Paying Yourself Before You Know

The capital a wage requires

One identity carries the whole page and it has no free parameters left in it. In a year you take some number of round trips. Each is worth the edge in R. Each R is the risk per trade, which is a fraction of the account. So the money the account is expected to make in a year is the round trips multiplied by the edge multiplied by that fraction multiplied by the capital. Set that equal to a wage and the capital falls out: the capital you need, measured in years of your own wage, is one divided by the round trips times the edge times the risk per trade.

Everything on the right of that is already measured or already fixed. The edge is lesson 67’s tenth of an R, which is a hypothesis rather than a measurement and the rest of this page is about exactly that. The risk per trade is lesson 21’s R and lesson 75’s cap. The round trips are what lesson 76 counted, and they are the term that used to be guessed.

Every cell is years of wage. The bottom right corner says a wage costs slightly more than a year of itself in capital, which is roughly what the encouraging version of this subject implies, and the top left says thirty-five years of it. The distance between those two corners is not a disagreement about risk appetite. It is lesson 65’s forty trades a month, which was stated rather than derived, against lesson 76’s measurement of the same rule family, which is 56.5 round trips a year. A reader who took the forty on trust is reading the bottom row of that table when they belong in the top one.

Now the second question, which is the one the first table cannot answer: how much of that capital do you spend before you know whether the edge was ever there? Lesson 67 needs 589 trades. At a pace of n round trips a year that is 589 over n years, and in each of those years you draw one wage. So the wage-years consumed before the verdict, divided by the capital measured in wage-years, is 589 over n divided by one over n times the edge times the risk per trade. The n cancels. The answer does not depend on how fast you trade.

Read the second column and remember that the pace is not in it. Trading four times as often does not reduce the share of capital you consume waiting for an answer, because a faster pace shrinks the capital you needed in the first place by exactly the factor it shortens the wait. The only lever is the risk per trade, and the fraction reaches the whole account at 1.70 per cent a trade. Above that, on the course’s own inputs, a wage-funding account is spent before lesson 67 returns a verdict, at any speed.

The third column is what the same capital owes at the same time. Lesson 67 measured a median worst drawdown of 8.82R over 156 trades, and at one and a half per cent a trade that is 13.23 per cent of the account, arriving during the same years and not instead of them. The fourth column adds them, and at the risk per trade lesson 75 licenses the sum is more than the account.

There is one honest reading of the second column that softens it and one that does not. The soft reading is that if the edge is real the wage is paid out of the gains, by construction, because the capital was sized so that the expected gains equal the wage; the account is then flat in expectation and the column overstates the loss. The hard reading is that the whole page is conditional on the edge being real, that lesson 67 exists because you cannot know whether it is, and that the second column is therefore exactly the amount you are staking on the answer being yes. The test is funded entirely by the possibility that its answer is no.

Almost nobody has divided their intended wage by their own edge, pace and risk per trade. It is one division, the inputs are the three numbers this course has spent seventy-eight lessons producing, and the answer is the size of the account the job requires before it is a job.

Module 10’s list of what the day contains that is not the decision gains its fourth item: the wage, and where it comes from during the years the verdict takes.

Two positions at one and a half per cent

Take the exact book module 9 finished with, because it is the only one this course licenses. Lesson 75’s answer was two rules at one and a half per cent a trade, carrying 1.06 bets, under a three per cent daily-loss limit. Lesson 76 measured that family at 113 orders a year, which is 56.5 round trips. Lesson 67 supplies the hypothetical edge and the test.

Capital: one divided by 56.5 times 0.10 times 0.015, which is 11.80 years of the wage you intend to draw.

Verdict: 589 trades at 56.5 a year, which is 10.42 years.

Drawn as wages in the meantime: 88.3 per cent of the capital, and the pace is not in that figure.

Median worst drawdown arriving during the same period: 13.23 per cent of the account.

Put those four lines in order and the shape is unmistakable. The capital required is 11.80 years of wage and the answer to whether the capital was well placed is 10.42 years away, so the two horizons are the same horizon. Over that horizon you draw 88.3 per cent of the capital and the ordinary path costs another 13.23, and 101.6 per cent is not a number an account can hold.

Which does not mean nobody is a full-time trader. It means the arithmetic has one term this page has kept out of it, and naming it is the whole lesson: the years are funded by something that is not the account. A salary, a partner’s salary, an earlier sale, a seat at a firm that pays a draw, capital that belongs to somebody else. Every version of the job that exists has that term in it, and every version that does not have it is the version that ends at some point inside the 10.42 years, with the account too small to test and the verdict never delivered.

Halve the risk per trade and the picture changes but not in the direction people expect. At 0.75 per cent a trade the drawn share falls to 44.2 per cent, which is survivable, and the capital required doubles to 23.6 years of wage. You do not escape the problem by sizing down; you move it from the column you can measure to the column you have to have.

So compute your own multiple before you set a date to leave anything, and write down which of your years to the verdict are paid for by something other than the account.

What this does not settle

That the tenth of an R exists. It is a hypothesis this course has carried since lesson 65 in order to have something to compute with, and the entire page is conditional on it. A larger edge divides the capital in the first table proportionally, so a system with half an R a trade needs a fifth of it. An edge of zero makes the whole page an account of how fast a wage empties an account. Which of those you have is the question lesson 67 answers in 589 trades, which is the second table.

That a wage cannot be drawn from an account. It can, and people do. What this page computes is what capital that takes and what fraction of it goes out of the door before the evidence comes in, and neither of those is an argument that the withdrawal is impossible. It is an argument that the number most readers carry in their heads is the bottom row of the first table, and that the measured pace puts them in the top one, which is a factor of 8.5 on every column.

That an expectation is a path. The soft reading above is a statement about expected value: size the capital so that expected gains equal the wage and the account is flat on average. Lesson 67’s 8.82R is there to say the path is not the average, and lesson 22’s arithmetic is what happens when a withdrawal and a drawdown arrive in the same quarter. The third column adds them because they add in life; it does not model the order they arrive in, which matters and which this page does not compute.

That deposits are cheating. The worked example ends by naming an outside source of funds and treating it as the ordinary case rather than the exception, and that is deliberate. Nothing in this course says an account must be self-funding, and the version of this subject that assumes it is the version that produces the encouraging table. What deposits do not do is shorten the 10.42 years or shrink the 88.3 per cent; they pay for them, which is a different thing and worth being clear about with yourself.

That this is the only way the skill pays. It is the only way this page prices, which is an account paying its owner a wage. A seat at a firm, a salary for building the systems, teaching, or managing capital that belongs to somebody else are all real and none of them is in this arithmetic, because each replaces the term the page found missing rather than solving it. That is not a smaller job. It is a different one with the funding problem already answered.

And the concession that costs most: this page has again priced the money and not the person. It has said what the account owes and what the years cost and nothing at all about what a person does with ten years of an unanswered question, which is not an arithmetic problem and is the one most people actually fail. It has also assumed that a trader working alone is the unit, and lesson 80 asks what changes when the thing is set up as a business rather than as a person with an account.