Probability of Ruin

TL;DR. Probability of Ruin is the fraction of bootstrap-resampled paths where the running account balance hits zero. Different from drawdown — drawdown is recoverable, ruin is terminal. Target below 1% for retail strategies; anything above 5% means the strategy is one bad cluster from being unrecoverable at the current size.

What you'll be able to do

• Distinguish ruin from drawdown and understand why the difference matters for sizing.
• Read a P(ruin) number and translate it directly into a position-size constraint.
• Recognize the most common mistake: using max drawdown as a proxy for ruin risk.

#The absorbing state

A drawdown of 50% can be recovered with a 100% gain. A drawdown to zero cannot be recovered with anything — there's no capital left to compound from. That asymmetry is what makes ruin a fundamentally different risk than drawdown, and why it deserves a separate metric.

Think of an account balance as a particle moving on a number line. Each trade nudges it up or down. Most strategies have a positive drift, so on average the particle moves up. But the particle can hit zero, and zero is an absorbing boundary — once it's there, it stays. The strategy is over. The account is closed.

Probability of Ruin is the fraction of bootstrap-resampled paths where the particle hits zero before the resample ends. Conceptually simple. Strategically important.

#Why drawdown isn't enough

Max drawdown across the resampled distribution tells you something — it bounds the largest equity decline you should plan around. But it's the wrong tool for the absorbing-state question.

A 30% max drawdown can mean:

• The path peaked, dropped 30%, recovered, and ended profitable. Survivable.
• The path peaked, dropped 30%, then drifted to zero. Not survivable.
• The path was 30% below peak for the entire backtest. Survivable but psychologically brutal.

The first and third paths look similar in the drawdown statistic but have very different ruin implications. The second is what ruin probability catches. Max drawdown averages survivors and casualties together; P(ruin) counts only the casualties.

#How it's computed

For each resampled path, the Robustness Lambda walks the running balance trade-by-trade. If at any point the balance reaches zero or below, that path is marked as ruined and execution short-circuits (a ruined account can't trade further).

P(ruin) = (count of ruined paths) / total_resamples

Ruined paths are removed from terminal-balance statistics so the median terminal isn't contaminated by paths that hit zero early. But the count of ruined paths drives this metric specifically.

#In AlgoLift

P(ruin) appears prominently:

• The Path Luck KPI strip — headline number, color-coded by severity (green below 1%, amber 1-5%, red above 5%).
• The Tail Risk panel's annotation on the drawdown envelope chart.
• The Sizing panel's frontier chart — P(ruin) is the right y-axis, plotted against position-size multiplier. The cross-over from acceptable to unacceptable is one of the chart's key reads.
• The Tail Discipline component of the Robustness Score — P(ruin) is one of the three inputs, and the only one with a hard 100-point ceiling at under 1%.

#Reading the score

The 1% target isn't arbitrary. It comes from the cost-of-error analysis: at 1% ruin probability, you'd expect to blow up once every hundred deployments. Most traders deploy multiple strategies over a career, so even a 1% target produces a non-trivial blow-up probability over a career horizon. Below 1% is the safety margin that makes the career-level math work.

#Worked example

What this shows. The strategy's median return is the same in absolute terms across all three starting balances — the trades make the same dollars. But the proportional drawdowns are larger relative to a smaller account, so the same trade list produces dramatically different P(ruin) numbers. The strategy that's perfectly safe at $100k is borderline at $50k and unsafe at $25k. This is why the Sizing panel exists as its own analysis: the right size depends on a tradeoff curve, not a single number.

#Common misunderstandings

• "P(ruin) of 0% means I'm completely safe." Not quite. The Robustness Lambda runs ten thousand resamples; the noise floor of measurement is 0.01%. A reported 0% means "below the measurement floor," which is "very low" not "literally impossible." Real-world risks like fat-finger errors and broker outages remain.
• "I should optimize parameters to minimize P(ruin)." Be careful. P(ruin) responds to position size and stop-loss layer more strongly than to entry/exit parameter tuning. Tuning entry parameters to reduce P(ruin) usually means over-fitting to the specific drawdowns in the historical sample, which doesn't generalize.

#When P(ruin) is the binding constraint

• Leveraged futures strategies. The combination of leverage and absorbing-state risk makes P(ruin) the right primary risk metric.
• Prop firm evaluations. Most firm-failure rules act as a proxy for ruin — hitting them ends the account. The Prop Fitness component is downstream of P(ruin) for this reason.
• Sizing decisions. The Sizing panel's frontier curve uses P(ruin) as the right-axis ceiling.

#When it matters less

• Long-only equity strategies on small position sizes. When the largest loss is bounded by the position size and the position is small relative to capital, ruin is mechanically impossible.
• Strategies with conservative stop-losses. A hard stop-loss at 2% of starting capital makes ruin require a long string of consecutive maximum losses, which is exponentially unlikely.