Risk of Ruin

What is Risk of Ruin?

Risk of ruin is the probability that an account falls to a level from which it cannot, or is not allowed to, continue trading. The idea comes from classical gambling mathematics, where a bettor with a known win rate and payoff faces a computable chance of losing the entire bankroll before the edge can express itself. Traders adapted the same streak math to answer the question that expectancy alone cannot: an edge is worthless if the path to realizing it passes through a drawdown the account does not survive.

The framework connects four inputs: win probability, payoff ratio, risk per trade, and the ruin threshold. The uncomfortable result is how nonlinear it is. Halving risk per trade does not halve ruin probability; it typically collapses it by orders of magnitude, because ruin requires a long adverse run and each extra unit of cushion lengthens the run required, cutting the probability roughly geometrically. Conversely, oversizing a genuinely positive-expectancy system can push ruin probability toward certainty.

In practice, ruin rarely means literal zero. Traders define it as the drawdown at which they would stop, lose funding, or breach prop-firm rules, and compute the probability of touching that barrier. Under fixed-fractional sizing, the account never reaches absolute zero in theory, but it can still cross any practical ruin threshold, so the concept survives the sizing scheme.

How it's calculated

The classical closed form covers a fixed bet with even payoff; realistic trading distributions are usually handled by simulation.

The closed form assumes independent trades, constant size, and 1:1 payoff; extensions exist for unequal payoffs but become unwieldy.

For real trade distributions with variable R-multiples, Monte Carlo resampling of the strategy's own trades is the standard estimation method.

Defining ruin as a drawdown threshold (for example 30 percent) rather than zero raises the computed probability substantially and is usually the more relevant number.

How traders use it

• Setting risk per trade: traders solve the problem backwards, choosing the largest per-trade risk at which the estimated ruin probability stays below a tolerance such as 1 percent, which typically lands well below full Kelly sizing.
• Stress-testing via simulation: resampling historical trades with Monte Carlo methods produces distributions of maximum drawdown and touch probabilities for any ruin barrier, capturing skew and streaks the closed form ignores.
• Evaluating funded-account viability: with ruin defined at a firm's trailing drawdown, the same math estimates the chance of breaching before hitting the profit target, often revealing that popular sizing is far too aggressive for the rule set.
• Sanity-checking win-rate claims: streak math shows, for example, that a 50 percent win rate makes a 7-loss streak likely within a few hundred trades, so any sizing plan that cannot absorb such a streak carries hidden ruin risk.
• Honest limitation: every estimate assumes the input edge is real and stationary. If the true expectancy is lower than the backtest suggests, or trades are correlated, actual ruin probability is higher than any of these calculations report.

Risk of Ruin vs related concepts