When the Drawdown Arrives

This module priced the drawdown you are in. It has not priced what you are about to do about it, and that is the larger number: at 5 per cent a trade, sizing up to recover returns you to the high in nine careers out of ten, and along the way digs the hole to twice its depth in nearly half of them.

Prerequisites: Lesson 18, for how deep an ordinary bad run goes, and lesson 22, for what the fraction does to the tail once it is deep.

The same drawdown, four responses

Take the account at lesson 18’s median: down 8.7 per cent, a 9R hole at 1 per cent risk a trade, on the system this module has carried throughout — a 45 per cent win rate at b = 2, an expectancy of +0.35R. It is an ordinary drawdown, it happens to half of all careers on this system, and nothing has gone wrong. Now simulate the next twenty trades four hundred thousand times, seed 20260901, changing nothing except the fraction risked from here on.

Risk a trade	Back to the old high within 20 trades	Hole at twice its depth	Equity at the 5th percentile
1%	45.8%	1.3%	0.867
2%	76.9%	14.6%	0.820
3%	84.0%	23.4%	0.774
5%	90.0%	48.1%	0.681

The first column is why this is hard, and it needs saying plainly: sizing up works. At 1 per cent you are back at the old high inside twenty trades in fewer than half of the careers. At 5 per cent you are back in nine of every ten. The impulse is not a delusion and it is not innumeracy, and telling somebody in a drawdown that trying to recover faster does not work is simply false. It does work. That is the entire problem.

The second column is the price, and it does not move at the same rate. Going from 1 per cent to 2 per cent multiplies your chance of standing at a new high by about 1.7, and multiplies your chance of standing in a hole twice as deep by eleven. Going to 5 per cent multiplies the first by two and the second by thirty-seven. Every step buys a little more of what you want and a great deal more of what you were trying to escape, and the exchange rate gets worse the further along you go — which is the shape lesson 20 found in the drag and lesson 22 found in the tail, arriving a third time in one module from a third direction.

The third column settles it. The fifth percentile is the bad-but-not-unthinkable case, the one career in twenty that comes out at least this badly. At 1 per cent it is 0.867, so the hole is 13.3 per cent rather than 8.7 per cent, and by the first table it needs 15.3 per cent to undo. At 5 per cent it is 0.681, so the hole is 31.9 per cent and needs 46.8 per cent. Put both of those back on 1 per cent risk and climb out: from 13.3 per cent down it takes a median of 36 trades, and from 31.9 per cent down it takes 107. Twenty trades spent shortening the climb tripled it.

Four rules that do not need you

So the fix is not to be better during the hour. It is to have four things decided already, each of which something other than you can enforce.

1. A cap on how many times you can be wrong in a session. Three losing trades and the session is over. Not three and then be careful — over. One loss is noise and two is a bad morning; by the third, the honest position is that you cannot tell whether the problem is the session or you, and you are not at that moment the right person to work it out. The number matters far less than the fact that it was fixed before the session started. A sticky note is the weakest version of this rule, a broker-side day-trade limit is better, and handing the platform password to somebody else for the rest of the day is better still.
2. A cap on what each of those times may cost. A cash figure, fixed in advance, past which you stop regardless of how few trades it took to get there. Two per cent of the account is a common place to start. It is a different rule from the first and it catches a different failure: one oversized trade can spend two per cent on its own while the first rule still has two losses left to give. Most brokers will enforce this server-side if you ask, and that is the version that works, because a figure held in your head is not a circuit breaker but an intention, and the section above is about what happens to intentions.
3. A gap after every loss. Thirty minutes before you may place another order, no exceptions, and least of all for a setup that looks perfect. Thirty is not a magic number; it is long enough to be worth something and short enough that you will keep to it. The mechanism is physical rather than mental: a timer you have to stand up and walk to, in a different room. The trade you do not take is the one you were not sitting in front of.
4. A lock on size while the account is below its high. This is the one the table prices. The first three limit how long a spiral can run; this one limits how fast it accelerates, and the distance between the top and bottom rows of that table is the whole of what it is worth. Work out tomorrow’s 1× size tonight, in shares or contracts, and write the number down. Done the night before, the arithmetic is done by someone with no stake in its answer. Done in the hour, it is not.

Notice what the four have in common. None asks you to make a good decision in a bad hour. Each is an if-then fixed in advance, and each has a version that somebody or something else holds on your behalf. That is not a stylistic preference; it is the form of rule the research above actually supports.

What this does not settle

That the exchange rate is the same at every edge. Both tables are computed at a 45 per cent win rate, b = 2, independent trades and a 9R starting hole, and every cell moves when those move. What survives is the direction: run the same simulation at 55 per cent with b = 1, and again at 35 per cent with b = 3, and in all three the second column rises faster than the first. By how much varies enormously — at 55 per cent and b = 1, going to 5 per cent multiplies the chance of a new high by eleven and the chance of doubling the hole by fifty-seven. So the sign of the trade-off is general and its size is not: the cells worth acting on are the ones you recompute at your own p and b from lesson 17.

That twenty trades is the horizon. It is a session-to-a-week window, chosen because that is the window in which the decision actually gets made. Stretch it to two hundred trades and the edge dominates everything: every row recovers, and even the 5 per cent row ends up far above where it started. That is true, it is not consoling, and it is not the question on the table at the time: the choice in a drawdown is what to do next, not which two-hundred-trade horizon to prefer.

That the drawdown is also where the record stops. Lesson 23’s two decaying fields — the stop as it was placed, and whether the trade was in the plan — are exactly the two a tilted trader does not fill in, which means the period you would most want to examine afterwards is the period least likely to have been written down. The fix there is structural in the same way: the log entry belongs to placing the order, not to reviewing the day.

That the four rules are free. This lesson prices the failure they prevent and never prices them. Take the session cap: at a 45 per cent win rate, stopping on the third loss removes 4.2 per cent of a four-trade day, 19.2 per cent of a six-trade day and 34.3 per cent of an eight-trade day, and every trade it removes was worth +0.35R on lesson 17’s arithmetic. At six planned a session that is 0.40R given away a day, and about 74R over a year of four sessions a week. The defence is not that the price is nothing. It is that the price is a known number and what it buys is not — and that the trades a cap removes are exactly the ones taken after two losses, which is a slice lesson 23’s record lets you cut. If your own log says those trades are as good as the rest, the cap is charging you the full rate for cover you may not need, and you will have found that out by measuring rather than by feeling it in the hour.

That this is the only state worth having rules for. Size creeps up after a winning run as well, and standards slip when nothing has set up for days. Both are real, neither is a drawdown, and neither is here. What carries across is the form of the fix rather than its content: decided in advance, written down, held by somebody else.

The drawdown has been in the arithmetic since lesson 18. What it finally costs you is not, and that part is still being decided — by four rules you either wrote down last week or did not.

Problems

1. Write tomorrow’s size down tonight. Take today’s closing equity, take your fraction, and convert it into a number of shares or contracts for each instrument you are likely to trade. Put the numbers somewhere you will see them before the open. The point of doing it the night before is not organisation, it is that the arithmetic is done by the version of you that has no stake in the answer.
2. Find out which two your broker will hold. Ask for a server-side daily loss limit and a limit on trades per day. Some brokers will set both, some one, some neither. Whichever they will enforce, take, because that rule now works without you. The ones they refuse are the ones you have to hand to a timer or a person instead, and knowing which is which is the difference between a plan and a list of good intentions.
3. Price your own unplanned trades. Lesson 23 put “in the plan, or not” in the record precisely so that this could be answered. Split your log on that column and compute the win rate, the payoff ratio and the expectancy of each half separately. If the unplanned half has a worse expectancy, you now know what the response costs you in your own currency rather than in a simulation’s. If it has a better one, you have found something far more interesting and should say so in the record, because it means your plan is leaving something out.

Sources. Daniel Kahneman and Amos Tversky, “Prospect Theory: An Analysis of Decision under Risk” (Econometrica, 1979), for the reflection effect this lesson turns on: the preference for a certain outcome over a gamble of equal value reverses when both are losses, which makes risk-seeking in a drawdown the predicted behaviour rather than a personal failing. Lars Schwabe and Oliver T. Wolf, “Stress Prompts Habit Behavior in Humans” (Journal of Neuroscience, 2009), for the finding that acute stress shifts behaviour from goal-directed to habitual, which is the reason a rule has to be built before it is needed rather than summoned when it is. Peter M. Gollwitzer, “Implementation Intentions: Strong Effects of Simple Plans” (American Psychologist, 1999), for what an if-then plan decided in advance does that an ordinary intention does not, which is the form every rule in the second half of this lesson is written in.

That closes the module. Everything in it was computed from two numbers and a fraction, and none of it said a word about what the market was doing while it happened. The next module is about exactly that: where the orders actually rest, why price runs at the levels everybody can see, and what a book full of size is really advertising.

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