Drawdown is the number that decides whether you survive

A drawdown is the fall from a high-water mark to the low that follows it, measured before the account gets back to the high. The maximum drawdown is the worst of them. Of all the numbers in a track record it is the one that decides whether you are still there at the end, and it is the one most often left out — because it is the one that does not sell. This page is the arithmetic of drawdowns: how much it costs to recover from one, how long the losing streaks that cause them are allowed to be, and how bet size turns into a probability of going broke.

Recovery is not symmetric

Lose 10% and you need to make 11.1% to get back to where you were, because you are now earning on a smaller base. Lose half and you need to double. The table every trader should be able to recite:

The formula is loss ÷ (1 − loss). The curve is gentle until about 20% and then it is not: the second 25% of a 50% drawdown costs far more to recover than the first, which is why the first job of every risk rule is to keep drawdowns in the top half of the table. It is also why a system's return cannot be judged without its drawdown. A 30% year that followed a 40% drawdown left the account still 22% below its high.

Losing streaks are not a sign that something is broken

Every system loses several times in a row, regularly, when nothing is wrong. How many in a row is not a matter of luck but of arithmetic, and it was worked out for coin flips long before anyone applied it to trading. Mark Schilling's result: in n trials where a loss has probability q, the longest run of losses you should expect is about

log(n × (1 − q)) ÷ log(1 ÷ q)

Which gives, for a run of trades:

Read the 50% row. A system that wins half its trades will string together six losses in a hundred trades as a matter of course, and nine in a thousand, with no edge lost and nothing broken. A trend-following system that wins 40% — common, because its winners are large and its losers small — should expect seven in a row every hundred trades and twelve somewhere in a thousand. Multiply the streak by your risk per trade and you have the drawdown the arithmetic has already promised you, before any bad luck: at 2% a trade, that 40% system's ordinary thousand-trade streak is a 24% drawdown, which the first table says costs 32% to recover.

This is the number the sizing page is built around. Risk per trade is chosen so that the expected streak — not the worst imaginable one — leaves an account that can keep trading.

The backtest's worst drawdown is a floor

Notice the table's columns. The expected longest streak grows with the number of trades: it is a property of how long you keep going, not of how good the system is. A backtest over a few hundred trades reports the worst drawdown that happened in those few hundred; a system traded for a thousand more will, by the same arithmetic, meet a longer streak than any it has shown. The maximum drawdown in a track record is one draw from a distribution whose tail keeps extending the longer you trade. Treat it as the least you should expect, not the most, and size so that half again as much would still be survivable.

The desk learned this on its own hands and keeps re-learning it: every system on the rack posts the deepest drawdown its record showed, and the standing evaluation re-measures each hand against that posted number on a schedule, so that a drawdown deeper than the record is raised as a finding rather than discovered in an account.

Risk of ruin: the formula that turns bet size into a probability

One of the oldest results in probability is about a gambler with an edge who nevertheless goes broke. Bet a fixed unit each time against an opponent with unlimited money, with probability p of winning each bet and q of losing, starting with i units. If p is no better than a coin flip, ruin is certain, eventually. If p is better, the probability of ever going broke is

(q ÷ p) ^ i

The edge is in the base; the number of units is in the exponent, and the exponent is the part you control.

Units are your account divided by your risk per trade. Risking 20% of the account per trade is five units; risking 5% is twenty; risking 1% is a hundred. The table says the same thing from two directions: a thin edge with large bets is a near-certain ruin, and halving the bet size squares the probability of ruin rather than halving it. Edward Thorp's figures for the optimal-growth bettor make the same point from the other end: even betting the mathematically optimal fraction, the probability of ever halving your capital is one half; at half that fraction it is one eighth.

Real trading is messier than the formula — losses are not one fixed unit, and the edge is estimated rather than known — but every refinement moves the answer in the same direction, toward smaller bets than the raw edge suggests.

The number you can actually sit through

All of this is arithmetic, and the arithmetic is the easy part. The maximum drawdown that matters is the one you can watch without touching the system, because a drawdown you abandon at the bottom is a loss that never gets its recovery. The honest way to pick a system is to look at its worst stretch first — its depth, and its length in months — and ask whether you would have kept it running through that, knowing only what you would have known at the time. The factors page has thirteen years of that question in one line. If the answer is no, the system is wrong for you however good its average, and no win rate will fix it.

• Position sizing from the stop, not the account
• How to read a track record (and the ten ways it lies)
• Leverage: the arithmetic of being wrong

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