Monte Carlo Tools
Risk-of-Ruin Calculator
Investment Education, Research & Tools for Smarter Decisions.
Enter your strategy's win rate, average win and loss size, risk per trade, and the drawdown level you consider "ruin" to compute the probability of capital depletion. Compares the analytical Gambler's Ruin approximation against a full Monte Carlo simulation so you can see both estimates side by side.
Direct Answer
A risk-of-ruin calculator estimates the probability that a trading account depletes to a specified drawdown threshold before it recovers, using either an analytical formula or Monte Carlo simulation of win rate, payoff ratio, and position size. It converts a strategy's edge and volatility into a single probability of catastrophic loss rather than a return expectation. That number should directly shape position sizing, a risk of ruin above a few percent typically means the bet size is too large for the edge.
Tool
Enter your strategy parameters above and click Calculate to see the risk-of-ruin estimate.
Uses simplified analytical formula and synthetic Monte Carlo simulation. Does not use real market data or account for regime changes.
How to Use This Tool
For the underlying math, analytical formulas, and a worked example behind these numbers, see the companion guide: Risk of Ruin and Capital Depletion.
Enter your strategy's win rate as a percentage. Enter the average winning trade size and average losing trade size as percentages of capital at risk (for the average win/loss inputs, these represent trade outcomes relative to the amount risked per trade, so if you risk 1% of capital per trade and your winner recovers 2%, enter "2.0". This means you earn 2× your risk on a win). The "Risk per Trade" field is the fraction of your total capital you put at risk on each trade. This is the key sizing parameter for ruin probability.
The "Ruin Threshold" is the drawdown percentage from your starting capital that you define as ruin. A 50% ruin threshold means: "if my capital falls to 50% of its starting level, I consider myself ruined and stop trading." A more conservative trader might set this at 25%; a more aggressive one might set it at 75%. Note that unlike a fixed ruin amount in classical Gambler's Ruin, this threshold adjusts downward as capital grows with compound sizing.
The analytical formula provides an instantaneous estimate. The Monte Carlo simulation draws each trade from your win/loss distribution and tracks whether any path hits the ruin threshold within the specified trade count. The two methods will generally agree closely for strategies with small edge; they diverge when edge is very high (where the analytical formula overestimates ruin risk) or when trade count is limited (where the Monte Carlo gives the finite-horizon estimate and the analytical formula gives the infinite-horizon estimate).
Understanding the Outputs
Expectancy per trade: The average return per trade in percentage terms. Positive expectancy is required for a finite risk of ruin over infinite trades. With negative expectancy, ruin probability approaches 100% over a sufficiently large trade count regardless of starting capital.
Analytical risk of ruin: Computed via the standard approximation RoR ≈ ((1 − edge) / (1 + edge))^(capital_units), where edge is computed from the win/loss parameters and capital_units is the number of risk units in the ruin threshold capital. This formula assumes infinite trades, independent outcomes, and equal win/loss sizes, the equal-size assumption is relaxed by scaling the win/loss into a common risk unit. The analytical result is most reliable when win probability is near 0.5 and win/loss amounts are similar.
Monte Carlo risk of ruin: Estimated as the fraction of simulated paths that reach the ruin threshold within the specified number of trades. This is the finite-horizon estimate: even a strategy with positive expectancy can reach ruin within 500 trades if volatility is high and edge is small. The Monte Carlo result depends on the trade count setting, increase trades to see how ruin risk accumulates with more trading.
Monte Carlo SE: The standard error of the Monte Carlo ruin probability estimate. Given N simulation paths and estimated RoR probability p, SE = sqrt(p × (1−p) / N). With 5,000 paths, SE is typically ±0.4-1.0 percentage points. Increasing paths to 10,000-20,000 halves the SE for a more precise estimate when ruin probability is near zero.
The gauge bar visually shows the risk of ruin: green below 5%, amber from 5-15%, red above 15%. These bands are not a regulatory or professional standard, no regulator or licensing body sets a numeric risk-of-ruin ceiling. They reflect a common industry convention among discretionary and systematic traders for how much finite-horizon ruin probability is worth tolerating in exchange for expected growth. Many practitioners treat a risk of ruin above 10% as a signal to reduce risk per trade or improve edge, but the "right" ceiling depends on your capital base, time horizon, and tolerance for drawdown, treat these thresholds as a starting heuristic to adapt, not a fixed rule.
Assumptions and Limitations
- Independent trades: Both the analytical formula and Monte Carlo assume each trade outcome is independent of prior trades. Serial correlation or momentum effects, common in trending markets, can cause consecutive losses that increase realized ruin risk beyond what either method predicts.
- Binary outcomes: Each trade is modeled as either the full average win or the full average loss. Real strategies have variable trade sizes; this simplification understates the fat tail of the loss distribution and may underestimate ruin probability for strategies with occasional catastrophic losses.
- Compound sizing: Risk per trade is applied as a fraction of the current capital (Kelly-style). This means losses reduce the absolute risk amount, which technically makes ruin impossible in the mathematical sense (capital approaches zero asymptotically rather than reaching zero). The ruin threshold parameter simulates a practical "ruin" at a defined drawdown level rather than true zero-capital ruin.
- No regime change: Win rate and average win/loss are held constant. In reality, strategy edge erodes, market regimes shift, and parameters change, all of which increase real-world ruin risk beyond what static-parameter models show.
- Analytical formula approximation: The formula used (Gambler's Ruin derivative) is a simplification. The exact ruin probability for strategies with asymmetric win/loss amounts and continuous compounding requires more complex formulas. For precise calculation, rely on the Monte Carlo estimate with high path counts.
A Probability That Moves With Your Assumptions
The value of a calculation like this is comparative. Entering a set of inputs and then changing one at a time shows which variable the outcome is most sensitive to, and for most parameter sets that variable is position size rather than the edge. That is a more durable lesson than any single probability the tool reports.
Reading the output as a forecast asks too much of it. The figure is conditional on inputs estimated from a limited record, and those estimates carry uncertainty of their own that the calculation does not carry forward.
The assumptions are the usual ones and they lean optimistic. A fixed win rate, a fixed payoff, independent outcomes and unchanging conditions describe a tidier process than any real trading record, and each simplification understates the chance of a punishing sequence.
A low reported probability is therefore weak reassurance while a high one is a strong warning. That asymmetry is worth respecting when deciding what to do with the number.
Frequently Asked Questions
Why do the analytical and Monte Carlo estimates sometimes differ substantially?
The analytical formula estimates infinite-horizon ruin probability, given unlimited trades, what fraction of paths eventually ruin? The Monte Carlo estimate is horizon-specific, what fraction ruins within the specified trade count? For a strategy with positive expectancy, the Monte Carlo ruin probability increases with more trades and eventually approaches the analytical estimate (never exactly reaching it for truly positive expectancy). If the two estimates differ by more than a few percentage points, check whether your trade count is low relative to your strategy's volatility, a large gap signals that most ruining paths need more than the specified trade count to reach the threshold.
What is an acceptable risk-of-ruin percentage for a trading strategy?
There is no regulatory or universally agreed answer, risk-of-ruin tolerance is a personal or firm-level risk-management choice, not a mandated standard. As an industry convention rather than a formal rule, many discretionary traders informally target RoR below 1-5%, and systematic strategies managed on behalf of others are often held to a tighter band, roughly 0.5-2%, because of client capital-preservation expectations. This heuristic assumes independent trade outcomes, fixed position sizing, and a realistic trading horizon (250-500 trades), it does not account for regime change or correlated losses, which raise real-world ruin risk above the modeled estimate. A RoR above 10% over any reasonable horizon is a common practitioner signal that either the risk per trade is too high or the edge is insufficient to justify trading this strategy at the given size. But you should set your own threshold based on your capital, goals, and drawdown tolerance rather than treating any single number as authoritative.
How does reducing risk per trade affect the risk of ruin?
Ruin risk is highly sensitive to risk per trade. Halving your risk per trade typically reduces ruin probability by far more than half, the relationship is exponential, not linear. This is because with smaller risk per trade, you need more consecutive losing trades to reach the ruin threshold, and the probability of that many consecutive losses falls exponentially with each additional trade required. The effect is most dramatic when your edge is small (near 50% win rate): cutting risk per trade from 2% to 1% may reduce ruin probability by 80% or more.
Does positive expectancy guarantee no risk of ruin?
Over infinite trades, positive expectancy does guarantee that ruin probability is strictly less than 100%, but it does not make ruin impossible or even unlikely for moderate trade counts and high risk per trade. A strategy with 51% win rate and equal win/loss amounts (edge of +2%) with 5% risk per trade can still have a 20-40% chance of hitting a 50% drawdown within 500 trades due to normal variance. Positive expectancy is a necessary condition for long-run survival; it is not sufficient without adequate capitalization relative to variance.
What ruin threshold should I use?
The ruin threshold represents your personal definition of "I will stop trading this strategy if I lose X%." A threshold of 25% is appropriate for a strategy within a larger portfolio where other capital exists to rebuild. A threshold of 50% is common for stand-alone strategy accounts. A threshold of 80-100% represents near-total capital depletion. Lower thresholds give higher ruin probabilities for the same edge and sizing. There is no formal rule requiring it, but as a matter of common practice many risk managers treat a drawdown beyond 25% as a trigger to review or pause a strategy, which is why 25-30% shows up often as a real-world working ruin threshold even when the account's stated stop point is deeper.
Does the calculator assume every trade risks the same fraction of capital?
Yes, and that assumption is doing significant work. Fixed-fractional risk means position size falls automatically as equity declines, which slows depletion and is the mechanism behind much of the calculated survival probability. An account that sizes in fixed share counts, or that keeps risking the same dollar amount after losses, depletes faster than the model shows. Where sizing does not follow the assumed rule, the output should be treated as a lower bound on risk.
What inputs should be used for a strategy with a lot of scratch trades?
Trades that finish near breakeven fit awkwardly into a win-or-lose framework, and the classification changes the answer. Counting them as wins inflates the win rate while dragging the average win down; counting them as losses does the reverse. A cleaner approach is to exclude them from both averages and reduce the trade count accordingly, then note that the model now describes only the decisive trades. Whichever convention is used should be stated with the result.
How many historical trades are needed before the win rate input is trustworthy?
A win rate from a small sample carries wide uncertainty, and the calculator treats whatever is entered as exact. Thirty trades can easily produce an observed rate several points away from the underlying one, and ruin probability is sensitive to that gap. Rather than seeking a threshold, the practical step is to run the calculation across the plausible range of win rates and payoff ratios, then work from the least favourable corner rather than the point estimate.
Can this be applied to a portfolio holding several positions at once?
Only loosely. The model assumes sequential, independent outcomes, while a portfolio takes several risks simultaneously and those risks may move together. Correlated positions can produce a combined loss far larger than any single trade in the input, which the sequential model has no way to generate. Treating the whole portfolio's periodic return as one composite outcome is a closer fit than treating each position as a separate trade, though it still assumes independence between periods.
References
- Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd ed. Wiley. Chapter 14 provides the classical Gambler's Ruin derivation and exact ruin probabilities for symmetric and asymmetric random walks.
- Vince, R. (1992). The Mathematics of Money Management. Wiley. Covers risk of ruin in the context of compound position sizing, Kelly criterion, and its relationship to drawdown depth and trade-by-trade risk.
- Tharp, V. K. (2006). Trade Your Way to Financial Freedom, 2nd ed. McGraw-Hill. Chapter 12 covers risk of ruin estimation for active traders, including the role of expectancy and trade variance.
- Ruin probability formula: Browne, S. (1997). Survival and Growth with a Liability: Optimal Portfolio Strategies in Continuous Time. Mathematics of Operations Research. Provides a continuous-time derivation that underpins the exponential approximation used here.
Educational Disclaimer
This tool is for educational purposes only. Risk-of-ruin estimates are based on simplified analytical and Monte Carlo models using user-entered parameters. Actual ruin probability depends on factors this tool does not model, including regime change, serial correlation, parameter instability, and tail events. This is not financial advice. Consult a qualified financial professional before making trading decisions.