The Rule That Trades the Most

The column this lesson adds

Two columns are on the card: what each rule earned, and where that money came from. This one is the first that takes something away. A rule does not pay to hold a position, it pays to change one, so the quantity to count is not days in the market but crossings, and the two are unrelated enough that counting the wrong one is how a fast rule keeps looking good.

The charge is lesson 63’s and it has not moved: a penny of spread, five basis points of slippage a side on a price near 103, and half a cent of commission, which is 0.1230 a share for a round trip. A position change is a round trip: one exit and one entry, or, at the edges of the window, one of the two. Charging the full round trip to every change is the conservative direction, and the page says so rather than quietly taking the cheaper convention.

Turnover across the grid

Count the changes each of the 253 rules makes over the twenty-eight moves, subtract 0.1230 for each, and the grid rearranges itself.

Every figure in the table is an average across the rules sharing that slow length. There is no winning row, and the spread between the corners is the lesson: the fastest family trades eight and a third times in twenty-eight moves and loses more than a quarter of what it earned to doing so, while everything from a fifteen-bar slow average outward trades once and loses three per cent.

Across the whole grid the median rule changes position once in the window and the busiest changes thirteen times. One rule changes position not at all. Because turnover is so unevenly spread, subtracting it does not shift the grid down, it shuffles it: a 2-bar average against a 3 sits 111th of 253 on gross return and 249th on net, and a 5 against a 6 goes from 141st to 251st. All ten of the largest falls belong to rules whose two averages are within three bars of each other, and the largest of them is 138 places.

Almost nobody you trade against has this column, because a backtest reports return and a broker reports commission, and the two arrive on different pages in different units. Joining them costs an evening and it is the cheapest evening in this module.

The four rules, net

Here is the same subtraction on the book. Each rule carries a quarter of the money, so each rule’s share of the return and of the cost is a quarter of its own.

The 2-bar against the 5 makes 4.90 gross, a full dollar more than the 3 against the 10 and 1.40 more than the 5 against the 20. It is the rule anybody would pick out of the four on the evidence lesson 91 printed. It also makes nine of the book’s thirteen position changes, which is 69.2 per cent of the turnover for 29.9 per cent of the gross return, and after paying for them it finishes second of the four.

The rule that finishes first is the 8-bar against the 30, which was third on gross return and is the slowest thing in the book. It changes position once in twenty-eight moves and keeps 97.0 per cent of what it earned. The fast rule keeps 77.4 per cent.

The cost of a rule is not in its return column, and the return column is the only one most people rank on.

Run the same subtraction across all 253 and the point lands harder. The best rule on the grid gross is a 9-bar average against a 10, at 7.00 a share; it changes position six times and nets 6.26. The best rule net is a 3-bar average against a 12, at 6.60 gross and 6.60 net, because over these twenty-eight moves it never changes position once. It goes long before the window opens, stays long to the end, and collects exactly what buying at bar 31 and selling at bar 59 collects. The winning rule in the grid, after costs, is the rule that does not trade.

So count your own position changes for a month and multiply by your round-trip cost before you rank anything.

What this does not settle

That 0.1230 is your cost. It is lesson 63’s, on one instrument near 103 dollars, and lesson 11 already showed the same round trip running from a fraction of a basis point to hundreds depending on what you are trading. A reader whose cost is half of this one halves every subtraction on the page, and the inversion between the fast rule and the slow one survives that particular halving but would not survive a tenth.

That charging a full round trip per change is right. It is the conservative reading. A change from long to flat is one side, not two, and a stricter accounting would charge 0.0615 in some places and 0.1230 in others depending on what the position was. The page takes the expensive convention deliberately, and a reader taking the other one should expect the fast rule to recover about half of what it lost here.

That the 3-and-12 rule is a discovery. It is not. A rule that never changes position over a particular twenty-eight moves is a rule that happened not to cross in that window, and on a different fortnight it crosses like everything else. What the finding establishes is about the accounting rather than about that rule: a grid searched on gross return will hand you the rule with the most turnover in it, because turnover and gross return are correlated on this data and only one of the two is being maximised.

That turnover is the only cost that behaves this way. It is the one this course can measure. Lesson 68 priced a second one, which is what the trade holds before the price moves against the size, and lesson 69 priced a third, which is the delay between the signal and the order. Neither is on this card and both are charged against the same fast rules.

And the concession that costs most: this page has now taken the return column apart three ways and has not once asked what any of it felt like to hold. A number net of costs is still a number at the end of a year, and lesson 67 spent an entire lesson on why the depth of the run to get there is the thing that decides whether anybody is still holding it. Lesson 94 puts that column on the card and finds the book’s worst run at 1.85 a share against 2.10 for the best single rule inside it, which is 88.1 per cent of the pain for 83.7 per cent of the return.