Module 13 Quiz: The Book
Module 9 measured how alike a book’s rules are. This one measured what the book does: what it earns, where that came from, what it costs to run and how deep it goes. Six questions, all arithmetic on the same twenty-eight moves, and the last one spends every column at once to find that three of the four deletions improve the book.
Covers: Lessons 91 to 95, and the card of four rules the module has been adding a column to since its first page.
Every question below hands you numbers and asks for a number back. Work all 6 with a calculator before you scroll to the answers; each answer shows the arithmetic, so a wrong result tells you which step to go back to rather than only that you were wrong.
The questions
1. Four rules, one book
Lesson 71 picked four moving-average rules chosen not to look alike, and lesson 91 ran them over the twenty-eight moves on which every rule in lesson 63’s grid is defined. This is what each of them made, gross, a share.
| Rule | What it made |
|---|---|
| 2 and 5 | 4.90 |
| 3 and 10 | 3.90 |
| 5 and 20 | 3.50 |
| 8 and 30 | 4.10 |
The book puts a quarter of the money in each. Over the same twenty-eight moves, buying at the first close and selling at the last makes 6.60 a share.
Ask. What does the book make, what share of the best member is that, and how does it compare with holding?
2. The three moves
The book’s twenty-eight moves, sorted largest first, begin 1.30, 1.00, 1.00. Its total is 4.10. Seventeen of the twenty-eight are positive and total 10.15; eleven are negative and total minus 6.05.
Ask. What share of the result is the best three moves, and what do the other twenty-five make between them?
3. What the turnover takes
A round trip costs 0.1230 a share. Over the twenty-eight moves the four rules change position this many times, and each carries a quarter of the book.
| Rule | Gross | Position changes |
|---|---|---|
| 2 and 5 | 4.90 | 9 |
| 3 and 10 | 3.90 | 2 |
| 5 and 20 | 3.50 | 1 |
| 8 and 30 | 4.10 | 1 |
Ask. What does each rule net, which of the four finishes first, and what does the book net?
4. The worst run
The book’s worst three consecutive moves run from bar 36 to bar 39, where the price goes 103.4, 103.1, 102.4, 101.3. On the first two the 8-and-30 rule is flat and the other three are long; on the third all four are long.
Ask. What is the book’s worst run, what is a fully long position’s, and what did the diversification buy?
5. The rule that does not trade
Across all 253 rules over the same twenty-eight moves, the best on gross return is a 9-bar average against a 10, at 7.00 a share, and it changes position six times. One rule in the grid, a 3-bar average against a 12, changes position not at all: it is long from the first move to the last. It makes 6.60 gross.
Ask. Which of the two is better after costs, and what is the second one equivalent to?
6. Delete one member
Here is the finished card for the four-rule book and for the book with the 5-and-20 removed, over the same twenty-eight moves.
| Book | Net | Worst run |
|---|---|---|
| All four | 3.7002 | 1.85 |
| Without 5 and 20 | 3.8080 | 1.77 |
Ask. What does each book return for each unit of depth, how much does the deletion improve it, and what does the 8-and-30 alone return on the same measure?
The answers
Each one is worked in full. Where a figure comes from a lesson rather than from this page, the lesson is named.
1. Four rules, one book
An equal-weight book of four is the average of the four: (4.90 + 3.90 + 3.50 + 4.10) ÷ 4 = 16.40 ÷ 4 = 4.10 a share.
Against the best of its own members, 4.10 ÷ 4.90 = 0.8367, so the book kept 83.7 per cent of what the single best rule earned. Against the benchmark, 4.10 ÷ 6.60 = 0.6212.
The averaging is the whole point and it is why lesson 91 found the median return flat at every book size from one rule to 253. A book of one family cannot earn more than its members average, and the only thing it can do is narrow the range around that average.
Answer. 4.10 a share, 83.7 per cent of the best member’s 4.90, and 62.1 per cent of holding’s 6.60.
2. The three moves
The best three sum to 1.30 + 1.00 + 1.00 = 3.30, and 3.30 ÷ 4.10 = 0.8049, so 80.5 per cent.
The rest is subtraction: 4.10 − 3.30 = 0.80 across twenty-five moves, which is 0.032 a move against a bar-to-bar standard deviation of 1.5443.
The check worth doing is the benchmark’s. Holding’s best three moves are 3.80 of its 6.60, which is 57.6 per cent, so the undiversified single position is the less concentrated of the two. Four rules did not spread the result over more days; they shrank the total the same good days are measured against.
Answer. 80.5 per cent, and the other twenty-five make 0.80.
3. What the turnover takes
Charge each rule its own turnover at the full round trip: 9 × 0.1230 = 1.1070, 2 × 0.1230 = 0.2460, and 0.1230 for each of the two that change once. Subtract from the gross: 3.7930, 3.6540, 3.3770 and 3.9770.
The ranking inverts. The 2-and-5 is the best of the four gross by a full dollar and finishes second, because it makes nine of the book’s thirteen changes, which is 69.2 per cent of the turnover for 29.9 per cent of the gross return. The 8-and-30 was third gross and finishes first, keeping 97.0 per cent of what it earned against the fast rule’s 77.4 per cent.
The book pays the same thirteen changes on a quarter of the money each: 13 × 0.1230 ÷ 4 = 0.3997, so 4.10 − 0.3997 = 3.7002.
Answer. 3.79, 3.65, 3.38 and 3.98. The 8-and-30 finishes first, and the book nets 3.7002.
4. The worst run
The three moves lose 0.30, 0.70 and 1.10, so anything long throughout loses 2.10, which is 1.360 of an R at 1.5443 a share. That is what holding loses, what the best rule in the whole grid loses, and what three of the four members lose.
The book has three quarters of its money long for the first two moves and all of it for the third: 0.75 × 0.30 = 0.225, then 0.75 × 0.70 = 0.525, then the full 1.100. That totals 1.85, or 1.198 of an R.
So the entire diversification benefit is 2.10 − 1.85 = 0.25 a share, and it is one rule being out of the market for two days. Set that beside what it cost: the book kept 88.1 per cent of the pain and 83.7 per cent of the return.
Answer. 1.85 a share against 2.10, so the whole benefit is 0.25.
5. The rule that does not trade
The 9-and-10 pays 6 × 0.1230 = 0.738, so 7.00 − 0.738 = 6.262. The 3-and-12 pays nothing at all inside the window and keeps its 6.60.
A rule that is long from bar 31 to bar 59 and never changes is holding a position from bar 31 to bar 59, which is exactly the benchmark. Its 6.60 is the benchmark’s 6.60 because it is the same trade.
The point is about the accounting rather than about that rule. A grid searched on gross return hands you the rule with the most turnover in it, because on this data turnover and gross return move together and only one of the two is being maximised.
Answer. 6.60 against 6.262, so the rule that never trades wins, and it is buying and holding.
6. Delete one member
Divide the net by the worst run: 3.7002 ÷ 1.85 = 2.000 and 3.8080 ÷ 1.77 = 2.155. The deletion raises the ratio by 2.155 ÷ 2.000 − 1 = 7.8 per cent, and it raises the net return at the same time, so nothing was traded away for it.
The 8-and-30 run alone nets 3.9770 on a worst run of 1.10, which is 3.615. It beats the four-rule book and every three-rule book you can make out of it, on net return, on turnover and on depth at once.
Three of the four deletions improve the book and the fourth, removing the 8-and-30, is the only one that makes it worse, at 1.718. The member the return column ranked third is the one the book cannot afford to lose, and it takes all four columns to see it.
Answer. 2.000 and 2.155, an improvement of 7.8 per cent, against 3.615 for the single rule.
What this quiz was testing
Whether a book can be told apart from its parts. Every question above handed you the same four rules and asked one more thing of them, and the answer changed each time: the return column preferred the fastest rule, the turnover column reversed that, the depth column reversed it again, and the concentration column said the whole ranking rests on three moves out of twenty-eight. A single number about a book cannot survive any of those four questions being asked.
What you take away is the card rather than the verdict. Four columns, one row per rule and one for the book, and a deletion test that asks whether any member beats the whole. On this data one of them does, on every column at once, and it is the rule that trades least.
Educational only. Trading involves substantial risk of loss. Not financial advice. Past performance does not guarantee future results.