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Risk of ruin

Risk of ruin is the probability that capital reaches a defined ruin threshold within a given horizon. It does not depend on a losing streak alone: the return model, sizing, costs, dependencies, leverage and ruin boundary all matter.

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Who this entry is for — Anyone who wants to distinguish a severe loss from ruin and understand why there is no universal percentage that can be calculated from win rate and risk/reward ratio alone.

Risk of ruin (RoR) is the probability that a capital process reaches a ruin threshold within a defined horizon. Before calculating it, one must specify what “ruin” means.

Boundary Example
Absolute ruin Capital equal to zero or a negative balance
Operational ruin Capital insufficient to execute the strategy
Regulatory/contractual ruin Breach of a margin requirement and liquidation
Trader-defined ruin Maximum drawdown beyond which the programme is suspended

Without a boundary, horizon and model, “my RoR is 0%” is not a verifiable measure.

What it depends on

Risk of ruin is not determined by a single streak of losses. It depends at least on:

  1. distribution of outcomes — the probabilities and sizes of gains and losses, including tails, gaps and costs;
  2. sizing rule — fixed amount, fraction of capital, leverage and position limits;
  3. initial capital and ruin threshold;
  4. horizon — number of trades or time observed;
  5. dependence between outcomes — autocorrelation, volatility clustering and regime changes;
  6. real-world mechanics — slippage, liquidity, margin, financing and the possibility that a stop is not executed at its expected price.

The classic gambler's ruin problem uses discrete steps, constant probabilities and absorbing boundaries. It is a useful model for reasoning, but it is not a ready-made formula for a strategy with variable payoffs.

Losing streak and compounded drawdown

A series of losses illustrates the effect of sizing; by itself, it does not calculate RoR. If every loss is a constant fraction f of current capital and there are no gaps or additional costs:

Cₙ = C₀ × (1 − f)ⁿ

and the drawdown after n losses is:

DDₙ = 1 − (1 − f)ⁿ

For eight consecutive losses:

Fraction lost per trade Capital remaining Drawdown
1% 0.99⁸ = 92.27% 7.73%
10% 0.90⁸ = 43.05% 56.95%

The previous version of this entry reported approximately −65% in the second case: that was arithmetically incorrect. Values of −8% and −80% would also be only linear sums; with percentage sizing on current capital, the calculation is compounded.

With a fraction strictly below 100% and perfectly bounded losses, capital approaches zero without reaching it in a finite number of trades. In practice, however, an operational or margin threshold may be crossed much earlier.

Why a losing streak is not a “statistical certainty”

The probability of observing at least one run of k losses in N trades depends on the loss probability and on the independence of outcomes. The probability of one specific block of eight losses with a 50% loss probability is 0.5⁸, but across hundreds of trades there are many possible, overlapping blocks.

Saying that “eight or ten losses are inevitable” without specifying a model and horizon is therefore incorrect. Regimes and dependencies can also make real outcomes very different from an independent Bernoulli sequence.

How to estimate it transparently

For a real strategy, a reproducible estimate states:

  1. the ruin threshold and horizon;
  2. the distribution of trades net of costs;
  3. the exact position-sizing and leverage rule;
  4. the treatment of gaps, slippage, margin calls and losses beyond the stop;
  5. the simulation method or formula and its assumptions;
  6. the uncertainty interval and stress tests.

A common procedure is to simulate many equity paths, count how many cross the boundary and divide by the total number. A bootstrap or Monte Carlo simulation does not eliminate model risk: if the sample does not represent future regimes and tails, the estimate may be too optimistic.

The Kelly criterion studies the logarithmic growth of capital under explicit assumptions and shows how central sizing is. It does not guarantee a zero RoR in real markets and does not replace leverage limits, stress tests and margin controls.

Operational risk — With leverage or margin, practical ruin may occur through forced liquidation before the balance reaches zero. The broker may also apply stricter “house” requirements and liquidate positions without waiting for a recovery.

What to use in a risk plan

  • an operational ruin threshold defined in currency and percentage terms;
  • limits per trade and for aggregate exposure;
  • scenarios with losses exceeding the stop;
  • stress tests on streaks, costs, correlations and regime changes;
  • a reduction or suspension rule that activates before the boundary;
  • an updated estimate whenever the strategy, market or leverage changes.

“Practically zero” is an objective conditional on the model, not a promise. The correct result to communicate is: under these assumptions, within this horizon, with this threshold.

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