The probability of ruin is the mathematical risk that a trader's capital falls to zero before their strategy generates enough profit to survive. According to ESMA, between 74% and 89% of retail clients lose money trading CFDs across European brokers: a figure that shows how systematically underestimated this risk is. The core formula: P(ruin) = ((1 - edge) / (1 + edge))^(capital / risk_per_trade), where edge represents your net statistical advantage per trade.
What is the probability of ruin?
Mathematical definition
Ruin theory is a branch of actuarial mathematics applied to trading by quantitative managers since the 1970s. The exact formula for a series of bets with positive expectancy is:
P(ruin) = ((1 - a) / (1 + a))^N
where:
- a = edge per unit of risk, calculated as
(win_rate x avg_win - loss_rate x avg_loss) / avg_loss - N = number of risk units your capital contains (capital / risk per trade)
Concrete example: a trader with a 55% win rate, a 1:1 reward-to-risk ratio, and 2% risk per trade on a $10,000 account has an edge of 0.10 and N = 50 risk units.
P(ruin) = ((1 - 0.10) / (1 + 0.10))^50 = (0.818)^50 = approximately 0.00008, or 0.008%
That number changes dramatically if risk per trade increases to 5%: N drops to 20 units, and P(ruin) rises to approximately 1.2%.
Why this calculation matters before going live
Most traders evaluate strategies solely on the maximum observed drawdown in backtest. That figure says nothing about actual probability of ruin: two strategies can show the same maximum drawdown but radically different probabilities of ruin depending on the distribution of their results.
Difference between drawdown and ruin
Drawdown and probability of ruin measure two distinct risks:
| Criterion | Maximum drawdown | Probability of ruin |
|---|---|---|
| Definition | Largest peak-to-trough decline observed | Risk of capital reaching zero |
| Nature | Historical and descriptive | Probabilistic and predictive |
| Use | Measure past pain | Anticipate future survival |
| Limitation | Ignores unobserved loss sequences | Requires stable return distribution |
| Corrective action | Reduce leverage or frequency | Adjust both edge AND position size |
A 20% drawdown may be acceptable. A 15% probability of ruin means that running your strategy 100 times over different periods, you blow your account in 15 of those scenarios. Ruin theory literature (Actuarial Society) shows that even profitable strategies can have high probabilities of ruin when position sizing is poorly calibrated.
Factors that influence probability of ruin
Position size
Position size is the most powerful lever on probability of ruin. The relationship is not linear: doubling risk per trade does not double probability of ruin: it increases it exponentially.
Illustration with a constant edge of 0.08:
| Risk per trade | N risk units ($10k account) | Approx. probability of ruin |
|---|---|---|
| 1% | 100 | < 0.01% |
| 2% | 50 | 0.04% |
| 3% | 33 | 0.4% |
| 5% | 20 | 4.2% |
| 10% | 10 | 20% |
This table shows why quantitative traders and prop firms typically cap risk per trade at 1-2%: probability of ruin remains mathematically negligible. See our guide on position sizing and the Kelly criterion for more detail.
Mathematical expectancy
Negative mathematical expectancy makes ruin certain in the long run. But even positive expectancy does not guarantee survival: if edge is thin and positions are too large, probability of ruin stays dangerous.
The expectancy formula per trade:
E = (win_rate x avg_win) - (loss_rate x avg_loss)
Positive edge is necessary but not sufficient. Read more in our article on backtesting metrics and expectancy.
Variance of results
A highly volatile strategy with a good average edge can have a higher probability of ruin than a less performant but more consistent strategy. Variance amplifies consecutive loss streaks and increases the risk of hitting zero before the recovery. This is precisely what Monte Carlo simulation captures better than the analytical formula.
Calculating probability of ruin with Monte Carlo
The reshuffling method
The Monte Carlo reshuffling (or bootstrap) simulation is the method recommended by quantitative traders. The process:
Collect backtest results
Randomly shuffle (reshuffle)
Simulate each trajectory
Calculate the ruin proportion
This method has the advantage of using the actual distribution of your strategy's results, without assuming normality of returns (an assumption that is often false in trading).
Reading the results
A Monte Carlo simulation produces a distribution of equity curves. The key indicators to extract:
3 key numbers to pull from your simulation
- Probability of ruin: percentage of trajectories reaching zero (or your threshold)
- 95th-percentile drawdown: the drawdown you will experience in 95% of scenarios
- Expected capital after N trades: the median of final trajectories
Practical example
A trader has a backtest of 200 trades: 52% winning trades, average reward-to-risk ratio of 1.3. Fixed 2% risk per trade on a $10,000 account. The analytical formula gives a theoretically very low probability of ruin.
But after 10,000 Monte Carlo simulations, the results show:
- 3.2% of trajectories experience a drawdown exceeding 30% at some point
- 0.4% of trajectories reach the ruin threshold at -50%
- The median drawdown at the 95th percentile is 22%
These figures allow precise calibration of a prop firm stop-out threshold or defining your own emergency halt level. See how to stress-test your backtest for robustness to complement this analysis.
Backtrex integrates this calculation directly in its backtest report: 10,000 Monte Carlo simulations run automatically after each backtest, with no code to write. Explore Backtrex features or check out the pricing plans.
Strategies to reduce ruin risk
Optimal position sizing (Kelly, fractional Kelly)
The Kelly criterion defines the theoretically optimal position size to maximize capital growth over the long term without ruin risk. The formula:
f = (p x b - q) / b
where f = fraction of capital to risk, p = probability of winning, q = probability of losing, b = reward-to-risk ratio.
In practice, traders use a fractional Kelly (typically 1/4 or 1/2 Kelly) for three reasons:
- Full Kelly maximizes growth but generates psychologically unsustainable drawdowns
- Estimates of p and b from backtest carry significant statistical uncertainty
- Fractional Kelly keeps probability of ruin well below 1%
The practitioner's rule of thumb
Quantitative literature recommends targeting a probability of ruin below 1% for any live trading. For prop firms like FTMO or MyForexFunds, where ruin means immediate loss of the funded account, many traders target 0.1%. This typically translates to a maximum risk of 0.5% to 1% per trade, depending on the result distribution.
Strategy diversification
Correlation between strategies is a key factor in reducing the overall probability of ruin of a portfolio. Two uncorrelated strategies each with 2% individual probability of ruin can have a combined probability of ruin below 0.5%, because their loss sequences do not occur simultaneously. This approach is central to backtesting vs. forward testing methodology and quantitative portfolio management.
Important Risk Warning
Conclusion
Probability of ruin is the most important number most traders never calculate. The analytical formula gives a quick approximation; Monte Carlo simulation reveals the full distribution of possible scenarios. For any live strategy (and especially for accounts funded by a prop firm), targeting a probability of ruin below 1% through properly calibrated risk per trade is a survival condition, not an option.
Professional quantitative managers typically target less than 1% probability of ruin. Above 5%, the strategy or money management must be revised before any live use. For prop firm funded accounts (FTMO, MFF), some traders target 0.1% because ruin immediately terminates access to capital. In practice, 1% or less risk per trade on a strategy with positive edge generally yields a negligible probability of ruin.
Probability of ruin increases exponentially with position size, not linearly. Moving from 2% to 5% risk per trade can multiply the probability of ruin by 50 or more, depending on your edge. Conversely, halving risk per trade reduces probability of ruin far more than proportionally, because each loss sequence consumes less capital and gives the strategy more time to recover.
No. A classical backtest produces a single trajectory: the one that actually occurred in the market in the order signals appeared. Monte Carlo simulation generates thousands of trajectories by reshuffling the same trades in different orders. It reveals drawdown and ruin scenarios the backtest never observed but that remain perfectly possible with the same strategy. It is the difference between "what happened" and "what could have happened."
Full Kelly defines the position size that maximizes capital growth over the long term. In practice, it generates very large drawdowns (30-50%) and is highly sensitive to estimation errors. Fractional Kelly (often 1/4 or 1/2 Kelly) reduces position size proportionally: growth is slower, but drawdowns and probability of ruin are considerably reduced. Most practitioners use 1/4 Kelly or even less.
In practice, 10,000 simulations yield a stable probability of ruin estimate for most strategies. Beyond 50,000 simulations, the precision gain is negligible. The limiting factor is not the number of simulations but the quality and quantity of trades in the original backtest: a Monte Carlo simulation on 30 trades will be far less reliable than one on 500 trades.
Yes. Backtrex automatically calculates probability of ruin and Monte Carlo simulations in the backtest report, with no code required. Traders using platforms like TradingView or MetaTrader generally need to program the simulation in Pine Script or Python, or use a third-party tool. Backtrex integrates this analysis directly into the visual backtesting workflow.
Probability of ruin calculated on a backtest remains an estimate based on historical data. In forward testing, it should be recalculated periodically as new trades are added. If the probability of ruin rises significantly in live trading compared to backtest, it signals the strategy may have curve fitting or that market conditions have changed.