Risk of ruin and drawdown recovery
A positive edge does not make ruin unlikely. Two numbers that show why size matters more than most traders think.
What this model assumes
One-barrier gambler's ruin. There is a floor and no ceiling: it asks whether the account ever reaches the loss you named, with no point at which you stop and walk away. That is a larger number than "ruin before doubling", the two-barrier form, though by less than it sounds: the two are nearly equal while ruin is unlikely, and a third apart only once it nears 50%.
The arithmetic. With a win probability p, a loss probability
q and a reward-to-risk R, it solves
p·zR+1 + q = z for the z between 0 and
1, then raises it to the number of risk units between you and ruin:
zN, where N is the ruin percentage divided by
the risk percentage. It is not q/(p·R), which is only correct
when a win and a loss are the same size and understates ruin badly above that.
Fixed size, off the starting base. Risk per trade is that percentage of the balance you started with, every trade, not a shrinking percentage of what is left. Real position sizing that shrinks with the account survives longer than this.
Independent trades, one fixed edge. Every trade has the same win rate and the same reward to risk, and none of them depends on the last. Real trading has neither of those properties, which is why this is a model and not a measurement.
Which way it is wrong. It ignores overshoot past the barrier, which makes it read high against simulation, by up to about 15% in the cases we ran. On a risk calculator that is the correct direction to be wrong in.
- Net losing trades to the floor
- —
- A drawdown of
- —
- needs a gain of
- —
The asymmetry nobody plans for
Losses and gains are not symmetric. Down 10% needs 11.1% to get back. Down 30% needs 42.9%. Down 50% needs 100%: a doubling, from a smaller base, after the drawdown that just shook your confidence in the method. This is the arithmetic that turns a bad month into a different career.
What this model assumes
Constant risk per trade, independent trades, and a constant edge. Real trading has none of those cleanly, so treat the number as a comparison tool rather than a forecast. Its value is in the direction it moves: hold your edge constant, double your risk per trade, and watch the probability climb. That relationship is real even where the exact percentage is not.
Constant risk means the same amount every time, which is what a fixed stop and a fixed contract count produce. It is not percent-of-current-equity sizing: under that the account compounds downward and never reaches exactly zero, so a whole-number count of losing trades to the floor would not mean anything.
Ruin does not have to mean zero. Set it to whatever ends your trading, which is rarely an empty account. On an evaluation account it is the drawdown limit; for most people funding themselves it is the loss they would stop after. Leave it at 100% for the textbook version. The guide to sizing against a drawdown limit is the long version of why that number is usually much closer than the balance suggests.
No edge is a different problem
If the win rate and reward-to-risk you enter do not clear break-even, the calculator says ruin is certain, because it is. At negative expectancy, position size determines how long the account lasts, not whether it survives. Fixing size is not a fix for that; the expectancy calculator is where that problem is visible.
Your own numbers beat any calculator. Drop a NinjaTrader export on the Trade Lab and it works these figures out from the trades you actually took. It reads the file in your browser and nothing uploads.