Sequence of returns risk, with real returns

When you save, only the average return matters. When you spend from savings, the order of returns matters too. A fall in the first years of retirement does more damage than the same fall twenty years later, because you are selling investments to pay the bills while prices are low, and the money you sold cannot take part in the recovery. This is sequence of returns risk, and it is why two retirees with the same average return can end up in very different places. It is one of the ideas behind our calculators.

The idea in one formula

Each year the calculator takes out the year’s withdrawal $W$ at the start of the year, and the rest earns that year’s return $r_{t}$ :

F_{t} = \left(F_{t-1} - W\right)\left(1 + r_{t}\right)

$F_{t}$ is the balance at the end of year $t$ . With no withdrawals ( $W = 0$ ) the final balance is $F_{0}\,(1 + r_{1})(1 + r_{2})\cdots(1 + r_{n})$ , and a product is the same in any order. With withdrawals, each year’s $W$ is multiplied only by the returns that come after it, so early returns act on a bigger share of the money.

Returns here are real, after inflation: $1 + r_{t} = (1 + \text{nominal return}) / (1 + \text{inflation})$ , so the withdrawal stays the same in today’s dollars.

Worked example: two retirees, the same 30 years

Both retirees start with $1,000,000, hold 60% in US stocks and 40% in 10-year Treasury bonds, and take $50,000 a year (5% of the starting balance) in today’s dollars. Both get exactly the same 30 yearly returns, the real US returns from 1966 to 1995. Retiree A gets them in calendar order. Retiree B gets them backwards, starting with 1995.

The average return is the same for both: 4.8% a year after inflation (4.1% compounded). Without withdrawals both would end with $3,304,883. With withdrawals:

Retiree A meets the weak years of the late 1960s and 1970s first. The first five years average -0.8% a year after inflation, and the money runs out in year 19.
Retiree B meets the strong 1980s and 1990s first, with the first five years averaging 11.6%. After 30 years, $1,230,136 is left.

The chart above lets you pick any first year from 1928 and swap which retiree gets which order. Some runs barely change when reversed; others, like this one, change completely.

How Monte Carlo simulation works

One worked example shows that order matters. It cannot show how likely a bad order is. A Monte Carlo simulation answers that by running the same plan through thousands of made-up market histories and counting the results. The retirement savings calculator does this when you switch on “Show market ups and downs”:

It builds 10,000 histories of yearly returns (and, in the historical model, inflation) from a seeded random number generator, so the same inputs always give the same answer.
It runs your savings, spending and income through each history with the same rules as the fixed-return projection.
It records the age the money runs out in each history and reports the share of histories in which savings last past each age, and percentile bands for the balance.

It then combines market and lifespan risk exactly, without simulating deaths. For each history $i$ with depletion age $D_{i}$ , it takes the chance that someone in the household is still alive at that age from the SSA period life table (see survival probability) and averages over the histories:

\bar{P} = \frac{1}{N} \sum_{i=1}^{N} {}_{D_{i} - x}p_{\overline{xy}}

Histories in which the money lasts past 110 count as 0. $N$ is the number of histories and $x$ is your age today.

For the calculator’s example couple (aged 65 and 63 with $750,000), a steady 5.5% return runs out at about 91. With the normal model’s ups and downs, savings last past 91 in 40% of simulated market histories; the middle history runs out at 88, and someone is still alive when the money runs out in 54% of simulated markets and lifespans, against 49% with a steady return. In the tool’s own words: In 40% of simulated market histories, savings last past 91, the age they run out with a steady 5.5% return. Allowing for lifespan too, someone is still alive when the money runs out in about 5 in 10 simulated retirements.

The historical model and the normal model

The historical model replays whole calendar years of US history, 1928–2025: the S&P 500 return, the 10-year Treasury bond return and CPI inflation from the same year travel together, so a year like 1974, with falling stocks and high inflation, arrives as one piece. Years are drawn at random with replacement, one at a time or in runs of 5 or 10 years to keep streaks of good and bad years. The data come from Aswath Damodaran’s dataset at NYU Stern (retrieved 2026-10-22). Over 1928–2025, a 60/40 mix averaged 9.0% a year before inflation, with a standard deviation of 12.1%; stocks alone averaged 11.9% with 19.4%. For the example couple, savings last past 91 in 77% of historical histories and the middle one runs out at 110, because history’s average beats the steady 5.5% the example assumes.

The normal model draws each year’s return from a bell curve (lognormal, so a year can never lose more than everything) with the average return you enter and a volatility you can set. By default the volatility is the historical figure for a 60/40 mix, 12.1%, and inflation stays at your fixed rate. Because the average is yours, switching the market view on changes only one thing: the ups and downs.

The limits of both

One country, one century. The historical model replays one market’s record over 1928–2025. Other countries’ markets, and the future, can deliver returns that look nothing like it.
Few data. 98 years of history hold only 3 separate 30-year retirements. Resampling makes new combinations, not new information.
Bell curves have thin tails. The normal model gives fewer crashes and booms than markets have shown, and treats every year as independent of the last.
No behavior. Real retirees cut spending after a bad year, and markets change after a crash. Both models keep spending fixed.
Fees and taxes are left out, as in the rest of the calculator.

A simulated share describes the model, not anyone’s future: it says how often the money lasted across the simulated histories, under these assumptions.

Where this is used

How long will my money last?

Questions

What is sequence of returns risk?

It is the risk that poor returns arrive early in retirement, while you are taking money out. Withdrawals made after a fall sell more of the portfolio at low prices, so less is left to recover. Two people with the same average return can end up with very different outcomes because of the order alone.

Does sequence risk matter before retirement?

Much less. While you are only adding money or leaving it alone, the order of returns does not change the final balance for a lump sum, because multiplication gives the same answer in any order. It starts to matter once regular withdrawals begin, and matters most in the first ten years or so.

What does a Monte Carlo success rate mean?

It is the share of simulated market histories in which the money lasts past a given age, under the model's assumptions. It describes the simulation, not your future. A different model, data period or set of assumptions gives a different share, so it is best read as a comparison between plans rather than a forecast.

Is the historical model better than the normal model?

Neither is better in every way. The historical model uses real US years, including crashes, inflation shocks and streaks, but it can only replay what happened in one country over one century. The normal model can explore any average and volatility, but its bell curve gives fewer extreme years than markets have shown.

Sequence of returns risk