Risk of Ruin and Drawdown Maths

The short answer

A drawdown costs more to repair than it cost to create, because returns multiply rather than add. Lose 50% and the 100% gain you need is calculated on the smaller balance that is left.

Risk of ruin is what happens when you put that asymmetry next to the losing streaks any win rate produces. It is the probability that a perfectly normal run of losses — not a mistake, not a bad entry — reduces the account to a state you cannot trade back from.

Why the maths is multiplicative

Add and subtract percentages and everything looks symmetric: down 20, up 20, back where you started. That is not how an account works.

equity after a sequence = start × (1 + r1) × (1 + r2) × … × (1 + rn)
recovery gain needed    = drawdown ÷ (1 − drawdown)

Each result is applied to whatever survived the last one. A 20% loss leaves 0.8 of the account, and 0.8 × 1.2 is 0.96 — still 4% down after an equal-sized gain.

The previous lessons in this course give the recovery table. The formula above is where that table comes from, and it is worth being able to compute in your head: divide the drawdown by what remains. A 25% loss needs 25 ÷ 75, or one third. A 60% loss needs 60 ÷ 40, or 150%.

The same multiplication explains something else. The order of your wins and losses does not change the final figure, but it changes the size of every position along the way, because sizing is a percentage of current equity. Losses early make every subsequent position smaller. That is a feature — it slows the bleed — but it also means recovery is not the mirror image of the decline.

Streaks are not anomalies

A losing streak is not a signal that something has broken. It is a scheduled event.

The numbers below are invented for teaching. They describe no real strategy and are not a prediction.

Take a method that wins 45% of the time, so any given trade loses with probability 0.55. The chance that eight losses land back to back, starting from any particular trade, is 0.55 raised to the eighth power — a little under 1%. Across 200 trades, you would expect that run to appear roughly once or twice.

So an eight-loss streak is not evidence of anything. It is the ordinary behaviour of a 45% win rate over a realistic number of trades. A trader who abandons a method after such a run has not diagnosed a problem; they have met the variance the win rate always implied.

What varies is not whether the streak arrives but what it costs.

Illustrative arithmetic only, based on the compounding formula above.

Four traders, one streak, four completely different situations — and the difference was decided before any of them placed a trade. At 1% the streak is an inconvenience. At 10% it is close to a career-ending event, and the trader still has to find a 132% gain while trading positions that are now less than half their previous size.

What risk of ruin actually combines

Ruin probability is driven by three things:

1. Per-trade risk. The dominant term, and the one entirely under your control.
2. Win rate and payoff. Together these determine whether the drift is upward at all. A negative expectancy makes ruin a certainty given enough trades; see risk/reward and expectancy.
3. The number of trades. More trades means more opportunities for a bad sequence, and also more opportunity for an edge to assert itself. Both grow together.

Two things follow that are not obvious.

The first is that improving your win rate is a much weaker lever than reducing your risk. Moving from 45% to 50% is a serious change in skill and hard to achieve. Moving from 3% risk to 1% takes one edit to a spreadsheet and cuts the drawdown of every future streak by roughly two thirds.

The second is that ruin probability is not linear in risk. Doubling per-trade risk does far more than double the chance of a catastrophic sequence, because the drawdown from any streak compounds.

What a year of trades actually does to an account

Formulas describe one streak. To see what a whole year of ordinary variance does, we simulated it: 100,000 separate years for each combination below, 250 trades per year, every winner paying 1.5 times the amount risked, and risk taken as a fixed share of current equity. Three win rates stand in for three kinds of trader — 40% (no edge at all: the payoff exactly offsets the losses), 45% (a modest edge of +0.125R per trade) and 50% (a strong one, +0.25R).

Read the middle line. A trader with a genuine, modest edge who risks 1% per trade sees a 30% drawdown in 0.6% of years. The same trader, same edge, same trades, risking 3% sees one in 68.3% of years — and at 5% it is 98.9%. Nothing about the skill changed. Only the size did.

Our own simulation, seed 20260922. "30% drawdown" means equity fell at least 30% below its running peak at some point in the year, even if it recovered afterwards.

Two rows deserve a second look.

The no-edge column is what most beginners are actually trading, whether they know it or not. At 3% risk, 51.8% of those years contain a 50% drawdown — half the account gone from the top, with no bad luck beyond the ordinary.

The median column shows why large risk is tempting. With a modest edge, the typical year ends at 1.32× at 1% risk and 2.78× at 5%. That is the number people see in a spreadsheet. The drawdown column is the price of it, paid in advance by nearly everyone who chooses it — 98.9% of those years include a 30% fall, and more than half include a 50% one.

A year that hit its win rate exactly

Averages hide what a drawdown feels like from the inside, so here is one simulated year, chosen to be uncomfortable.

This account did exactly what its method promised: 113 wins in 250 trades, a 45% win rate, at a sensible-looking 2% risk. It climbed to 1.88 times its starting balance, then gave back 39% of that peak before finishing the year at 1.77×. Its longest losing streak all year was 7 trades — survivable on its own. The drawdown was built from losses scattered between small wins, which is why counting streaks underestimates how deep a hole can get.

It is a bad case on purpose: the deepest drawdown among the 183 years (out of the first 2,000) that landed on exactly 45%. Most years at 2% risk are gentler. But roughly 25.1% of them reach a 30% drawdown, so this is not a freak.

How this was calculated, and where it breaks down

The model is deliberately simple, and every simplification makes the real numbers worse, not better:

• Trades are independent. Real results cluster: a method that suits one market regime loses repeatedly in the next. Clustering produces longer, deeper drawdowns than independent coin-flips.
• The win rate is known and fixed. In reality you estimate it from a small sample and it drifts. Most traders overestimate it.
• No fees, no slippage, no gaps. Each of these shaves every trade, and gaps can make a single loss larger than the amount you meant to risk.
• Risk is recalculated on current equity every trade. That automatically shrinks positions during a drawdown, which is protective. Traders who size off their starting balance, or who increase size to "get back", do much worse than these tables.

So treat the figures as a floor on the danger, not an estimate of it. The script that produced them is in the site's repository (scripts/sim/risk_of_ruin.py) with a fixed seed, so anyone can reproduce every number here.

Mathematical ruin versus practical ruin

If you always risk a fixed percentage of current equity, you can never mathematically reach zero. Each loss takes a slice of what remains, so the balance approaches zero without arriving.

This is cold comfort. The real threshold is practical ruin: the point at which the return needed to recover is so far outside what your process has ever produced that assuming it is fantasy. An account down 70% needs to more than triple. If the method was producing modest gains before the drawdown, nothing about being down 70% makes it produce triple-digit ones now.

Practical ruin also has a human component that the formula ignores entirely. Traders in deep drawdowns raise size to recover faster, abandon rules that were working, and take trades they would not otherwise take. The arithmetic gets worse exactly when behaviour does — a pattern examined in why discipline fails.

This is why a drawdown limit is a separate control from a per-trade limit. The per-trade limit bounds one outcome. The drawdown limit says what happens when several of them arrive in a row: at a stated level — some traders use 10%, others 20% — you stop, review, and only resume at reduced size. It converts an open-ended decline into a bounded one.

Variance, not bad entries

Most accounts that fail do not fail because the trader could not read a chart. They fail because the sizing could not survive a run of outcomes that the strategy's own win rate made likely.

That is a hopeful conclusion, in a limited way. It means the failure mode most likely to remove you is the one most completely under your control, and it is controlled before the trade, not during it.

What to do with this

Work out, for your own method, the longest losing streak that is plausible rather than the one you hope for — then check what that streak does to your equity at your current risk percentage. The position size calculator gives you the per-trade number; the compounding formula above turns it into a drawdown.

If the answer puts you in the bottom rows of the recovery table, the fix is not a better entry technique. It is a smaller number.

Frequently asked questions

What is a reasonable amount to risk per trade?

There is no universal number, but the simulation above shows why most educational sources settle between 0.5% and 1% for people still proving their method. At 1% risk, a trader with no edge at all hits a 30% drawdown in about one year in eight; at 3% it happens in nearly every year.

Does a higher win rate protect me?

Less than it seems. Moving from a 45% to a 50% win rate is a large improvement in skill, yet at 3% risk it only cuts the chance of a 30% drawdown from about two years in three to about one in three. Cutting risk from 3% to 1% does more, and it costs nothing.

Why can't I just count how many losses in a row I can survive?

Because drawdowns are rarely one streak. The example year above never lost more than seven in a row and still fell 39% from its peak, through losses spread between small wins.

Is risk of ruin the same as losing money?

No. With a modest edge at 3% risk, 85% of the simulated years that suffered a 30% drawdown still finished the year in profit. Risk of ruin is about the path — whether the account falls far enough, at any point, that you cannot or will not continue — not only about where it ends.