Risk of ruin calculator

Worked example

You win an illustrative 40% of trades, and a win pays 2 times what you risk. That is an edge of +0.20 R a trade: over many trades each one adds 0.2 of the risk on average. You risk 2% of the balance per trade and call a 20% loss of the starting balance ruin.

Over 500 trades the chance of falling to that level at some point is 13.04%, even with the edge. The chance of ending the 500 trades above the start is 86.94%. A run of 12 losses in a row does it on its own.

The risk per trade moves it most. The same trader at 1% per trade has a 1.46% chance, and at 5% per trade 47.74%. Risking a fixed amount, 2% of the start every time, gives 14.23%. With no edge at all, a 40% win rate at 1.5 to 1, the chance is 74.56%.

The formula

Each trade wins with the win rate p and pays R times the risk, or loses the risk. Risking a share f of the balance, w wins and l losses leave start × (1 + R × f)ʷ × (1 − f)ˡ; risking a fixed amount they leave start × (1 + (w × R − l) × f). Ruin is the first time that falls to start × (1 − ruin level).

We work it out exactly: the balance depends only on how many wins and losses came so far, so the calculator walks every trade over all of those counts at once and adds up the chance of the paths that touch the ruin level. There is no random simulation, so the same inputs always give the same answer. The classic formula ((1 − edge) ÷ (1 + edge))ⁿ only covers wins and losses of the same size with no limit on trades, so we do not use it. Real results also depend on streaks, fees and changing markets, so treat the number as a guide to sizing, then size each trade with the lot size calculator.

Questions and answers

What is risk of ruin in trading?

The chance that a run of losses takes the account down to a level you cannot or will not trade from. Here you set that level as a loss of the starting balance, like 20% or 50%.

How is risk of ruin calculated here?

Exactly, over every possible order of wins and losses within the number of trades, with the win rate, the reward to risk and the risk per trade you enter. A win rate of 40% at 2 to 1, risking 2% with ruin at a 20% loss, gives 13.04% over 500 trades.

What is a safe risk per trade?

There is no single safe number, but the chance falls fast as the risk shrinks. In the example it goes from 47.74% at 5% to 13.04% at 2% and 1.46% at 1%.

Can the risk of ruin be zero?

Risking a share of the balance never reaches zero, so a 100% ruin level is never hit and the losses in a row read never. Any smaller ruin level can be reached by a long enough losing streak, so the chance is never exactly zero.

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