Sequence-of-returns risk: why average returns mislead

Sequence-of-returns risk is the risk that poor returns arrive early in retirement, while you are withdrawing. Without withdrawals, the order of returns doesn’t change where you end up. With them, it does: in the example below, the same ten yearly returns, averaging 6%, leave $822,957.19 or $1,125,047.84 after ten years depending only on their order. A projection at a flat 6% shows $1,092,265.56.

Why doesn’t the order of returns matter without withdrawals?

Growth multiplies, and multiplication gives the same product in any order. A balance that falls 20% and then rises 25% ends where it started (0.80 × 1.25 = 1), and so does one that rises 25% first. The ten returns in the example multiply to a growth factor of 1.6806014, so $1,000,000 left alone becomes $1,680,601.37 whichever order they arrive in.

Why does the order matter once you withdraw?

A fixed withdrawal taken after a loss is a bigger slice of a smaller balance. To raise the same cash after prices fall, you sell more of your investments, and what you sell isn’t there for the recovery. William Bengen’s 1994 study gives a historical case: a retiree who began in 1929 by withdrawing 4% of the portfolio was taking about 7.6% of it by the end of 1932, even though deflation had lowered the dollar amount.

The algebra shows exactly where order enters. With a starting balance $B_0$, the same withdrawal $W$ at the start of each year and yearly returns $r_1, \dots, r_n$:

The first term is the balance with no withdrawals, and it doesn’t depend on order. The second is what the withdrawals would have grown to had they stayed invested: each one misses every return from its own year onward. When the good years come late, every withdrawal misses them and the second term is large. In the example below it is $857,644.18 when the losses come first and $555,553.53 when they come last, so the balances are $1,680,601.37 − $857,644.18 = $822,957.19 and $1,680,601.37 − $555,553.53 = $1,125,047.84.

Worked example: the same ten returns in two orders

Example assumptions, not a forecast: $1,000,000 at the start of retirement, $50,000 withdrawn at the start of each year and not raised for inflation (a 5% initial withdrawal rate), and no fees or taxes. The returns are made up: −20%, −10%, +5%, +12%, +15%, +18%, +10%, +8%, +14% and +8%, an arithmetic average of exactly 6.00%. Retiree A gets them in that order. Retiree B gets them reversed, so the two losses come last.

Each year, the new balance is (balance − $50,000) × (1 + return). For A’s first year: ($1,000,000 − $50,000) × 0.80 = $760,000. Figures are calculated at full precision and rounded to the cent, so a row recomputed from the rounded numbers can differ by a cent.

Both retirees withdrew $500,000, yet B finishes $302,090.65 ahead. A’s $50,000 grew from 5.00% of the balance in year 1 to 8.08% in year 4 ($50,000 ÷ $618,450), while B’s shrank to 3.00% by year 9. Going into year 11, the same $50,000 is 6.08% of A’s balance and 4.44% of B’s.

These ten returns can be arranged in 1,814,400 distinct orders (the two 8% years are interchangeable). Checking every one, the ending balance runs from $774,633.07, with the returns in rising order, to $1,161,904.35 in falling order. About 89% of the orders end below the flat 6% projection.

What does a constant-return projection hide?

• The spread. A flat rate gives one number. The same average return produced anything from $774,633 to $1,161,904 here.
• Its tilt. Fed the arithmetic average, it lands above most orders because it also skips volatility drag (next section).
• When the money runs out. Keep the example, but raise each withdrawal 3% a year for inflation and give every year after year 10 a 6% return:

The same first-decade average and the same later returns move the end from year 23 to year 31. The flat projection says year 30, seven years later than A’s path.

Which average should a constant-return projection use?

If you use one rate, the geometric average is the fairer one. The arithmetic average (add the returns, divide by 10) is 6.00%. The geometric average is the constant rate that reproduces the actual growth:

Here that is $1.6806014^{1/10} - 1 = 5.3286\%$. A figure labeled simply “average” is usually the arithmetic mean, so check which kind a source reports before using it as a projection rate.

At 6% a year, $1,000,000 would grow to $1,790,847.70 in ten years with no withdrawals, $110,246.33 more than these returns actually produce. The gap, often called volatility drag, reflects the fact that losses need larger gains to recover: after a 20% fall it takes a 25% rise to get back, as covered in common percentage mistakes. With withdrawals, the geometric rate gives $1,007,945.37, which sits near the middle of all 1,814,400 orders (about 51% end below it). That removes the tilt but not the spread: it is still $184,988.18 more than retiree A ends with.

Why do the first years of retirement matter most?

A loss early shrinks the balance that every later withdrawal comes out of. To isolate this, take nine years at +9% and one year at −21% (average 6.00%), the same $1,000,000 and $50,000 withdrawals, and move only the year of the loss:

Every year of delay helps, and the first delay helps most ($29,888.44 from year 1 to year 2). Still, one bad year explains only part of the $302,090.65 between A and B: moving the loss from year 10 to year 1 costs $195,315.55. Nearly all the rest comes from A’s second early loss. Moving just A’s −20% year to year 10 recovers $198,752.89 of the gap; moving both losses to the end, −10% then −20% as in B, recovers $300,269.08.

On historical data, a poor first decade, more than a single crash, is the main danger: Kitces found that stock returns over the first ten years of retirement correlated with the safe withdrawal rate more than twice as strongly as first-year returns.

How do the withdrawal-rate studies behind the 4% rule handle it?

They test actual historical sequences instead of an average. Bengen argued that planning with average returns and average inflation is a fallacy, and ran withdrawals through every starting year from 1926 onward. For a portfolio of 50% stocks and 50% intermediate-term Treasuries, a 4% first-year withdrawal, raised each year for inflation, lasted at least 33 years in every period he tested. At 5%, retirees starting in the late 1960s and early 1970s might have had only about 20 years. The 1998 AAII study (often called the Trinity study) measured a “portfolio success rate”: the share of past payout periods, using 1926–1995 returns, in which a withdrawal rate did not exhaust the portfolio.

In both studies, the withdrawal rates that held up were limited by the worst historical sequences, not by the average return. That is sequence risk at work. The figures describe the past, not a promise about the future, and this site doesn’t recommend a rate.

How do flexible withdrawals change the outcome?

Flexibility moves the risk rather than removing it. Take the ten-year example again, but withdraw 5% of the current balance at the start of each year instead of a fixed $50,000. Each withdrawal then removes the same fraction of the balance, so $B_n = B_0 (1 - p)^n \prod (1 + r_t)$ with $p$ = 0.05, and the order no longer changes it:

A’s balance now ends where B’s does, but A’s withdrawal is 35% lower by year 4, and A’s ten-year total is $94,267.55 less than fixed withdrawals would have paid. The sequence risk now shows up in the income instead.

Other approaches make similar trades:

• Trimming after losses. Skipping an inflation raise, cutting withdrawals or postponing a large expense after a decline means fewer investments sold at low prices. The cost is lower spending when markets are down.
• Guardrail rules. Jonathan Guyton and William Klinger (2006) tested rules that cut withdrawals when the current withdrawal rate rises well above its starting level and raise them when it falls well below. The cost is an income that changes from year to year.
• A cash or short-term bond reserve (a “bucket” strategy). A few years of spending held outside stocks means no forced stock sales in a decline. The cost is the lower return on the reserve. Research summarized by Kitces found that, on historical returns, such reserves more often left retirees with less money than holding none; Kitces adds that a rebalanced portfolio already sells whatever has held up.
• A lower starting withdrawal. More room for a poor sequence, paid for with less income every year, including the good ones.

Which trade suits you depends on how far your spending can bend, what other income you have, such as Social Security or a pension, and how long the money must last.

What does this example leave out?

• Actual market returns. The returns are invented to isolate order. Real markets don’t deliver a known average.
• Inflation’s own sequence. High inflation early raises every later inflation-adjusted withdrawal, even if inflation averages the same over the whole retirement. See nominal vs. real returns for today’s-dollar projections.
• Taxes, fees, required minimum distributions and asset mix. One return stands in for the whole portfolio; how fees compound covers fees.
• Timing within the year. Withdrawals here are yearly, at the start of the year.
• Probabilities. Two orders are illustrations, not odds. Historical and Monte Carlo tests estimate how often a plan would have survived; a single flat-rate projection can’t.

Try it

1. Retirement withdrawal calculator: its main projection uses one constant return, so it reproduces the flat-rate rows. Below it, the “Same average return, different order” illustration runs made-up returns that average the return you enter. At 6% they are this guide’s ten returns: “Weak years first” is retiree A, “Weak years last” is retiree B, and every later year earns 6%.
   • Starting balance $1,000,000, first-year withdrawal $50,000, expected annual return 6%, withdrawals at the start of each year and “Raise withdrawals with inflation each year” unchecked: the money lasts more than 100 years, and the year-10 balance is $1,092,265.56. The illustration shows A with $822,957.19 and B with $1,125,047.84 after year 10.
   • Check that box and set the inflation rate to 3%: the money lasts 29 years, with $1,001,269.04 after year 10 and $9,168.34 left for year 30. The illustration gives A’s and B’s rows of the table above: A has $713,836.27 after year 10 and lasts 22 years, then $44,032.81 in year 23; B has $1,059,033.10 and lasts 30 years, then $70,077.64 in year 31.
2. CAGR calculator: a starting value of 1,000,000, an ending value of 1,680,601.37 and a period of 10 years give a CAGR of 5.33%, the geometric average.
3. FIRE calculator: spending in retirement of $50,000 a year (set its frequency to Yearly) at a 5% withdrawal rate gives an FI number of $1,000,000, the starting balance used here; at 4% it is $1,250,000. Its projections also use one constant return, so they share the blind spot described above.