Risk of Ruin
Trading Intelligence
9 min read
riskOfRuin
Compute the probability of account wipeout given your win rate, payoff ratio, and risk per trade to ensure long-term survival.
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9 min read
Compute the probability of account wipeout given your win rate, payoff ratio, and risk per trade to ensure long-term survival.
Risk of Ruin (RoR) is the mathematical probability that a trader's account hits a critical loss threshold (typically 50–100%) before recovering. It is a function of win rate, payoff ratio, risk per trade, and trade-outcome correlation.
Every edge can fail if you risk too much. This is the math that tells you how likely it is to survive long enough to win.
Prerequisites: Distribution of Trade Returns, Risk Per Trade & Position Sizing.
You’ve got a system. You’ve got a positive edge. You’ve got your journal full of +0.5R and +2R wins.
But there’s a lurking question every pro eventually faces:
❓ “How likely am I to lose so much in a row that I can’t recover?”
That’s what Risk of Ruin (RoR) answers — mathematically.
And if you’re trading without knowing it?
You may be optimizing toward performance — but gambling with survival.
Let’s fix that.
Risk of Ruin is the probability that your account hits a critical loss level (e.g. 50%, 80%, 100%) before recovery.
In other words:
This isn't fear-mongering — it’s pure math.
Even with a solid edge, risking too much can guarantee failure over time.
The classical closed form holds only for equal-size, binary bets (1R win or 1R loss):
RoR = ((1 - edge) / (1 + edge))^N
where edge = 2p - 1 (p is win probability, binary case) and N = Capital / Risk per trade (units of risk before ruin)
This formula breaks for asymmetric R:R. For a system with 2R wins and 1R losses, substituting expected-R into
edgeis dimensionally inconsistent and understates ruin probability. For asymmetric payoffs use the Vince formula (Ralph Vince, The Mathematics of Money Management, 1992) or a Monte Carlo simulation resampled from your journal.
Let’s walk through the binary-case example as an intuition pump.
Now estimate:
RoR ≈ [(1 – 0.35) / (1 + 0.35)] ^ (100 / 2)
RoR ≈ (0.65 / 1.35)^50
RoR ≈ (0.481)^50 ≈ 0.00000008 → effectively **0%**
With a good edge and conservative risk, your chance of ruin is nearly zero.
Try 10% risk per trade instead of 2%:
(0.481)^(100 / 10) = (0.481)^10 ≈ 0.0025 → RoR = **0.25%**
Now imagine 30% risk per trade. You only get ~3 units of cushion before ruin:
(0.481)^(100 / 30) ≈ (0.481)^3.33 ≈ 0.10 → RoR ≈ 10%
That is not certain death — but it is a one-in-ten chance of total wipeout with a winning system. Unacceptable for any serious operator.
Risk of Ruin grows exponentially with risk per trade (45% WR, 2R:1R system, 100% capital).
Same edge, three sizing choices: orders-of-magnitude difference in wipeout probability.
Edge doesn’t matter if your size is too big.
RoR is an exponential function of (Capital / Risk). Cutting risk from 5% to 2% does not cut RoR by 60% — it raises the survival base to the power 50 instead of 20, which is orders of magnitude difference. Halving risk roughly squares the survival probability. This is why every serious textbook (Vince, Brown, Tharp) lands in the same 0.5–2% risk-per-trade band.
For any system with asymmetric R:R or correlated trades, Monte Carlo is not optional — it is the right tool. The closed form is just an intuition pump. MC simulates thousands of trade sequences resampled from your journal, generating:
Useful for:
See Aaron Brown, Red-Blooded Risk (Wiley, 2011), Ch. 8, for the practitioner treatment of MC for survival probability.
| Principle | Recommendation |
|---|---|
| Use fixed % risk per trade | 0.5%–1.5% for most systems |
| Know your EV and variance | From backtest or real journaled data |
| Simulate worst streaks | Use rolling drawdowns or MC simulation |
| Accept a soft stop threshold | Pause at 15–20% drawdown, reduce size |
| Re-validate after 100+ trades | Edge may decay, RoR must adapt |
Risk of Ruin is the probability that your account hits a critical loss level (typically 50%, 80%, or 100%) before recovering — even if your trading system has a positive expectancy.
Yes. Positive expectancy only describes the average outcome over many trades. Variance and oversized risk can blow up an EV+ account before the edge has time to play out, especially when trades are correlated or position sizing exceeds 2% per trade.
For most systems with a real edge, fixed fractional risk in the 0.5%–1.5% range keeps RoR effectively at zero. This is the band Vince, Brown, and Tharp converge on across decades of practitioner research.
For asymmetric R:R systems and correlated trades — yes. The closed form is a binary-case intuition pump. Monte Carlo, resampled from your actual journaled trades, is the correct primary tool for estimating real-world ruin probability.
Risk of Ruin is the math behind why traders who “almost made it” disappear.
Don’t assume your edge will save you — design your risk so it survives long enough to matter.
Let others blow up trying to make 5% a day. You’ll still be here in 5 years — compounding confidently.
Next: Position Sizing Based on Confidence Intervals — turns the survival math here into a sizing rule.