Losing streaks and risk of ruin

Prerequisite: Size the risk before the position

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Learning objective

Calculate compounded drawdown and recognise assumptions behind streak probabilities.

Losing streaks occur even in a process with positive historical average outcomes. Their severity depends on position sizing, tail losses and dependence between trades. Define ruin operationally: it might mean reaching a minimum usable balance, breaching an account rule or losing the ability to continue the plan.

Fixed fractional sizing risks a proportion of remaining equity, so cash risk falls as equity falls. This slows decline under the model but does not protect against gaps or uncontrolled losses. Fixed cash risk behaves differently because it becomes a larger fraction of the shrinking account.

The probability q raised to n describes one specified run of n losses only when loss probability q is constant and trades are independent. It is not the chance of encountering any such run in a long sequence. Real trades may cluster by regime, making naive independent calculations misleading.

Common mistakes

Doubling risk after each loss can rapidly exhaust capital. Do not claim a precise ruin probability from a tiny or selected sample.

Practice

Compare ten-loss drawdowns under 0.5%, 1% and 2% hypothetical fractional sizing. Add one loss twice the planned amount and explain the changed assumptions.

Sources & further reading

• CME Group — Controlling Risk