Which risk-adjusted return ratio is the most useful?

The one whose definition of risk matches the question. To compare volatility-targeted strategies, the Sharpe ratio; to compare portfolios with skewed returns, Sortino or Omega; to judge how painful a strategy was to hold, the Calmar ratio or the Ulcer performance index. Reading two or three together, over the same window, shows more than any one of them.

Why can the Sortino ratio rank two portfolios differently from the Sharpe ratio?

Because it ignores months above the target. A portfolio whose volatility comes mostly from large gains is marked down by the Sharpe ratio and not by the Sortino ratio, so it moves up the Sortino ranking.

Is the Calmar ratio better than the Sharpe ratio for drawdowns?

It is closer to what investors feel in a crash, because it uses the deepest fall rather than average volatility. But it rests on one event, so it is noisier, and it ignores how long the portfolio stayed down; the Ulcer index covers duration.

Can I compare ratios from different websites?

Only after checking the conventions: risk-free rate or threshold, data frequency, annualization, sample or population standard deviation, and the window. MarketHeist uses 0, monthly data, √12 for Sharpe and Sortino, and the whole window for Calmar and Ulcer; other sources differ on each.

Sharpe, Sortino, Omega, Calmar and Ulcer ratios compared

By Jeffrey Lin · Published 2026-11-08 · Updated 2026-11-08 · Data through Sep 2026

On this page

Key takeaways

Every ratio here has the same shape, return over risk, and the same weakness: it is only as good as its definition of risk, and each one leaves something out.
The Sharpe ratio counts all volatility, up and down; the Sortino ratio counts only months below a target and gives large shortfalls extra weight; Omega counts every shortfall at its plain size. For roughly symmetric returns the three rank portfolios alike.
The Calmar ratio compares growth with the deepest decline, one event; the Ulcer performance index compares it with the Ulcer index, which counts every month spent below a previous high. They answer how painful the path was, which the first three do not.
None of them says how reliable the number is. The probabilistic Sharpe ratio adds that, using the track record's length and how lopsided and fat-tailed its returns are.
MarketHeist computes all of them on monthly total returns with no interest on cash subtracted and a threshold of zero; Sharpe and Sortino are quoted as yearly figures, Omega is not, and Calmar and Ulcer use the whole window.

Definition

A risk-adjusted return ratio divides a portfolio's return by a measure of the risk taken to earn it, so portfolios with different risk can be ranked on one scale. The common ratios differ in what they count as risk: all volatility (Sharpe), returns below a target (Sortino, Omega), the single worst decline (Calmar), or the depth and length of every decline (Ulcer performance index).

Also known as: risk-adjusted return, Sharpe vs Sortino vs Calmar, Sharpe vs Omega, Martin ratio vs Sharpe, which risk-adjusted ratio to use, return per unit of risk.

How it works

All five start from the same question: how much did a portfolio earn for the risk it took? They agree on the numerator, more or less, and disagree on the denominator. That choice is the whole difference between them, so the useful question about each ratio is what it treats as risk and what it ignores.

The Sharpe ratio (1966) divides the average return by the standard deviation of all returns. A large gain raises the standard deviation as much as a large loss, so the ratio penalizes upside surprises. The Sortino ratio (1994) keeps only the months below a target, squares their shortfalls and averages them; upside surprises cost nothing, and a few large losses cost a lot. The Omega ratio (2002) sets the total of all gains above a threshold against the total of all shortfalls below it, each at its plain size. Kaplan and Knowles (2004) showed that the Sortino ratio and Omega minus 1 are two members of one family: the same excess return divided by a lower partial moment of order 2 or 1.

The next two measure risk along the path instead of month by month. The Calmar ratio (1991) divides the compound annual growth rate by the maximum drawdown, the deepest fall from a peak; one event decides the denominator, and a second decline of the same depth costs nothing extra. The Ulcer performance index, or Martin ratio, divides growth by the Ulcer index (1987), the root mean square of the percentage drawdown in every month, so it charges for every month below a previous high, by how far below it was.

Choosing among them is like rating cars by fuel economy, by how hard they brake, or by how they did in a crash test: each measure is correct about what it measures, and a buyer who cares about crashes learns little from fuel economy.

In practice the ratios usually agree on large differences, a balanced portfolio against a stock index, and disagree on close calls; Eling and Schuhmacher (2007) found rankings of hedge funds by the Sharpe ratio and a dozen alternatives to be highly correlated. The disagreements carry information: a portfolio that ranks higher on Sortino than on Sharpe has had its volatility on the upside; one that ranks well on Sharpe and poorly on Calmar had a calm record broken by one deep fall. None of the five says whether the figure would hold up in another period; the probabilistic Sharpe ratio turns a Sharpe ratio into a probability that its true value beats a benchmark.

Formula

The five ratios as MarketHeist computes them (monthly returns, risk-free rate and threshold 0)

\begin{array}{l} Sharpe = \frac{\bar{r}}{s} \sqrt{12} & Sortino = \frac{\bar{r}}{\sqrt{\frac{1}{N} \sum \min {(r_{t}, 0)}^{2}}} \sqrt{12} \\ Ω = \frac{\sum \max (r_{t}, 0)}{\sum \max (- r_{t}, 0)} & Calmar = \frac{CAGR}{| MDD |}, UPI = \frac{CAGR}{UI / 100} \end{array}

rₜ, r̄: monthly total return in month t and its arithmetic mean
s: sample standard deviation of the monthly returns (divides by N − 1)
N: number of months
Ω: Omega ratio at a 0% monthly threshold, not annualized
CAGR: compound annual growth rate over the whole window
MDD: maximum drawdown over the whole window, the deepest fall from a running peak
UI: Ulcer index in percent: the root mean square of the monthly percentage drawdowns
UPI: Ulcer performance index (Martin ratio) at a risk-free rate of 0

One family: Kappa ratios (Kaplan and Knowles 2004)

K_{n} (L) = \frac{μ - L}{\sqrt[n]{E [\max {(L - R, 0)}^{n}]}}, Ω (L) = 1 + K_{1} (L), Sortino = K_{2} (L)

Kₙ(L): Kappa ratio of order n at threshold L
μ: mean period return
L: threshold or target return per period
E[max(L − R, 0)ⁿ]: lower partial moment of order n: the average shortfall below L raised to the power n

Order 1 weighs each shortfall by its size, order 2 by its size squared; a higher order punishes the largest losses more. The Sortino ratio here is per period, before the √12 annualization.

Worked example

Gold (GLD) and the S&P 500 (SPY), 262 monthly total returns from Dec 2004 to Sep 2026, with the probabilistic Sharpe ratio tested against an annualized Sharpe ratio of 0.50.

Over these months gold and the S&P 500 grew at almost the same rate, 10.3% and 10.9% a year, but gold swung more: its volatility was 17.3% against 14.8%. The ratios built on monthly returns put the S&P 500 ahead. Its Sharpe ratio was 0.78 against 0.65 for gold, and its Omega ratio 1.79 against 1.62.

The Sortino ratio narrowed the gap: 1.20 for the S&P 500 against 1.10 for gold, relatively closer than their Sharpe ratios. Gold's monthly returns were close to symmetric, a skew of 0.00, while the S&P 500's leaned toward large falls, a skew of -0.56. Much of gold's extra volatility was on the upside, which the Sharpe ratio charges for and the Sortino ratio does not.

The probabilistic Sharpe ratio asks a different question: how likely is the true Sharpe ratio above 0.50, given 262 months and the shape of the returns? It was 88.7% for the S&P 500 and 76.0% for gold. Neither reached 95%: over this record, neither Sharpe ratio can be told apart from 0.50 with that confidence.

The Calmar ratio and the Ulcer performance index are computed from the path of each fund's value, which this lab leaves out. The Ulcer index guide works through gold and the S&P 500 over these months, and the Calmar ratio guide explains how a single deep decline can reorder portfolios that the ratios above rank one way.

Data through Sep 2026. Reproduce id 59437083bb604652 (this guide, its lab setup and the data month).

Interactive lab

Sharpe, Sortino and Omega ratios, the probabilistic Sharpe ratio, skew and kurtosis for both picks over the same months. Switch portfolios to find pairs the ratios rank the same way and pairs they split on.

Annualized Sharpe and Sortino ratios of monthly returns. Dec 2004 to Sep 2026.

Probability that the true Sharpe ratio exceeds 0.50 as the record grows. The dashed line marks 95%.

Measure	GLD	SPY
Sharpe ratio	0.65	0.78
Sortino ratio	1.10	1.20
Probabilistic Sharpe ratio (against 0.50)	76.0%	88.7%
Skewness of monthly returns	0.00	-0.56
Excess kurtosis of monthly returns	0.22	1.26
Downside deviation (annualized)	10.3%	9.6%
Volatility (annualized)	17.3%	14.8%
Average return (mean monthly return x 12)	11.3%	11.5%
CAGR	10.3%	10.9%
Volatility drag (annualized)	1.5%	1.1%
Omega ratio (threshold 0%)	1.62	1.79
Months in the window	262	262

Risk-free rate 0, 12 periods a year. The probabilistic Sharpe ratio is the probability that the true Sharpe ratio exceeds the benchmark, given the record's length, skewness and kurtosis. Volatility drag: 12 times the arithmetic mean monthly return minus the geometric mean monthly return. Omega ratio: the sum of the monthly gains over the sum of the monthly losses, at a threshold of 0% a month. Dec 2004 to Sep 2026.

How MarketHeist computes it

Every choice an implementation has to make, as the code makes it today. The page is checked against the code each time it is built.

Choice	How it is computed	In the code
Data	Monthly total returns (dividends reinvested). Funds younger than the period shown are extended backward with older funds, spliced on returns, not prices.
Window	The worked example and the lab use the common window of the two portfolios compared, Dec 2004 to Sep 2026 (262 months), ending at the data month of this page. Another pick in the lab is read over its own common window.
Portfolio streams	A fund is its proxy-extended monthly return stream. A built-in portfolio is read as the MarketHeist MCP reads it: its composed stream with its own rebalancing rule and overlay. A custom mix is rebalanced yearly.
Ratios	Risk-free rate 0, 12 periods a year. Sharpe: mean of the monthly returns over their sample standard deviation, times the square root of 12. Sortino: the same mean over the downside deviation, the root of the average squared negative return over all N months. The probabilistic Sharpe ratio uses the per-period Sharpe ratio, the skewness and the kurtosis of the monthly returns; the benchmark Sharpe ratio is divided by the square root of 12 first.
Sharpe ratio	Mean monthly return over the sample standard deviation (N − 1), times √12; risk-free rate 0.	`sharpe`packages/shared/engine/metrics.ts
Sortino ratio	Mean monthly return over the downside deviation, the square root of the mean of min(r, 0)² over all N months, times √12; target 0.	`sortino`packages/shared/engine/metrics.ts
Omega ratio	Sum of the positive monthly returns over the absolute sum of the negative ones (threshold 0), not annualized; infinite with no losing month.	`omega`packages/shared/engine/metrics.ts
Calmar ratio	CAGR over the absolute maximum drawdown, both over the whole window (the MAR ratio in effect), not Young's trailing 36 months.	`calmar`packages/shared/engine/metrics.ts
Ulcer performance index	CAGR divided by the Ulcer index as a fraction, at a risk-free rate of 0. The Ulcer index is the root mean square of the monthly percentage drawdowns from the running peak since the window began.	`ulcerIndex`packages/portfolio/engine/metrics_extra.ts
Probabilistic Sharpe ratio	Probability that the true per-month Sharpe ratio exceeds the benchmark divided by √12, from the observed Sharpe ratio, the number of months, skewness and kurtosis (Bailey and López de Prado 2012).	`probabilisticSharpeRatio`packages/shared/engine/metrics.ts
Engine functions	The functions the portfolio app and the MarketHeist MCP tools run, called here on the same monthly returns.	`sharpe`packages/shared/engine/metrics.ts`sortino`packages/shared/engine/metrics.ts`probabilisticSharpeRatio`packages/shared/engine/metrics.ts`skewness`packages/shared/engine/metrics.ts`excessKurtosis`packages/shared/engine/metrics.ts

Risk-adjusted return ratios compared (Sharpe, Sortino, Omega, Calmar, Ulcer) compared with its neighbours

What each ratio counts as risk
Ratio	Risk in the denominator	Large gains count as risk	Order of returns matters	Use it to see
Sharpe	Standard deviation of all returns	Yes	No	Return per unit of overall swing
Sortino	Downside deviation below a target (squared shortfalls)	No	No	Return per unit of bad months, large ones weighted most
Omega	Average shortfall below a threshold	No	No	Total gains against total shortfalls
Calmar (MAR)	Maximum drawdown	No	Yes	Growth per unit of the single worst fall
Ulcer performance index (Martin)	Ulcer index: depth and length of every decline	No	Yes	Growth per unit of time spent below a high
Probabilistic Sharpe ratio	Not a ratio: the probability the true Sharpe ratio beats a benchmark	Inherits Sharpe's	No	Whether a Sharpe ratio is distinguishable from luck

Limitations

Each ratio is an estimate from one history. Over a few years a ratio's error band is wide, and none of the ratios except the probabilistic Sharpe ratio reports it.
The risk-free rate of 0 raises every ratio and favours low-volatility holdings most; subtracting a Treasury-bill rate can reverse rankings between bonds and stocks, especially for Sharpe, Sortino and Omega.
Calmar depends on one event and on the window: a window that starts after a crash gives a very different figure from one that includes it.
A single ratio cannot judge a holding inside a portfolio. A hedge that loses a little most months has poor ratios on its own and can still lower the risk of the portfolio that holds it; risk contribution measures that.
Long histories are extended backward with older funds or indexes where a fund is younger than the window, so early months approximate the fund rather than reproduce it.

Frequently asked questions

Which risk-adjusted return ratio is the most useful?: The one whose definition of risk matches the question. To compare volatility-targeted strategies, the Sharpe ratio; to compare portfolios with skewed returns, Sortino or Omega; to judge how painful a strategy was to hold, the Calmar ratio or the Ulcer performance index. Reading two or three together, over the same window, shows more than any one of them.
Why can the Sortino ratio rank two portfolios differently from the Sharpe ratio?: Because it ignores months above the target. A portfolio whose volatility comes mostly from large gains is marked down by the Sharpe ratio and not by the Sortino ratio, so it moves up the Sortino ranking.
Is the Calmar ratio better than the Sharpe ratio for drawdowns?: It is closer to what investors feel in a crash, because it uses the deepest fall rather than average volatility. But it rests on one event, so it is noisier, and it ignores how long the portfolio stayed down; the Ulcer index covers duration.
Can I compare ratios from different websites?: Only after checking the conventions: risk-free rate or threshold, data frequency, annualization, sample or population standard deviation, and the window. MarketHeist uses 0, monthly data, √12 for Sharpe and Sortino, and the whole window for Calmar and Ulcer; other sources differ on each.

References

Sharpe, W. F. (1966) Mutual Fund Performance. Journal of Business 39(1). The reward-to-variability ratio.
Sortino, F. A. and Price, L. N. (1994) Performance Measurement in a Downside Risk Framework. Journal of Investing 3(3).
Keating, C. and Shadwick, W. F. (2002) A Universal Performance Measure. Journal of Performance Measurement 6(3). The Omega function.
Young, T. W. (1991) Calmar Ratio: A Smoother Tool. Futures 20(1).
Martin, P. G. and McCann, B. B. (1989) The Investor's Guide to Fidelity Funds. Wiley. The Ulcer index and the Ulcer performance index.
Eling, M. and Schuhmacher, F. (2007) Does the Choice of Performance Measure Influence the Evaluation of Hedge Funds?. Journal of Banking and Finance 31(9). Rankings by Sharpe, Calmar, Omega, Sortino and other ratios compared.
Kaplan, P. D. and Knowles, J. A. (2004) Kappa: A Generalized Downside Risk-Adjusted Performance Measure. Journal of Performance Measurement 8(3). Omega and Sortino as members of one family.
Bailey, D. H. and López de Prado, M. (2012) The Sharpe Ratio Efficient Frontier. Journal of Risk 15(2). The probabilistic Sharpe ratio.

Try it on your own holdings

Compare portfolios side by side on these ratios →

Or ask an assistant connected to the MarketHeist MCP server (https://marketheist.io/mcp), which computes the same figures:

Using MarketHeist.io, compare GLD and SPY over the same months on the Sharpe, Sortino, Omega and Calmar ratios and the Ulcer index, and explain why the ratios that ignore upside volatility narrow the gap.

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The prompt opens in a new tab, already filled in. An assistant without the MarketHeist connector answers from its own knowledge, not from the figures on this page.

Historical simulation, not advice. Computed by the MarketHeist portfolio engine from monthly total returns, data through Sep 2026. Markdown version of this page: risk-adjusted-ratios.md.