How to Calculate Risk of Ruin in Trading

Risk of ruin is the probability that a run of losses takes the account below a level you have defined as unrecoverable, before the strategy’s edge has had time to express itself. It is calculated from three inputs: the win rate, the ratio of average win to average loss, and the fraction of capital risked on each trade.

The reason it matters is that expectancy and survival are different questions. Expectancy describes where a strategy ends up on average across many trades. Risk of ruin describes whether you are still trading when that average arrives.

Why positive expectancy is not enough

Take a strategy that wins 45 per cent of the time with an average win twice the average loss. Per trade, expectancy is positive: the wins more than pay for the losses over a long enough run.

Now risk 25 per cent of the account on each trade. Four consecutive losses, which a 45 per cent win rate produces regularly, removes most of the capital. What remains cannot recover, because a 25 per cent risk on a much smaller account is a much smaller absolute bet, and the arithmetic of recovery works against you: losing half demands a 100 per cent gain to get back.

The edge did not change. The strategy is still positive expectancy. It simply never got the chance to prove it, because the path crossed zero before the average had time to assert itself.

That gap between “profitable on average” and “survives the path” is the entire subject.

The inputs

Three numbers, and each has to come from real records rather than estimates.

Win rate. The fraction of trades that end positive, measured over enough trades to mean something. Thirty trades is not a sample; our guide to expectancy and sample size covers why, and what number begins to be informative.

Reward to risk. The average winning trade divided by the average losing trade, both measured after costs. Using planned ratios rather than realised ones is the most common way this calculation is made to flatter a strategy, because planned targets are hit less often than planned stops.

Fraction risked per trade. The portion of account equity at stake when a stop is hit, expressed as a decimal. One per cent is 0.01.

A fourth input is a decision rather than a measurement: what counts as ruin. Zero is the obvious answer and the least useful one, because no serious trader continues to zero. A more honest threshold is the drawdown at which you would stop trading the strategy, which for most people is somewhere between 25 and 50 per cent.

Reading the result

The output is a probability between zero and one. Interpreting it requires two adjustments.

First, it is a best case. The standard calculation treats every trade as independent of every other. Real trading does not work that way: correlated positions lose together, and strategies tend to produce losing streaks clustered in the market conditions that do not suit them. Both make the real probability higher than the formula says. Why correlation in particular breaks the independence assumption is covered in correlation and portfolio heat.

Second, it is extremely sensitive to the inputs, and the inputs are estimates. A win rate measured over fifty trades carries a wide error band, and shifting it a few points moves the ruin figure substantially. The number is a guide to the shape of the risk, not a precise forecast.

With both caveats applied, the practical reading is simple: anything above a few per cent means the position size is too large for the edge you have evidence of.

Position size moves it more than anything else

This is the finding worth internalising, because it contradicts where most effort goes.

Traders generally try to reduce ruin risk by improving the strategy: a better filter, a higher win rate, a cleaner entry. Those improvements are real but incremental, and they move ruin probability modestly.

Cutting the fraction risked per trade moves it sharply. The relationship is not linear. Halving the risk per trade does not halve the probability of ruin; it reduces it by far more, because ruin requires a longer unbroken run of losses to reach the threshold, and the probability of a run falls geometrically with its required length.

The practical implication is that a trader uncertain about their edge should respond by trading smaller rather than by searching for a better system. Smaller size buys the sample size needed to find out whether the edge is real, and a strategy cannot be evaluated by someone who has already run out of capital. Reducing size during a losing streak applies the same logic in the middle of a drawdown.

A worked comparison

Two traders run the same strategy. Both win 45 per cent of the time with an average win twice the average loss, so both have identical positive expectancy. Both define ruin as a 50 per cent drawdown. The only difference is the fraction risked per trade.

Trader A risks five per cent. A losing streak does not need to be remarkable to do serious damage: a run of eight losses, which a 45 per cent win rate produces more often than most people expect, takes roughly a third of the account. Two such runs in a year, separated by ordinary trading, reaches the threshold. The strategy never got a fair test.

Trader B risks one per cent. The same eight-loss run costs under eight per cent. It is unpleasant and entirely survivable, and the account is still large enough that the subsequent winning trades are meaningful in absolute terms.

Same edge, same win rate, same reward to risk, same market. One of these traders finds out whether the strategy works. The other finds out how long a losing streak can be.

The asymmetry is worth stating plainly: the trader risking five times as much per trade does not have five times the ruin probability. They have a vastly higher one, because the number of consecutive losses required to reach the threshold has fallen, and streak probability falls geometrically with required length. That non-linearity is the reason position size dominates every other input.

What the formula leaves out

Three real risks sit outside the calculation entirely.

Gap risk. The arithmetic assumes each loss is the size you planned. A position that gaps through its stop loses more, and a single large gap can do what several planned losses would not.

Correlation. Six positions that fail together are one loss of six times the size, not six independent losses. The formula counts them as six, which understates the clustering that actually destroys accounts.

Behaviour. The largest omission. The calculation assumes you keep following the rules through the drawdown. Most ruin in practice involves a trader abandoning position sizing after several losses and attempting to recover quickly, which is the mechanism by which a survivable drawdown becomes a terminal one. No formula captures that, and protecting mental capital is the part of the problem that arithmetic cannot reach.

Using it as a sizing constraint

The useful application is backwards. Rather than calculating ruin probability for your current size, decide the probability you are willing to accept, then solve for the position size that produces it.

That inverts the usual order of reasoning. Instead of choosing a size and discovering the risk, you choose the risk and derive the size. It tends to produce smaller positions than traders expect, particularly when the win rate is honest about costs and the reward to risk uses realised rather than planned figures.

A strategy worth trading should survive the assumption that your estimates are somewhat wrong. Sizing to a ruin probability well under one per cent, on inputs measured after costs, leaves room for that error. The position size calculator handles the arithmetic once the fraction is decided.