Risk of ruin: why a profitable strategy can still wipe out your account

Risk of ruin is the probability that a run of consecutive losses will push an account below the level at which trading can no longer continue, and it can happen even to a strategy with a positive expected value. What determines this probability is not the quality of the signal but the share of capital you put at risk on each individual trade: with a large enough stake, ruin is not a question of "if" but of "when". Position size is therefore not a comfort setting but a survival parameter of the system, and it has to be worked out before you choose a security.

Why a positive expected value is no protection

Expected value is the average outcome over a long run, calculated as if the order of trades did not matter. In a real account, order matters decisively. Losses are taken out of the capital you go on trading with: after a drawdown, every subsequent stake, sized as a share of what remains, becomes smaller in absolute money terms, and the recovery has to be made from a reduced base. This is the gap between the arithmetic mean and what actually happens to capital when it is reinvested trade after trade.

Hence the key conclusion: a strategy that is profitable on average and a strategy that survives are not the same thing. The distance over which the expected value shows itself has to be covered. If a losing streak knocks you out of the account halfway along that distance, the positive expected value will remain a true statement about the strategy and a false statement about you.

The asymmetry of drawdowns

Losses and recoveries are not symmetrical. To get back to your starting capital after a drawdown you need a gain larger than the loss was — and the deeper the hole, the disproportionately steeper the required recovery. A shallow drawdown can be won back by a move of almost the same size; a deep one demands a result that the strategy simply does not deliver over its normal horizon. There is a zone in which the account is still formally alive but in practice already dead: the remaining capital is not enough to earn the money back within a reasonable time.

Where the ruin threshold really lies

A zero balance is a rare scenario. The real threshold is higher and is made up of several constraints at once.

A margin position is closed out forcibly long before zero: the broker does not wait for your view on the stock's prospects. The minimum lot size and commissions set a floor below which a trade stops making economic sense. And there is a psychological threshold — the level beyond which a trader stops following the rules and starts trying to win it all back, which finishes the job faster than any mathematics. For the calculation it makes sense to take the highest of these thresholds, not the lowest.

The levers that control it

The probability of ruin depends on several variables, and your influence over them varies greatly.

The share of capital risked per trade is the only lever entirely under your control, and it is also the most powerful one: reducing the risk per trade lowers the probability of ruin disproportionately. The ratio of the average win to the average loss you set only partly — through your exit rules. The share of winning trades is decided by the market itself, and attempts to raise it usually end up worsening the win-to-loss ratio: trades get closed earlier, the profitable ones included.

Leverage works the other way: it does not increase the expected value, but it pulls the forced-liquidation threshold closer to the current price. The same strategy, the same signal, a different probability of surviving long enough to see the result.

The illusion of diversification

Several positions reduce the risk of ruin only when they move independently. A set of stocks from a single sector or tied to a single export chain is one bet spread across different tickers: in a stress scenario, correlations rise and the positions close at a loss at the same time. Before you call a portfolio diversified, look at the composition of the stock market and at what your holdings have in common with one another. Instruments with a different nature of risk — OFZ and the rest of the debt market — behave differently here from just one more stock added to the ones you already hold.

How to calculate it for your own system

Step 1 — define your ruin threshold in money terms: not zero, but the level below which you stop trading or get closed out.

Step 2 — use your own trading journal, not someone else's assumptions: the share of winning trades and the average size of wins and losses have to be calculated from your own history.

Step 3 — run these parameters through a simulation of random reshufflings of your trades. That way you see not the single path that has already happened, but the distribution of paths that could have happened with the same statistics.

Step 4 — choose the share of risk per trade so that the proportion of scenarios that break through the threshold becomes acceptable to you. That is the practical answer: not "how much will I make", but "what stake lets me survive long enough to realise my expected value".

An honest caveat

Any such calculation assumes that tomorrow's market is statistically similar to yesterday's and that trades are independent. Both assumptions are wrong. Market regimes change, losses cluster into streaks more often than in a random model, and liquidity disappears precisely when it is needed. It is therefore sensible to treat the resulting probability as an optimistic estimate and to build in a safety margin. Definitions of the terms used here can be found in the glossary.