Risk of ruin, explained with a slider

Risk of ruin is the chance that a run of losses takes away a set share of your capital before the strategy’s edge has time to show. “Ruin” does not have to mean zero. Most traders would call losing half the account ruin, because few keep trading after it.

It depends on three things: how much the strategy makes per trade on average, how much of the capital each losing trade costs, and how far down you call ruin.

The formula

Start with the edge: what one trade earns on average, measured in average losses. With a 55% win rate and an average win 1.2 times the average loss, the edge is 0.21. Each trade adds 0.21 of an average loss to the account, on average.

The classic formula then counts how many average losses fit into the amount you can lose. Call that the units. The chance of ruin is (1 − edge) ÷ (1 + edge), multiplied by itself once per unit. Here that ratio is 0.653. If each loss costs 2% of the capital and ruin is losing 50%, there are 25 units, and the chance is about 1 in 43,000.

Now risk 5% per trade. There are only 10 units, and the chance is 1.4%. At 10%, it is 11.9%. The strategy did not change. Only the bet size did.

Chance of ever losing 50%

under 0.1%

Edge per trade, in average losses

+0.21

Losses in a row that get there

25

12.8%8.2%3.6%−0.9%

0.5% risked per trade10%

Try a win rate a few points lower, or a smaller payoff. When the edge reaches zero, the chance of ruin is 100%: a strategy with no edge will, given enough trades, hit any loss you name.

What the formula leaves out

The formula assumes every loss is the same size, the average loss. Real losses are not. A strategy that cuts most losses small and lets a few run has a modest average loss and a few very large ones. The formula never sees the large ones.

There is a second way to estimate the same chance. Take the real trades of a history and build a new history from them, drawing one trade at random at a time, as many as there were. Do that many times, and count how often the account falls as far as you call ruin. This is a Monte Carlo simulation, and it keeps every loss at its real size.

Monetio’s engine computes both. For a signal it calls ruin a fall, from a peak, as large as the first deposit. Here are three anonymized live signals from our fixtures, each with a positive edge and more than a thousand trades.

Signal A: formula0.2%

Signal A: simulation1.4%

Signal B: formula0.0%

Signal B: simulation0.6%

Signal C: formula0.0%

Signal C: simulation1.0%

For Signal B, the formula put the chance at about 1 in 7,800,000. The simulation put it at 0.6%. Only shuffling the order of its real trades, the account fell half that far in 12.7% of the runs. Its largest single loss was 25% of its first deposit, where the formula assumed every loss was average.

And the real history? Signal B fell 92% of its first deposit from a peak. Signal C fell 96%. Signal A fell further, 178% of it: it went through the event the formula called a 0.2% chance.

What to do with your own report

1. Find the loss per trade as a share of your capital, not the signal’s. Copying with a smaller account raises it.
2. Use the calculator to see how fast the chance of ruin climbs as that share grows. Size so a long losing streak leaves you trading.
3. Compare the largest loss with the average loss. When the largest is many times the average, trust the simulation over the formula, and size down further.

Monetio runs the simulation on every report, with its real trades, and shows the chance of losing half the first deposit next to the chance of losing all of it.