Sortino Ratio
A Sortino ratio cannot tell you how big to trade — it comes out the same at every size — but its denominator can: a twenty-trade journal with a downside deviation of 0.50R, sized so the short side costs 0.50% of a 10,000.00 account per trade, risks 1.00% a trade, which is 100.00, and 100.00 behind a 20-pip stop on EUR/USD is 0.50 lots.
| Risk per trade | Money at risk | Lot size | Short-side cost per trade | Sortino ratio |
|---|---|---|---|---|
| 0.50% | 50.00 | 0.25 | 0.25% · 25.00 | 2.00 |
| 1.00% | 100.00 | 0.50 | 0.50% · 50.00 | 2.00 |
| 2.00% | 200.00 | 1.00 | 1.00% · 100.00 | 2.00 |
| 4.00% | 400.00 | 2.00 | 2.00% · 200.00 | 2.00 |
| 8.00% | 800.00 | 4.00 | 4.00% · 400.00 | 2.00 |
The last column never moves. Sixteen-fold change in size, five different sums of money, and one ratio — because the ratio is measured in R, and R is the size: the money one trade puts at risk. Whatever you pick for that, the journal's outcomes are quoted in it, and it cancels.
The consequence is the reason this page exists. A number that cannot see your size cannot choose it, and no amount of waiting for a better ratio will produce a lot count. What does produce one is the denominator on its own, once it is converted out of R and into a share of the account — and that conversion is one multiplication, because a trade's result in money is the risk you took multiplied by its result in R:
The denominator, counted by hand
Here are two journals of twenty trades, printed in full so every row can be checked. Results are in R: +1.50R is a trade that made one and a half times what it put at risk, −1.00R is a trade stopped out for the full amount. The shortfall column is how far each trade fell below a target of zero, squared; anything at or above the target is a zero, and the zeros are counted in the denominator too, which is the convention the CFA Institute paper below describes.
| Trade | A, in R | A shortfall² | B, in R | B shortfall² |
|---|---|---|---|---|
| 1 | +0.50 | 0.00 | +3.00 | 0.00 |
| 2 | +1.00 | 0.00 | +3.00 | 0.00 |
| 3 | +1.50 | 0.00 | +3.00 | 0.00 |
| 4 | +2.00 | 0.00 | +3.00 | 0.00 |
| 5 | +2.50 | 0.00 | +3.00 | 0.00 |
| 6 | +0.50 | 0.00 | +3.00 | 0.00 |
| 7 | +1.00 | 0.00 | +3.00 | 0.00 |
| 8 | +1.50 | 0.00 | +3.00 | 0.00 |
| 9 | +2.00 | 0.00 | +3.00 | 0.00 |
| 10 | +2.50 | 0.00 | +3.00 | 0.00 |
| 11 | +0.50 | 0.00 | +4.00 | 0.00 |
| 12 | +1.00 | 0.00 | +4.00 | 0.00 |
| 13 | +1.50 | 0.00 | +4.00 | 0.00 |
| 14 | +2.00 | 0.00 | +4.00 | 0.00 |
| 15 | +5.00 | 0.00 | +4.00 | 0.00 |
| 16 | −1.00 | 1.00 | −2.00 | 4.00 |
| 17 | −1.00 | 1.00 | −2.00 | 4.00 |
| 18 | −1.00 | 1.00 | −2.00 | 4.00 |
| 19 | −1.00 | 1.00 | −2.00 | 4.00 |
| 20 | −1.00 | 1.00 | −2.00 | 4.00 |
| Total | +20.00 | 5.00 | +40.00 | 20.00 |
Journal A: the twenty results add to +20.00R, so the mean is +1.00R; the squared shortfalls add to 5.00, over twenty trades that is 0.25, and the square root is 0.50R — the ratio is 1.00 divided by 0.50, which is 2.00. Journal B: the results add to +40.00R for a mean of +2.00R; the squared shortfalls add to 20.00, over twenty that is 1.00, and the square root is 1.00R — the ratio is 2.00 divided by 1.00, which is also 2.00. Two journals, the same ratio, and denominators twice apart.
One ratio, two sizes
Now size both of them two ways. The first is the flat rule most traders are told — risk one percent of the account per trade. The second is the rule this page is built on: name the short-side cost you are willing to carry per trade, and let the denominator decide the percentage. The instrument is the same in every row: a 10,000.00 account, a 20-pip stop, one pip worth 10.00 at one standard lot, so 200.00 of risk per lot.
| Journal A | Journal B | |
|---|---|---|
| Trades | 20 | 20 |
| Mean result | +1.00R | +2.00R |
| Sum of squared shortfalls | 5.00 | 20.00 |
| Downside deviation | 0.50R | 1.00R |
| Sortino ratio at MAR = 0 | 2.00 | 2.00 |
| Worst trade in the journal | −1.00R | −2.00R |
| Flat 1% rule — money at risk | 100.00 | 100.00 |
| Flat 1% rule — lot size | 0.50 | 0.50 |
| Flat 1% rule — short-side cost per trade | 0.50% · 50.00 | 1.00% · 100.00 |
| Flat 1% rule — worst trade costs | 1.00% · 100.00 | 2.00% · 200.00 |
| Denominator rule at 0.50% — risk per trade | 1.00% | 0.50% |
| Denominator rule at 0.50% — money at risk | 100.00 | 50.00 |
| Denominator rule at 0.50% — lot size | 0.50 | 0.25 |
| Denominator rule at 0.50% — worst trade costs | 1.00% · 100.00 | 1.00% · 100.00 |
The flat rule hands both journals 0.50 lots, and the cost of that indifference is in the two rows under it: journal B is carrying twice the short-side cost per trade and loses twice as much of the account on its worst trade, because its losses are twice as deep in R. The denominator rule does the opposite — it takes the cost you named as fixed and lets the size absorb the difference, so journal B trades half the size and both journals cap their worst trade at 100.00. Same ratio throughout, and the two answers are two apart. If you only ever look at the ratio, you will never see which journal you are holding.
What the target does to the denominator
The target you type into the ratio — the minimum acceptable return, the MAR — is the one input that changes the denominator without changing a single trade. Raising it pulls more trades into the shortfall column and makes the ones already there deeper, and since the size comes out of the denominator, the size moves with it. This is journal A at three targets, held to the same 0.50% of short-side cost:
| MAR | Trades below it | Sum of squared shortfalls | Downside deviation | Sortino ratio | Risk per trade | Money at risk | Lot size |
|---|---|---|---|---|---|---|---|
| 0.00 | 5 | 5.00 | 0.50R | 2.00 | 1.00% | 100.00 | 0.50 |
| 0.50 | 5 | 11.25 | 0.75R | 0.67 | 0.67% | 66.67 | 0.33 |
| 1.00 | 8 | 20.75 | 1.02R | 0.00 | 0.49% | 49.09 | 0.24 |
At a target of 1.00R the numerator is zero — the journal's mean is exactly its target — so the ratio reads 0.00 on a journal that made money on fifteen of twenty trades, and the size it implies is less than half the first row's. That is not a contradiction, it is what the ratio is: a measurement of one journal against one target, not a grade. Pick the target before you read the number, and pick it for a reason, because you are also picking the size.
The denominator in the third row is 1.02R: the squared shortfalls add to 20.75, over twenty trades that is 1.0375, and the square root of that is 1.0186. Everything else on this page is exact to two places; this row is the one that is not, and it is the only one where the shortfall column holds three different depths at once.
What the ratio is, and what the first page of results leaves out
The ratio is one line, and the sources that publish it do not agree on every part of it. The CFA Institute's paper by Deborah Kidd gives it as S = (Mean portfolio return − MAR) / Downside deviation, and says the target may be an absolute return, an index return, the risk-free rate, or zero. Schwab's page describes the numerator as the return minus the risk-free rate; StrategyQuant's reference says the same. Wikipedia defines the denominator as the square root of target semivariance and calls it downside deviation. This page uses the MAR form, because the target is the input that moves the denominator and the whole argument above runs through it.
Two conventions are worth knowing before you compare a number from one tool against a number from another, and both are documented rather than invented here. The first is what you divide by: this page divides the sum of squared shortfalls by every trade in the journal, winners counted as zero, which is the form the CFA paper describes for semideviation; some tools divide by the number of trades that fell short instead, which makes the denominator larger and the ratio smaller. The second is discrete against continuous: the CFA paper reports Sortino and Forsey's warning that using only the historical returns that fall below the target can significantly underestimate downside risk, because it measures only what did happen (discrete), instead of what could have happened (continuous); Wikipedia likewise prefers the continuous form and notes the discrete one needs monthly data to mean anything. Everything on this page is the discrete form, on purpose, because it is the one you can check by hand from a journal.
What none of the pages we could read does is take the next step. We searched each of the six for position size and position sizing, and for the word leverage; none of them contains any of the three. They explain the ratio, they compare it with Sharpe, they warn about its conventions — and they stop at the number. The step from the denominator to a lot count is below, on the same page as the ratio, and it is one multiplication and one division.
Where the size gets turned into units
Everything above ends at a percentage of the account, and the percentages are the part this page owns. Turning them into units is what the position size calculator is for: it starts from the balance and the stop distance you type and returns units, lots and notional, so the 0.50 lots this page arrives at is one screen of inputs there. The lot size calculator states the same conversion the other way round — lots to units, with the margin and the notional alongside — which is the check to run when a size looks small or large against the contract you actually trade.
The direction matters. This page produces the input, not the ticket: it answers what fraction of the account one trade should carry given the shape of your losing side, and it does it in the same unit every position-sizing rule on this site uses. The calculators turn that fraction into something you can place.
What people call this
Downside deviation is the denominator and the part that carries the size; it is also called downside risk and, in the academic form, target semideviation. The minimum acceptable return — the MAR — is the target the deviations are measured against, and it is what the CFA paper says may be zero, an index, the risk-free rate or an absolute number.
A Sortino ratio calculator is usually a box that takes a series of period returns and returns the ratio. The one on this page takes a journal in R and returns a lot count, which is a different output from the same arithmetic. Sharpe is the same shape with total volatility underneath instead of the downside half, and it is scale-free for exactly the same reason: both ratios divide a return by a deviation measured in the same unit.
Questions traders ask
Can I use a Sortino ratio to choose my position size?Not on its own — the ratio is the same number at every size, so it cannot distinguish one size from another. What chooses the size is the denominator taken by itself: a downside deviation of 0.50R with a short-side cost of 0.50% of the account gives a risk of 0.50% / 0.50 = 1.00% per trade, which is 100.00 on a 10,000.00 account, and 100.00 behind a 20-pip stop at 10.00 a pip is 0.50 lots.
Why does the ratio not change when I risk more per trade?Because it is measured in R, and R is the amount one trade puts at risk. Risking 8.00% instead of 0.50% makes every trade's loss and profit sixteen times larger in money and leaves every figure in R untouched, so the numerator and the denominator scale together and cancel. The table at the top of this page shows five sizes from 0.25 to 4.00 lots with the ratio reading 2.00 in every row.
Two journals, same ratio — should they be the same size?No, and that is the whole point. Both journals on this page have a ratio of 2.00; one has a downside deviation of 0.50R and the other 1.00R, because its losses run to −2.00R instead of −1.00R. Held to the same 0.50% of short-side cost, the first risks 1.00% per trade and trades 0.50 lots, the second risks 0.50% and trades 0.25 lots.
Is downside deviation the same as my average loss?No. It is the square root of the mean of the squared shortfalls, taken over every trade in the journal with the winners counted as zero — which is why journal A's is 0.50R when its losing trades each cost 1.00R. Squaring penalises deep shortfalls harder than shallow ones, and dividing by all twenty trades rather than by the five that lost is what pulls the figure down. It is a root-mean-square, not an average, and it is not a worst case: the worst trade in journal A still costs the full 1.00%.
What minimum acceptable return should I use?The one you actually hold the journal to, and you have to choose it before you read the number, because it moves the denominator and therefore the size. On journal A a target of 0.00 gives a downside deviation of 0.50R and 0.50 lots; a target of 1.00R gives 1.02R and 0.24 lots, with no trade in the journal changing. Zero is the common default, and it means every losing trade counts and no winning one does.
Does this account for gaps, slippage or compounding?No. The bridge from R to the account assumes every trade's result is the risk you took multiplied by its result in R, which is exact only while the loss is linear in size and the balance is treated as constant across the journal. A gap past the stop, a fixed commission, a margin call or a balance that has already moved all break it. The figure is a starting point for the size, not a risk forecast.
Where this page stops
Both journals are constructed to be checkable, not sampled from a market: twenty trades each, with the losing side set at one depth per journal and the winning side in round quarter-turns of R. Real journals have losses of several depths at once, and the third row of the target table is the only place on this page where that shows. Nothing here is a probability model — no figure says how often a journal like A or B occurs, only what each one implies for the size if it is yours. Twenty observations is a short journal for any statistic, and the denominator is the part that moves most when you add trades.
The conversion out of R assumes the loss is linear in size, the balance is constant across the journal, and every trade risks the same percentage; none of the three is exactly true once a balance is compounding, a fixed commission is being paid, or a loss runs past the stop. The size is rounded down to a 0.01 lot step, so 0.2454 lots appears as 0.24. No spread, financing, swap or tax is in any figure, and the pip value is one you type rather than one looked up, because contracts differ.
None of this is advice, and none of it is a claim that one size is right in general — the percentage you name as your short-side cost is a choice, and a different choice gives a different answer on the same journal. The sources quoted above were read on 22 October 2026, and pages change. Of the eight web results Google returned for this word, six were read: Wikipedia, Schwab, the CFA Institute paper, StrategyQuant, Groww and Corporate Finance Institute; two — Investopedia at number two and the CME Group paper at number six — returned 403 on every route we tried, plain fetch, a real browser and a mobile user agent, so we make no claim about what they say. The other two results in the top ten were videos, which we did not read.
Related guides
- Profit factor calculator — the same journal read from the other end: gross profit over gross loss, and what the ratio leaves out.
- Drawdown calculator — the deepest run of losses a size like the ones above can produce, and how long it takes to climb out.
- Risk of ruin calculator — what a given risk percentage does to the chance of the account going under.
- Kelly criterion — the share of the account a bet with this shape of outcome puts at risk, and the half-Kelly figure.
- Win rate calculator — the break-even win rate a payoff like journal A's demands.
- Risk reward ratio — the target side of the same arithmetic, and the win rate it needs.
- Trailing stop — how the exit rule changes the shape of the outcomes that feed this page's denominator.