed, but what the changed value does to a ranking by Sortino ratio of the world’s biggest managed futures programs – what do we see? Not much, to be honest, as the top four remained in the same order. However, there was some movement in the rankings, Transtrend and Lynx switching places, as well as Aspect and Cantab, but the ranking is pretty close across the two calculation methods.

So, as a practical matter – this doesn’t really move the needle that much, and is likely a more useful tool when analyzing unique track records where all monthly losses are exactly -%5 or the like.  The real discovery here seems to be Red Rock Capital – who sports a higher Sortino than some of the royalty of managed futures (i.e. AHL, Campbell, Transtrend) no matter which method is used.

You can view the full paper here: Sortino: A Sharper Ratio

1. We have used a combination of the Sortino and the Calmar for years and the combionation has alerted us to potential problems well ahead of any disasters.

The definition is clearly defined in Kim Avery’s book. It is available from Autumn Gold.

2. An argument for why we want to use the Sharpe ratio works as follows (and it is often heard). By the law of large numbers, a portfolio that is reasonably diversified should have normally distributed returns – and therefore, for symmetric distributions, the Sharpe and Sortino ratios rank portfolios similarly. However, for this argument to work, the law of large numbers’ assumptions must be satisfied. The thorniest of these assumptions is the relative uncorrelation of the many assets in the portfolio: in bad times, they become more correlated. Therefore, in bad times, downside risk and standard deviation rank risk differently, and Sharpe and Sortino ratios do the same.

Disclaimer
The performance data displayed herein is compiled from various sources, including BarclayHedge, and reports directly from the advisors. These performance figures should not be relied on independent of the individual advisor's disclosure document, which has important information regarding the method of calculation used, whether or not the performance includes proprietary results, and other important footnotes on the advisor's track record.

Benchmark index performance is for the constituents of that index only, and does not represent the entire universe of possible investments within that asset class. And further, that there can be limitations and biases to indices such as survivorship, self reporting, and instant history.

Managed futures accounts can subject to substantial charges for management and advisory fees. The numbers within this website include all such fees, but it may be necessary for those accounts that are subject to these charges to make substantial trading profits in the future to avoid depletion or exhaustion of their assets.

Investors interested in investing with a managed futures program (excepting those programs which are offered exclusively to qualified eligible persons as that term is defined by CFTC regulation 4.7) will be required to receive and sign off on a disclosure document in compliance with certain CFT rules The disclosure documents contains a complete description of the principal risk factors and each fee to be charged to your account by the CTA, as well as the composite performance of accounts under the CTA's management over at least the most recent five years. Investor interested in investing in any of the programs on this website are urged to carefully read these disclosure documents, including, but not limited to the performance information, before investing in any such programs.

Those investors who are qualified eligible persons as that term is defined by CFTC regulation 4.7 and interested in investing in a program exempt from having to provide a disclosure document and considered by the regulations to be sophisticated enough to understand the risks and be able to interpret the accuracy and completeness of any performance information on their own.

RCM receives a portion of the commodity brokerage commissions you pay in connection with your futures trading and/or a portion of the interest income (if any) earned on an account's assets. The listed manager may also pay RCM a portion of the fees they receive from accounts introduced to them by RCM.

Disclaimer
The performance data displayed herein is compiled from various sources, including BarclayHedge, and reports directly from the advisors. These performance figures should not be relied on independent of the individual advisor's disclosure document, which has important information regarding the method of calculation used, whether or not the performance includes proprietary results, and other important footnotes on the advisor's track record.

Benchmark index performance is for the constituents of that index only, and does not represent the entire universe of possible investments within that asset class. And further, that there can be limitations and biases to indices such as survivorship, self reporting, and instant history.

Managed futures accounts can subject to substantial charges for management and advisory fees. The numbers within this website include all such fees, but it may be necessary for those accounts that are subject to these charges to make substantial trading profits in the future to avoid depletion or exhaustion of their assets.

Investors interested in investing with a managed futures program (excepting those programs which are offered exclusively to qualified eligible persons as that term is defined by CFTC regulation 4.7) will be required to receive and sign off on a disclosure document in compliance with certain CFT rules The disclosure documents contains a complete description of the principal risk factors and each fee to be charged to your account by the CTA, as well as the composite performance of accounts under the CTA's management over at least the most recent five years. Investor interested in investing in any of the programs on this website are urged to carefully read these disclosure documents, including, but not limited to the performance information, before investing in any such programs.

Those investors who are qualified eligible persons as that term is defined by CFTC regulation 4.7 and interested in investing in a program exempt from having to provide a disclosure document and considered by the regulations to be sophisticated enough to understand the risks and be able to interpret the accuracy and completeness of any performance information on their own.

RCM receives a portion of the commodity brokerage commissions you pay in connection with your futures trading and/or a portion of the interest income (if any) earned on an account's assets. The listed manager may also pay RCM a portion of the fees they receive from accounts introduced to them by RCM.