Risk management

Risk of ruin

By Jarosław Wasiński • Published: Feb 15, 2026 • Updated: Oct 11, 2026

The probability, under a specified model, of reaching a defined capital or drawdown threshold over a stated horizon. Ruin need not mean a literal zero balance. Estimates depend on return distributions, sizing, dependence between trades and extreme losses; simplified formulas are not reliable guarantees about a live strategy.

Example. Simplified model: initial capital is USD 1,000; each independent trial gains USD 100 with 55% probability or loses USD 100 with 45%, without additional costs. The stake is fixed, not proportional; there is no upper stopping threshold and the horizon is unlimited. The probability of reaching zero is (0.45/0.55)¹⁰ ≈ 13.44%. This is not a forecast for an actual strategy or a risk over the next ten trades.

Define ruin and the horizon

Ruin can mean insufficient funds for the smallest position, breaching a drawdown limit or reaching a specified equity threshold, rather than zero alone. State whether the horizon is the next 100 trades, one year or unlimited time. Margin thresholds and cash flows alter the process. An ending value above the threshold does not prove it was never breached: an earlier breach may have required trading to stop before the modelled recovery.

Why a positive mean is insufficient

The example has expected payoff of +USD 10 per trial, yet an adverse random path can still exhaust capital. The power formula requires fixed independent trials, equal-sized gains and losses, a fixed stake and appropriate boundaries. See Yale’s lecture on gambler’s ruin. Do not insert historical win rate and the account’s number of R units directly into a formula for every strategy.

Model the actual constraints

Variable losses, dependence, gaps, costs, position size and margin requirements can materially change risk. Simulation should reproduce stopping rules and actual sizing, with uncertainty attached to its estimate. Resampling known trades does not create crises absent from the sample. Lower risk per trade can help but provides no guarantee; minimum contract size can also prevent further trading.

Changing the threshold changes the event

Under the same model, stopping at USD 500 rather than zero leaves five fixed stakes between initial capital and the threshold. The unlimited-horizon hitting probability is (0.45/0.55)⁵ ≈ 36.66%. The larger figure reflects a different event, not a change in the rule’s quality. State threshold and horizon beside the percentage, including when the report labels it risk of bankruptcy.

Use it in a risk plan

Report threshold, horizon, assumptions and extreme scenarios, rather than a percentage alone. Compare sizing and dependence alternatives while retaining costs. A fixed percentage of equity has different dynamics from the fixed stake in the example. In the course: loss mathematics and risk of ruin. Source checked on 11 October 2026.

FAQ

Does positive expectancy rule out ruin?

No. Capital, path, sizing, boundaries and horizon also matter.

Does fixed-fractional sizing prevent capital exhaustion?

An ideal model without losses of 100% or more may avoid exact zero, but real stopping thresholds, minimum volume and gaps remain relevant.

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