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MoneyWhat a million dollars actually pays

The math

What a million dollars actually pays.

This publication is named after a million dollars. It has never said what a million dollars actually pays you, which is a strange omission for a site with that name. The arithmetic takes one line. The confidence people attach to it does not survive contact with the model.

EDUCATION, NOT ADVICE · This essay is general education about a way of thinking, not financial advice and not a recommendation for your situation. The simulation below is a model built on assumptions that are stated openly and could be wrong. It is not a forecast and not a promise. Full disclosures →

The one line

Four percent of a million dollars is $40,000 a year, before tax.

That is the whole rule, and the arithmetic is not in dispute. Invert it and it becomes a target rather than an income: to draw 4% you need 25 times what you plan to spend. Every FI number you have ever seen is that multiplication.

Withdrawal rateIncome from $1,000,000Multiple of spending you need
3.0%$30,00033.3x
3.5%$35,00028.6x
4.0%$40,00025.0x
4.5%$45,00022.2x
5.0%$50,00020.0x

Read the middle column and a million dollars stops sounding like wealth and starts sounding like a job that pays $40,000 and never calls you. That is not nothing. It is also not what most people picture when they picture a millionaire, and the gap between those two pictures is responsible for a great deal of disappointment at exactly the wrong moment.

Income you wantAt 4% you needAt 3.5%At 3%
$40,000$1,000,000$1,142,857$1,333,333
$60,000$1,500,000$1,714,286$2,000,000
$80,000$2,000,000$2,285,714$2,666,667
$100,000$2,500,000$2,857,143$3,333,333

Half a point of withdrawal rate moves the target by roughly 14%. A full point moves it by 33%. The rate is not a detail attached to the plan. It is the plan, and the number on the door is downstream of it.

The part that is quoted as though it were a fact

The 4% figure gets repeated with a confidence it has not earned. So run it. A fixed real withdrawal, a random real return every year, 50,000 paths, and count how many portfolios last thirty years.

Expected real return10% volatility12% volatility16% volatility20% volatility
4%83.3%76.0%63.7%53.2%
5%92.3%86.1%73.6%62.0%
6%96.9%92.7%81.7%70.0%
7%99.0%96.7%88.3%77.3%

Every cell in that table is the same withdrawal rate, the same portfolio, the same thirty years. The only thing that changes is two numbers nobody can know in advance. The answer ranges from 53.2% to 99.0%, a spread of 45.8 percentage points.

The 4% rule is not a rule. It is a point estimate from a distribution 46 points wide, and which end of it you land on depends on assumptions you cannot check until it is far too late to act on them.

This is the same objection we made to our own scoreboard in a hit rate proves nothing. A single number that hides its error bars is not information. It is a decision that has been made for you and then rounded.

So the honest way to hold the 4% figure is as a planning convention rather than a promise. It is useful precisely as the table's middle rows are useful: a reasonable central case, with the explicit understanding that the tails are wide and live.

The rule was built for a thirty year retirement

Here is the part that matters most to anybody reading a site like this one, and it is usually left out. The 4% convention comes from studies of a retirement that starts in the sixties and runs about thirty years. Retire at forty and you are not running that experiment. You are running one almost twice as long.

At the base case, a 5% real return with 12% volatility:

HorizonSurvival at 4%
30 years86.1%
40 years73.5%
50 years64.7%

21 points of survival, gone, with no change to the portfolio or the spending. Only the number of years it has to last.

Put it the other way around, which is more useful. The rate that lasts fifty years about as reliably as 4% lasts thirty is 3.0%. On a million dollars that is $30,000 rather than $40,000. Retiring early costs $10,000 a year of permanent income, a quarter of the draw, before you have made a single other decision. That is the real price of the extra decades, and it is almost never quoted alongside the retire-at-forty arithmetic that makes them sound free.

Cost comes straight out of the income

We wrote earlier that a fee is quoted against your assets and paid out of your returns. In retirement it is worse than that, because the return is the income.

A 1% fee on a million dollars is $10,000 a year. Your income at a 4% draw is $40,000. So the fee is 25% of your retirement income, taken first, every year, in the years when you have no salary to make it up with.

All-in costIncome surrenderedSurvival, 30 yearsSurvival, 50 years
0.00%$086.1%64.7%
0.50%$5,00081.3%56.0%
1.00%$10,00076.0%46.7%
1.50%$15,00070.1%37.3%

Over fifty years a point and a half of cost takes survival from 64.7% to 37.3%. The fee does not reduce the odds a little. It is the single largest controllable variable in the table, larger than the difference between a thirty and a forty year retirement, and unlike the return assumption it is a number you can look up this afternoon with the fee drag calculator.

The one lever that is free

Everything above assumes you withdraw the same real amount every year no matter what the market does, which is what the rule specifies and what almost nobody would actually do. Watching a portfolio fall by a third and taking the full inflation-adjusted raise on schedule is not a plan. It is an instruction to a robot.

So model the crudest possible alternative. If the portfolio is down 20% from where it started, cut spending by 20% until it recovers. No optimization, no rules engine, no forecasting. One decision a reasonable person would make anyway.

HorizonFixed withdrawalWith the cutDifference
30 years86.1%94.6%+8.4 points
40 years73.5%86.1%+12.6 points
50 years64.7%77.7%+13.0 points

13 points of survival over fifty years, bought with nothing. No extra saving, no better returns, no lower fees, no market timing. Just a willingness to spend less in bad years, which is the same behavior that determines almost every other outcome in personal finance.

That is the most important row in this essay. The withdrawal rate debate consumes enormous attention and moves survival by a few points per half point of rate. Being willing to flex your spending moves it by more than a full point of withdrawal rate would, and it is available to everybody for free.

What this model does not know

Stating the limits properly, because a simulation that hides them is worse than no simulation.

Returns are drawn independently each year. Real markets mean revert somewhat, which means this model treats long horizons more harshly than history has. Read the levels as pessimistic and the comparisons between rows as the useful part.

It knows nothing about valuations on the day you retire. Starting into an expensive market and starting into a cheap one are different experiments, and this treats them identically. That is the order your returns arrive in, and it is the single biggest thing missing here.

There are no taxes in it, and no Social Security. Both are large. The first makes $40,000 less than $40,000. The second makes the required portfolio smaller for most people, sometimes dramatically, and the fifty year retiree gets it for only part of the horizon.

Nobody actually dies on schedule. A fifty year horizon is a planning assumption, not a prediction, and a plan that fails in year forty-eight fails differently from one that fails in year five.

What to take from it

The arithmetic is the reliable part. A million dollars pays $40,000 a year, you need 25 times your spending, and every extra dollar of annual spending costs you 25 more dollars of portfolio. That much you can build a plan on.

The confidence is the unreliable part. Anybody quoting a single success probability for a withdrawal rate is quoting one cell out of a table 46 points wide, and usually the comfortable one.

And the levers are not where the argument is. The debate is about whether the number is 3.5 or 4. The things that actually move the outcome are how long the money has to last, what you pay to hold it, and whether you are willing to spend less in a bad year. Two of those three are entirely within your control.

A million dollars is not an amount of money. It is a rate of pay, and the rate is lower and less certain than the number on the door suggests.

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