How to use the sortino, calmar and omega ratio calculator
- Paste the returns for each period, oldest first, as percentages. Separate them with commas, spaces or line breaks. The example holds twelve months.
- Enter the minimum acceptable return for one period. Zero counts every loss as downside. A positive target also counts a gain that falls short of it.
- Choose how many periods make a year, so the page can annualize the Sortino ratio and the compound return.
- Read the Sortino, Omega and Calmar ratios, the downside deviation and the largest drawdown, then look through the table of periods to see which ones caused the damage.
Formula
downside deviation = square root of (sum of min(0, return - target)^2 / n)
Sortino ratio = (mean return - target) / downside deviation
Omega ratio = sum of (return - target) above the target / sum of (target - return) below it
Calmar ratio = annualized compound return / largest peak-to-trough drop
The downside deviation squares each shortfall, adds them and divides by all n periods, including the periods that did not fall short. The annualized Sortino ratio is the per-period ratio times the square root of the periods in a year.
Twelve months of returns
The twelve returns in the page add up to 8.6 percent, a mean of 0.7167 percent a month. Four months fall below zero: -1.4, -3.5, -0.6 and -2.2 percent. Their squares add up to 19.41, so the downside deviation is the square root of 19.41 / 12, which is 1.2718 percent. The Sortino ratio is 0.7167 / 1.2718 = 0.5635 a month, or 1.95 after multiplying by the square root of 12.
The gains above zero add up to 16.3 percentage points and the shortfalls to 7.7, so the Omega ratio is 2.12. Compounding the twelve months gives 8.64 percent, and the deepest drop from a peak is 3.5 percent, so the Calmar ratio is 8.64 / 3.5 = 2.47.
Why downside ratios exist
The Sharpe Ratio Calculator divides excess return by the standard deviation of all returns, so a surprisingly large gain raises the risk figure just as a surprisingly large loss does. Most people do not mind upside surprises. The Sortino ratio keeps the same idea but measures risk only from the returns that fall below a target you choose.
The Omega ratio goes a step further and compares the total of everything above the target with the total of everything below it, so it uses the whole shape of the returns rather than one summary number. The Calmar ratio asks a different question: how much return did you earn for the worst drop you had to sit through?
Reading the table of periods
The Shortfall column shows how far each period fell below the target, and it is zero when the period met it. Those are the numbers that feed the downside deviation. The Drawdown column shows how far the compounded value sits below its highest earlier value after each period, which is where the largest drawdown comes from.
Use the table to check the ratios by hand. If one period explains most of the downside deviation, a single bad month is driving the answer, and the ratio will move a lot if you add or drop one observation. A short series gives unstable ratios, and the Drawdown Recovery Calculator shows what gain it takes to get back after a drop.
Choices that change the answer
The target matters most. A target of zero and a target equal to the risk-free rate for the period give different downside deviations from the same returns. The way you annualize also differs between sources, and some compute the Calmar ratio over the last 36 months only. Compare ratios only when they were built the same way.
Assumptions and limits
- Returns are percentages for equal-length periods, oldest first. They are compounded as entered, so contributions and withdrawals are not modeled.
- The downside deviation divides by all n periods. Some sources divide by the number of periods below the target, which gives a larger figure.
- The annualized Sortino ratio multiplies the per-period ratio by the square root of the periods in a year. The annual return compounds the whole series and scales it to a year.
- The Calmar ratio uses the largest drawdown of the whole series you entered, measured on the compounded value.
- Nothing typed here leaves your browser.
Frequently asked questions
Why does the page sometimes say the Sortino ratio is not defined?
When no return falls below the target there is no downside deviation, and dividing by zero has no meaning. The page says so instead of showing a huge number. The Omega and Calmar ratios can have no value for the same reason, when there are no shortfalls or no drawdown.
Can I use daily returns?
Yes. Pick 252 periods in a year for trading days. The annualized Sortino ratio then uses the square root of 252, and the annual return compounds the days you entered and scales them to one year.
Is a higher Calmar ratio always better?
Not by itself. A short series with one small drop can give a very large Calmar ratio, and a long series with a deep drop gives a small one. Compare series of similar length and similar market conditions.
What should the minimum acceptable return be?
It is the return per period below which you count a result as a miss. Zero, the risk-free rate for the period and the return needed to reach a goal are all reasonable choices, and each one tells you something different.