Risk of Ruin

Risk of ruin can be calculated using several formulas depending on the assumptions:

Simple risk of ruin formula (fixed bet size): RoR = ((1 - Edge) / (1 + Edge))^N, where Edge = (Win Rate x Average Win - Loss Rate x Average Loss) / Average Loss, and N = number of units in the account (account size / risk per trade).

Example: You risk $500 per trade on a $25,000 account (N = 50 units). Your win rate is 55% with a 1.5:1 reward-to-risk. Edge = (0.55 x 750 - 0.45 x 500) / 500 = (412.5 - 225) / 500 = 0.375. RoR = ((1 - 0.375) / (1 + 0.375))^50 = (0.455)^50 = essentially 0%. Your account is safe.

Same example with 5% risk per trade: N = 20 units. RoR = (0.455)^20 = 0.00004 = 0.004%. Still very safe.

Now with $2,500 risk per trade (10%): N = 10 units. RoR = (0.455)^10 = 0.034 = 3.4%. Getting dangerous.

With $5,000 risk (20%): N = 5 units. RoR = (0.455)^5 = 0.019 = 1.9%. One bad streak of 5 losses and you are wiped out.

The takeaway: Reducing position size from 10% to 2% of account doesn't just reduce risk by 5x — it reduces risk of ruin exponentially, from dangerous levels to near zero. This is why professional traders obsess over position sizing more than any other variable.

The 1% rule: Risk no more than 1% of total account equity on any single trade. With a $50,000 account, your maximum loss per trade should be $500. This gives you 100 units of risk — enough to survive an extremely unlikely losing streak of 20+ consecutive losses.

The 2% maximum: More aggressive traders may risk up to 2% per trade, giving 50 units of risk. This is the absolute maximum recommended by most risk management experts. At 2%, a 10-trade losing streak (which happens to every trader eventually) costs 20% of the account — painful but recoverable.

Kelly Criterion and Half-Kelly: The Kelly Criterion calculates the mathematically optimal bet size to maximize long-term growth: Kelly % = (Win Rate x Avg Win / Avg Loss - Loss Rate) / (Avg Win / Avg Loss). In practice, traders use half-Kelly (50% of the Kelly recommendation) because Kelly assumes perfect knowledge of true win rates and payoffs. Overestimating your edge with Kelly sizing can dramatically increase risk of ruin.

Portfolio heat limits: Even with 1% risk per trade, holding 20 correlated positions creates 20% total risk exposure. Limit total portfolio heat (sum of all open position risk) to 6-10% of equity. This prevents correlated losses from creating unacceptable drawdowns.

Adaptive sizing after drawdowns: Reduce risk per trade proportionally during drawdowns. After a 10% drawdown, cut risk to 0.5% per trade. This slows the drawdown rate and preserves capital for recovery. Resume normal sizing only after equity recovers.

Scenario 1 — Oversized positions: A trader risks 10-20% per trade, hits a 5-trade losing streak, and loses 50-100% of their account. This is the most common cause of ruin. It happens because the trader's edge is real (55% win rate) but position sizing is too aggressive for the volatility of outcomes.

Scenario 2 — Averaging down without limits: A trader buys a declining stock, adds at a lower price, adds again, and again. Each add increases position size and total exposure. When the stock continues falling, the concentrated position destroys the account. This is how Nick Leeson blew up Barings Bank.

Scenario 3 — Correlated bets: A trader holds 10 different positions that all look independent but are all long the same factor (growth, tech, momentum). When that factor reverses, all 10 positions lose simultaneously. 10 positions at 2% risk each that all lose is a 20% hit — equivalent to one massive oversized bet.

Scenario 4 — Revenge trading: After a significant loss, the trader increases size trying to recover quickly. This increases risk per trade precisely when emotional state is worst and decision-making is impaired. The larger bets amplify losses, accelerating the death spiral.

Scenario 5 — Tail risk (gap events): A stock held overnight gaps down 30% on unexpected news (fraud, earnings disaster, FDA rejection). Even with a 2% risk stop, you can lose 10-15% of your account if the gap blows through your stop. This is why day traders who flatten positions at close, and diversified portfolios, have fundamentally lower ruin risk than concentrated overnight holders.

The common thread: Every blown-up account involves either too much risk per trade, too much correlated risk, or both. Risk of ruin is always a position sizing problem, never a strategy selection problem.