Module 10 Quiz: The Profession

This module kept a list of what the day contains that is not the decision: twelve operations, a chain, a rate, a wage and an overhead. Seven questions, all arithmetic, and every one of them starts from a count the earlier modules produced rather than from a number anybody assumed. The last one puts the whole list beside a record of seven trades.

Covers: Lessons 76 to 81, and the five-item list of subtractions the module has been keeping since lesson 76.

Every question below hands you numbers and asks for a number back. Work all 7 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. A pace, and the wait it buys

Lesson 76 ran lesson 71’s four rules over the twenty-nine moves on which all of them are defined. The 2-and-5 rule asked for 9 orders, the 3-and-10 for 2, and the 5-and-20 and 8-and-30 for 1 each.

Take a year as 252 trading days. Two orders make a round trip. Lesson 67 needs 589 trades to settle whether an edge of a tenth of an R is real, and lesson 65 assumed forty trades a month.

Ask. How many orders and how many round trips a year does the book ask for, what share of its workload does the fastest rule carry, and how long does lesson 67’s verdict take at that pace? How long would it take at the assumed pace?

2. The quiet week and the busy one

On the same twenty-nine moves the 2-and-5 rule had a six-day stretch, moves 44 to 49, in which the position never changed and no order was sent, and it earned 1.90 in the instrument’s units. It then had five consecutive days, moves 50 to 54, of exit, entry, exit, entry, exit, and it earned 0.20 while the price moved 0.40 across the whole stretch.

A typical daily move over those twenty-nine is 0.7172. Five orders are two and a half round trips. Lesson 12 priced a round trip at a fifth of one per cent of a typical day’s movement on its index ETF and at 52 per cent of one on its micro cap.

Ask. What is each stretch worth in typical daily moves, what is the ratio between them, and what do the five orders cost on each of the two instruments as a share of what the busy week made?

3. The link you do not own

An order reaches the market through your equipment and then through the broker, and availability along a chain multiplies. Take the broker at 99.9 per cent and a year as 8,760 hours. The book asks for 113 orders a year.

A second connection is not two independent links. With a share c of failures common to both, a pair of links each down a fraction q of the time is down c q + (1 − c) q². Take q as one per cent and c as one in five.

Ask. What is the chain’s availability and its downtime a year at your side of 99.0, 99.9, 99.99 and 99.999 per cent, and how many orders a year does your own side alone cost you at each? Then: what does a second connection do to your side, and what does a stop resting at the broker do to the hours a position spends unprotected?

4. The rate that changes nothing, and the relief that does

Lesson 67’s trade outcome has a mean of a tenth of an R and a standard deviation of one R. Split it and the winning part averages 0.4509 R a trade and the losing part 0.3509 R, and the edge is the difference.

A rate takes a slice off the first number and relief gives a slice back on the second. Write the share of a loss that actually reduces what you pay as a fraction of the full rate. Lesson 67’s verdict takes 589 trades on an edge of a tenth of an R and a standard deviation of one.

Ask. Why does the verdict stay at 589 trades at every rate when relief is full? At what rate does the edge vanish with no relief at all? What share of losses must be relieved at a rate of thirty per cent and at forty? And what is the edge, the standard deviation and the trade count at thirty per cent with half the losses relieved?

5. The capital a wage requires

In a year an account takes some number of round trips, each worth the edge in R, and each R is the risk per trade as a fraction of the account. Set the expected annual gain equal to a wage and the capital falls out: the capital, in years of that wage, is one divided by the round trips times the edge times the risk per trade.

Use lesson 76’s 56.5 round trips a year, lesson 67’s edge of a tenth of an R and its 589 trades and median worst drawdown of 8.82R, and the one and a half per cent a trade lesson 75 licenses.

Ask. What capital does the wage require, how far away is the verdict, what share of that capital is drawn as wages before it lands, and why does the pace not appear in that share? At what risk per trade does the share reach the whole account, and what do the wages and the drawdown come to together?

6. The cost that does not scale

Every cost the course has priced so far arrives with a trade. A fixed cost does not: it arrives in a year you traded four hundred times and in a year you traded none.

Lesson 79 sized the capital so that the expected annual gain equals the wage, which means a cost base measured as a share of the wage is the same share of the edge. Take a cost base of a quarter of the wage on the book lesson 79 priced: 11.80 years of capital, 56.5 round trips a year, a tenth of an R, and lesson 67’s verdict at 5.8888 divided by the edge squared.

Ask. What capital does the wage plus the cost base require, what edge is left, how many trades does the verdict take, and how many years is that at 56.5 round trips a year against 480? And why does the wait move so much faster than the capital?

7. Seven trades against the bars the course wrote

The book module 9 licensed has one record: the seven trades lesson 63’s winning cell took on sixty closes. Three bars ask for a count of trades and each names a different one. Lesson 65 fixes a horizon of 156 before the first trade. Lesson 67 wants 589. Lesson 80’s quarter-wage cost base wants 1,047.

The pace is lesson 76’s 56.5 round trips a year.

Ask. What is each of those four in years at that pace, and what is each as a multiple of the record the book actually has? Which of them is the one to work on, and what do the five items on this module’s list have in common?

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. A pace, and the wait it buys

Thirteen orders in twenty-nine days is a rate: 13 ÷ 29 × 252 = 113 orders a year, which is 56.5 round trips. The fastest rule asked for 9 of the 13, which is 9 ÷ 13 = 69.23 per cent of every order the book sent.

The verdict is one division: 589 ÷ 56.5 = 10.42 years. Forty trades a month is 480 round trips a year, so the same 589 would have taken 589 ÷ 480 = 1.23 years, and at the 240 round trips a mid-table pace gives, 2.45.

The gap between 10.42 and 1.23 is not a disagreement about patience. It is a count that was assumed against a count that was made, on the same rule family, and the assumed one is eight and a half times the measured one. A reader carrying lesson 65’s wait in their head is carrying somebody else’s numerator.

Answer. 113 orders and 56.5 round trips a year, 69.23 per cent of the workload on one rule, and a verdict 10.42 years away against 1.23 at the assumed pace.

2. The quiet week and the busy one

Two divisions. 1.90 ÷ 0.7172 = 2.65 typical daily moves for the six days that asked for nothing, and 0.20 ÷ 0.7172 = 0.28 for the five days that asked for an order every session. The ratio is 1.90 ÷ 0.20 = 9.5.

Then the bill. Two and a half round trips at a fifth of one per cent of 0.7172 is 2.5 × 0.002 × 0.7172 = 0.0036, which is 1.8 per cent of the 0.20. The same two and a half round trips at 52 per cent of 0.7172 is 0.93, which is 4.7 times the whole gain.

Identical rule, identical week, identical orders. The only thing that changed is the instrument, and the six days that felt like a system that had stopped working made nine and a half times what the week that felt like work made, before either bill.

Answer. 2.65 typical daily moves against 0.28, a ratio of 9.5, and five orders costing 0.0036 on the index ETF against 0.93 on the micro cap, which is 1.8 per cent of the gain against 4.7 times it.

3. The link you do not own

The chain is one multiplication a row.

Your side	Chain, at a broker of 99.9%	Chain down a year	Orders missed a year
99.0%	98.901%	96.3 hours	1.13
99.9%	99.800%	17.5 hours	0.11
99.99%	99.890%	9.6 hours	0.011
99.999%	99.899%	8.8 hours	0.001

Read the third column down and the purchases price themselves. The first, from 99.0 to 99.9, is worth 78.8 hours a year. The second is worth 7.9. The third is worth 0.8, and there is no fourth, because the 8.8 hours that remain belong to the broker and no equipment of yours can reach them.

The second connection: at one failure in five common to both, the pair is down 0.2 × 0.01 + 0.8 × 0.0001 = 0.00208, so your side goes to 99.792 per cent, the chain to 99.692, and a position spends 8,760 × 0.00308 = 27.0 hours a year unprotected rather than 96.3.

The resting stop: a submitted order is executed by the machine holding it, so the position is protected at the broker’s 99.9 per cent whatever your equipment does, which is 8.8 hours. The free move is worth 87.5 hours a year and the paid one 69.3, and the free one is larger before the bill is subtracted rather than after.

Answer. 98.901, 99.800, 99.890 and 99.899 per cent, which is 96.3, 17.5, 9.6 and 8.8 hours a year and 1.13, 0.11, 0.011 and 0.001 orders missed; the second connection takes your side to 99.792 per cent and the position to 27.0 unprotected hours, and the resting stop takes it to 8.8 for nothing.

4. The rate that changes nothing, and the relief that does

The first part is one observation. A proportional rate with full relief multiplies every outcome by one minus the rate, so the mean becomes 0.0700 and the standard deviation 0.7000 at thirty per cent. The test runs on the mean divided by the standard deviation, and a factor that multiplies both cancels: 0.0700 ÷ 0.7000 = 0.10, unchanged, and the verdict stays at 589 trades at any rate short of confiscation.

With no relief the edge is what the rate leaves of the winning part after the whole losing part is subtracted, so it vanishes when the rate times 0.4509 equals 0.10: 0.10 ÷ 0.4509 = 22.18 per cent.

Between the two, the relief needed is the winning part minus the edge over the rate, all over the losing part. At thirty per cent that is (0.4509 − 0.3333) ÷ 0.3509 = 33.5 per cent, and at forty it is (0.4509 − 0.2500) ÷ 0.3509 = 57.3 per cent. The question to ask about a tax system is therefore not what the rate is but how much of a loss comes back.

And at thirty per cent with half the losses relieved the mean is 0.10 − 0.30 × (0.4509 − 0.5 × 0.3509) = +0.0174 R against a standard deviation of 0.7703, so the drift per trade falls from 0.10 to 0.0225 and the verdict takes 11,596 trades. The rate did not change the shape. The relief did.

Answer. Full relief multiplies the mean and the standard deviation by the same factor and the test is a ratio, so 589 stands; with no relief the edge vanishes at 22.18 per cent; thirty per cent needs 33.5 per cent of losses relieved and forty needs 57.3; and at half relief the edge is +0.0174 R on a standard deviation of 0.7703, which is 11,596 trades.

5. The capital a wage requires

The capital is one division: 1 ÷ (56.5 × 0.10 × 0.015) = 11.80 years of the wage. The verdict is another: 589 ÷ 56.5 = 10.42 years. The two horizons are the same horizon.

The share drawn is where the pace disappears. Wages drawn before the verdict are 589 over n years, and the capital is one over n times the edge times the risk per trade, so the ratio is 589 × 0.10 × 0.015 = 88.3 per cent and the n has cancelled. Trading four times as often does not reduce what the wait costs you, because a faster pace shrinks the capital by exactly the factor it shortens the wait.

Which leaves the risk per trade as the only lever, and it runs out quickly: the share reaches the whole account at 1 ÷ (589 × 0.10) = 1.70 per cent a trade. Lesson 67’s median worst drawdown of 8.82R at one and a half per cent is another 13.23 per cent of the account, arriving during the same years rather than instead of them, and 88.3 + 13.23 = 101.6 per cent is not a number an account can hold.

Answer. 11.80 years of wage, a verdict 10.42 years away, 88.3 per cent drawn as wages, a share the pace cancels out of, the whole account reached at 1.70 per cent a trade, and 101.6 per cent with the drawdown added.

6. The cost that does not scale

The capital is the wage and the cost base together: 11.80 × 1.25 = 14.75 years of wage, an extra 2.95. The edge is the same fraction gone: a quarter of the wage is a quarter of the edge, so 0.10 becomes 0.075.

The verdict is 5.8888 ÷ 0.075² = 1,047 trades, and at 56.5 round trips a year that is 18.53 years rather than 10.42. The same bill on the same account at 480 round trips a year takes 0.0029 R from each trade rather than 0.0250, leaves an edge of 0.0971, and costs 1.30 years against 1.23. Eight years at the pace you actually trade at, and a month at the pace you assumed.

The reason the wait moves so much faster than the capital is the square. The capital grows in proportion to the cost base and the trade count goes as one over the edge squared, so leaving three quarters of the edge multiplies the trades by sixteen ninths and leaving a quarter multiplies them by sixteen. A fixed cost is not a bill the account settles out of its profits. It is a piece of the edge, and the pace decides how big a piece.

Answer. 14.75 years of wage, an edge of 0.075 R, 1,047 trades, and 18.53 years at the measured pace against 1.30 at the assumed one; the wait moves faster because it goes as one over the edge squared.

7. Seven trades against the bars the course wrote

Two divisions a row.

What it takes	Trades	Years at 56.5 a year	Times the record
The book’s whole record	7	0.12	1
Lesson 65’s fixed horizon	156	2.76	22.3
Lesson 67’s verdict	589	10.42	84.1
Lesson 80’s cost base	1,047	18.53	149.6

The last column is what ranks the work. A record twenty-two times the one you have is two years and nine months of trading the rule you already have, which is a plan. A record eighty-four times the one you have is a decade, and one a hundred and fifty times is a working life. The reachable bar is the one to start on, and it is reachable precisely because it is the one that was fixed before the first trade rather than demanded after it.

And the list this module kept has one property worth saying out loud. Twelve operations, a chain, a rate, a wage, an overhead: every entry on it is a subtraction. Nothing the day contains outside the decision adds to the edge. The whole of what a profession does with the arithmetic is to find out how much of the edge survives the things that are not the trade.

Answer. 0.12, 2.76, 10.42 and 18.53 years, which is 1, 22.3, 84.1 and 149.6 times the record; the fixed horizon at 22.3 times is the reachable one; and every item on the list is a subtraction.

What this quiz was testing

Whether you can put a count where an assumption was. Handed a grid, you count the orders it actually asked for and turn that into a pace; handed a quiet stretch and a busy one, you price both and find the quiet one worth nine and a half times the other; handed a chain, you multiply it and stop buying at the link you do not own; handed a rate, you ask what share of a loss comes back rather than what the rate is; handed a wage, you divide it by the edge, the pace and the risk per trade and read the years off; handed a fixed cost, you divide it among the trades there actually are; and handed a record, you set it against every bar the course wrote and work on the smallest gap that is not already closed.

Module 11 is where the candidates come from, and it starts where this book is weakest. This one carries 1.06 independent bets on a single instrument, and lesson 82 asks what a second instrument does to it: two rules on each of two instruments is four positions, and at a cross-correlation of zero that is 2.13 bets rather than four.

Educational only. Trading involves substantial risk of loss. Not financial advice. Past performance does not guarantee future results.