Sortino vs Sharpe Ratio: Formulas, a Worked Example and When to Use Each

The Sortino vs Sharpe ratio comparison comes down to one question: how should risk be measured? Both ratios show how much return an investment earned for each unit of risk it took. The Sharpe ratio divides excess return by total volatility, so a large gain counts as risk just like a large loss. The Sortino ratio divides by downside deviation, which only counts returns that fall below a target you choose.

That one difference can change which of two funds looks better, as the worked example below shows.

Sortino vs Sharpe ratio: the key difference

• Nearly the same numerator. Sharpe uses the return above the risk-free rate; Sortino uses the return above a minimum acceptable return (MAR). Set the MAR to the risk-free rate and the numerators are identical.
• Different denominator. Sharpe uses the standard deviation of all returns. Sortino uses downside deviation, built only from shortfalls below the target.
• Different view of a good year. For Sharpe, a +25% year and a −25% year both raise the risk figure. For Sortino, only the −25% year does.

The Sharpe ratio formula

Introduced by William F. Sharpe in 1966, the Sharpe ratio measures excess return per unit of total volatility:

Sharpe ratio = (Rp − Rf) / σp

• Rp: average return of the portfolio over the period
• Rf: risk-free rate over the same period, for example a short-term Treasury bill yield
• σp: standard deviation of the portfolio’s returns (strictly, of its excess returns; the two are identical when the risk-free rate is constant)

A higher ratio means more excess return per point of volatility. The Sharpe ratio uses every observation and is central to modern portfolio theory, which often looks for the mix of assets with the highest Sharpe ratio. Its limits:

• It penalizes upside volatility exactly like downside volatility, so a fund with a few very strong years can look riskier than one with steady, mediocre returns.
• It treats standard deviation as a full description of risk, which works best when returns are roughly symmetric. With skewed returns (option strategies, concentrated growth portfolios, some hedge funds) it can mislead in either direction.
• It depends on the period measured. Three calm years say little about how a portfolio behaves in a crisis.

The Sortino ratio formula

The Sortino ratio, named after Frank A. Sortino, whose work on downside risk made it widely known, keeps the same logic but replaces total volatility with downside deviation:

Sortino ratio = (Rp − MAR) / DD

• Rp: average return of the portfolio
• MAR: minimum acceptable return, the target below which a result counts as a shortfall (often 0%, the risk-free rate or a required return)
• DD: downside deviation, the typical size of the shortfalls below the MAR

How to calculate downside deviation

DD = √( Σ min(0, Ri − MAR)² / n )

1. For each period, compute the shortfall: Ri − MAR if the return is below the MAR, otherwise 0.
2. Square each shortfall.
3. Add the squares and divide by n, the total number of periods, including those with no shortfall.
4. Take the square root.

A common mistake is to take the standard deviation of the negative returns only. That measures how much the losses differ from one another, not how large they are: a fund that lost exactly 10% in each of three bad years would show a “deviation” of zero and an infinite Sortino ratio.

Choosing the target return (MAR)

The MAR changes the result: a higher target turns more periods into shortfalls and lowers the ratio. Use the risk-free rate to line Sortino up with Sharpe, 0% if your concern is losing money, or your required return to test a portfolio against a goal.

Worked example: two funds with the same average return

Take two hypothetical funds over ten years. Both average 9% a year (simple average). The risk-free rate is 3% a year and the MAR is set equal to it, so both ratios share the same numerator. The figures are illustrative, not data from real funds.

Year	Fund A	Fund B
1	21%	28%
2	−6%	4%
3	15%	−2%
4	3%	26%
5	18%	6%
6	−2%	3%
7	12%	27%
8	22%	−4%
9	−9%	−1%
10	16%	3%
Average	9%	9%

Step 1: excess return

For both funds: 9% − 3% = 6 percentage points.

Step 2: Sharpe ratio

Standard deviation measures how far each year lands from the 9% average. For Fund A, the squared deviations add up to 1,194; divided by 10 years, that is a variance of 119.4 and a standard deviation of 10.93%. For Fund B, they add up to 1,470: a variance of 147 and a standard deviation of 12.12%.

Sharpe A = 6 / 10.93 = 0.55
Sharpe B = 6 / 12.12 = 0.49

Step 3: Sortino ratio

Only shortfalls below the 3% MAR count. Fund A has three: −6% (9 points below the target), −2% (5 points) and −9% (12 points). Squared and added: 81 + 25 + 144 = 250; divided by 10: 25; square root: 5.0%. Fund B’s shortfalls are −2% (5 points), −4% (7 points) and −1% (4 points): 25 + 49 + 16 = 90; divided by 10: 9; square root: 3.0%. Years at or above 3% count as zero.

Sortino A = 6 / 5.0 = 1.20
Sortino B = 6 / 3.0 = 2.00

Measure	Fund A	Fund B
Standard deviation	10.93%	12.12%
Downside deviation (MAR 3%)	5.00%	3.00%
Worst year	−9%	−4%
Sharpe ratio	0.55	0.49
Sortino ratio	1.20	2.00

What the example shows

The two ratios rank the funds in opposite order. Sharpe prefers Fund A because Fund B’s returns are more spread out, but that spread comes from its best years (+28%, +27%, +26%). Sortino looks only at the shortfalls, where Fund B is clearly milder. If your concern is the size of losses, Sortino gives the more relevant ranking; if you need to know how far a year can land from the average in either direction, Sharpe still matters.

Two caveats. We divided by n (10) throughout; a spreadsheet’s STDEV.S divides by n − 1 and gives 11.52% and 12.78%, so Sharpe ratios of 0.52 and 0.47. And ten years of data is far too little to judge a real fund. With monthly data, convert the MAR and the risk-free rate to monthly figures (3% a year is about 0.25% a month), then annualize the monthly ratio by multiplying it by √12 (about 3.46), a convention that assumes independent monthly returns.

When the Sortino ratio is the better measure

• Returns are clearly skewed: concentrated growth portfolios, strategies with occasional large gains, funds that use options to limit losses.
• You care about a specific threshold, such as not losing money or earning the return a plan requires. The MAR builds that threshold into the ratio.
• You compare funds whose upside volatility differs a lot and do not want strong years to count against a fund.

When the Sharpe ratio is the better measure

• Returns are roughly symmetric, as with broad diversified equity or balanced funds, where both ratios usually tell a similar story.
• You have little data. Standard deviation uses every observation; downside deviation rests on the below-target periods, which may be few.
• You are building or combining portfolios. Mean-variance analysis works with standard deviations and correlations.
• You need a widely published figure. Many fund factsheets show a Sharpe ratio; Sortino is less standard and its MAR is not always disclosed.

Often the best answer is to read both, together with maximum drawdown. The gap between them is informative too: Sortino ends up far above Sharpe when few periods fall below the target or when most of the swings come from strong periods, as with Fund B; when the two are close, below-target results drive most of the variability.

Sharpe vs Sortino vs Calmar vs Treynor

Each ratio in this family keeps return on top and puts a different definition of risk underneath.

Ratio	Formula	Risk measure	Most useful for	Main blind spot
Sharpe	(Rp − Rf) / σp	Standard deviation of all returns	Diversified portfolios with roughly symmetric returns	Treats gains as risk
Sortino	(Rp − MAR) / DD	Downside deviation below a chosen target	Skewed returns; investors with a minimum return goal	Depends on the MAR; unstable with few shortfalls
Calmar	Annualized return / |max drawdown|	Largest peak-to-trough loss, classically over 36 months	Strategies judged on their worst loss, such as managed futures	Rests on a single episode and on the window chosen
Treynor	(Rp − Rf) / βp	Beta (market, or systematic, risk)	A diversified portfolio held within a larger one	Ignores diversifiable risk; meaningless when beta is near zero or negative

The Calmar ratio, introduced by Terry W. Young in 1991, asks a blunter question than Sortino: how much annual return per point of worst historical loss? Sortino looks at every below-target period; Calmar looks at one worst stretch. Our guide to the Calmar ratio covers its calculation. The Treynor ratio, proposed by Jack Treynor in 1965, divides excess return by beta, which only makes sense for a portfolio that is already diversified; see the Treynor ratio explainer. For the Sharpe ratio on its own, read our Sharpe ratio guide.

Pitfalls when comparing risk-adjusted ratios

• Compare like with like: same period, same data frequency, same risk-free rate and, for Sortino, the same MAR. Factsheets do not always state these choices. Never set one fund’s Sortino against another fund’s Sharpe: the Sortino figure is normally the larger one.
• Watch for hidden tail risk. A strategy that sells insurance-like options can show smooth returns and high Sharpe and Sortino ratios until a rare large loss arrives. If that loss is not in the sample, neither ratio sees it.
• Both ratios describe the past. They summarize how a return path behaved, not how it will behave.

Where risk ratios fit in stock research

Sharpe and Sortino ratios are mostly used to compare portfolios and funds. Applied to a single stock, they describe its past return path but say nothing about whether the price is above or below what the business is worth. In our scanner, risk is one input among several: the 15% risk component looks at leverage, liquidity, volatility, downside risk, missing data and accounting warning signs, next to valuation, quality, growth and technical context. The scoring methodology explains how these components are combined to help prioritize deeper research, not to recommend trades.

Frequently asked questions

Is the Sortino ratio better than the Sharpe ratio?

Not in every case. Sortino is more informative when returns are skewed or when falling short of a specific target is what matters, because it does not count strong gains as risk. Sharpe is more robust with short histories and roughly symmetric returns.

What is a good Sharpe and Sortino ratio?

There is no universal threshold. As a rough rule of thumb, a Sharpe ratio above 1 is often called good. Sortino figures run higher for the same fund: with the target at the risk-free rate, a Sortino ratio of 1 means a Sharpe ratio of 1 or lower. Both depend on the period, the data frequency and the target, so compare them only with peers calculated the same way.

Why is the Sortino ratio usually higher than the Sharpe ratio?

When the target equals the risk-free rate and the average return is above it, downside deviation cannot be larger than standard deviation, because it leaves out every above-target swing. Same numerator, smaller denominator: the Sortino ratio comes out at least as high as the Sharpe ratio.

How do you calculate the Sortino ratio in Excel?

Put the returns in A2:A11 and the target (here also the risk-free rate) in B1. In C1, calculate downside deviation with =SQRT(SUMPRODUCT((A2:A11<B1)*(A2:A11-B1)^2)/COUNT(A2:A11)). The Sortino ratio is then =(AVERAGE(A2:A11)-B1)/C1 and the Sharpe ratio =(AVERAGE(A2:A11)-B1)/STDEV.P(A2:A11). With Fund A’s returns and 3% in B1, C1 shows 5% and the Sortino ratio 1.20.

Are Sharpe and Sortino ratios used for mutual funds?

Yes. Many fund factsheets and data platforms show a Sharpe ratio, and some also show a Sortino ratio. Compare them only between funds in the same category, over the same window and from the same source.

Educational content, not investment advice.