Where the Result Came From

The column this lesson adds

Module 13 is filling in a card, one row per rule and one column per lesson. Lesson 91 supplied the first column, which is what each rule and the book of them earned. This is the second: where that money came from, move by move, so that a reader can see whether a total is a description of twenty-eight days or a description of three.

The arithmetic is the least sophisticated in this module and that is deliberate. Sort the book’s twenty-eight moves from largest to smallest, add them up from the top, and see how far down the list you have to go before you have the whole result. No model, no assumption, no seed. It is the one measurement on the card a reader can do in a spreadsheet in four minutes, and it is the one that changes what the other three mean.

Twenty-eight moves, sorted

The book is a quarter in each of a 2-bar average against a 5, a 3 against a 10, a 5 against a 20, and an 8 against a 30, over the moves from bar 31 to bar 59. Seventeen of the twenty-eight moves are positive and total 10.15. Eleven are negative and total minus 6.05. The book is never flat, because the four rules are never all out at once, and on eleven of the twenty-eight all four are long together, which is one position at full size rather than four at a quarter.

The third row is the one worth sitting with. The best quarter of the book’s moves made more than half again what the book made all year, which means the other three quarters, taken together, lost 2.20. That is not a defect in the rules. It is what a positive expectancy looks like from close up on any record short enough to read: a few moves carry it and the rest are the cost of being there for them.

What is a defect, or at least a surprise, is the last column. Holding is a single position in a single instrument, the least diversified thing on this page, and every row of it is less concentrated than the book beside it. Its best move is 19.7 per cent of its result where the book’s is 31.7. Its best three are 57.6 per cent where the book’s are 80.5.

The reason is arithmetic rather than luck, and it is one line. Concentration is measured against the total, and the book’s total is smaller. The book and holding have their best moves on very nearly the same days, because on eleven of the twenty-eight the book is fully long and is holding; what the book does with the other seventeen is sit partly out and collect a fraction. So the numerator barely changes and the denominator falls, and the ratio rises. Diversifying inside one family cannot move the good days. It can only dilute the total they are being compared against.

Almost nobody you trade against has sorted their own year this way, and it takes four minutes, because it needs one column of daily results and one sort. The reason it is not done is not difficulty. It is that the answer is unpleasant and no platform volunteers it.

The three moves

They are not exotic and none of them is a gap or an event. The best move is bar 54 to bar 55, where the price goes from 105.8 to 107.1 and all four rules are long, so the book collects the whole 1.30. The second is bar 45 to bar 46, from 105.6 to 106.6, again with all four long, for 1.00. The third is bar 57 to bar 58, from 106.0 to 107.0, for another 1.00.

Every one of the three is a move on which the book was fully long, which is to say a move on which the book was not a book at all. It was one position, the same position holding would have had, at the same size. The four rules earned 80.5 per cent of their year on the eleven moves where they had stopped disagreeing.

Take those three moves out and run the numbers again. The remaining twenty-five moves make 0.80 a share, which over a stretch of twenty-five bars is 0.032 a bar, against a bar-to-bar standard deviation of 1.5443. Holding, over the same twenty-five, makes 2.80. The rules that spend twenty-five of twenty-eight moves disagreeing with each other produce, over those twenty-five moves, less than a third of what doing nothing produces.

A book is not diversified on the days that pay for it.

That is the finding, and it puts a bound on how much any of this module’s other columns can matter. If a book’s year is three moves, then its correlation, its weights and its turnover are all being estimated from a sample in which the thing being explained happened three times. Lesson 19 fixed what a result resting on three observations is worth long before any of this, and the answer was that it is worth a hypothesis and not a decision.

So sort your own year, largest day first, and find how many days it takes to reach your total.

What this does not settle

That concentration is a fault. It is not, and a reader who leaves with that has taken the wrong thing. Every positive-expectancy record in this course is concentrated, including the ones the course endorses: the seven trades lesson 86 lays out put 2.70 of their 10.70 into one trade, and the rest of the module 12 sheet is worse. Concentration is what a small edge looks like when you can see individual days. What the last column establishes is narrower and it is comparative: this book is more concentrated than the thing it is supposed to improve on.

That twenty-eight moves can support a statement about concentration at all. They cannot, in the sense that the ranking of the top three would change on a different fortnight. What survives a change of window is the mechanism rather than the magnitude, and the mechanism is the one line above: the book and holding share their good days, so diluting the total raises the ratio. That is arithmetic and it does not need a longer sample.

That the four rules are a fair representative of a book. They are the four lesson 71 chose to be as unalike as this family allows, which makes them the best case rather than a typical one. A book of four rules picked without that care would be more alike, not less, and its numbers here would be worse.

That the days can be identified in advance. Nothing on this page is a rule for finding the three moves before they happen, and there is no such rule in this course. The measurement is a description of a record, and its use is to tell you what your own record is made of, not to tell you what to do on Monday.

And the concession that costs most: this page has counted gross moves and has still not subtracted a penny of what it cost to be in position for them. The book changes position thirteen times over the twenty-eight moves and every change costs 0.1230 a share. Lesson 93 puts that column on the card and finds the ranking of the four rules inverting on it: the 2-bar against the 5 is the best of the four gross, at 4.90, and after its own nine position changes it nets 3.79, behind the 8-bar against the 30, which trades once and nets 3.98.