Sharpe Ratio vs. Sortino vs. Calmar – Risk Adjusted Return

In this post I explore what risk-adjusted return is and some different ways to measure it, including Sharpe, Sortino, and Calmar ratios.

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Introduction – What Is Risk Adjusted Return?

So we explored the concept of portfolio risk here recently. A good armchair definition of risk is the permanent loss of capital, though many erroneously conflate volatility – the variability of return – and risk.

Risk-adjusted return refers to the performance measure of the excess return of an investment or portfolio per unit of risk over a given time period. As the name suggests, it is quite literally the return of an investment adjusted for its risk (above the risk-free rate of T bills). It is usually expressed as a number.

An investment may deliver a high return, but at what cost? If the investment is extremely risky, investors may not be adequately compensated for taking on that risk. Risk-adjusted return allows us to assess whether or not this is the case.

Risk-adjusted return also provides arguably the best way to compare different portfolios. Simply comparing total return doesn't tell the full story, as one portfolio may be much riskier than another and thus may not be suitable for a risk-averse investor. When a portfolio has a comparatively greater risk-adjusted return, we say it is more efficient. As such, for two portfolios with the same return, we should obviously prefer the more efficient one with lower risk.

Let's explore some different ways to measure risk-adjusted return.

Measuring Risk-Adjusted Return – 4 Ratios

So there are a few metrics we can use to measure risk-adjusted return. This list is not exhaustive; there are other, more complicated measurements out there.

Sharpe Ratio

The first and by far the most popular – but what I would also submit is the worst (sorry, Bill!) – is called the Sharpe ratio, developed by American economist and Nobel laureate William F. Sharpe, who also contributed to the CAPM.

The Sharpe ratio is the ratio of excess return of an investment to its volatility.

Sortino Ratio

The Sortino ratio, named after Frank A. Sortino, is a variation of the Sharpe ratio that only considers downside volatility.

Treynor Ratio

The Treynor ratio, developed by American economist Jack Treynor, looks at the excess return of an investment relative to its beta, or its sensitivity to the market. This tells investors if they are being compensated for taking on risk greater than the systematic market risk. Because an investment's beta is simply its volatility relative to the market, the ratio of the Treynor ratios of two portfolios should be nearly the same as the ratio of their Sharpe ratios.

Calmar Ratio

The Calmar ratio was developed by fund manager Terry W. Young in 1991. It is simply the ratio of the investment's average compounded annual return to its maximum drawdown over a given time period. As such, it's also referred to as the Drawdown ratio.

Sharpe Ratio vs. Sortino Ratio vs. Calmar Ratio

Let's compare these risk-adjusted return ratios. Thankfully, they're all pretty easy to glance at, understand, and compare between investments, as they're just expressed as numbers. I'm leaving out Treynor simply because I noted it's so similar to Sharpe, which is vastly more popular.

Recall that the formula for the Sharpe ratio is the excess return of an investment versus its volatility. This should immediately raise some red flags. First and most importantly, I've discussed elsewhere that while they're often erroneously conflated, volatility is not risk. As such, risk-adjusted return is somewhat of a misnomer for the Sharpe ratio. “Volatility-adjusted return” would be more appropriate.

Volatility is just the variability of return around the mean. It's the measure of price movement. All things being equal, risk and return are positively correlated. But there are high volatility assets that exhibit low returns, such as commodities, which have a real expected return of about zero. So in terms of asset pricing and expected returns, volatility is a poor proxy for risk.

We actually want volatility on the way up, because that's where returns come from. Specifically, a small handful of days of huge gains are responsible for most of the market’s performance over an entire year. Investors only complain about volatility when it happens on the downside, and rightfully so. It would be rare to find an investor who, after seeing a highly volatile day of a 10% gain, would exclaim “my portfolio is too risky!”

Secondly, and this one is admittedly a bit nitpicky, using standard deviation as a measure of volatility assumes that the returns of financial markets are Normally distributed; they're not.

In fairness, volatility is usually pretty even on both sides, so results across different ratios should be pretty similar (Sharpe and Sortino should be fairly linearly correlated) on average, but I figure if we have the ability to isolate downside risk just as easily, why not go ahead and do so? That's where the Sortino and Calmar ratios come in, which are my preferred metrics.

Remember, the Sortino ratio is just a slight variation on the Sharpe ratio. Whereas Sharpe looks at both upside and downside volatility, Sortino only cares about the downside. Again, results should be pretty similar on average between the two, but to me this is an obvious improvement in precision that requires no extra time, effort, complexity, or computing power.

Now let's talk about Calmar, one of the least popular risk-adjusted return measurements. I happen to think it's probably the best. Whereas Sortino looks at all the downside volatility over a given time period, Calmar looks at the maximum drawdown for that time period.

This has both some benefits and drawbacks. I maintain that a good definition for risk is permanent loss of capital. That risk is obviously most apparent and most impactful during drawdowns, or crashes. As such, it is a superior and much more “pure” measurement of risk than volatility. Consequently, I would submit that Calmar is superior to Sortino, and, as mentioned, Sortino is superior to Sharpe.

This quality of the Calmar ratio can also be its downfall, however. If the time period we're investigating happened to not experience a major drawdown, such as the steady bull market between 2010 and 2017 for U.S. stocks, the Calmar ratio is going to look unrealistically juicy and is not going to tell the full picture. In fairness, Sortino wouldn't really either.

Put another way, Calmar inherently uses much fewer data points than Sharpe or Sortino, making it less statistically significant. We could extend this to say that Calmar may only be appropriate for long time periods. Calmar also obviously ignores general volatility. But this is why I advocate for looking at both Sortino and Calmar together.

Glance at Risk Adjusted Return Metrics, But Don't Focus On Them

In fairness to Bill Sharpe, just like with Bengen and his 4% “rule,” he never intended for investors to become obsessed with his ratio or to make predictions about the future based on it. Just as past returns do not indicate future returns, past Sharpe ratios do not indicate future Sharpe ratios. Hedge funds have also seemingly bastardized Sharpe's metric, as they tend to calculate it improperly – effectively juking the stats – before plastering it all over their marketing materials, as it's a shiny object to which institutional eyes are drawn.

Moreover, Sharpe ratios fluctuate based on the time period looked at. The Sharpe ratio for your portfolio today will likely look different than the one for it 10 years from now. Remember that these are just quick and dirty ratios and may not tell the full story of the riskiness of a particular portfolio or strategy. Do your due diligence. There's a famous saying in finance that “you can't eat Sharpe.”

Also remember one important rule. Just like Modern Portfolio Theory tells us, and just like I've preached in every other post on this website, view the portfolio holistically, not each asset or security in isolation. Consequently, in this context of discussing risk-adjusted return, only apply and compare your measure thereof for the entire portfolio, not for each individual asset. Just as two very volatile assets can magically make for a less volatile portfolio when combined due to their uncorrelation, so too can two assets with low risk-adjusted returns in isolation combine to make a portfolio with a high risk-adjusted return.

Here's an example to illustrate. Over the past half-century, the U.S. stock market has delivered a risk-adjusted return as measured by the Calmar ratio of 0.85. 10-Year U.S. Treasury bonds came in pretty close at 0.82 for that same time period. Equally weighting those 2 assets 50/50 in a portfolio gives us a Calmar ratio of 1.80.

Here's another example of the folly of looking at the risk-adjusted return of individual assets. Looking at the past 50 years, as we'd expect, short-term treasury bonds – which are much less volatile and less risky than longer-term bonds – have had Sharpe, Sortino, and Calmar ratios of 0.47, 0.77, and 5.52 respectively, while long-term treasury bonds were worse across the board, delivering 0.41, 0.66, and 1.13 for those. However, a diversified 60/40 portfolio (60% stocks, 40% bonds) using short treasuries came in at 0.57, 0.85, and 0.86 for the aforementioned ratios, while one using long treasuries fared better at 0.65, 0.99, and 1.51.

What's your risk-adjusted return metric of choice? Let me know in the comments.

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