Risk of Ruin

Ruin is computable from three numbers you already have: your edge, the fraction you risk, and how far you are allowed to fall. And it is not a story about bad luck. On the same winning system, risking 1 per cent of the account ruined nobody in two hundred thousand simulated careers and risking 10 per cent ruined sixteen in a hundred.

Prerequisites: Lesson 17, for p and b, and lesson 20, for the fraction, which turns out to matter more than either of them.

The same edge, five fractions

Take lesson 18’s system again — a 45 per cent win rate at b = 2, an expectancy of +0.35R a trade, a system that makes money — and simulate two hundred thousand careers of a thousand trades each, seed 20260901, sizing as a fixed fraction of current equity. Ruin means the account touched half its starting value at any point. The second column asks what happens if the edge is three points worse than you believe, which lesson 19 established is well inside what fifty trades can hide.

Risk per trade	Ruin, if the win rate really is 45%	Ruin, if it is really 42%
1%	0.00%	0.00%
2%	0.00%	0.03%
3%	0.06%	0.52%
5%	1.52%	5.29%
10%	15.98%	30.80%

The zeros in the first two rows are literal rather than rounded. At 1 per cent not a single one of the two hundred thousand careers halved the account, under either win rate. At 2 per cent with the true edge, three did.

Then read down. The edge is identical in every row and the method is identical in every row; only the fraction moves, and it moves the answer from nothing at all to one career in six. That is the whole of what this lesson has to say about size, and it is the same claim lesson 20 made from the other direction, now with the tail attached instead of the median.

Now read across, because the second column is the one that should worry you. At 1 per cent and 2 per cent being wrong about the edge changes nothing you would notice. At 5 per cent it more than triples the risk of ruin, and at 10 per cent it takes it to nearly a third. The sensitivity is not in the edge alone and not in the size alone — it is in the two together, and the fraction is what decides how much an error in the edge is allowed to cost you. You will never know p exactly. You do get to choose how much that ignorance is worth.

One more thing the simulation says, and it is the one nobody expects. Almost all of this risk arrives early. At 5 per cent a trade the ruin probability is 0.91 per cent after fifty trades and 1.52 per cent after two hundred, and the remaining eight hundred add fourteen ruined careers out of two hundred thousand. At 10 per cent it is 12.94 per cent after fifty and 15.98 per cent at the end. In both cases most of a career’s entire ruin risk is concentrated in its first fifty trades — three-fifths of it at 5 per cent, four-fifths at 10 per cent.

The reason is that a positive edge drifts you away from the barrier. Survive the opening stretch and the account is far enough above the level that ordinary variance can no longer reach it. Which lands the two halves of this module on top of each other: the period in which ruin is most likely is precisely the period in which, by lesson 19, you cannot yet tell whether you have an edge at all. You are most exposed exactly when you know least, and the only instrument that works in that window is the fraction.

What this does not settle

That the numbers are yours. Every figure above is computed at a 45 per cent win rate and b = 2, on independent trades. Your own two numbers move the table, and problem 1 below is how you build your own rather than borrowing this one.

Nor is three points a stress test. The second column moves the win rate by three because three is a comfortable amount to move it, and lesson 19’s interval is far wider than that: fifty trades reading 45 per cent are consistent with anything from 31 to 59. Run the same simulation at 35 per cent — still a profitable system, still +0.05R a trade — and the top row stops being zero. It becomes 2.28 per cent, and the 5 per cent row becomes 74. Worse, that interval reaches down past 33.3 per cent, which at b = 2 is exactly where the expectancy turns negative and every cell here goes to certainty given enough trades. So the honest reading of the second column is not that being wrong is survivable. It is that this table means something only once you have enough trades for the first column to be true, and the fraction is what you set in the meantime.

That trades are independent. They are not, and lesson 18 said so in its own bounds. Positions taken on the same idea fail together, so the real distribution has fatter tails than this one and the real ruin probability is higher than every cell here. Read the table as the optimistic case.

That the barrier is yours to set. It is your barrier only if nobody else can close you first, and lesson 15 was the list of five published rules that let them: a maintenance call does not consult your drawdown protocol, and a gap through a stop can take you past a level you had promised yourself you would stop at. For an account on borrowed money the effective barrier is set by the broker and is usually much shallower than the one you would have chosen.

That a low number is permission. A 1.52 per cent chance of halving the account is not the same as a 1.52 per cent chance of a bad outcome; it is the probability of the single worst one. Everything short of it — the drawdowns of lesson 18, the years that go nowhere — is still on the table and is far more likely than ruin ever was.

And that knowing the number is a plan. This lesson computes what a fraction costs you in the tail. What to actually do when the drawdown is happening, in the state of mind it produces, is lesson 24, and it has to be written down before rather than during for reasons that are the subject of that lesson rather than this one.

Ruin is not the market’s decision. It is the product of an edge you estimated and a fraction you chose, and of the two, the fraction is the one you control exactly.

Problems

1. Find the fraction where your own table turns. Simulate ten thousand careers of five hundred trades at your own p and b from lesson 17, sizing at 1, 2, 3, 5 and 10 per cent, and record how often the account ever halves. You are looking for the row where the answer stops being a rounding error, because that row is the edge of the region you are allowed to trade in. That row moves with your edge, not with your confidence.
2. Price your own ignorance. Run the same simulation twice more with your win rate three points lower and three points higher. The spread between those two columns at your current fraction is what not knowing your edge is worth to you, in units of ruin. If that spread is wide, the fix is not a better estimate — it is a smaller fraction, because the fraction is the term you can change today.
3. Ask who else can close you. Write down your own barrier as a percentage, then find the two numbers your broker uses: the maintenance requirement from lesson 14 and any daily or overall loss limit on the account. If either of them bites before your own barrier does, then your barrier is decoration and the real one belongs to somebody else. That is worth knowing before it is enforced rather than after.

Sources. William Feller, An Introduction to Probability Theory and Its Applications, Volume I (3rd edition, 1968), chapter XIV, which is the standard derivation of the gambler’s ruin problem and of the result that an unfavourable game ends in ruin with certainty against an opponent of unlimited means. Nassim Nicholas Taleb, “The Logic of Risk Taking” (in Skin in the Game, 2018), for the distinction this lesson turns on: an average computed across many people says nothing about a single person who has to survive in sequence, and a strategy with a positive expectation can still be certain to end you. Perry J. Kaufman, Trading Systems and Methods (5th edition, 2013), whose treatment of ruin for unequal payoffs is where to go when the even-money formula above stops applying, which for most real systems is immediately.

Every number in this module has now been computed from p, b and a fraction — and all three came from a record you may not be keeping. The next lesson is the ten fields that decide whether any of this can be answered about your own trading at all.

Educational only. Trading involves substantial risk of loss. Not financial advice. Past performance does not guarantee future results.