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.

Disclosure:  Some of the links on this page are referral links. At no additional cost to you, if you choose to make a purchase or sign up for a service after clicking through those links, I may receive a small commission. This allows me to continue producing high-quality content on this site and pays for the occasional cup of coffee. I have first-hand experience with every product or service I recommend, and I recommend them because I genuinely believe they are useful, not because of the commission I may get. Read more here.

Introduction – What Is Risk Adjusted Return?

So we explored the concept of portfolio risk here recently. A good armchair definition of risk is, in my opinion, the probability of permanent loss of capital and the potential magnitude thereof, 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 – 5 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 by looking only at negative returns.

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.

Treynor is not very useful for standalone portfolios and is more meaningful if the investment is one piece of a larger allocation. It was designed for portfolio construction, not evaluation, and cross-fund Treynor comparisons are apples-to-oranges due to it focusing on beta. For these reasons, Treynor has little to no practical use for retail investors, so it will not be included in our comparison below.

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.

Ulcer Performance Index

Ulcer Index is a standalone risk measure developed by Peter Martin in 1987 that quantifies how far a portfolio falls below its prior peak and how long it stays there, capturing both the depth and duration of drawdowns simultaneously.

The Ulcer Performance Index (UPI) aka Martin Ratio is the ratio of excess return to the Ulcer Index. As such, UPI penalizes sustained underwater periods far more harshly than Sharpe, Sortino, or Calmar. Basically, whereas Calmar only looks at degree of drawdown, UPI looks at degree and duration of drawdown.

I like UPI a lot, but it is more complex than the previous ratios and will get its own dedicated blog post on this site, so I'm not going to focus on it too much here, but I figured it'd be remiss not to at least mention it in this context.

How To Calculate Sharpe, Sortino, and Calmar Ratios

Now we'll briefly cover how to calculate the Sharpe, Sortino, and Calmar ratios. Backtesting tools will usually do this for you, so it should be rare that you have to do it yourself. But if so, here are the formulas.

Calculate Sharpe Ratio

To calculate Sharpe Ratio, use this formula:

Sharpe = (Rp - Rf) / σp

where R_p = portfolio return, R_f = risk-free rate, and σ_p = portfolio volatility (measured by standard deviation).

Calculate Sortino Ratio

To calculate Sortino Ratio, use this formula:

Sortino = (Rp - Rf) / σd

where R_p = portfolio return, R_f = risk-free rate, and σ_d = negative return (downside) volatility (measured by standard deviation).

Calculate Calmar Ratio

To calculate Calmar Ratio, use this formula:

Calmar = (Rp - Rf) / MaxDD

where R_p = portfolio return, R_f = risk-free rate, and MaxDD = max drawdown.

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.

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. Sharpe penalizes those huge gains, just as it penalizes huge losses. 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 over Sharpe in this context.

Remember, the Sortino ratio is just a slight variation on the Sharpe ratio. Whereas Sharpe looks at and penalizes 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, at least now in the 21st century.

When Harry Markowitz published Modern Portfolio Theory in 1959, he actually acknowledged as much, saying that Sortino's use of that semi-variance (downside only) was conceptually superior to full variance (Sharpe) for measuring risk. But he had to use full variance anyway, because semi-variance optimizations were computationally unfeasible in 1959. The Sortino ratio was essentially Markowitz's preferred measure.

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. Again, I maintain that a good definition for risk is related to the 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 characteristic 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.

Structural Shortcomings of Sharpe, Sortino, and Calmar

The previous section covered a fairly surface-level comparison of the Sharpe, Sortino, and Calmar ratios with respect to how retail investors would use them. In this section, I'll briefly touch on what financial academia has had to say about some of the shortcomings of these ratios. All 3 have their own unique issues.

Novices may want to skip this somewhat technically-heavy section.

I've broken it out into 3 subsections for the 3 main ratios.

Sharpe Shortcomings

1. Bill Sharpe didn't want his name on the ratio and didn't endorse its widespread usage.

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.

William Sharpe didn't even his name on the ratio. In his original 1966 Journal of Business paper, he called it the “reward-to-variability ratio.” Doesn't have quite the same ring to it, does it?

Other people started calling it the Sharpe ratio. Even Morningstar adopted it in the early 90's. But Sharpe himself continued resisting the namesake label for almost 3 decades. When he finally relented in his 1994 Journal of Portfolio Management update, he wrote that he was “bowing to increasingly common usage” with respect to the name but still did not endorse how it was being used everywhere.

2. Sharpe can be overstated.

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.

In his 2002 Financial Analysts Journal paper “The Statistics of Sharpe Ratios,” MIT's Andrew Lo showed that the monthly-to-annual Sharpe conversion is only correct when monthly returns are serially uncorrelated. When returns are smoothed, which is exactly what happens with hedge funds, private equity, real estate, and anything else that reports appraised values rather than marked-to-market values, the simple month-to-annual 12x multiplication overstates the true annual Sharpe.

And the magnitude of that potential overstatement is not insignificant. Lo found that the annual Sharpe ratio for a hedge fund with serially correlated returns can be overstated by as much as 65%! A reported annual Sharpe of 1.0 might be a true Sharpe of 0.6. Lo suggests a correct formula using a complex adjustment factor that accounts for the autocorrelation of the return series.

Practically, this boils down to a pretty simple lesson: be especially skeptical of high reported Sharpe ratios for any strategy that doesn't trade in liquid, continuously marked-to-market instruments.

3. Hedge funds can also game Sharpe with options.

Goetzmann, Ingersoll, Spiegel, and Welch proved in their 2007 Review of Financial Studies paper that the Sharpe-maximizing strategy when options are available is to sell out-of-the-money calls and puts, called a short strangle.

Collecting option premium generates steady small gains, and since tail events happen infrequently, the measured standard deviation stays low. The result is an inflated Sharpe that looks great right up until the market blows through one of those strikes.

Goetzmann put it plainly: “The Sharpe ratio is very sensitive to options-like strategies. Many hedge funds essentially sell out-of-the-money options, which every once in a while go boom.” Even Sharpe agreed this was a real problem. The paper proposed a “manipulation-proof” performance measure using power utility functions, which is theoretically elegant – albeit comparatively complex – and has been almost entirely ignored by the industry.

If you ever see a hedge fund with a suspiciously high Sharpe and a strategy description that involves “generating income” or “capturing premium,” ask what's on the other side of those trades.

4. Bad returns can raise Sharpe.

This one is counterintuitive enough that it's worth spelling out. Benjamin Auer documented in a 2013 Financial Markets and Portfolio Management paper that a fund with a negative Sharpe ratio can actually improve its Sharpe by reporting a sufficiently bad return.

Here's the math: when Sharpe is already negative, an extreme negative observation pulls the numerator (return) down only slightly, but it inflates the standard deviation substantially, which makes the negative number less negative, i.e., higher. Auer found using hedge fund data that a significant number of funds had at some point reported a return bad enough that it improved their Sharpe ratio.

The opposite is also true: an extremely good return can decrease a positive Sharpe by inflating the SD denominator more than it raises the numerator. This is one of the reasons “Sharpe-maximizing” behavior in practice sometimes looks strange; as with most things, the metric behaves oddly at the extremes.

Sortino Shortcomings

Just like with Sharpe, the Sortino ratio was named after Frank Sortino, but Frank Santio didn't name the Sortino ratio.

He developed the underlying downside-risk framework at the Pension Research Institute (PRI), which he founded at San Francisco State University in 1981. The actual computation code was written by his collaborator Hal Forsey, an SFSU mathematics professor. The name came from Brian Rom of Investment Technologies LLC, the firm that marketed PRI's software.

According to Sortino himself, it was Rom's idea to call it the Sortino ratio as part of the commercialization effort. The first published reference to the underlying measure appeared in Financial Executive Magazine in August 1980; the ratio by name came later via software marketing. For what it's worth, Rom also coined “Post-Modern Portfolio Theory” in 1993.

1. Miscalculation

Tom Rollinger and Scott Hoffman of Red Rock Capital published a paper titled “Sortino: A ‘Sharper' Ratio” documenting that most spreadsheet implementations, financial blogs, and even some commercial software calculate the Sortino ratio incorrectly.

Looking at only downside volatility sounds simple enough, but it shouldn't mean simply taking the standard deviation of negative returns. Their illustrative example is a return stream of [−10%, −10%, −10%, −10%] which gives a “downside deviation” of zero under the wrong method, because the standard deviation of four identical numbers is zero. By that logic, a fund that loses 10% every single period is risk-free.

The correct method calculates Target Downside Deviation (TDD) as:

TDD = √[ (1/N) × Σ min(0, R_i − T)² ]

where T is a target return, R_i is the return series, and returns above the target T are set to zero, not removed from the calculation. The count in the denominator is total N, not just the number of below-target periods.

This means deviations are measured from the target return T, not from the mean return, and the squaring happens to the full deviation from T, not to the return itself.

This calculation results in a TDD of 10% for the example above, which is exactly right.

The takeaway here is if you're comparing Sortino ratios from different publications, there's a reasonable chance they're not using the same calculation.

2. Choosing Target Return

As you can imagine, the Sortino ratio is highly sensitive to the Minimum Acceptable Return (MAR) you choose, and there is no industry standard. The ratio is monotonically decreasing in MAR. Raise the target and you simultaneously shrink the numerator and increase the denominator. A fund that looks solid with MAR of 0% can look mediocre with MAR of 5%.

To illustrate the magnitude using S&P 500 data, the ratio with MAR = 0% vs. MAR = 5% differed by more than 40%. When comparing Sortino ratios across managers or publications, verify they're using the same target before drawing any conclusions. Most tools default to zero or the risk-free rate, but neither is definitively “correct.”

3. Sortino moved on.

In his 2009 book The Sortino Framework for Constructing Portfolios, Sortino effectively argued that the ratio bearing his name was incomplete. His statement was that Sortino tells you how badly you missed the target, but says nothing about how much you exceeded it. His preferred successor was the Upside Potential Ratio – upside potential above the desired target divided by downside deviation below it. The ratio bearing his name, he suggested, should be considered a floor, not a ceiling. Is that practically useful? Who's to say?

Calmar Cons

CALMAR stands for CALifornia Managed Accounts Reports, the name of the newsletter Terry Young published out of Santa Ynez, California. He introduced the ratio in Futures magazine in October 1991 in an article titled “Calmar Ratio: A Smoother Tool.”

The newsletter itself was sometimes branded “CMA Reports.” It was a small regional publication, which makes it somewhat amusing that its name became permanently embedded in institutional performance analytics.

1. Calmar has a data point problem.

Calmar's main issue is a data point availability problem that's pretty easy to understand, which I hinted at earlier. You might think 5 years is plenty of time to assess the performance of an investment, but if you just so happened to not see a major drawdown during that period, Calmar is going to look great, and then you may have a major crash in year 6 that takes Calmar to the toilet for the whole 6-year period.

The Sterling ratio actually remedies this somewhat by averaging the annual max drawdowns over the period rather than using the single worst drawdown, but you'll typically only find Sterling when looking at literature on managed futures.

2. Calmar suffers from survivorship bias.

Calmar looks at max drawdowns. Funds that suffer catastrophic drawdowns generally close and drop out of databases. The average Calmar ratio you see in industry reports and marketing materials reflects the survivors, not the full distribution. The average looks better than reality because the worst outcomes removed themselves from the sample.

Recap Comparison Table – Risk-Adjusted Ratios at a Glance

Here's a quick recap of all that comparison of Sharpe, Sortino, and Calmar in a table:

Does the Risk Adjusted Return Metric You Choose Even Matter?

I've blabbered on about surface level issues and deep technical issues of various risk-adjusted return metrics and why we might want to use one over another, but here's the blunt truth: for most investors evaluating most investments, the choice here simply doesn't matter.

Martin Eling and Frank Schuhmacher ran the numbers in a 2007 Journal of Banking & Finance paper comparing the Sharpe ratio against 12 alternatives – Sortino, Calmar, Sterling, Omega, Kappa 3, and several others – across over 2,500 hedge funds. Their finding was: “despite significant deviations of hedge fund returns from a normal distribution, our comparison of the Sharpe ratio to the other performance measures results in virtually identical rank ordering across hedge funds.” Correlation coefficients between Sharpe and the alternatives were above 0.97 across the board.

This is what I hinted at earlier in saying Sharpe and Sortino are always going to be highly correlated.

Eling followed up in a 2008 Financial Analysts Journal paper covering nearly 40,000 mutual funds across 7 asset classes over a decade and said the same thing: “choosing a performance measure is not critical to fund evaluation and the Sharpe ratio is generally adequate.”

CAIA's Linus Nilsson ran a similar analysis in 2024 on 2,000+ funds and reached the same conclusion, adding the important caveat: “The off-the-line observations are managers with short track records or managers using option strategies.”

And there's the rub that this all boils down to: it depends on strategy.

For a plain vanilla stock or bond fund, the kind most investors – especially a Boglehead audience – are dealing with, Sharpe, Sortino, and Calmar will score it nearly identically to each other, so use whichever is available. (I realize this is largely moot anyway because tools nowadays are going to report all 3 plus more that you can easily glance at simultaneously.)

The small percentage of cases where these metrics meaningfully disagree are the areas where the disagreement matters most: option-selling strategies, tail-risk products, funds with short track records, leveraged instruments, and anything with smoothed or appraised valuations (private equity, interval funds, non-traded REITs).

For those, get out the full toolkit, use all 3 metrics, look at the actual return distribution, and treat any suspiciously high Sharpe with extra skepticism.

Like I hinted at earlier, think of these not as “this one instead of that one,” but rather “this one in addition to that one.”

We basically came around full circle at this point. Sharpe is the most popular > Sharpe is the worst > Sharpe is perfectly acceptable for most situations.

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

As you've now seen, risk-adjusted return 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.

References

Auer, B. R. (2013). The low return distortion of the Sharpe ratio. Financial Markets and Portfolio Management, 27(3), 273–296.

Eling, M. (2008). Does the measure matter in the mutual fund industry? Financial Analysts Journal, 64(3), 54–66.

Eling, M., & Schuhmacher, F. (2007). Does the choice of performance measure influence the evaluation of hedge funds? Journal of Banking & Finance, 31(9), 2632–2647.

Goetzmann, W., Ingersoll, J., Spiegel, M., & Welch, I. (2007). Portfolio performance manipulation and manipulation-proof performance measures. Review of Financial Studies, 20(5), 1503–1546.

Lo, A. W. (2002). The statistics of Sharpe ratios. Financial Analysts Journal, 58(4), 36–52.

Martin, P., & McCann, B. (1989). The investor's guide to Fidelity funds: Winning strategies for mutual fund investors. John Wiley & Sons.

Rollinger, T., & Hoffman, S. (2013). Sortino: A “sharper” ratio. Red Rock Capital.

Sharpe, W. F. (1966). Mutual fund performance. Journal of Business, 39(S1), 119–138.

Sharpe, W. F. (1994). The Sharpe ratio. Journal of Portfolio Management, 21(1), 49–58.

Sortino, F. A., & van der Meer, R. (1991). Downside risk: Capturing what's at stake in investment situations. Journal of Portfolio Management, 17(4), 27–31.

Young, T. W. (1991). Calmar ratio: A smoother tool. Futures, 20(12), 40.

Interested in more Lazy Portfolios? See the full list here.

Disclaimer:  While I love diving into investing-related data and playing around with backtests, this is not financial advice, investing advice, or tax advice. The information on this website is for informational, educational, and entertainment purposes only. Investment products discussed (ETFs, mutual funds, etc.) are for illustrative purposes only. It is not a research report. It is not a recommendation to buy, sell, or otherwise transact in any of the products mentioned. I always attempt to ensure the accuracy of information presented but that accuracy cannot be guaranteed. Do your own due diligence. I mention M1 Finance a lot around here. M1 does not provide investment advice, and this is not an offer or solicitation of an offer, or advice to buy or sell any security, and you are encouraged to consult your personal investment, legal, and tax advisors. Hypothetical examples used, such as historical backtests, do not reflect any specific investments, are for illustrative purposes only, and should not be considered an offer to buy or sell any products. All investing involves risk, including the risk of losing the money you invest. Past performance does not guarantee future results. Opinions are my own and do not represent those of other parties mentioned. Read my lengthier disclaimer here.