Drawdown math and risk of ruin: why small risk per trade survives

The arithmetic of drawdowns: recovery gains, what losing streaks do at each risk level, how often streaks happen, and drawdown rules to write down before one.

Most traders think about risk one trade at a time. Drawdowns do not happen one trade at a time. They happen in streaks, and the arithmetic of a streak is less forgiving than it looks: losses compound, recoveries need larger percentage gains than the loss that caused them, and losing runs that feel impossible turn up regularly over a few hundred trades. This guide works through the numbers so you can set risk and drawdown rules before the streak arrives.

Why a loss needs a bigger gain to recover

A percentage loss and a percentage gain are measured from different starting points. Lose 50% of $20,000 and you have $10,000; a 50% gain on $10,000 only brings you back to $15,000. To get back to $20,000 you need a 100% gain.

The rule: if the drawdown is d (as a decimal), the gain needed to get back to the old peak is:

recovery gain = d / (1 - d)

Gain needed to recover from a drawdown (recovery = d / (1 - d))

Drawdown	Gain needed to recover
10%	11.1%
20%	25.0%
30%	42.9%
40%	66.7%
50%	100.0%
60%	150.0%
70%	233.3%
80%	400.0%
90%	900.0%

Up to about 20% the gap is small. Past 30% it grows fast, and past 50% recovery becomes a years-long project. The job of risk control is to keep drawdowns in the shallow part of this table.

How risk per trade turns into a drawdown

If you risk a fixed fraction r of the current account on every trade (fixed-fractional sizing, the approach in position sizing with 1R), then after n full losses in a row the account is multiplied by (1 - r)ⁿ. The drawdown is:

drawdown after n straight losses = 1 - (1 - r)^n

Drawdown after 10 consecutive full 1R losses, fixed-fractional sizing

Risk per trade	Account left (x start)	Drawdown	Gain needed to recover
0.5%	0.9511	4.89%	5.14%
1%	0.9044	9.56%	10.57%
2%	0.8171	18.29%	22.39%
5%	0.5987	40.13%	67.02%

Two things stand out. First, at 0.5% or 1% a ten-loss streak is unpleasant but survivable; at 5% the same streak takes away 40% of the account and needs a 67% gain to repair. Second, compounding helps on the way down: ten losses at 2% is an 18.29% drawdown, not 20%, because each loss is taken on a slightly smaller account.

These figures assume every loss is exactly 1R. Slippage, gaps and commissions often make real losses larger, so treat the table as a floor.

How likely is a losing streak?

Two different questions get mixed up here.

A specific run

If your win rate is p and trades are independent, the chance that a particular set of N trades are all losses is:

P(next N trades all lose) = (1 - p)^N

Illustrative example: with a 50% win rate, the next 5 trades all losing has a probability of 0.5⁵ = 3.1%. With a 40% win rate it is 0.6⁵ = 7.8%.

At least one run somewhere in a sample

The question that matters is different: over the next 100 or 250 trades, what is the chance that a run of N or more losses happens somewhere? There are many overlapping windows, so the probability is much higher. There is no neat one-line formula, but it can be computed exactly by tracking the current losing-run length trade by trade (a short recurrence in a spreadsheet or a few lines of code). The table was computed that way, assuming independent trades and a constant win rate.

Probability of at least one losing streak of N or more (illustrative, independent trades)

Win rate	Streak of 5+ in 100 trades	Streak of 8+ in 100 trades	Streak of 8+ in 250 trades	Streak of 10+ in 250 trades
40%	97.6%	49.0%	82.5%	45.2%
50%	81.0%	17.0%	38.4%	11.2%
60%	45.9%	3.6%	9.2%	1.5%

Read the 40% row carefully, because many breakout and trend-following styles win less than half the time. Over 250 trades, a trader with a 40% win rate has better than a four-in-five chance of seeing eight or more losses in a row at some point, and close to even odds of ten or more. A ten-loss streak is not by itself a sign the method is broken.

Real results can be worse than this table. Trades are often not independent: a market that stops respecting your setup can produce clusters of losses, and a trader on tilt takes lower-quality trades after a loss. Use these numbers as a minimum to plan around.

Risk of ruin, in plain terms

Risk of ruin is the chance that a sequence of losses takes the account to a level where you can no longer (or will no longer) trade the plan. In practice ruin is rarely zero: it is the drawdown at which you abandon the method, a margin call, or sizes too small to trade one micro contract.

Three ideas carry most of the weight:

• Edge decides the direction, size decides the speed. If expectancy after costs is negative, no sizing rule prevents eventual ruin; smaller size only slows it. If expectancy is positive, sizing decides whether you survive the streaks long enough for the edge to show.
• Thin edges need small size. Illustrative example: a 45% win rate with winners averaging 1.5R has an expectancy of 0.45 x 1.5 - 0.55 x 1 = 0.125R per trade. If costs and slippage cut the average winner to 1.3R, expectancy falls to 0.035R, almost nothing. A thin edge plus large risk is a short path to a deep drawdown.
• Define ruin as a number. Pick the drawdown you would treat as "stop and rebuild", for example 20% or 50%, and count how many straight losses reach it.

Consecutive full 1R losses needed to reach a drawdown, fixed-fractional sizing

Risk per trade	Losses to reach -20%	Losses to reach -50%
0.5%	45	139
1%	23	69
2%	12	35
5%	5	14

The count uses n = ln(1 - target) / ln(1 - r), rounded up. Compare it with the streak table: at 5% risk, a five-loss run (more likely than not over 100 trades at a 50% win rate) is enough to put the account down 20%. At 0.5%, it takes 45 straight losses.

Why fixed-fractional sizing shrinks bets in a drawdown

Because risk is a percentage of the current account, each loss reduces the next bet. Illustrative example: a $25,000 account at 1% risks $250 on the first trade. After ten straight losses the account is about $22,610, so the eleventh trade risks about $226. The account bends downward instead of falling in a straight line, which is why the 10-loss drawdown at 1% is 9.56% rather than 10%.

The trade-off is real: smaller bets also mean a slower climb back, because winners are sized off the smaller account. That is intended: the instinct to "size up and win it back" is how a recoverable 15% drawdown becomes a 40% one.

One practical limit for futures traders: with micro contracts the count is a whole number, so in a small account the formula can round down to zero contracts. That is a signal to skip the trade or choose a setup with a tighter valid stop, never to round up. The contract details are in the micro E-mini contract specs guide.

Practical rules you can write down today

1. Cap risk per trade. Pick a number between 0.25% and 1% of the account and write it in your plan. Could you take ten straight losses at that size and still follow the plan?
2. Set a drawdown circuit breaker. Illustrative ladder, measured from the account peak: at -10%, halve risk per trade (1% becomes 0.5%); at -15%, halve again and trade only your best-documented setup; at -20%, stop live trading and review your journal before restarting.
3. Restore size in steps. Return to the next size up only after the account recovers to a set level (for example, back above -5% from peak), not after one good day.
4. Count losses in R, net of costs. Record each loss including commissions and slippage, so a "1R" loss that was really 1.3R shows up. The trade journal template has columns for this.
5. Add a daily limit. A loss limit for the day (for example 2R or 3R) stops one session from creating most of a drawdown.

Illustrative example of the circuit breaker: a $25,000 account at 1% risk drops 10% to $22,500. Risk is halved to 0.5%, or $112.50 per trade. Reaching -20% from there now takes about 24 more straight losses instead of 12. That buys time to judge whether the drawdown is variance or a broken setup.

Common mistakes

• Sizing from the best month. Risk set during a winning streak ignores the losing streak that follows.
• Treating a streak as proof. Eight losses at a 40% win rate is common; abandoning a sound method after a normal run resets the sample and adds costs.
• Moving the circuit breaker. A drawdown rule that gets loosened when it triggers is not a rule.
• Ignoring costs and gaps. Stops are not fills. Overnight gaps and fast markets can turn 1R into 2R or more, which pushes every number in this guide in the wrong direction.
• Adding correlated positions. Two trades that move together are one larger trade for drawdown purposes.

All numbers here are illustrative arithmetic, not a forecast of any method's results. More on sizing and loss limits is on the risk topic page.

Examples use round, illustrative numbers and are not actual trades or results. Education only — not investment, tax or legal advice.

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