The Month That Loses

What a month is made of

A month is not a unit the market recognises. It is a unit a landlord recognises, and the entire difficulty of this module is that those two facts have to be reconciled by somebody. The market delivers trades; the calendar demands rent; and the number of trades that fall inside a calendar month is small enough that the month is mostly noise.

Two inputs settle everything on this page and both were measured rather than assumed. The first is the pace. Lesson 76 counted the four-rule book’s orders over the twenty-eight moves every lesson since 71 has been working on and found thirteen of them, which is thirteen position changes in twenty-eight trading days. Scale that to a twenty-one-day month and it is 9.75 changes a month. A completed trade is two changes, an entry and an exit, so the pace is 4.875 trades a month.

The second is the edge. 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, which it is: it is roughly twice what lesson 18’s system delivers once you divide its 0.35R by its 1.4925R of spread. So a month has an expected result of 0.10 multiplied by 4.875, which is 0.4875 of an R, and a standard deviation of the square root of 4.875, which is 2.2079 of an R. The month is worth about half an R and it moves about two and a quarter.

That ratio is the whole lesson and it does not need a simulation. The chance a month comes out negative is the chance a draw falls more than 0.4875 divided by 2.2079 below its own mean, which is 0.2208 of a standard deviation, and the normal distribution puts 41.26 per cent of its weight there.

The same edge at other paces

Nothing above depends on the edge being small. It depends on the pace being small, and the way to see that is to hold the edge at a tenth of an R and move only the number of trades.

Read the first column down. The losing-month rate falls with the square root of the pace and nothing else, so quadrupling the trades halves the distance to certainty rather than removing it. Between the pace lesson 76 measured and the pace lesson 65 assumed there are eight percentage points of losing months, which is one extra losing month a year: 4.95 against 3.16. The forty a month was not a small liberty. It was the difference between a year with three bad months and a year with five.

The last column is the one to take home. At any pace on this table, a year in which every single month makes money is a rare event, and at the measured pace it is a once-in-six-hundred-years event. A trader who has had twelve clean months has almost certainly not got a tenth-of-an-R edge at five trades a month. They have got something else, and the something else is usually more trades, more leverage or a shorter record than they think.

Almost nobody you trade against has done this arithmetic on their own pace, because the pace is the one input that never appears in a backtest report. A report gives a return and a drawdown; the trade count is in a footnote if it is anywhere.

The year, month by month

Twelve months at 41.26 per cent each is a binomial, so the year’s shape can be printed exactly.

Five is the single most likely answer and it is not close to a majority: 22.85 per cent of years land there and 77.15 per cent land somewhere else. Six or more losing months happen in 36.87 per cent of years, which is more than one year in three, and three or fewer happen in 19.95 per cent, which is one year in five. So a trader with a genuine edge, running it correctly, at the pace this course measured, spends about two years in five having a year that looks broken.

The run matters more than the count, because a run is what empties an account and a count is what fills a spreadsheet. Twenty thousand simulated years of twelve months each, at the same 41.26 per cent, put three consecutive losing months somewhere inside 39.91 per cent of them. Two years in five contain a quarter in which nothing worked.

Set that beside what the previous module just finished measuring. Module 13’s book made 3.70 a share net over twenty-eight moves and its worst run was 1.85, and both of those are statements about a fortnight of trading. This page is the same arithmetic stretched to the horizon a person actually lives on, and the stretching does not smooth anything: the month is short enough that the edge is invisible inside it and long enough that a bill arrives at the end.

A losing month is not evidence. At the measured pace it is the expected outcome of two months in five, and a trader who changes the system after one has changed it on noise. Lesson 67 gives the test that separates the two, and it needs 589 trades rather than five.

So count your own trades for a month, take the square root, divide your edge by it, and read the losing-month rate off the normal distribution before you promise anybody an income.

What this does not settle

That trade outcomes are normal. They are not, and lesson 44 said so plainly: returns carry fatter tails than the formula assumes, so events far from the centre happen more often than a normal implies. The losing-month rate sits near the centre of the distribution rather than out in a tail, so the figures on this page are close, but they are the tidy version of a messier truth. The normal is used because it is the distribution lesson 67 ran its drawdown harness on, and using a different one here would make this page incomparable with that one for no gain in honesty.

That the pace is 4.875 for you. It is 4.875 for lesson 71’s four rules on lesson 63’s data, and lesson 76 was explicit that the aggregate across all 253 rules is nearer half a dozen entries a year than forty a month. A reader running an intraday system takes hundreds of trades a month and reads the bottom of the table rather than the top. What transfers is the square-root relationship, not the row.

That the edge is a tenth of an R. It is lesson 67’s stated example and it is generous. Lesson 98 puts module 13’s 0.1230 round trip back into it and finds the cost takes about four fifths of that edge, which moves the losing-month rate from 41.3 per cent to 48.2. This page is the gross version and the next two pages are the ones that make it net.

That months are the right unit. They are the unit rent is charged in, which is why this page uses them, but nothing about the market changes at a month boundary. A quarter is less noisy and a week is worse, and the only reason the month wins is that it is the period a household budget is written in.

And the concession that costs most: this page has priced a month and said nothing about what a person does inside one. A 41.3 per cent losing-month rate is a fact about a distribution; whether a specific reader keeps following the rule through the fifth losing month of a year is a fact about a person, and no page in this course can measure it. Lesson 97 does the next best thing and asks what leaves the account while that is going on, because the withdrawal is the one number in this business that does not care what the market did.