Risk of Ruin is the probability of reaching a specified lower capital threshold within a given time or before another stopping condition, under explicitly stated rules and a probability model.
Risk of Ruin expresses the probability of reaching a predefined capital threshold under stated conditions. In the simple gambler’s ruin problem, the lower boundary is zero and the process also ends upon reaching an upper target. When evaluating a trading account, however, a different level below which the chosen rules no longer allow trading to continue may matter. This practical threshold must be explicitly defined; it is not automatically equivalent to legal insolvency or a zero balance. A figure without a threshold, starting capital and stopping rules is incomplete. [1] [3]
Reaching a boundary within a limited number of steps and reaching it at any time before the upper target are different events. Paths that have reached neither boundary by the end of the chosen period remain unresolved. They cannot automatically be classified as successes or failures. Our example therefore records the lower boundary, continuing paths and upper target separately. Extending observation under the same rules cannot erase an already recorded arrival at the lower boundary; it does change the share of still unresolved paths. This is a property of the defined event, not a market forecast. [1]
A fixed monetary loss represents an increasing share of an account as capital falls. A rule based on current capital, by contrast, changes the size of the next position. CME shows how a fixed risk percentage during a losing streak also reduces the monetary amount risked on the next trade. A calculation using fixed steps therefore cannot be transferred unchanged to variable positions. Rounding, minimum trade sizes and any capital replenishment must also be specified. We present no particular percentage here as a universally safe rule. [2]
Expectancy describes the expected outcome under a model, whereas Risk of Ruin asks whether a boundary is reached along the path. Maximum drawdown measures a decline from a previous peak; it is not itself a probability of ruin. Our own simple counterexample: a single bet that wins twice the amount at risk or loses the entire amount at risk, with equal probabilities for both outcomes, has a positive expected result. Yet if the entire account is risked, it can still be lost completely in that very step. This counterexample is neither a trading recommendation nor the model used in the graph below. [1] [3]
A mathematical model can stop a process exactly at a boundary, but a real order must be executed in the market. Coinbase distinguishes triggering a stop-limit order from subsequently filling the limit order; downside protection may fail to execute during high volatility. A market order may also miss the expected price and have multiple fills. When applying a model to trading, it is therefore insufficient to record the planned loss as a fixed step. Differences between the trigger price, execution prices and the unclosed remainder can change the account’s entire path. [4]
Our example uses independent, identically distributed outcomes with fixed probabilities. Repeatedly observing a similar historical frequency does not itself establish these assumptions. If outcomes influence one another or conditions change, the original calculation may no longer describe the new situation. NFA notes that hypothetical results benefit from hindsight and cannot fully capture actually bearing losses. CFTC also distinguishes simulated executions from real trading. We therefore do not describe our model’s result as a measured risk of a strategy. [5] [6]
A separately calculated risk for one sequence of trades does not automatically describe an account holding other positions. CME’s trading-plan guidance distinguishes individual trade risk, simultaneous positions, total exposure, leverage and daily loss. When several positions decline together, their combined outcome may matter. Assessing an account threshold therefore requires all relevant cash flows and open obligations. Simply adding percentages from separate models without knowing how they relate does not provide the probability of reaching a shared threshold. [3]
State the starting capital, lower boundary, upper target, observation length, position sizes, costs and stopping rules alongside a calculation. Separate model probabilities from estimates obtained from data and from actual observed outcomes. A hypothetical calculation can help explore sensitivity to assumptions, but cannot replace checking them. NFA stresses disclosing material assumptions and limitations of hypothetical results. A small calculated number is no guarantee of safety, especially if the model omits events that could end the ability to continue. [5]
The same boundaries, a different horizon
For the clearest picture, read this entry together with Expectancy, Position Sizing, Max Drawdown, Stop-loss, Risk Management. The reverse links also lead from Risk Management, Kelly Criterion, Max Drawdown, Portfolio Risk.
01Why does the example give both 37.5 % and 50 %?+
The first value concerns reaching zero by the fourth step. The second applies when continuing until zero or the upper target without a fixed time limit. After the fourth step, some paths have still reached neither boundary.
02Does positive Expectancy eliminate the risk of ruin?+
No. The expected result does not tell you whether some possible paths hit the account threshold. Position sizes, the sequence of outcomes, costs, the horizon and stopping rules also matter.