The Ride You Actually Bought

The column this lesson adds

Three columns are on the card: what each rule earned, where that came from, and what it cost to run. This is the fourth and the last, and it is the only one a person actually experiences. Lesson 67 spent a whole page establishing that the depth of the run is what switches a system off, and that the median worst drawdown of a genuine tenth-of-an-R edge over 156 trades is 8.82R. Nobody quits because of an annual return. They quit in the middle of a drawdown, which means the depth column is the one that decides whether the return column is ever collected.

The measurement is the plainest available and it is the one lesson 18 defined. Run the cumulative result move by move, track the highest point reached so far, and record the largest distance below it. No annualising, no scaling, no ratio: a number of dollars a share, and the same number divided by the 1.5443 that lesson 63 measured one bar’s standard deviation at, so it can be read in the units the rest of the course uses. The run is measured on the gross series rather than the net one, because a change costs 0.1230 at the moment it happens and adds a step to the curve rather than a slope to it, and what this column is trying to see is the shape of the price path the rules share. Doing it the other way moves the book from 1.85 to 1.88, the 2-and-5 from 2.10 to 2.22 and the 8-and-30 from 1.10 to 1.22, which changes no ordering on the page and sharpens the finding it ends on.

The four rules and the book

The 8-and-30 row is the one to look at twice. Its gross return over the window is 4.10 a share, which is the four-rule book’s 4.10 to the penny, and lesson 93 already showed it keeping more of that than any other member because it changes position once. Here it also carries half the depth. Same return, a third of the pain, one trade.

Three of the four rules have a worst run of exactly 2.10, and so does holding, and so does the book’s benchmark, and so does the best rule in the entire grid of 253. That is not a coincidence and it is the whole mechanism of this page. A run of 2.10 a share is what the instrument itself did between bar 36 and bar 39, and any rule that was long through those three moves took all of it. Lesson 72 measured how often positions move together and found four of them going the same way on 40.53 per cent of days. This is what that looks like when you stop counting days and start counting the worst three in a row.

The book’s 1.85 is smaller than 2.10, and it is smaller for one reason: on those three moves the 8-and-30 rule happened to be flat, so a quarter of the book sat out and the other three quarters took the full hit. That is diversification working, and the size of it is 0.25 a share on a 2.10 drawdown, which is 11.9 per cent.

The last column is the one to rank on and it is the one nobody prints. Net return for each unit of worst run puts the book at 2.000, ahead of three of its four members and behind the fourth by a distance that is not close: 3.615 against 2.000. Holding is at 3.084.

Almost nobody you trade against has computed the depth of their own book against the depth of the best rule inside it, because a platform reports the book, and the members exist only in the spreadsheet where they were designed.

The three moves, again

The book’s worst run is three consecutive moves, from bar 36 to bar 39. The price goes 103.4, then 103.1, then 102.4, then 101.3, losing 0.30, then 0.70, then 1.10, and 2.10 in total. The 2-and-5 rule, the 3-and-10 and the 5-and-20 are long through all three and each takes the whole 2.10. The 8-and-30 is flat for the first two, because a thirty-bar average of a series that spent bars 16 to 30 falling still sits above an eight-bar average that has only just turned up, and it is long for the third. So the book loses 0.225, then 0.525, then the full 1.100, which is 1.85.

The entire diversification benefit on this page is therefore 0.25 a share, and it is one rule being out of the market for two days. Not four return streams offsetting one another: one rule asleep, and awake again in time for the largest of the three losses. The rule that was asleep is also the one that dominates the book on every column of the card, which means the book’s single best property was contributed by the member it least resembles.

Then look at the same three moves in lesson 92’s column. The book’s three best moves are bars 54 to 55, 45 to 46 and 57 to 58, and on all three all four rules are long together. The book is undiversified exactly when it is winning and diversified exactly once, for three days, when it is losing. Both facts have the same cause, which is that these rules disagree only in the middle of a turn, and the middle of a turn is where small moves live.

A book of one family diversifies on the days that do not matter.

That sentence is the module’s, not this lesson’s, and it is why the card exists rather than a single number. Return alone said the book was fine, at 83.7 per cent of the best member gross and 97.6 per cent of it net. Depth alone said the book was good, at 88.1 per cent of the pain. It takes the four columns together to see that a single member of the book beat it on all of them at once.

So compute the worst run of your own book and of each rule inside it, on the same days, and put the five numbers in a column.

What this does not settle

That a worst run measured on twenty-eight moves means anything. It does not, and this is the bound that costs the page most of its force. Lesson 67 needed 156 trades to say what a median worst drawdown was, and it said so about a distribution rather than about a record. Twenty-eight moves produce one number with no distribution behind it, and the 2.10 that four different things share is one episode in one fortnight. A reader who takes the ranking home rather than the method has taken the wrong thing.

That the 8-and-30 rule is the answer. It is the answer on this window and there is no reason to expect it on another. It was flat for three days because of where two averages happened to sit, and lesson 74 already showed that this family’s whole correlation structure reverses between the first fourteen moves and the last fourteen. The general claim is only that a book can be dominated by one of its members on every column at once, which is worth checking on your own record and is not a fact about slow moving averages.

That depth is measured correctly here. It is measured on closes, on a quarter-weighted book, with no intrabar path, and lesson 87 already conceded what that hides: a real position experiences the low, not the close, and the low is lower. Every worst run on this page is therefore the shallow version of itself.

That holding’s 3.084 settles the argument. Holding wins every column on this page and it has won every column since lesson 91, and it is still one instrument over one twenty-eight-move window in which the price rose from 99.9 to 106.5. Lesson 66 fixed it as the benchmark precisely so that it could not be argued with after the fact, and lesson 63’s shuffle is the reason a single window flattering one side proves very little.

And the concession that costs most: four columns have now been measured one at a time, and no page has yet asked what happens when a reader has to act on all four at once. They do not point the same way. The return column prefers the fast rule, the turnover column prefers the slow one, the concentration column says the whole result is three days and the depth column says the book is dominated by one of its members. Lesson 95 puts the finished card in front of a reader with a decision to make and finds that the four columns do not vote: they queue, and the one that binds is the one nobody ranks on.