Trader Toolkit · Calculator

Risk of Ruin

The approximate chance that a method ever loses a chosen share of the account.

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Risk a little, trade by trade:see how far a run can fade.

A method, described by three numbers

Result

Win rate

The share of trades that gain. A placeholder until you type yours.

Payoff ratio

Average win ÷ average loss. A placeholder until you type yours.

Risk per trade

The share of the balance lost when a trade loses. Shared with the other tools.

Share of the account lost

The loss you are asking about: 50 for half the account.

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Chance of ever losing 50% of the account

less than 0.01%

an approximation, under the assumptions listed beside this

Losses in a row that get there

from the start, at 1% a trade; the chance of that exact run is less than 0.01%

Balance after one win: × 1.015
Balance after one loss: × 0.99
Average change in the logarithm of the balance, per trade: 0.002419
Break-even win rate for this payoff ratio, at very small risk: 40%

The same win rate, payoff ratio and loss at other risk sizes
Risk per trade	Losses in a row	Chance, approximately
0.5%	139	less than 0.01%
1%	69	less than 0.01%
2%	35	less than 0.01%
3%	23	0.11%
5%	14	2.2%
10%	7	20.44%

The table is the same formula at six risk sizes. It ranks nothing: a smaller chance of a large loss is not a statement about any real method, whose win rate and payoff are not constants.

SimulationA calculation on the figures you entered. An approximation of a model, not a forecast of an account: real trades are not independent and their results are not of fixed size. Educational information, not investment advice or a recommendation to trade.

How it works

Formula

P ≈ (1 − D)^(2μ ÷ σ²); μ = p·ln(1 + b·f) + (1 − p)·ln(1 − f); σ² = p·(1 − p)·(ln(1 + b·f) − ln(1 − f))². p = win rate, b = payoff ratio, f = share risked per trade, D = share of the account lost. P = 1 when μ ≤ 0.

With your numbers

1A win multiplies the balance by 1 + payoff × risk1 + 1.5 × 0.01 = 1.015; ln = 0.014889
2A loss multiplies it by 1 − risk1 − 0.01 = 0.99; ln = −0.01005
3Drift: the average of the two logarithms, weighted by how often each happens0.5 × 0.014889 + 0.5 × −0.01005 = 0.002419
4Variance: win rate × loss rate × (the distance between the two logarithms)²0.5 × 0.5 × (0.024939)² = 0.00015549
5Exponent: 2 × drift ÷ variance2 × 0.002419 ÷ 0.00015549 = 31.1168
6Probability: (1 − share lost) to that power(1 − 0.5)^31.1168 = 0.5^31.1168 = less than 0.01%
7Losses in a row, from the start, that reach the levelthe smallest n with 0.99ⁿ ≤ 0.5: n = 69; chance of that run = 0.5^69 = less than 0.01%

Assumptions

This is an approximation, not a measurement. It treats the balance as moving smoothly when it really moves in steps, so the true figure for the same inputs differs a little, and more so when the risk per trade is large.
Every trade risks the same share of the balance as it then stands (fixed-fraction sizing). Every loss is exactly that share and every win exactly the payoff ratio times it. Real results vary in size, and a stop can be filled beyond its level.
The win rate and the payoff ratio never change, and each trade is independent of the one before. Real trades come in runs, and a method’s past win rate is not a property of its future.
There is no limit on the number of trades: the figure is the chance of ever reaching the level, however long it takes. The loss is measured from the starting balance, not from a later peak.
Costs are left out unless they are already inside the win rate and the payoff ratio you type.
The starting figures are placeholders that make the working visible. They do not describe any method, and no setting here is recommended.

Terms used

In plain language

A long enough run of losses is always possible. The question is how likely.

Any method that sometimes loses can lose several times in a row. Risk of ruin puts a number on how much that matters: given how often the method wins, how large its wins are beside its losses, and how much of the balance each trade puts at risk, how likely is it that the account ever falls by a chosen share?

The figure on this page is an approximation, and it is called one wherever it appears. It supposes that every trade risks the same share of whatever the balance then is, that every loss is exactly that share and every win exactly the payoff ratio times it, that the win rate never changes, and that one trade tells you nothing about the next. On those terms the logarithm of the balance takes a random step each trade, and the chance of it ever falling a given distance has a short formula.

Real trading keeps none of those terms exactly. Results vary in size, losses come in clusters, a stop can be filled beyond its level, and a win rate measured on past trades is not a constant of nature. The figure is useful for seeing how steeply the chance of a deep loss rises with the share risked per trade. It is not a measurement of any account.

When the method’s average step is not upward, the approximation gives one hundred per cent for every level: with no drift to carry it away, the balance reaches any lower mark sooner or later.

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Fetching the page

The same win rate, payoff ratio and loss at other risk sizes

Risk per trade

Losses in a row

Chance, approximately

0.5%

139

less than 0.01%

0.11%

2.2%

10%

20.44%

How it works

Formula

With your numbers

1A win multiplies the balance by 1 + payoff × risk1 + 1.5 × 0.01 = 1.015; ln = 0.014889

2A loss multiplies it by 1 − risk1 − 0.01 = 0.99; ln = −0.01005

3Drift: the average of the two logarithms, weighted by how often each happens0.5 × 0.014889 + 0.5 × −0.01005 = 0.002419

4Variance: win rate × loss rate × (the distance between the two logarithms)²0.5 × 0.5 × (0.024939)² = 0.00015549

5Exponent: 2 × drift ÷ variance2 × 0.002419 ÷ 0.00015549 = 31.1168

6Probability: (1 − share lost) to that power(1 − 0.5)^31.1168 = 0.5^31.1168 = less than 0.01%

7Losses in a row, from the start, that reach the levelthe smallest n with 0.99ⁿ ≤ 0.5: n = 69; chance of that run = 0.5^69 = less than 0.01%

Assumptions

This is an approximation, not a measurement. It treats the balance as moving smoothly when it really moves in steps, so the true figure for the same inputs differs a little, and more so when the risk per trade is large.

Every trade risks the same share of the balance as it then stands (fixed-fraction sizing). Every loss is exactly that share and every win exactly the payoff ratio times it. Real results vary in size, and a stop can be filled beyond its level.

The win rate and the payoff ratio never change, and each trade is independent of the one before. Real trades come in runs, and a method’s past win rate is not a property of its future.

There is no limit on the number of trades: the figure is the chance of ever reaching the level, however long it takes. The loss is measured from the starting balance, not from a later peak.

Costs are left out unless they are already inside the win rate and the payoff ratio you type.

The starting figures are placeholders that make the working visible. They do not describe any method, and no setting here is recommended.

Terms used