Risk of Ruin: The Formula Every Systematic Trader Should Know

Risk of ruin is the probability that your account falls to a level from which you stop trading - whether that's zero, a broker's margin floor, or simply the drawdown at which you'd give up. It's the single most useful number in systematic trading because it reframes the question from “how much could I make?” to “what's the chance I'm still here in five years?” And unlike most trading questions, it has a formula.

The classic formula

For the simplified case - every trade risks one fixed “unit”, wins and losses are equal in size, and trades are independent - the risk of ruin with win probability p (and loss probability q = 1 − p, with p > 0.5) is:

Risk of ruin = (q / p)^N

where N is how many risk units your capital contains. Two levers jump out immediately: your edge (the q/p ratio) and your unit count N - which is set entirely by position sizing.

An illustrative example

Illustrative numbers only. Suppose a system wins 55% of the time with equal-sized wins and losses, so q/p = 0.45/0.55 ≈ 0.818.

• Risking 5% per trade gives N = 20 units: 0.818²⁰ ≈ 1.8% risk of ruin.
• Risking 2% per trade gives N = 50 units: 0.818⁵⁰ ≈ 0.004%.
• Risking 10% per trade gives N = 10 units: 0.818¹⁰ ≈ 13%.

Same strategy, same edge - and the survival probability swings from near-certainty to a meaningful chance of ruin purely on sizing. This is the mathematical spine of the 1% rule: small units make N large, and N sits in the exponent.

What the simple formula leaves out

1. Unequal wins and losses. Real systems have asymmetric payoffs; extended versions of the formula (or simple Monte Carlo simulation) handle this.
2. Estimation error. Your 55% win rate is a backtest estimate. If the true rate is 52%, ruin probabilities jump sharply - which is why sample size in backtests matters so much before trusting any input.
3. Correlated losses. The formula assumes independent trades. Losses that cluster - correlated positions, regime shifts - behave like one big unit, effectively shrinking N.
4. Psychological ruin. Most traders abandon systems at a drawdown far shallower than zero. Compute ruin against your real quitting point, not the theoretical one.

Risk of ruin vs Kelly

The Kelly criterion answers a different question - what size maximises long-run growth - and full Kelly sizing accepts brutal drawdowns on the way. Risk of ruin is the constraint you check first: growth optimisation is meaningless if the path to it includes an unacceptable chance of not surviving. Practitioners often size well below Kelly precisely to keep ruin probability negligible; see Kelly and volatility scaling.

Common mistakes

• Computing it once and never updating. Edge estimates drift; re-run the numbers as live data accumulates.
• Using backtest win rates uncritically. Haircut your inputs - the formula is exquisitely sensitive to them.
• Ignoring it because the strategy “feels” safe. Feelings don't exponentiate; formulas do.

This is why Nebula enforces hard risk caps on every system it builds: whatever the strategy logic, the per-trade unit stays small, which keeps N large and the ruin exponent working for you rather than against you.

Trading carries a high level of risk. Nothing here is financial advice; past performance does not predict future results.