What Is Sortino Ratio and How Is It Different From Sharpe?

In short. The Sortino ratio is the average return above a target, divided by the downside deviation – a measure of how far and how often returns fell below that target. Unlike the Sharpe ratio, it does not penalize large winning periods. It is most useful when a strategy's results are lopsided, but it is easy to miscalculate: the downside deviation must be averaged over all periods, not only the losing ones.

The Sharpe ratio answers one question well: how much return a strategy produced per unit of volatility. Its weak spot is that it treats a big up month and a big down month as the same kind of risk. The Sortino ratio was built to fix that one thing, and the fix changes how two strategies with the same average return can rank against each other.

The formula

The Sortino ratio follows the same structure as the Sharpe ratio, with two substitutions. As a CFA Institute article on the measure puts it, the minimum acceptable return (MAR) replaces the risk-free rate in the numerator, and downside deviation replaces standard deviation in the denominator:

Sortino ratio = (average period return – target return) / target downside deviation

The target is chosen by the person doing the measuring. It can be 0% (no tolerance for losing money in a period), the risk-free rate, or a required return such as a monthly goal. The ratio is named after Frank Sortino, and the original framework was set out by Sortino and Price in the Journal of Investing in 1994.

Downside deviation is not "standard deviation of the losses"

Target downside deviation is the root-mean-square of each period's shortfall below the target. Periods at or above the target count as a shortfall of zero, and those zeros stay in the average. Rollinger and Hoffman's paper "Sortino: A 'Sharper' Ratio", hosted by CME Group, lists the two differences from standard deviation:

• Reference point: deviations are measured from the target, not from the average of all returns.
• Zeros are kept: every return above the target becomes 0, but it still counts in the number of periods you divide by.

That second point is where most errors come from. The same paper says the authors had seen downside deviation calculated incorrectly "more often than not", most often by throwing away the positive returns and taking the standard deviation of the negative ones.

A worked example from a trading journal

Take the same six months of net returns used in the Sharpe ratio walkthrough: +4.2%, -1.8%, +3.1%, +0.5%, -2.4%, +5.0%, with a target of 0%.

1. Average return minus target: 1.43% – 0% = 1.43%.
2. Shortfall below target for each month: 0, -1.8, 0, 0, -2.4, 0.
3. Square each shortfall: 0, 3.24, 0, 0, 5.76, 0. The sum is 9.00.
4. Divide by all six months, not by the two losing ones: 9.00 / 6 = 1.50.
5. Take the square root: downside deviation of about 1.22%.
6. Sortino ratio: 1.43 / 1.22 = about 1.17 per month.

For the same series, the sample standard deviation is about 3.14%, so the monthly Sharpe ratio is about 0.46. The Sortino ratio comes out higher because most of the volatility in this series came from the winning months.

Here is how much the calculation mistakes move the result on these same six numbers (our own arithmetic):

The third method nearly triples the result. On a short track record with few losing months, it can make an ordinary strategy look exceptional.

Why the target return matters

Change the target and the ratio changes with it. With a target of 0.5% per month instead of 0%, the same series has a numerator of 0.93% and a downside deviation of about 1.51%, because the +0.5% month now counts as a small shortfall too. The Sortino ratio drops to about 0.62.

Neither number is wrong. The point is that a Sortino ratio is meaningless without its target. The CFA Institute article notes that funds can only be compared on this ratio when each one uses the same MAR, and Rollinger and Hoffman make the same point for comparing trading systems. In a personal journal, pick one target, write it down next to the ratio, and keep it fixed.

Sortino vs Sharpe: same average return, different ranking

The difference between the two ratios shows up most clearly on strategies with the same average return but differently shaped results. All three series below average 1.43% per month (illustrative numbers, target 0%):

By Sharpe, B looks better than C. By Sortino, C is far ahead and B is last. The Sharpe ratio penalizes C for its +9.4% month, because standard deviation does not care which direction a swing goes. Rollinger and Hoffman describe the same effect on positively skewed strategies such as trend following: removing the largest winning returns can raise the Sharpe ratio, which makes little sense to anyone who actually holds the account.

Strategy B is the case to watch. Its steady months make the equity curve look calm until the one large loss. Rollinger and Hoffman point to option-selling programs as a typical example of this negatively skewed profile, and it is exactly where a single number based on symmetric volatility understates the real risk.

Reading the two ratios side by side is more useful than picking one. A Sortino ratio far above the Sharpe ratio means most of the volatility was on the upside. Ratios that sit close together mean the swings were roughly balanced. The CFA Institute article makes the same suggestion: comparing the two shows what portion of the volatility came from outperformance versus underperformance.

Annualizing: handle with care

Many analytics tools annualize a monthly Sortino ratio the same way as a Sharpe ratio, by multiplying by the square root of 12. On the example above, that turns 1.17 into roughly 4.05. The CFA Institute article flags this as a known problem: downside deviation does not scale with time the way standard deviation does, and using monthly versus annual periods can produce dramatically different downside figures for the same history.

The practical rule for a journal: report the ratio for the period you actually measured, state the period and the target, and compare only ratios built the same way. A monthly Sortino ratio of 1.17 and an "annualized" 4.05 describe the same six months, not two different levels of skill.

What the Sortino ratio still misses

The Sortino ratio is better than the Sharpe ratio at describing lopsided results, but it is still a summary of the past:

• Few losing periods, little information: with only two months below target, the downside deviation rests on two numbers. One extra bad month can move the ratio a lot.
• Losses that have not happened yet: a strategy with a rare but large loss can show a high Sortino ratio until that loss appears. Sortino's own warning, quoted by the CFA Institute: "Just because nothing bad happened doesn't mean you didn't take any risk."
• Order and clustering: the ratio ignores whether losing periods came one after another. For that, look at maximum consecutive losses and drawdown.
• Size of a bad day: for an estimate of how much a position could lose over a short horizon, value at risk answers a different question.

Logging what the Sortino ratio needs

Like the Sharpe ratio, the Sortino ratio is built from period returns, not from a list of individual trades. The journal needs a consistent period-end balance or return (daily, weekly or monthly, but always the same), the target return written down once, and a note of the period length. Win rate, profit factor and the other trading performance metrics come from trades; risk-adjusted ratios come from this separate return series. If deposits and withdrawals are not logged separately, the period returns will be wrong before any ratio is calculated.

This article is for educational purposes only and is not financial or investment advice. The Sortino and Sharpe ratios describe past returns, not future risk, and trading, especially with leverage, can result in the loss of some or all of your capital.

Log each trade in the BitStat trading journal and review results by period and drawdown on the BitStat performance dashboard.