Risk of Ruin

The probability that an account's equity drops below a critical threshold (zero, a margin floor, or a personal capitulation level) before the strategy realizes its expected return. The dominant risk metric for leveraged trading — much more important than expected return for assessing real-world deployment.

In plain English

If a strategy has positive expected return over many trades but a max drawdown that exceeds your bankroll, you have a positive probability of being ruined before the expected return materializes. "In the long run, this works" is irrelevant if you don't survive to see the long run.

The classic gambler's-ruin framework formalizes this: even with a positive edge, betting too much per trade relative to your bankroll guarantees ruin with probability 1 over long enough time. The optimal bet sizing — the Kelly criterion — maximizes long-run growth while keeping ruin probability bounded.

For trading strategies, risk of ruin captures the answer to "would I still be in the game when the winners arrive?"

Formula / mechanic

For a simple win-rate-p, payoff-ratio-b game with bet fraction f of bankroll per trade, the long-run growth rate is:

G(f) = p × log(1 + b × f) + (1 − p) × log(1 − f)

The optimal Kelly fraction f* maximizes G(f):

f* = (b × p − (1 − p)) / b

For a strategy with WR = 30%, win/loss ratio b = 3 (winners 3× larger than losers), Kelly = (3 × 0.3 − 0.7) / 3 = 0.067 = 6.7% of bankroll per trade. Risking more than this is statistically worse, not better — extra leverage past Kelly increases ruin probability faster than it grows expected return.

Realistic deployment is usually at half-Kelly or less, both because Kelly assumes you know p and b exactly (you don't), and because the volatility at full Kelly is psychologically intolerable.

Why it matters for this fleet

Fleet variants run at fixed leverage (a position-size multiplier that scales both profit and loss) — 1×, 2×, 10×, 50×, 100× — regardless of the implied Kelly fraction for their actual win-rate and payoff ratio. High-leverage variants are betting far above Kelly, so they have intrinsically high risk of ruin.

The leverage cliff is visible in the fleet's median max drawdown (the deepest peak-to-trough equity fall): −4.4% at 1×, −28% at 2×, −84% at 10×, −98% at 50×, −98.5% at 100×. As leverage climbs, heavy-loss becomes the modal (most common) outcome — fleet-wide, 110 of 210 strategies end in heavy_loss (a deep, near-total equity wipe) versus 100 that "survived".

The lived shape of ruin RISK is strategy 628 (id628 — EMA 9/21 · BTC · 1-minute · 2× · short — a fast crossover pair run short on the noisiest candles): win rate 10.6% (only about one trade in ten closed in profit), a 145-trade losing streak (the fleet maximum), and a −98% drawdown. The account technically "survived" only because of the 5%-position-sizing floor (each trade risks 5% of equity, so no single trade can zero the account). Strip that floor, or let a real trader add margin, and id628 is the textbook ruin path: a system with no edge, run at leverage, on pure noise.

Why drawdown vs starting equity is the most important fleet screen

Risk of ruin is hard to compute formally without knowing the exact win-rate and payoff distributions, but a useful proxy is the max drawdown percentage — how far equity fell, peak-to-trough, as a share of the peak:

• < 20%: very low risk of ruin (psychologically tolerable, well below any margin call) — the regime of the fleet's 1× rows.
• 20–50%: moderate risk (uncomfortable but survivable for disciplined traders) — roughly where the 2× rows sit.
• 50–100%: high risk (likely triggers capitulation or margin calls) — the 10×/50×/100× regime, where the fleet median is −84% to −98.5%.
• ≈ 100%: effective ruin under real conditions; the strategy "survives" in the simulator only because the 5%-sizing floor stops a single trade from zeroing the account.

Updated 2026-05-17 (phase 121.1): The simulator now models bankruptcy explicitly — a (strategy, symbol) pair stops trading when its equity crosses a configurable floor. RoR remains a useful summary metric (and the max-drawdown-% screen is still the right fleet-level lens), but it is no longer a proxy for un-modeled behavior — the underlying mechanism now exists in-simulator. (In this dossier, the 5%-sizing floor means no row actually reached the bankruptcy gate; see bankruptcy.)

How to reduce risk of ruin

1. Lower leverage. The single biggest lever.
2. Position-size on Kelly-fraction-of-equity, not on fixed fraction.
3. Set hard stop-losses inside the liquidation distance.
4. Diversify across uncorrelated strategies — portfolio drawdown is far below sum of individual drawdowns when strategies are uncorrelated.
5. Reserve a "DO NOT TOUCH" portion of the bankroll that the strategy can never access. Caps absolute downside even at the cost of upside.

Refined 2026-05-17 (Q11)

Is RoR a numeric metric?

Yes — strictly a probability in [0, 1]. But no riskOfRuin field is returned by /api/analytics. There is no single closed-form value because RoR depends on parameters you don't have ground truth for (true WR, true payoff distribution, margin-call threshold, trade independence). Practitioners either:

1. Model it — gambler's-ruin closed form RoR ≈ ((q/p)/b)^N for constant-bet games, or Monte-Carlo trade-resampling (shuffle the historical trade list N times, count fraction of paths that hit zero).
2. Use an observable proxy — |maxDrawdownDollar| / initialEquity, both fields available in /api/analytics.

The closed-form RoR is extremely sensitive to payoff ratio b: at WR 35%, b=2.5, 20-unit bankroll, RoR ≈ 0.3%. Drop b to 1.5 and RoR jumps to ~22%. Tiny changes in payoff swing the answer by orders of magnitude — which is why the drawdown-% proxy is preferred for fleet-level screening.

Worked proxy example from this dossier

• id628 (EMA 9/21 · BTC · 1m · 2× · short) — −98% max drawdown, win rate 10.6%, the fleet's worst losing streak (145 trades). Under the drawdown-% screen this is the ruin-risk archetype: equity all but gone, edge nonexistent. The simulator records it as heavy_loss rather than a literal bankruptcy only because 5% position sizing keeps the last sliver of equity off zero. That nuance is exactly the trap — "survived" ≠ "did fine". Risk of ruin is the probability of being wiped out before any edge can materialize, and id628 never had an edge to wait for.

Related

• bankruptcy
• drawdown
• liquidation
• path dependence
• leverage
• edge

Sources

• wiki/qa-sessions/2026-05-17-session.md#q9 (first asked here)
• Kelly, J. (1956), "A New Interpretation of Information Rate"
• Standard gambler's-ruin probability theory (Feller, Vol. 1)
• Thorp (1962), Beat the Dealer, Ch. on bet sizing