BUILD: COURSE 2 | LESSON 3
Drawdown maths and risk of ruin
Learning objectives
Compute the gain required to recover from any drawdown, and explain why losses and gains are asymmetric.
Estimate the depth of normal losing streaks from win rate, and translate that into expected drawdown at a given risk-per-trade.
Use risk-of-ruin intuition to choose a per-trade risk level that makes account destruction mathematically remote.
Every trading account that dies, dies the same way: a drawdown it could not recover from — financially or psychologically. The previous lessons gave you an edge measure (expectancy) and a way to keep risk constant (ATR sizing). This lesson answers the question those two leave open: how much can I risk per trade before normal bad luck destroys me? The answer comes from arithmetic that is simple, brutal, and worth memorising.
The recovery asymmetry
Losses and gains are not symmetric, because a loss shrinks the base your recovery is calculated on. Lose 10% of $10,000 → $9,000. To get back to $10,000 you must make $1,000 on a $9,000 base = +11.1%. The general formula:
Required gain = drawdown ÷ (1 − drawdown)
| Drawdown | Gain needed to recover |
|---|---|
| −5% | +5.3% |
| −10% | +11.1% |
| −20% | +25% |
| −30% | +42.9% |
| −40% | +66.7% |
| −50% | +100% |
| −70% | +233% |
| −90% | +900% |
Read the shape of that table, not just the numbers. Up to about −20%, recovery is a similar-sized job to the loss. Beyond −30%, the curve bends viciously: a halved account must double just to break even, and doubling an account is the kind of performance that takes even good traders years. Deep drawdowns also arrive with a second tax the table doesn't show: you now trade a smaller account with damaged confidence, so the very edge you need to recover is usually operating below its normal level. Conclusion one of this lesson: your entire risk framework should be designed to make −30%+ drawdowns close to impossible.
Losing streaks × risk per trade = your expected drawdown
From P2.1: with win rate w, the chance of n consecutive losses starting at a given trade is (1−w)ⁿ. Over a few hundred trades, streaks that look "impossible" are near-certainties. Rules of thumb for the worst streak you should plan for in ~100–300 trades:
- 50% win rate → expect a worst streak around 7–8 losses
- 40% win rate → around 9–10
- 30% win rate → around 12–13
Now multiply by risk per trade (streak losses compound, but at small risk sizes simple multiplication is a good first approximation):
- Risk 1%, 40% win rate: a 10-loss streak ≈ −9.6% drawdown (1 − 0.99¹⁰). Annoying. Survivable. Recovery needs +10.6%.
- Risk 3%: same streak ≈ −26.3%. Now you need +35.7% to get back, and you're deep in the bad zone of the table.
- Risk 5%: ≈ −40.1%. Recovery needs +67%. Most traders' discipline fails long before the maths does.
And this is only the pure streak; real drawdowns are streaks interleaved with choppy small wins and are typically 1.5–2× deeper than the naive streak estimate. This is the quantitative case for the 1–2% rule you were given in Foundations as a commandment: at 1% risk, the ordinary worst-case of a decent system is a drawdown in the −10% to −15% range — recoverable arithmetic and recoverable psychology. At 5%, the same system with the same edge produces −40% to −60% episodes. Risk size doesn't change your expectancy per trade in R; it changes whether you live to collect it.
Risk of ruin: the intuition
Risk of ruin is the probability that your account hits a level you (or the margin engine) define as dead — before your edge has time to express itself. The exact formula involves some algebra, but the intuition rests on three levers, and you should know the direction and rough weight of each:
- Edge (expectancy). Negative expectancy → ruin probability is 100% at any size; it's only a question of when. No sizing scheme rescues a losing system.
- Risk per trade (fraction of account). This is the lever with nonlinear power. Ruin probability rises roughly exponentially with size. For a modest positive-edge system (say 45% win rate, 1.5:1 payoff), risking 1% per trade puts ruin risk near zero (fractions of a percent); at 5% it climbs into the single digits; at 10% it becomes a coin-flip-ish gamble over a few hundred trades. Halving your size does far more than halve your ruin risk.
- Ruin threshold. If "ruin" for you is −50% (the point you'd realistically quit) rather than −100%, effective ruin risk is much higher than the naive calculation. Be honest about your real threshold — for most people it's the drawdown their conviction can't survive, not zero.
Two protective consequences follow. First, fractional-of-current-balance sizing (1% of current equity, not starting equity) means losses shrink your bet size automatically — mathematically, you can't hit zero, and drawdowns decelerate themselves. Second, an equity circuit-breaker caps behavioural ruin: e.g. "if I'm down 8% in a month, I stop and review; down 15% total, I drop to half size until back at the high-water mark." The maths above assumes you keep executing your system flawlessly through a 10-loss streak. Nobody does. The circuit-breaker is a rule that assumes you're human.
Your personal risk policy — write it down
Turn this lesson into three written numbers before the next one. (1) Risk per trade: 0.5–2% of current equity, chosen from your own worst-streak estimate: take your realistic win rate, find the plan-for streak above, and pick the risk % that keeps that streak's drawdown inside −15%. (2) Monthly stop: the drawdown at which you pause trading and review (commonly 6–10%). (3) Half-size threshold: the total drawdown at which you cut risk in half until you make a new equity high (commonly 10–15%). This document is the difference between a drawdown being a data point and being an ending. In P2.4 we manage individual trades; in P2.5 we make sure five "1% risks" aren't secretly one 5% risk.
Key takeaways
Recovery is asymmetric: required gain = drawdown ÷ (1 − drawdown). −10% needs +11.1%; −50% needs +100%. Beyond −30%, the maths turns against you fast.
Losing streaks are a certainty, not a tail risk: a 40%-win-rate system should plan for ~10 straight losses within a few hundred trades.
Expected worst drawdown ≈ streak length × risk per trade (and real drawdowns run deeper). At 1% risk that's uncomfortable; at 5% it's account-threatening.
Risk of ruin scales nonlinearly with position size: halving risk per trade cuts ruin probability by far more than half. With negative expectancy, ruin is certain regardless of sizing.
Size as a % of current equity and pre-commit circuit-breakers (monthly stop, half-size threshold) — the maths assumes discipline the drawdown will test.