Which Limit Binds First

The card, filled in

Here is the whole of module 9 on one object. Three of the four columns are per rule and are printed below; the fourth is a property of the book rather than of any row, so it is stated after.

The book-level column is lesson 72’s: four positions at two per cent each are eight per cent of heat, and at the worst correlation lesson 74 measured that eight per cent arrives on 35.67 per cent of days, one day in 2.8.

Read the columns in order. The first says one rule is a duplicate of another at 0.9648. The second says that on the fortnight that matters, three of the four rules are the same series, so the first column was the optimistic version. The third says the same thing in a different currency: told it may not short, the optimiser puts nothing at all in two of the four rules, and the two it drops are two of the three that hit 1.0000.

So the three columns that are about correlation agree, and they narrow four rules to two. That is a useful answer and it is not the binding one, because nothing in those three columns says how large the two may be.

The fourth number does. A daily-loss limit means nothing unless the heat fits inside it, so the number of positions is the limit divided by the risk per trade, and at three per cent and two per cent a trade that is 1.5. Not two rules at two per cent. One.

Every row after the first carries the full three per cent of heat, so the comparison is like for like. The count is not something you choose and then size around. It is what the size per trade leaves room for, and the whole of the argument about which rules to run happens inside a number the loss limit fixed before the argument started.

Almost nobody has divided their loss limit by their risk per trade and then compared the answer against the number of rules they run. It is one division and one count, and if the second is larger than the first, no correlation work will help, because you are already past the limit on a day when everything moves together.

Which is why the count is the control and the loss limit is the reading. Lesson 69 established that a loss limit is a postcondition: it reads a loss, and a loss exists only after exposure does, so it cannot stop the fifth order. The position count derived from it is a precondition. You can ask the broker how many positions are open before you send anything, and refuse on the answer, and that check runs at the first order rather than after the damage.

What four rules buy over one

Take the last row of that table against the first, because they are the two ends of the argument. Four rules at three quarters of a per cent each, and one rule at three per cent. Both are three per cent of heat, both fit the limit, and the only difference is how the risk is spread.

One position at three per cent: the day’s standard deviation is 3.00 per cent, and the full three per cent arrives whenever that one position loses, which is half the time.

Four positions at three quarters of a per cent, at lesson 74’s worst-window correlation of 0.8800: the day’s standard deviation is 2.86 per cent, and the full three per cent arrives 35.67 per cent of the time.

So the entire benefit of running four rules rather than one, after four pages of measurement, is a day 4.61 per cent smaller and a full-loss day that arrives 28.7 per cent less often. That is the answer, it is real, and it is small.

It is worth seeing what it would have been if the correlation had been what people assume. At the full-window 0.7695 the same swap buys a day 9.05 per cent smaller and a full-loss day 40.0 per cent less often. If the four rules were independent it would be a day 50 per cent smaller and a full-loss day 87.5 per cent less often, which is the number the word diversification is usually carrying when somebody says it.

The gap between 50 per cent and 4.61 per cent is what module 9 has been measuring. It is not that diversification does nothing. It is that on four rules of the same family on one instrument it does about a tenth of what the word implies, and it costs you a quartering of the size per trade to collect.

Which settles what to do with the card. Two rules survive the correlation columns, and at three per cent and one and a half per cent a trade the limit permits exactly two. The card and the cap agree at two positions of one and a half per cent, carrying 1.06 bets, a day of 2.91 per cent and a full-loss day one in 2.4. That is the book module 9 actually licenses, and it is smaller than the one anybody starts with.

So divide your daily-loss limit by your risk per trade before you argue about rules, and make the broker refuse the order past that count.

What this does not settle

That three per cent is the right limit. It is lesson 69’s number and lesson 69 took it as a convention rather than a measurement, and nothing in this course has derived it. Everything above is a division, so it runs on whatever number you use: at two per cent and one per cent a trade the answer is two positions, at five per cent and one it is five. What the page fixes is the order of operations, not the input.

That the count is a precondition in practice. It is one in principle, because a broker can be asked what is open before an order goes out. Whether your broker exposes that in time, whether your own hand obeys the answer, and what happens when the fifth setup is the good one are the parts this page cannot help with, and lesson 69’s finding about the person between the signal and the order applies to the person enforcing the cap as much as to the one placing the trade.

That four columns is a risk system. A desk has forty, and the ones missing here are the ones that catch what a card cannot: an instrument that stops trading, a broker that fails, a rule that keeps firing because a data feed is stale. This module has priced the risk you can compute from a return series, and every failure that is not in a return series is absent from it by construction.

That the card tells you who may override it. It does not, and this page is not going to invent a governance procedure it has no evidence for. What it can say is the shape of the problem: a cap that anyone may lift on the day is not a cap, and the only version of it that has ever held is one where lifting it takes longer than the setup lasts.

That 4.61 per cent is the value of diversification. It is the value of these four rules at the worst correlation measured on sixty closes of one instrument, which is the least favourable case this course can construct and not the general one. Four instruments, or rules that can be short, would give a number much closer to the 50 per cent the independent story promises, and lesson 39 already argued for the first of those.

And the concession that costs most: the whole of module 9 has assumed the rules are worth running. Every threshold that decides that sits earlier in the course and applies to each rule alone: lesson 64’s bar, lesson 67’s test, lesson 70’s filter condition, lesson 68’s capacity. A book of four dead rules, correlated at 0.88, sized to three per cent of heat and enforced as a precondition, is a very well governed way of losing money slowly. Module 10 leaves the arithmetic and starts on the day: what the hours are actually spent on, and which of them can be given to a machine.