Risk of Ruin
Risk of ruin is the probability that a losing streak destroys enough capital to end a trading career before an edge has time to express. It measures survival, not profitability — a positive-expectancy system can still go broke if position size is too large.
The Non-Linear Explosion
Risk of ruin does not scale proportionally with risk per trade. It accelerates:
| Risk per trade | Probability of 50% drawdown |
|---|---|
| 0.5% | low |
| 1% | ~18% |
| 2% | ~65% |
| 5% | approaches certainty |
Doubling risk per trade does not double ruin probability — it multiplies it. This non-linearity is the core warning. The math works against you faster than intuition suggests.
Loss Asymmetry
Recovery from a drawdown requires a larger percentage gain on the reduced capital:
| Loss | Gain required to recover |
|---|---|
| 10% | 11% |
| 30% | 43% |
| 50% | 100% |
| 75% | 300% |
Losing half the account requires doubling the remaining balance just to return to the starting point. This asymmetry means each additional point of drawdown is progressively harder to claw back — which is why preventing large drawdowns matters more than capturing extra upside.
The Practical Rule
A single bad week or bad month should not be able to destroy the account. Common guidance: keep risk per trade between 0.25% and 2%. At that range, a normal losing streak produces a painful but survivable drawdown. At 5% risk per trade, a modest run of losses can wipe the account before the system's edge has any chance to express.
This maps directly to ergodicity: for a career of repeated bets, what matters is path-dependent survival across time, not average expected value across all possible worlds. A path that includes a ruin event cannot continue.
Connections
- position-sizing — the direct lever; risk of ruin is controlled by keeping size small enough
- ergodicity — the theoretical ground; time-average survival vs. ensemble average; ruin is a path-dependent event
- kelly-criterion — Kelly maximizes long-run growth but at full Kelly the drawdowns are severe; fractional Kelly trades off growth rate for survival probability
- expectancy — positive expectancy is necessary but not sufficient; ruin is the survival constraint that must be satisfied first