Even a strategy with a genuine statistical edge can go bust if it bets too large relative to that edge. Risk of ruin quantifies this precisely, and the Kelly Criterion tells you the theoretical growth-optimal bet size — though almost no serious trader uses full Kelly in practice.
Simplified Risk of Ruin Formula
Risk of Ruin ≈ ((1 − Edge) / (1 + Edge)) ^ (Capital Units)Where Edge is your win probability advantage (e.g. Win% − Loss%, for equal-sized bets) and Capital Units is how many 'risk units' your account is divided into. More capital units (i.e. smaller risk per trade) drives risk of ruin toward zero exponentially.
| Edge | Risk per Trade | Approx. Risk of Ruin |
|---|---|---|
| 10% | 5% | ~13% |
| 10% | 2% | ~0.2% |
| 10% | 1% | ~0.0004% |
| 5% | 5% | ~36% |
| 0% | Any | 100% (eventually) |
If your expectancy is zero or negative, risk of ruin approaches 100% over enough trades no matter how small you size — sizing only delays the inevitable. Position sizing cannot fix a broken strategy; it can only manage a good one.
The Kelly Criterion
Kelly % = W − ((1 − W) / R)Where W is win probability (as a decimal) and R is the win/loss ratio (average win ÷ average loss). This gives the fraction of capital to risk per trade that maximizes long-run compound growth.
Worked Example
W = 45% (0.45), average win/loss ratio R = 2. Kelly % = 0.45 − (0.55 / 2) = 0.45 − 0.275 = 0.175, or 17.5% of capital per trade. This is dramatically higher than the 1-2% most traders use — and that gap is deliberate.
Full Kelly assumes your win rate and win/loss ratio estimates are exactly correct forever — in live trading they're estimates from a limited, noisy sample. Even small estimation errors at full Kelly size produce extreme volatility and drawdowns of 50%+ are common even when the edge is real.
Fractional Kelly in Practice
Most professional sizing frameworks use 10-25% of full Kelly. In the example above, 17.5% full Kelly becomes roughly 1.75-4.4% at quarter to half Kelly — much closer to the 1-2% commonly recommended, and consistent with why that range persists as a practical standard.
| Kelly Fraction | Risk per Trade (from 17.5% full Kelly) | Growth vs. Volatility |
|---|---|---|
| 100% (full) | 17.5% | Max growth, extreme volatility |
| 50% | 8.75% | ~75% of growth, much lower volatility |
| 25% | 4.4% | ~44% of growth, smooth equity curve |
| 10% | 1.75% | ~19% of growth, very stable |
Practical Takeaways
- ▸Kelly requires accurate win rate and win/loss ratio inputs — garbage in, garbage out.
- ▸Use Kelly as a ceiling, not a target — trade well below it (quarter-Kelly or less) to survive estimation error.
- ▸Recalculate periodically as your actual win rate and R:R evolve with more trade data.