2 COMMA,,INVESTOR @2commainvestor

MoneySequence of returns

The math

The order your returns arrive in

Two retirees earn exactly the same average return over thirty years and spend exactly the same amount. One finishes with nearly three times as much money. Nothing separates them but the order.

Every retirement calculator you have ever used asks for an expected return. You type in 7%, or 8%, and it draws you a smooth curve upward. That curve is a lie, and not in the way you think. The problem is not that the average is wrong. The problem is that there is no such thing as an average year.

Markets do not deliver 8% thirty times. They deliver a sequence: down 15, down 12, up 22, up 9, down 18, up 27. The average of that sequence might be exactly 8%. But the order in which those numbers arrive can change your retirement more than the average itself does, and almost nothing in personal finance prepares you for it.

This is called sequence of returns risk. It is the single most important idea in the withdrawal phase, and it is barely discussed compared with the endless argument about which index fund to own.

The demonstration

Take a thirty-year run of annual returns. Five losing years, the worst of them down 18%, the best up 27%. The arithmetic mean is 9.40% and the compound annual growth rate is 8.80%.

Now run that identical set of thirty numbers twice. The first time, the three losing years at the start arrive first. The second time, run the exact same numbers in reverse order, so the bad years land near the end. Same numbers. Same average. Same compound growth rate, to the decimal. Only the order differs.

Both retirees start with $1,000,000 and withdraw $40,000 in year one, raising it 3% a year for inflation. That is the classic 4% rule.

Same thirty returns, two orders

$1,000,000 starting portfolio, $40,000 first-year withdrawal, 3% annual increases, 30 years

Compound annual return, both cases
8.80%
Balance after 10 years, bad years first
$954,898
Balance after 10 years, bad years last
$1,793,857
Final balance, bad years first
$2,218,518
Final balance, bad years last
$6,229,131

Both retirees survived. Both took exactly the same money out. One ended with 2.8 times what the other did. The gap opens in the first decade and never closes, because the money withdrawn during the early decline is gone before the recovery arrives.

Why it happens

The mechanism is simple enough to state in one sentence: a withdrawal during a decline permanently removes shares that would otherwise have participated in the recovery.

If your portfolio falls 15% and you take out $40,000 anyway, you are not selling from a $1,000,000 balance. You are selling from a smaller one, which means you sell a larger fraction of what you own. Those shares are gone. When the market comes back, it comes back on a smaller base. Do that three years running and the damage is locked in for the rest of your life, no matter how good the following twenty-seven years are.

In the demonstration above, the retiree who hit the bad years first was down to $954,898 after a decade, having started with a million. The other was at $1,793,857. Every subsequent year of identical returns compounded on those two very different numbers.

The version where somebody goes broke

Both retirees above survived because 4% is a conservative rate. Now consider someone who looks at that 8.80% compound return, reasons that spending 7% still leaves room for growth, and retires on $70,000 a year.

The same two sequences at a 7% withdrawal rate

$1,000,000 starting portfolio, $70,000 first-year withdrawal, same 3% increases

Bad years first
Broke in year 14
Bad years last
$1,485,463 remaining
Highest safe rate, bad years first
4.86%
Highest safe rate, bad years last
7.94%

Identical returns. Identical average. One person runs out of money at age 14 years into retirement and the other never comes close. The honest reading of the last two rows is that the safe withdrawal rate is not a property of the market. It is a property of the market and your timing together, and you do not control the second one.

The part that gets the sign backwards

Here is the thing almost nobody says out loud, and it changes what you should worry about and when.

If you are still saving, sequence risk works in your favor. A crash early in your accumulation years is not a disaster. It is a discount. Every contribution you make during the decline buys more shares than it otherwise would, and those shares participate fully in the recovery.

Run the same two sequences again, but instead of withdrawing, contribute. Start with $100,000 and add $20,000 a year, rising with inflation:

Same sequences, contributing instead of withdrawing

$100,000 starting balance, $20,000 contributed annually, rising 3% a year, 30 years

Bad years first
$6,423,153
Bad years last
$4,417,847
Advantage to the early crash
$2,005,306

The exact ordering that cost the retiree most of their money made the saver $2,005,306 better off. Same market, same thirty years, opposite sign. Which side of that line you are standing on is the entire difference.

This is why "buy the dip" is genuinely good advice for a thirty-year-old and genuinely dangerous advice for a sixty-five-year-old, and why generic market commentary aimed at everyone at once is close to useless.

What to actually do about it

You cannot control the order the market delivers returns in. You can control four things, and they are roughly in order of effectiveness.

Be flexible about spending. This is the big one and it is not close. A retiree who cuts withdrawals by 10% during a bad year avoids selling the most shares at the worst prices. Nearly every study of withdrawal rules finds that modest flexibility buys more safety than any amount of clever asset allocation. A rigid inflation-adjusted withdrawal is the assumption that makes the 4% rule fragile, not the 4%.

Hold a cash buffer. One to three years of spending in cash or short-term bonds lets you stop selling equities entirely during a decline. It costs you return in the average year and buys you survival in the bad one. That is a trade most people should take at the point of retirement and not a day before.

Start lower than you think. The difference between 4.86% and 7.94% above is not a rounding error, it is the difference between two lives. Starting at a rate that survives the bad ordering costs you some spending in the good one. That is the price of not knowing which one you got.

Know that the risk concentrates early. The first decade after you stop earning is when this is decided. A portfolio that gets through ten years intact is usually far ahead and can absorb almost anything afterward. That is worth knowing because it means the caution has an expiry date, and you do not have to live like this forever.

The bottom line

The average return is the number everyone quotes and it is the least useful number in the calculation. Thirty years of 8.80% compound growth produced two completely different retirements here, and the variable that separated them was not skill, cost, allocation, or fund selection. It was the calendar.

Which is uncomfortable, because it means a meaningful part of your outcome was decided by when you happened to be born. The only sane response is to build a plan that survives the bad ordering rather than one that requires the good one, and then stop optimizing the third decimal place of your expected return.

A note on the numbers. The return sequence used above is constructed, not a historical backtest, and it is used in both directions so that the average and the compound growth rate are identical by construction. That is the point: the comparison isolates ordering and nothing else. Real historical sequences behave the same way and often worse, but quoting one would invite an argument about which thirty years to pick, which is not the argument this essay is making.

Follow @2commainvestor