Guide · Risk
Losses and recoveries are measured against different bases, so they are never the same size. That single fact drives almost every serious risk rule: why per-trade risk is small, why losing streaks matter more than single losses, and why the drawdown you can survive is a smaller number than the one you think you can survive.
A drawdown is a fall from a peak in account equity, expressed as a fraction of that peak. If you lose fraction d, the capital still standing is 1 - d, and that survivor has to produce the entire missing piece on its own.
The two numbers differ because they are percentages of different bases. The loss is a percentage of the peak. The recovery is a percentage of what is left after the loss, and what is left is smaller. The deeper the hole, the smaller the shovel you have to dig with.
| Drawdown | Capital remaining | Gain required to recover | Recovery / drawdown |
|---|---|---|---|
| 5% | 95.0% | 5.26% | 1.05x |
| 10% | 90.0% | 11.11% | 1.11x |
| 15% | 85.0% | 17.65% | 1.18x |
| 20% | 80.0% | 25.00% | 1.25x |
| 25% | 75.0% | 33.33% | 1.33x |
| 30% | 70.0% | 42.86% | 1.43x |
| 35% | 65.0% | 53.85% | 1.54x |
| 40% | 60.0% | 66.67% | 1.67x |
| 50% | 50.0% | 100.00% | 2.00x |
| 60% | 40.0% | 150.00% | 2.50x |
| 70% | 30.0% | 233.33% | 3.33x |
| 80% | 20.0% | 400.00% | 5.00x |
| 90% | 10.0% | 900.00% | 10.00x |
Read the right-hand column. Out to roughly 10% the ratio sits near 1, so ordinary intuition is close enough: a 10% loss and an 11% gain really are almost the same object. By 30% the required gain is 1.43 times the loss. By 50% it is double. By 80% it is five times, and by 90% you need a tenfold return simply to break even.
The curve is convex, and convexity is the point. Small drawdowns are cheap to repair and large ones are ruinously expensive, so the cost of a losing sequence rises faster than the sequence itself. That is why professional risk limits look absurdly conservative from the outside: they are not trying to avoid losing, they are trying to stay in the flat part of that curve where recovery is still arithmetic rather than fantasy.
It also explains why per-trade risk of 0.5% to 1% is not timidity. A trader risking 1% per position needs a long, unlucky run to reach the steep part of the curve. A trader risking 5% gets there in eight bad trades. The expectancy of the system barely enters into it, because the recovery penalty is imposed by arithmetic regardless of how good the edge is. The measurement of that edge is a separate exercise, covered in the R-multiple and expectancy guide.
Standard deviation summarises how spread out individual period returns are. Volatility is usually that same dispersion annualised. Neither one knows, or cares, what order the returns arrived in. Drawdown cares about nothing else.
Take two six-period return series built from exactly the same numbers. Series A alternates: +5%, -5%, +5%, -5%, +5%, -5%. Series B clusters them: +5%, +5%, +5%, -5%, -5%, -5%. Both have a mean period return of 0.00%, both have a standard deviation of 5.00%, and both finish at -0.75% cumulative. Series A has a maximum drawdown of 5.47%. Series B has a maximum drawdown of 14.26%, more than two and a half times as deep.
Drawdown is path dependent, volatility is not. Two systems with identical Sharpe ratios can produce completely different lived experiences, because Sharpe is built from a dispersion measure that has been deliberately stripped of sequence. A ratio can look respectable while the equity curve underneath it is one you would have abandoned in month four.
This is also why a summary statistics block is not enough to judge a system. You want the equity curve, the underwater curve, and the maximum drawdown alongside the averages. What to insist on seeing is set out in reading a backtest report.
Drawdowns rarely arrive as a single catastrophic trade. They arrive as a run of ordinary ones. If trades are independent with win rate w, the probability of exactly k losses in a row starting at any given trade is straightforward.
Those look reassuringly small, and that is the trap. It is the probability at one specific starting point, and a hundred-trade year gives you roughly a hundred starting points. The question that matters is whether such a run appears anywhere in your sample, which is a much larger number.
| Win rate | 5 losses in a row | 8 losses in a row | 5-run somewhere in 100 trades | 8-run somewhere in 100 trades | Expected longest run (100 / 500 trades) |
|---|---|---|---|---|---|
| 40% | 7.78% | 1.680% | 97.6% | 49.0% | 7.9 / 11.0 |
| 45% | 5.03% | 0.837% | 92.0% | 30.7% | 6.9 / 9.5 |
| 50% | 3.12% | 0.391% | 81.0% | 17.0% | 6.0 / 8.3 |
| 55% | 1.85% | 0.168% | 64.7% | 8.4% | 5.3 / 7.3 |
| 60% | 1.02% | 0.066% | 45.9% | 3.6% | 4.6 / 6.4 |
At a 55% win rate, eight straight losses is a 0.168% event at any given trade, but there is an 8.4% chance of seeing one somewhere in a hundred trades. Push the sample to 500 trades and the expected longest losing run alone is around seven. A trend-following system running at 40% wins should plan for a run of about eight in a hundred trades and about eleven in five hundred, not as a disaster scenario but as the expected case.
Two caveats keep this honest. The maths assumes trades are independent and the win rate is constant, and live trading violates both. Correlated positions lose together, so five open trades in the same sector can behave like one, and market regimes cluster outcomes so losses bunch more than a coin flip would. Treat the table as a floor on streak length rather than a ceiling, and check your own realised streaks in a trade log rather than trusting the model.
Risk of ruin asks: what is the probability of losing everything before the edge has time to work? For fixed-size bets at even money it collapses to the classic gambler's ruin result, where N is how many betting units you hold.
Fixed 1R units, 1:1 payoff, win rate w > 0.5: Risk of losing N units = ((1 - w) / w)^N w = 0.55, N = 20 units -> (0.45/0.55)^20 = 1.81% w = 0.55, N = 33 units -> 0.13% w = 0.52, N = 20 units -> 20.17% w = 0.50, N = any -> 100%Nobody actually trades down to a zero balance, so literal ruin is the wrong question. Reframe N as your drawdown budget measured in R. If you cap tolerable drawdown at 20% and risk 1% per trade, you hold 20 units, and the relevant probability is the chance of hitting that limit rather than the chance of going broke. Same formula, an answer you can act on.
Look at the sensitivity in those numbers. Dropping the win rate from 55% to 52%, a difference most traders could not detect in fifty trades, takes the 20-unit failure probability from 1.81% to 20.17%. At exactly 50% with even payoffs, the probability of eventually hitting any finite limit is 1. Risk of ruin is far more sensitive to a small error in your edge estimate than to anything else in the calculation.
That sensitivity is exactly why an unvalidated edge is dangerous to size against. In my own walk-forward testing the anchored-VWAP reclaim setup produced +0.117R over 4,933 trades on a 129-symbol, 10-year universe, 95% CI [+0.057, +0.174]. A risk-matched random entry on the same universe already captured +0.086R, so the signal contributed roughly +0.030R with a confidence interval that crosses zero. That is not a validated edge, and plugging an optimistic win rate into a ruin formula would have made it look far safer than the evidence supports. How that testing was run.
With no deposits or withdrawals, the order of returns cannot change your final balance, because multiplication commutes. It can, and does, change everything about the path. Take four period returns of -20%, -20%, +50%, +10%. Every ordering finishes at +5.6% cumulative. Order them so the two losses sit at the end and the maximum drawdown is 36%. Order them so a gain separates the losses and the maximum drawdown is 20%. Identical results, nearly double the pain.
Add cash flows and the ending number moves too. Start with $100,000, earn +30%, -30% and +10% in some order, and withdraw $10,000 at the end of each year. Best ordering (+30%, +10%, -30%) ends at $75,400. Worst ordering (-30%, +10%, +30%) ends at $62,800. That is a $12,600 spread, 12.6% of starting capital, produced by nothing except the order in which identical returns arrived.
Contributions flip the sign of the effect. With $10,000 added at each year end instead of withdrawn, the losses-first ordering finishes best at $137,400 and the gains-first ordering finishes worst at $124,800, because the contributions bought in after the decline. Withdrawing during a drawdown is the damaging case, because you are converting a paper loss into a permanent one by selling shares that never come back.
For a trader this is not an abstraction about retirement portfolios. You add capital when you can and take money out when you need it, and both actions interact with where you are in the drawdown cycle. It is also the strongest practical reason not to increase size immediately after a hot streak, since the sequencing risk of a large position early in a decline is severe. The transition problem is discussed in going from paper to live.
This is the payoff of everything above. If you know the drawdown you refuse to exceed and you know the losing streak the maths says to expect, per-trade risk is not a preference. It falls out.
Equity after k consecutive full losses at risk r: (1 - r)^k Drawdown from that run: D = 1 - (1 - r)^k Solve for r given a drawdown cap D and a planned streak k: r = 1 - (1 - D)^(1/k) D = 0.20, k = 10 -> r = 1 - 0.80^0.1 = 2.21% D = 0.20, k = 15 -> r = 1.48% D = 0.10, k = 10 -> r = 1.05%| Planned losing streak | Cap DD at 10% | Cap at 15% | Cap at 20% | Cap at 25% | Cap at 30% |
|---|---|---|---|---|---|
| 5 losses | 2.09% | 3.20% | 4.36% | 5.59% | 6.89% |
| 8 losses | 1.31% | 2.01% | 2.75% | 3.53% | 4.36% |
| 10 losses | 1.05% | 1.61% | 2.21% | 2.84% | 3.50% |
| 12 losses | 0.87% | 1.35% | 1.84% | 2.37% | 2.93% |
| 15 losses | 0.70% | 1.08% | 1.48% | 1.90% | 2.35% |
Worked all the way through. Say your drawdown cap is 20% and your system runs near a 50% win rate, where the expected longest run in 500 trades is about eight and the tail reaches further, so you plan for ten. The table gives 2.21% per trade. On a $40,000 account that is $884 of risk per position. Ten straight full stops take the account to $31,995, exactly the 20% you budgeted, and no further.
Compare that with the common habit of risking whatever feels right. At 2% per trade a ten-loss run costs 18.3%, which is close enough. At 3% it costs 26.3% and you have blown through the cap. At 5% it costs 40.1%, requiring a 66.9% gain to recover from a run that a 50%-win-rate system will hand you roughly once every few hundred trades.
Two honest limitations. First, the model assumes every loss is exactly 1R, and real losses are not: gaps, slippage, and correlated positions closing together produce losses larger than planned. Plan for a longer streak than the table suggests, or treat the resulting risk figure as a maximum rather than a target. Where the stop goes, and therefore what 1R actually equals, is covered in stop-loss placement and applied in position sizing per trade.
Second, it models a pure losing run with no interleaved wins, which is conservative, while ignoring that drawdowns can also be built from many small net-negative clusters rather than one clean streak, which is optimistic. It is a sizing floor, not a forecast. Growth-optimal sizing answers a related but different question and generally lands on a larger number than most people should trade, for reasons set out in the Kelly criterion guide.
There are two drawdown limits and they are not the same. The mathematical limit is the depth from which recovery is still plausible in a reasonable time. The psychological limit is the depth at which you stop following your own rules. The second is always smaller, and it is the one that binds.
A system that can mathematically tolerate a 30% drawdown is worthless to a trader who abandons it at 15%, because the abandoned version has different statistics: it locks in the loss and forfeits the recovery. Sizing to the mathematical limit while carrying a psychological limit half as deep is the single most common way a tested system produces an untested result.
The symptoms of hitting the psychological limit are behavioural, not emotional, and therefore countable: cutting size after a loss and never restoring it, skipping valid signals after two losers, widening a stop to avoid booking a loss, adding to a position that is already at maximum planned risk. Each one is a rule violation with a timestamp.
You do not find your real limit by asking yourself, because the answer you give while flat is not the answer you live at down 18%. You find it by looking at what you did during your last drawdown. That requires the log to already exist, which is the least glamorous and most useful argument for keeping a trading journal with a violation tag on every trade.
A 35% drawdown is usually described as a 53.85% recovery problem. It is better described as a time problem, because that gain has to be earned at whatever rate your system actually produces.
Years to recover at compound rate g: t = ln(1 + d/(1 - d)) / ln(1 + g) At g = 12% per year: d = 20% -> ln(1.2500) / ln(1.12) = 2.0 years d = 30% -> ln(1.4286) / ln(1.12) = 3.1 years d = 35% -> ln(1.5385) / ln(1.12) = 3.8 years d = 50% -> ln(2.0000) / ln(1.12) = 6.1 yearsSix years to get back to a previous high is not a statistic, it is a decade of a working life spent producing nothing new. It is also six years of continuing to execute a system that has spent the entire period reminding you it lost half your money. The underwater period, meaning how long the equity curve stays below its prior peak, is usually a better predictor of whether a trader quits than the depth of the drawdown itself.
This is the specific reason instruments with structural decay deserve tighter drawdown budgets: the recovery rate is working against a headwind. The mechanism is worked through in the leveraged ETF decay guide.
A backtest gives you one path: the specific order in which your trades happened to occur. Since drawdown is path dependent, that single maximum drawdown figure is a sample of size one drawn from a distribution you have not looked at.
Monte Carlo fixes this cheaply. Resample your trade results with replacement, or simply shuffle their order, run several thousand synthetic equity curves, record the maximum drawdown of each, and read the percentiles. The output is not a prediction. It is the range of outcomes your own trade distribution is capable of producing.
Here is a simulation of a hypothetical system: 55% win rate, wins of +1.5R, losses of -1R, 200 trades per path, fixed-fractional sizing, 20,000 paths.
| Risk per trade | Median max DD | 95th percentile | 99th percentile | Worst of 20,000 paths | Median final equity |
|---|---|---|---|---|---|
| 0.5% | 3.5% | 5.9% | 7.3% | 11.9% | 1.45x |
| 1.0% | 6.9% | 11.4% | 14.2% | 21.1% | 2.08x |
| 2.0% | 13.4% | 21.9% | 26.9% | 41.1% | 4.19x |
Two things to take from that. Doubling per-trade risk roughly doubles the median drawdown but stretches the tail further than proportionally, so the worst observed path at 2% risk is 41.1% against 21.1% at 1%. And the median drawdown is a bad planning number: at 1% risk the median path drew down 6.9%, while one path in twenty exceeded 11.4%. Size against the 95th percentile, not the median, because you only get one path.
The obvious caution is that the simulation inherits every assumption you feed it. The 55% win rate and +1.5R payoff above were assumed, not measured, so the output describes an imaginary system precisely. Feed it an overfitted backtest and it returns an overfitted distribution with more decimal places, which is exactly the failure described in backtest overfitting. It also assumes independent trades, so it understates real drawdowns whenever positions are correlated. You can run the sizing and simulation arithmetic in the risk toolkit.
None of this arithmetic reduces risk. It only makes risk legible before it arrives, and every figure above is a model of trading rather than a record of it. Backtested and simulated drawdowns are systematically shallower than live ones, because models do not include gaps through stops, liquidity vanishing at the worst moment, correlated positions failing together, or a trader deviating from the plan. Assume your real maximum drawdown will exceed the tested one, and size for that gap rather than against it.
Educational content, not financial advice. No live profit-and-loss figures are claimed anywhere on this site; backtest and walk-forward results are always labelled as such. Full terms: /terms.html
FAQ
You need a 100% gain. After losing half your capital, the remaining half has to double to return to the previous peak. The formula is gain required equals drawdown divided by one minus drawdown, so 0.50 divided by 0.50 equals 1.00.
A 30% drawdown requires a 42.86% gain to recover. The 70% of capital that survives must produce the entire missing 30 percentage points, and 30 divided by 70 is 0.4286. The ratio of required gain to loss is 1.43 at that depth, rising to 2.0 at a 50% drawdown.
Because the two percentages are measured against different bases. The loss is a percentage of the account peak, while the recovery is a percentage of the smaller amount left after the loss. The deeper the drawdown, the smaller that base, which is why the required gain accelerates rather than rising in a straight line.
Volatility and standard deviation measure the dispersion of individual period returns and ignore the order those returns arrived in. Drawdown depends entirely on that order. Two series with an identical mean and an identical standard deviation can have very different maximum drawdowns, for example 5.47% when gains and losses alternate versus 14.26% when the same losses are clustered together.
At a 50% win rate the expected longest losing run is about six trades in a hundred and about eight in five hundred. At a 40% win rate it is roughly eight in a hundred and eleven in five hundred. Those figures assume independent trades with a constant win rate, so real streaks tend to be longer because correlated positions and market regimes cluster losses together.
Use r equals one minus the quantity one minus D raised to the power one over k, where D is your drawdown cap and k is the losing streak you plan for. Capping drawdown at 20% while planning for ten consecutive losses gives 2.21% risk per trade. On a 40,000 dollar account that is 884 dollars of risk per position.
Risk of ruin is the probability of losing your capital before an edge has time to work. For fixed one-unit bets at even money it equals the loss rate divided by the win rate, raised to the number of units you hold. At a 55% win rate with 20 units the figure is 1.81%, but at 52% it jumps to 20.17%, which shows how sensitive the result is to a small error in your estimated win rate.