Module 14 Quiz: The Business

Every module before this one measured what a rule does. This one measured what a person living off it can take out. Six questions, all arithmetic on the pace lesson 76 counted and the tenth of an R lesson 67 defined, and the last one puts five numbers in the order they fail.

Covers: Lessons 96 to 100, and the two inputs the whole module rests on: thirteen orders in twenty-eight days, and a tenth of an R a trade.

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. Thirteen orders, one month

Lesson 76 counted the four-rule book’s orders over the twenty-eight moves every lesson since 71 has used, and found thirteen of them. A month holds twenty-one trading days. A completed trade is two position changes, an entry and an exit.

Ask. How many completed trades a month is that, and how does it compare with the forty a month lesson 65 assumed?

2. The month that loses

Lesson 67 fixed one R as one standard deviation of a trade’s outcome and called a tenth of an R a trade a genuine edge. At 4.875 trades a month, each trade is an independent draw with a mean of 0.10 R and a standard deviation of 1 R.

Ask. What does the month earn, how much does it move, and how often does it lose money?

3. What the round trip leaves

Module 13 charged 0.1230 a share for a round trip. Lesson 63 measured one bar’s standard deviation at 1.5443 a share, and this module takes that as one R. The gross edge is a tenth of an R a trade.

Ask. What is the cost in R, what share of the edge is it, and what is left?

4. What the account supports

An account of 100,000 risks one per cent a trade, so one R is 1,000. The pace is 4.875 trades a month and the gross edge is a tenth of an R. A household takes 500 a month out of it.

Ask. What does the account earn a month, and what balance would that withdrawal actually need?

5. The trial, and what leaves during it

Lesson 65 fixes 156 trades as a fair trial before you start. Lesson 67 puts the median worst drawdown of a genuine tenth-of-an-R system over 156 trades at 8.82 R. The account is the same 100,000 at one per cent, and the same 500 a month leaves it.

Ask. How long is the trial, what does the market take at the median, and what does the household take?

6. The row that binds

Here is the finished card, with the figures each row came from.

Row	Figure
Pace	4.875 trades a month
Cost	0.0796 R of a 0.10 R edge
Net earning	99 a month on 100,000
Withdrawal	500 a month
Verdict	18,952 trades

Ask. Which row fails first, and what does repairing it do to the rest?

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. Thirteen orders, one month

Thirteen changes in twenty-eight days is 13 ÷ 28 = 0.4643 a day. Over twenty-one trading days that is 9.75 position changes a month, and 9.75 ÷ 2 = 4.875 completed trades.

Against forty: 4.875 ÷ 40 = 0.1219, so the measured pace is 12.2 per cent of the assumed one. Lesson 65 said in the same breath that its forty was stated rather than derived, and lesson 76 derived it. The gap is a factor of eight.

Everything in this module is that one number multiplied by something. It is worth writing down before the rest.

Answer. 4.875 trades a month, which is an eighth of lesson 65’s forty.

2. The month that loses

The mean adds: 0.10 × 4.875 = 0.4875 R. The standard deviation adds in quadrature, so it is the square root: √4.875 = 2.2079 R.

A month loses money when the draw falls more than its own mean below zero, which is 0.4875 ÷ 2.2079 = 0.2208 standard deviations. The normal distribution puts 41.26 per cent of its weight below −0.2208.

Twelve months at that rate expect 4.95 losing months, and the chance of twelve clean ones is 0.5874 to the twelfth power, which is 0.169 per cent. A year with no losing month in it is a once-in-six-hundred-years event at this pace.

Answer. 0.4875 R earned against 2.2079 R of movement, so 41.3 per cent of months lose.

3. What the round trip leaves

0.1230 ÷ 1.5443 = 0.0796 of an R for a round trip.

Against the edge: 0.0796 ÷ 0.10 = 0.7965, so the round trip takes 79.7 per cent of a tenth-of-an-R edge and the net edge is 0.10 − 0.0796 = 0.0204 R a trade.

Now put it through lesson 19’s sample size, which is 7.85 divided by the square of the edge. At 0.10 that is 785 trades; at 0.0204 it is 18,952. The cost did not reduce the verdict by four fifths. It multiplied the wait by twenty-four, because the formula squares.

Answer. 0.0796 R, which is 79.7 per cent of the edge, leaving 0.0204.

4. What the account supports

The month earns 0.4875 R, and one R is 1,000, so it earns 487.50.

The withdrawal is 500, which is 500 ÷ 487.50 = 1.0256 of the whole edge. The account that breaks even is the one whose monthly earning is 500: the earning is 0.004875 of the balance, so the balance is 500 ÷ 0.004875 = 102,564.

And the withdrawal cannot be seen while it happens. One month moves 2.2079 R, which is 2,207.94 on this account, so the 500 is 0.227 of one month’s noise. Withdrawals grow with the months and noise grows with their square root, so they cross at (2,207.94 ÷ 500)² = 19.5 months.

Answer. 487.50 a month earned against 500 taken, so the balance needed is 102,564.

5. The trial, and what leaves during it

156 ÷ 4.875 = 32.00 months exactly.

The market’s median worst take is 8.82 R, and one R is 1,000, so 8,820. The household’s take is 32 × 500 = 16,000.

16,000 ÷ 8,820 = 1.81. The withdrawal is nearly twice the drawdown over the same stretch, and it is the one that never comes back. Every plan models the first of those two and almost none model the second.

Answer. 32 months, in which the market takes 8,820 and the household takes 16,000.

6. The row that binds

Read down and stop at the first row that is worse than the one below it can survive. Row one sets frequency and cannot fail on its own. Row two takes 79.7 per cent of the edge, and everything below it is arithmetic on what is left, so row two binds.

Repair it and nothing else. Hold each trade long enough that one R is two bars rather than one, 3.0886 rather than 1.5443, and the cost falls to 0.1230 ÷ 3.0886 = 0.0398 R, which is 39.8 per cent of the edge. The net edge rises from 0.0204 to 0.0602, and the monthly earning from 99 to 0.0602 × 4.875 × 1,000 = 294.

The withdrawal is still 500, and 7.85 ÷ 0.0602² = 2,168 trades is still 37 years at this pace. Tripling the best row on the card moves the business from impossible to infeasible, which is the answer this module was written to be able to give.

Answer. Row two. Halving the cost in R triples the net earning, from 99 to 294, and still leaves the business unviable.

What this quiz was testing

Whether a rule and a business are the same object. They are not, and the six questions above are the arithmetic that separates them: a pace, a month, a cost, a withdrawal, a trial and a card. None of them is about whether the rule works. All of them are about how often it gets to, and what leaves the account while it does.

What you take away is the order of the rows. The account arithmetic in questions four and five is the arresting part, and it is downstream: it describes a business whose edge was already reduced by four fifths in question three. Fix the row that binds, not the row that frightens you.

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