What Is Risk of Ruin?
Risk of ruin is the probability that a strategy loses enough capital to stop being viable, given its edge and its bet size. A positive expectancy does not make ruin impossible — it makes it unlikely, and how unlikely depends almost entirely on how much is risked per trade.
What is the formula?
For a series of equal-sized bets at even money, the classic form is ((1 − A) ÷ (1 + A))^U, where A is the edge (win rate minus loss rate) and U is the number of bet units of capital.
Worked example. A 55% win rate at a 1:1 payoff gives A = 0.10. Risking 5% of the account per trade gives U = 20 units. Risk of ruin = (0.90 ÷ 1.10)^20 = 0.818^20 = 1.8%.
Halve the bet size to 2.5% and U becomes 40: 0.818^40 = 0.03%. The edge did not change at all; the survival probability changed by a factor of about 55.
Why does bet size dominate?
Because ruin probability falls exponentially in the number of units, and only linearly in the edge. Compare, all at a 1:1 payoff:
| Win rate | Risk per trade | Units | Risk of ruin |
|---|---|---|---|
| 55% | 10% | 10 | 13.4% |
| 55% | 5% | 20 | 1.8% |
| 55% | 2% | 50 | 0.004% |
| 60% | 10% | 10 | 1.7% |
Cutting risk from 10% to 2% at a 55% win rate improves survival more than raising the win rate from 55% to 60% at unchanged size — and one of those is under your control today.
What does the model leave out?
Correlated positions. Five trades in the same sector are one bet with five tickets. Ruin models assume independence, and correlated risk breaks that assumption exactly when it matters.
Gaps and slippage. A 2% risk is 2% only if the stop fills. Overnight gaps and fast markets do not respect it.
Changing edge. The formula assumes the edge is constant and known. In practice it is estimated from a sample and can decay.
Practical ruin. Most traders stop long before the account reaches zero. A 40% drawdown ends more trading careers than a 100% loss does.
How does this connect to a track record?
The reason bet size dominates edge here was established in the same 1956 paper that gave the Kelly criterion its name: the growth-optimal fraction of a bankroll is finite and betting above it reduces long-run growth even when the edge is real.[1] Risk of ruin is the tail of that same relationship.
For a sense of how often the tail is reached in practice: following Taiwanese day traders from 1992 to 2006, under 1% predictably earned positive abnormal returns net of fees.[2] Most of that population was not ruined by a single catastrophic bet but by a negative expectancy applied at a size that left no room to find out.
A metric is a summary of a record, so it inherits every weakness of that record. Computed from trades selected after the fact, it is a number about the selection. kappi commits each trade before it resolves and publishes it on a Merkle-anchored log, so PnL, RME, correlation to SPX, mean R:R and trade count over 30, 100 and 200-day windows are computed over everything that was committed, losses included. $15/month to keep a record; reading one is free.
Sources
- Kelly, 'A New Interpretation of Information Rate', Bell System Technical Journal 35(4), 1956, 917–926 read 2026-08-16
- Barber, Lee, Liu & Odean, 'Do Day Traders Rationally Learn About Their Ability?' — of Taiwanese day traders 1992–2006, under 1% predictably earned positive abnormal returns net of fees read 2026-08-16
Frequently asked questions
How do you calculate risk of ruin?
For equal-sized even-money bets, ((1−A)/(1+A))^U where A is the edge and U the number of bet units of capital. A 55% win rate risking 5% per trade gives (0.9/1.1)^20 = 1.8%.
Does a profitable strategy have zero risk of ruin?
No. Positive expectancy makes ruin unlikely, not impossible. At a 55% win rate and 10% risk per trade the probability is still 13.4%, which is not a small number.
What matters more, edge or position size?
Position size. Ruin probability falls exponentially in the number of bet units and only linearly in the edge, so cutting risk from 10% to 2% helps more than raising a win rate from 55% to 60%.
What does the risk of ruin formula assume?
Independent trades, a constant known edge, and stops that fill at the intended price. Correlated positions, gap risk and edge decay all make the real number worse than the model's.