Risk of Ruin: Probability of Going Broke
⚡ Read this before you open your next trade
Risk of ruin (RoR) is the probability that a trading strategy will eventually lose all capital given its edge and position sizing. It's one of the most important risk metrics — much more important than expected return, Sharpe ratio, or win rate. A strategy with excellent expected return but high risk of ruin will eventually blow up; a strategy with modest expected return but near-zero risk of ruin can compound reliably for decades. Calculating RoR involves simple math once you know win rate, payoff ratio, and risk per trade. Understanding RoR transforms position sizing decisions — you stop asking "how much can I win?" and start asking "how do I avoid zero?"
The Risk of Ruin Formula
Simplified formula for equal-sized risk per trade: RoR = ((1 - edge) / (1 + edge))^N where edge = (win_rate × payoff_ratio) - loss_rate, and N = number of "units" in account (account balance / risk per trade). Example: 55% win rate, 2:1 payoff. Edge = (0.55 × 2) - 0.45 = 1.1 - 0.45 = 0.65 (65% edge per unit). With 100 units (1% risk per trade), RoR = ((1-0.65)/(1+0.65))^100 = (0.21)^100 ≈ 0 (effectively zero). With 20 units (5% risk per trade), RoR = (0.21)^20 ≈ 0.0000001 (still essentially zero with this edge). Now a weaker strategy: 50% win rate, 1:1 payoff. Edge = (0.5 × 1) - 0.5 = 0 (zero edge). RoR = (1/1)^N = 1 (100% — guaranteed ruin over infinite time). Even tiny edges compound over many trades; zero edge is certain ruin. More complex formulas account for different win/loss amounts per trade, maximum simultaneous positions, and other realistic factors.
Inputs Matter: Edge Sensitivity
Small changes in edge estimation produce large changes in RoR. Using 1% risk per trade (100 units): 60% win rate, 1:1 payoff → Edge 20%, RoR ≈ 0. 55% win rate, 1:1 payoff → Edge 10%, RoR ≈ 0.0000001 (still negligible). 52% win rate, 1:1 payoff → Edge 4%, RoR ≈ 0.0001 (0.01%, still safe). 51% win rate, 1:1 payoff → Edge 2%, RoR ≈ 0.04 (4%, meaningful risk). 50% win rate, 1:1 payoff → Edge 0%, RoR = 100% (certain eventual ruin). The margin between "safe" and "ruined" is narrow, especially for mechanical strategies with modest edge. Practical implication: if your win rate estimate might be 2% off, don't size as if your central estimate is true. Use lower bound of confidence interval. If you estimate 55% win rate with 95% CI of [51%, 59%], size position as if win rate were 51% — safer margin for error.
Position Size Impact on RoR
RoR drops exponentially as position size decreases. With 55% win rate, 1:1 payoff: 10% risk per trade (10 units) → RoR ≈ 0.13 (13% chance of ruin). 5% risk per trade (20 units) → RoR ≈ 0.018 (1.8% chance of ruin). 2% risk per trade (50 units) → RoR ≈ 0.0003 (0.03%). 1% risk per trade (100 units) → RoR ≈ 0.0000001 (negligible). 0.5% risk per trade (200 units) → RoR ≈ 10^-14 (essentially zero). Each halving of position size roughly squares the safety margin. This is why reducing position size from 5% to 2.5% isn't just "50% safer" — it's roughly 500× safer measured by RoR. Professional traders converge on 1-2% risk per trade specifically because this range produces negligible RoR across most edge estimates while still allowing meaningful account growth. Sub-1% sizing provides extreme safety but extends time to meaningful returns; above 2% increases RoR materially as edge estimates get close to zero.
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RoR vs Expected Drawdown
Risk of ruin and expected drawdown are related but distinct. RoR is the probability of eventually going to zero (theoretical infinite horizon). Expected max drawdown is the expected worst decline from peak equity over a specific time horizon (e.g., 1 year, 5 years). A strategy can have: (1) Low RoR but high expected drawdown — e.g., trend-following with 1% per trade. RoR is negligible but 20-30% drawdowns are normal. (2) Moderate RoR and moderate drawdown — e.g., mean-reversion with 2-3% per trade. RoR might be 1-5%; drawdowns might be 30-40%. (3) High RoR regardless of drawdown — typical for undersized or negative-edge strategies. For practical trading, expected max drawdown is often more important than RoR because drawdowns cause psychological abandonment even when mathematical ruin is impossible. A strategy with 0.001% RoR but 45% expected max drawdown will typically get abandoned at drawdown, producing emotional "ruin" without mathematical ruin.
How to Drive RoR to Effectively Zero
Practical framework: (1) Confirm positive edge — without positive expected value, any RoR > 0 becomes 100% over long enough horizon. Verify edge through out-of-sample testing, forward testing, or real trading results over 200+ trades. (2) Size conservatively — 1% risk per trade produces negligible RoR even with modest edges. For extra safety, use 0.5-1% range. (3) Diversify to independent strategies — two uncorrelated strategies each with low RoR have aggregate RoR approximately equal to product of individual RoRs. If each is 0.001%, combined is 0.000001% (assuming true independence). (4) Respect stops — psychological discipline to accept losses at defined levels is what makes RoR calculations valid. Traders who "widen stops" or "average down" invalidate the RoR framework. (5) Monitor regime changes — RoR assumes stable edge. If market regime shifts and edge deteriorates, recalculate RoR with new parameters; may require reducing position size. (6) Account size management — withdraw gains periodically to a separate safe account. If trading account blows up, the withdrawn portion survives.
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Frequently Asked Questions
What risk of ruin is acceptable?
For serious long-term trading: under 0.01% (1 in 10,000). This ensures that even over 10,000+ trade careers, ruin is extremely unlikely. For active day trading with constant reinvestment: under 0.1%. For recreational trading with money you can afford to lose entirely: under 5% might be acceptable as the account failing doesn't affect broader financial life. Professional money managers targeting institutional capital aim for RoR < 0.001% (1 in 100,000) because investor redemptions during drawdowns amplify ruin probability significantly.
Does RoR formula work for trading with variable R:R?
The simple formula assumes constant risk per trade. For variable trade outcomes, use "average R" approach: calculate average R-multiple of winners and losers from historical trades, use these in formula. More precise alternatives: Monte Carlo simulation — run 10,000+ random sequences of trades using historical outcome distribution, count how many sequences reach zero. More accurate but requires more data and computation. Commercial platforms like NinjaTrader and TradingView offer backtesting tools that include Monte Carlo RoR analysis.
What if my edge declines over time?
RoR formulas assume constant edge. In reality, edges can decline as markets evolve, more traders adopt the same strategy, or structural changes occur. Solutions: (1) Rolling-window RoR calculation — recompute RoR using most recent 200-500 trades rather than all-time. Provides updated RoR based on current performance. (2) Reduce position size if edge indicators (win rate, avg win/loss) show deterioration of 20%+ from historical baseline. (3) Retire strategy if edge fully vanishes — no position size makes negative-edge strategy safe. (4) Continuous monitoring — weekly review of rolling performance statistics flags edge decay before it becomes catastrophic.
Should RoR be calculated per trade or per day?
Typically per trade, as that's the fundamental unit of risk. However, for day traders taking multiple trades daily, daily aggregated RoR provides meaningful second view. Daily RoR accounts for correlation between same-day trades (often higher than between-day trades) and psychological reality of daily P&L. Some traders track both: per-trade RoR for theoretical foundation, daily RoR for practical position management. If daily RoR exceeds per-trade RoR significantly, it signals correlation risk in daily position stack.
Is RoR the same as risk of drawdown?
No. RoR is probability of total ruin (account goes to zero). Risk of drawdown is probability of specific decline levels (e.g., 20% drawdown, 30% drawdown). A strategy with 0% RoR can still have 50% probability of 20% drawdown. Both metrics matter: RoR ensures mathematical survival, drawdown probability affects psychological sustainability. For practical trading, calculate both — RoR for long-term safety, drawdown probabilities for tolerance management. If drawdown probabilities exceed your psychological tolerance, reduce position size even if RoR is already near zero.
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Kacper MrukXAUUSD & ETHUSD Trader | Macro + options data | Think, don't follow
Creator of Take Profit Trader's App. Specializes in XAUUSD and ETHUSD, combining macro analysis with options data. He teaches not how to trade, but how to think in the market. Actively trading since 2020.
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