Risk of Ruin Calculator

What counts as ruin in this calculator?

Ruin means reaching your chosen loss boundary. With $10,000 of starting capital and a 30% threshold, that boundary stays at $7,000. If equity first rises to $12,000, the boundary still stays at $7,000. A 30% peak-to-trough drawdown would instead stop at $8,400. Use the maximum drawdown calculator to examine that separate historical measure.

The formula and its assumptions

Let p be win probability, b the reward/risk ratio, f the risk percentage of starting capital, and d the loss-threshold percentage. Each trade is modeled as +b risk units on a win or -1 unit on a loss. Trades are independent and their probabilities and payoffs stay constant.

The exponential expression is the infinite-horizon boundary probability for a Brownian model with drift, applied here as a diffusion approximation to discrete trades. It is not an exact solution for arbitrary trade payoffs. The calculator returns 100% when μ is zero or negative and 0% when p is exactly 1. A historical 100% win rate does not prove future losses are impossible.

Cash risk stays fixed: 2% of $10,000 means $200 for each trade, including after losses. Percentage-of-current-equity sizing has a different wealth process. The sample-trades field is a note only; it does not enter this formula or provide a confidence interval.

A worked example you can reproduce

Use the defaults: p = 0.50, b = 1.5, f = 2%, d = 30%. Expected profit μ = 0.50 × 1.5 − 0.50 = 0.25 risk units. Variance σ² = 0.50 × 0.50 × 2.5² = 1.5625, and u = 30 / 2 = 15. The estimate is exp(−2 × 0.25 × 15 / 1.5625) = exp(−4.8) = 0.0082297, or about 0.823%. The display rounds this to 0.82%.

The colored bands use cutoffs of 10%, 30%, and 50% solely to group outputs. They are not empirically validated safety levels or recommendations to trade.

Stress-test clustered losses and position sizing

At $200 fixed cash risk, 15 consecutive losses take $10,000 to $7,000. If risk is 2% of current equity instead, 15 losses leave $10,000 × 0.98¹⁵ = $7,385.69, a 26.14% loss; 18 consecutive losses are needed to cross 30%. These are deterministic stress paths, not the probability of ruin.

With independent 50% loss probability, one specified block of 15 losses has probability 0.5¹⁵ = 0.00305%. In a hypothetical clustered-loss scenario with a 50% chance of the first loss and an 80% chance of each following loss conditional on a loss, the same block has probability 0.5 × 0.8¹⁴ = 2.199%. This comparison shows why independence matters. Neither number gives the chance of a losing streak anywhere in a longer history.

1. Estimate win rate and average net win/loss from comparable trades. Include commissions, spread, financing, and slippage in the outcomes.
2. Repeat the calculation with a lower win rate and lower payoff ratio. A small sample can make both inputs unstable.
3. Inspect overlapping positions, losses grouped by date, and shared market exposure. One market move can affect several trades together.
4. Test gaps and losses larger than one risk unit separately. A stop order can fill beyond its trigger price.

The risk of ruin simulator shows sampled paths with current-equity sizing and a chosen number of trades. Its zero-balance ruin definition differs from this fixed loss threshold, so the two headline percentages are not interchangeable.

Sources and model limits

• Karl Sigman, Columbia University: Notes on Brownian Motion, section 1.8 provides the drifted Brownian boundary result. Matching its mean and variance to the two-outcome trade model is this calculator's approximation.
• FINRA: Stop Orders, Factors to Consider During Volatile Markets explains why the stop price can differ from the execution price.

Sources checked October 17, 2026. This tool does not model changing market regimes, variable payoff tails, correlated positions, margin liquidation, or future parameter uncertainty. Educational estimates only, not investment advice or a guarantee of returns.

Risk of ruin FAQ