Risk of Ruin and Drawdowns: The Maths That Keeps Traders Alive

Risk of ruin is the probability that a run of losses takes your account down to a level from which you cannot, or will not, keep trading. It depends on your win rate, your average win compared with your average loss and, above all, on how much you risk per trade. Even a strategy with a genuine edge can be ruined by betting too large, because long losing streaks are normal, not rare.

Expectancy: do you have an edge at all?

Measure results in R, the amount you planned to risk on a trade. A trade that loses its full planned risk is -1R; a trade that makes twice the planned risk is +2R.

Expectancy = (win rate x average win) - (loss rate x average loss)

A positive expectancy is necessary but not sufficient. How you size the bets decides whether you survive long enough to collect it.

Losing streaks are normal

With a 40% win rate, each trade has a 60% chance of losing. The probability of 10 losses in a row starting at any one point is 0.6 to the power of 10, about 0.6%, which sounds tiny. But over hundreds of trades there are hundreds of starting points. Calculated exactly, for a 40% win rate:

Losing streak of at least...	Chance over 100 trades	Chance over 200 trades	Chance over 500 trades
6 losses	about 87%	about 98%	almost certain
8 losses	about 49%	about 75%	about 97%
10 losses	about 21%	about 38%	about 71%
12 losses	about 8%	about 15%	about 35%

A trend follower who trades for a few years should expect a streak of 8 or more losses and should not be surprised by 10 or 12.

How streaks damage different risk sizes

Losses compound. After each loss you risk a percentage of a smaller account, but the damage still builds quickly:

Risk per trade	Account left after 10 straight losses	Drawdown
1%	0.99^10 = 90.4%	-9.6%
2%	0.98^10 = 81.7%	-18.3%
5%	0.95^10 = 59.9%	-40.1%
10%	0.90^10 = 34.9%	-65.1%

Drawdown arithmetic

The deeper the hole, the harder the climb out:

Loss	Gain needed to recover
10%	11.1%
20%	25.0%
30%	42.9%
50%	100%
75%	300%

A strategy that earns, say, 10% in a good year needs many good years to repair a 50% loss. Avoiding deep drawdowns matters more than squeezing out extra return.

Risk of ruin, simulated

To see the effect of bet size, we can simulate the example system (40% win rate, +2R wins, -1R losses) many times. In a simulation of 5,000 runs of 500 trades each:

Risk per trade	Runs with a 50% drawdown from a peak	Runs that fell to half of starting capital
0.5%	none	none
1%	none	none
2%	about 2%	almost none
5%	about 84%	about 12%
10%	all of them	about 48%

The edge is identical in every row; only the bet size changes. At 1% per trade, a 50% drawdown never happened in this simulation. At 5%, most runs suffered one, even though the system makes money on average. Real trading is harsher than this simple model: win rates drift, costs vary, gaps exceed stops and positions in correlated markets lose together.

Kelly sizing and why professionals bet less

The Kelly criterion gives the bet size that maximises long-run growth if you know your edge exactly:

Kelly fraction = W - (1 - W) / R, where W is the win rate and R is the average win divided by the average loss.

In practice nobody knows their true edge; it is estimated from a backtest that is probably optimistic. Overestimating your edge with Kelly sizing is very costly. Many traders use a quarter or less of the Kelly fraction, and the Turtle rules sized each unit at about 1% of equity per unit of volatility, as described in the trend-following lesson.

Personal ruin comes before mathematical ruin

Most traders do not wait for their account to reach zero. They stop after a drawdown that hurts too much, often at the worst time. Other forms of ruin arrive sooner:

• Margin calls and broker liquidation at the low point.
• Correlated losses: five positions at 1% each in related markets can behave like a single 5% bet, as the diversification lesson explains.
• Gaps and limit moves that make a 1% planned loss into a 3% actual loss.

Define your personal ruin level honestly, for example "I would stop trading after a 30% drawdown", and size so that reaching it is very unlikely.

Setting your limits

A starting framework (adjust after your own testing):

• Risk per trade: 0.25% to 1% of equity.
• Total open risk: 4% to 6% of equity.
• Drawdown circuit breakers: at -10% from the equity peak, halve position risk; at -20%, stop opening new trades and review the system against its backtest.
• Recovery rule: return to normal size only after a set recovery, for example half the drawdown regained.