The Book on One Card

What a card is for

A column is a measurement and a card is a decision. Module 9 finished the same way, in lesson 75, with four columns that did not argue but queued, and the one that bound was the one that could be enforced before an order went out. This module’s four columns queue differently, and the reason is worth naming before the table: none of these four can be enforced in advance. Return, concentration, turnover and depth are all measured after the fact, on a record, which means the card cannot tell you what to run. It can only tell you what to stop running, and that turns out to be enough.

So the operation is deletion rather than selection. Take the book as it stands, remove one member, and recompute all four columns on the three that are left. Do it four times, once per member. Every figure below is on the same twenty-eight moves, at the same 0.1230 a share per position change, weighted equally across whatever remains, and the last column is net return divided by worst run, which is the only number on the card that needs three of the four columns to exist.

The card, and the card with one row removed

Read the last column down the first five rows. Every deletion but one improves the book, and the improvements are not small: the best of them raises net return per unit of depth by 7.8 per cent while raising the net return itself. A four-rule book is worse than three of the four three-rule books you can make out of it, which means the fourth rule was never paying for itself in the first place.

The exception is the row that matters. Deleting the 8-and-30 is the only deletion that makes the book worse, and it makes it worse on three columns at once: the net falls to 3.61, the depth goes back to the 2.10 that every long position in this window shares, and the ratio drops by 14.1 per cent. That rule was third of four on gross return, which is the column a reader arrives at this module already ranking on, and it is the one member the book cannot afford to lose.

The sixth row is the one that ends the argument. Run the 8-and-30 alone, with no book around it at all, and it nets 3.98 against the four-rule book’s 3.70, on one position change instead of thirteen, with a worst run of 1.10 instead of 1.85. It beats the four-rule book and all four three-rule books on net return, on turnover and on depth simultaneously. There is no column on this card on which running the book is better than running one of its members.

The queue, and what is at the front of it

Take the card to the decision it exists for. A reader has these four rules and has to choose what to run on Monday.

Rank on return alone, which is what lesson 91 supplied and what almost everybody stops at, and the answer is the 2-and-5 at 4.90 gross. Add lesson 93’s turnover column and that answer is wrong: nine position changes cost 1.11 and the 2-and-5 falls to second at 3.79. Add lesson 94’s depth column and it falls again, because it carries the full 2.10 run while the 8-and-30 carries 1.10. Add lesson 92’s concentration column and the entire ranking loses its support, because 80.5 per cent of the four-rule book’s result is three moves and no ordering resting on three observations is an ordering.

So the queue is: the return column proposes, the turnover column reverses it, the depth column reverses it again, and the concentration column says none of the three had enough evidence to be making claims. Four measurements, four different answers, and the first three of them are the ones a platform prints.

What survives all four is the one statement none of the columns contradicts: this book should not exist. Its best available version is one of its own members, and that member wins by not doing things. It changes position once. It is out of the market for the first two moves of the worst run and in for the rest. It has no diversification benefit, no weighting scheme, no rebalancing, and no answer to the question of what to do when it is wrong.

A card is not a scoreboard. It is a list of the ways a book can be worse than one of its parts.

Then there is the seventh row, and this module has been putting it at the bottom of every table since lesson 91 for a reason. Holding nets 6.48 over the same twenty-eight moves, which is 63 per cent more than the best thing on this card, on one position change and the same 2.10 worst run that four of the six other rows carry. It loses only one column, the last, where the 8-and-30’s 3.615 beats its 3.084, and it loses that one because it takes a deeper run to make more money. That is the honest summary of module 13: four lessons of measurement on a book of four rules produced one rule that is better per unit of pain than doing nothing, and nothing that is better in dollars.

So take your own book, delete each member in turn, and recompute all four columns on what is left.

What this does not settle

That deletion is a strategy. It is a diagnostic. Deleting the member that improves the card most, on a record of twenty-eight moves in which the result is three of them, is a spectacular way to overfit, and it is the same error lesson 63 measured when it searched 253 rules and found the winner below the median of what a structureless series produces. The correct use of this card is to notice that the book is dominated, not to run the deletion the card recommends.

That four rules is a book. It is four settings of one idea, and the module has said so on every page. Lesson 71 measured what that costs at 0.9472, and a book of genuinely different objects is a different question that this course has no data to answer. What transfers is the card and the deletion test, not the verdict.

That the last column is a respectable statistic. Net return divided by worst run is not a Sharpe ratio, is not comparable across records of different lengths, and rewards a record that happened to avoid one bad fortnight. Lesson 94 cited the reason: expected maximum drawdown grows with the length of the record, so this ratio flatters short samples and this sample is very short.

That holding wins. It won every column in this module because the price rose from 99.9 at bar 31 to 106.5 at bar 59, and lesson 63’s shuffle is the whole reason a single rising window settles nothing. What the benchmark is for is to stop a book being graded against zero, and this book was graded against 6.48 and lost. That is a fact about this window and it is the fact lesson 66 said to record rather than to argue with.

And the concession that costs most: this module measured a book and never once asked what the person running it was going to live on. Every figure on this card is dollars a share on one instrument, with no account size, no withdrawals and no fixed costs, which is exactly the abstraction lesson 79 and lesson 80 spent their pages dismantling. Module 14 puts the account back and starts where this card stops: at the pace lesson 76 measured, a system with a genuine edge of a tenth of an R a trade loses money in 41.3 per cent of its months, and the first thing a trading business has to survive is not a drawdown but an ordinary year.