How Long the Money Lasts

Two withdrawals, only one of which anybody models

An account loses money two ways at once and traders model one of them. The market takes some and gives it back, and the household takes some and does not. Over any given stretch both are running, and the arithmetic of which one dominates is a division nobody does.

Lesson 65 fixed 156 trades as the length of a fair trial before you start, and at 4.875 trades a month that is exactly 32 months. Over those 32 months, lesson 67 says the median worst drawdown of a genuine tenth-of-an-R system is 8.82R, which at one per cent risk on a hundred thousand is 8,820. Over the same 32 months, a 500 withdrawal takes 16,000.

The withdrawal is 1.81 times the drawdown, and it is the one that never comes back. That ratio is the finding, and it does not need a simulation: it is a multiplication and a division on figures two earlier lessons already printed.

What ten years of paths look like

The rest of this page does need one, because the ratio above is an average and the account experiences an order. Here is the harness, in full. Each month the account earns a normal draw whose mean is the edge multiplied by 4.875 multiplied by one per cent of the current account, and whose standard deviation is the square root of 4.875 multiplied by one per cent of the current account. Then 500 leaves. Risk is resized to one per cent of the current balance every month, which is the disciplined convention and the generous one. That is 20,000 independent paths of 120 months, on seed 20260905.

Read the top row first, because it is the good news and it is not good. With a genuine, uncosted tenth-of-an-R edge, taking out 500 a month against an account that earns 487.50, the median decade ends 6.2 per cent below where it started and 57.52 per cent of paths finish below the opening balance. Nothing went wrong in those paths. The withdrawal was 2.6 per cent larger than the edge and ten years of compounding did the rest.

Now read down. The middle row is the same business after the round trip lesson 98 priced, and it is much closer to the bottom row than to the top one. Net of cost, ten years of this business is nearer to having no edge at all than it is to having the edge the backtest reported.

Where the money actually went

Separate the two forces by switching one off. Run the same paths with no withdrawal at all and the gross business ends at a median of 174,206 with no path ever halving, and the net business ends at 109,447 with 0.10 per cent halving. So on the gross edge, the withdrawal costs the median decade 80,435 of ending balance and lifts the chance of halving from nothing at all to 5.23 per cent.

That is the number to hold. The 500 a month is 60,000 taken over ten years, and it costs 80,435 of ending balance, because every dollar withdrawn is also a dollar that stops compounding. The gap between the two, 20,435, is what the withdrawal costs beyond its face value.

Halving is not the same as ruin, and it is worse. An account that halves has not failed; it has been forced to halve its position size to keep one per cent meaning one per cent, which halves the earning power that has to fund the same 500 a month. Ruin is an event you can plan for. This is a ratchet.

Watch the ratchet in the middle row. At the net edge the account earns roughly 99 a month at the opening balance, and the withdrawal is 500. Once the balance falls, one per cent of it is smaller, so the earning falls while the withdrawal does not, and 58.67 per cent of paths reach the halfway line inside ten years. The median path ends at 46,526, which means the median business has taken 60,000 out of an account that is now worth less than half its opening value and can support a withdrawal of 46 a month.

The 0.03 per cent of paths that reach zero are the least interesting number in the table. Nobody trades an account to zero; they stop somewhere above it, and where they stop is a question about a person that lesson 96 already conceded this course cannot answer.

Set the whole table against the two figures that opened this page. Over the 32-month trial period lesson 65 asks for, the market’s median worst take is 8,820 and the household’s certain take is 16,000. Every planning document a trader writes models the first and none model the second, and the second is nearly twice as large and has no recovery.

So run your own two numbers side by side: your withdrawal over the length of your own trial, and your median expected drawdown over the same stretch. If the first is larger, your business is not a trading problem.

What this does not settle

That the monthly draws are independent and normal. They are neither. Lesson 44 said returns carry fatter tails than a normal, and lessons 63 and 85 both established that volatility clusters, so real bad stretches are both deeper and longer than this harness makes them. Every figure in the table is the tidy version, and the direction of the error is against the trader in all three rows.

That the risk is resized every month. The harness resizes one per cent to the current balance, which is the disciplined thing and also the thing that produces the ratchet. A trader who keeps risking a thousand dollars a trade as the account falls earns more in the recovery and reaches zero far more often, and lesson 22 is the page that prices that path rather than this one.

That the 8.82R and the paths belong to the same model. Lesson 67 measured its drawdown on 156 trades of a fixed-size R; this page compounds a percentage of a moving balance. The two agree closely at these sizes and would not at larger ones. The comparison in the opening claim is an order-of-magnitude statement, and it is the ratio of 1.81 that carries it rather than either figure alone.

That a decade is the right horizon. It is the horizon lesson 98’s 589 trades takes at this pace, which is why it is here. It is also longer than most trading careers and shorter than most retirements, and a business plan that cannot survive its own measurement period is not made viable by shortening the plan.

And the concession that costs most: five pages have now measured a business and none has said whether to run it. That is deliberate, and lesson 100 does not say either. What it does instead is put the five numbers on one card, in the order in which they bind, so the reader can see which one fails first for them rather than which one this course happened to measure hardest.