Risk management
Risk of Ruin: Why a Winning Edge Can Still Fail
Risk of ruin explained for traders: why positive expectancy can still blow up an account, fixed vs fixed-fractional sizing, and closed-form vs Monte Carlo.
Risk of ruin is the probability that an account falls to a level you define as failure before the edge has time to work. A strategy can have a genuine positive expectancy and still carry a high risk of ruin if each trade risks too much of the account. Expectancy tells you which way the average points. Risk of ruin tells you whether you survive long enough to collect it.
Defining ruin
Ruin does not have to mean a zero balance. It is better defined as a threshold that ends the strategy in practice:
- a drawdown you have decided you will not trade through, such as 30% or 50%
- a prop-firm maximum loss limit that closes the account
- the point where position sizes become too small to trade at the broker's minimum lot
The probability you calculate depends heavily on where you put that line, so state it explicitly before running any numbers.
Positive expectancy is not enough
The classic gambler's ruin problem gives a clean closed-form answer for the simplest case. Each trade wins one unit with probability p or loses one unit with probability q = 1 − p, every trade risks the same fixed amount, and you start with N units of capital. If p is greater than q, the probability of ever losing all N units is:
Risk of ruin = (q ÷ p)^N
Take a strategy that wins 55% of the time with equal-sized wins and losses. Its expectancy is 0.55 − 0.45 = +0.10 units per trade, a solid edge. Here is its risk of ruin for different capital buffers:
| Capital in units of risk (N) | Risk per trade as % of starting capital | Risk of ruin |
|---|---|---|
| 5 | 20% | 36.7% |
| 10 | 10% | 13.4% |
| 20 | 5% | 1.8% |
With N = 5, the arithmetic is (0.45 ÷ 0.55)^5 = 0.8182^5 = 0.367. More than a third of traders running this positive-expectancy system with 20% risk per trade would lose everything. The edge is identical in every row. Only the bet size changes.
The formula describes the probability of ruin at any point over an unlimited number of trades. Over a finite horizon the probability is lower, but much of the risk sits in the early trades, before profits have built a buffer.
Fixed sizing versus fixed-fractional sizing
The closed-form result above assumes fixed sizing: the same money at risk on every trade regardless of account growth. A run of losses eats into a fixed number of units, and the account can reach zero.
Fixed-fractional sizing risks a constant percentage of current equity. After each loss, the next risk amount shrinks. Mathematically the account approaches zero but never reaches it, so for fixed-fractional sizing ruin must be defined as a drawdown threshold.
A simple way to see how risk per trade drives that threshold is to count how many consecutive losses take the account to a 50% drawdown:
| Risk per trade | Consecutive losses to reach −50% |
|---|---|
| 1% | 69 |
| 2% | 35 |
| 5% | 14 |
The calculation is n = ln(0.5) ÷ ln(1 − risk). At 2%, that is −0.6931 ÷ −0.0202 = 34.3, so the 35th loss crosses the line. Straight losing runs of that length are rare, but mixed sequences with slightly more losses than wins reach the same place, and they are far more common. Fixed-fractional sizing slows the descent; it does not remove it.
Closed-form versus Monte Carlo
Closed-form formulas are useful for intuition and fast to compute, but they require simplified inputs: fixed win probability, fixed payoff sizes and independent trades. Real trade results are messier. Wins and losses vary in size, and the occasional loss is larger than planned because of gaps or slippage.
Monte Carlo simulation handles that by working from your actual trade distribution:
- Express each historical trade as a multiple of initial risk (R), so a full stop-out is −1R and a trade that made twice the risk is +2R.
- Draw trades at random, with replacement, to build a long sequence.
- Apply your sizing rule to that sequence and track equity.
- Record whether equity crossed your ruin threshold within the horizon, for example 500 trades.
- Repeat thousands of times. The share of paths that crossed the threshold is the estimated risk of ruin.
The same simulation also gives you the distribution of maximum drawdowns, which is often more useful than a single ruin probability. The risk of ruin calculator runs a simplified version of this simulation, with fixed win and loss sizes, from your win rate, payoff ratio, risk per trade and ruin threshold.
Assumptions that break
Both methods assume the future trade distribution looks like the one you fed in. Several things commonly violate that:
- Estimation error in the edge. A 55% win rate measured over 100 trades has a standard error of about 5 percentage points, so the true rate could plausibly sit anywhere from roughly 45% to 65%. At 50% with equal payoffs there is no edge, and fixed-size betting is eventually ruined with certainty.
- Dependence between trades. Losing streaks cluster when market regimes change, which makes long runs of losses more likely than independent draws suggest.
- Edge decay. Strategies degrade as conditions change or as more participants trade the same pattern.
- Losses beyond 1R. Weekend gaps and fast markets can fill stops well past their level.
- Correlated positions. Several open trades on related pairs behave like one larger bet.
Estimation error can cut either way, but the others all push real-world ruin risk above the modeled figure, so treat the output as an optimistic estimate rather than a precise number.
Using the numbers
Risk of ruin is most useful as a comparison tool. Run your strategy's figures at 0.5%, 1% and 2% risk per trade and see how quickly the probability of hitting your threshold rises. Start from a realistic expectancy estimate, which the expectancy calculator and the guide to expectancy and profit factor cover, and haircut the win rate to allow for estimation error. Then compare the simulated drawdowns with what you can tolerate, as discussed in the maximum drawdown guide.
Key points
- Risk of ruin is the probability of reaching a failure threshold you define, not only a zero balance.
- With fixed sizing, ruin = (q ÷ p)^N for even payoffs; a 55% edge with 5 units of capital still fails 36.7% of the time.
- Fixed-fractional sizing never reaches zero, so define ruin as a drawdown level.
- Monte Carlo on your own R-multiple history handles uneven payoffs; closed-form results suit quick intuition.
- Uncertainty in the edge, streaky results and gaps all make real ruin risk higher than the model.