Sequence Risk, With Real Numbers

Same Returns, Different Retirement

Two people retire with $1,000,000. Both withdraw $40,000 in year one and raise it with inflation. Both earn the exact same 25 annual returns, with the same arithmetic average and the same geometric average. One ends with $1,173,055. The other ends with $2,254,954.

The only difference is the order of the returns. That is sequence of returns risk, and this post is the numbers version. No hand-waving about “early losses hurt more.” You get year-by-year tables built from real S&P 500 and bond data, plus the one-line reason it happens.

Where the Numbers Come From

Everything below comes from a Python script I ran against Aswath Damodaran’s NYU Stern dataset (“Historical Returns on Stocks, Bonds and Bills”). It has S&P 500 total returns including dividends, 10-year Treasury bond returns, and annual CPI-U inflation (the FRED series CPIAUCNS, measured December to December). The data runs through 2025.

The setup:

1. Portfolio is 60% S&P 500, 40% 10-year Treasuries, rebalanced every January.
2. The withdrawal comes out at the start of each year: $40,000 in year one, then raised each January by the prior year’s CPI-U change.
3. No fees, no taxes. Real life is worse on both.
4. Retiree 1 retires in January 2000 and lives through the real 2000 to 2024 returns.
5. Retiree 2 gets the same 25 returns in reverse order, so 2024 happens first and 2000 happens last.
6. Both retirees take the identical dollar withdrawals in the identical year order. Only the return order changes.

The core loop is short enough to read in one breath:

bal = 1_000_000
w = 40_000
for (stock, bond), cpi in zip(returns, inflation):
    bal -= w                                  # withdraw first
    bal *= 1 + 0.6 * stock + 0.4 * bond       # then grow what's left
    w *= 1 + cpi                              # raise next year's withdrawal

Feed it returns and then returns[::-1]. That is the entire experiment.

The Control: No Withdrawals, No Difference

Run the same two return sequences with zero withdrawals. Both retirees end with exactly $5,034,973. The 60/40 mix averaged 7.17% per year (arithmetic) and 6.68% per year (geometric) in both orders.

This is the key insight, and it is just multiplication. A 1.20 times a 0.70 equals a 0.70 times a 1.20. If nothing moves in or out of the account, order is irrelevant.

Sequence risk only exists when money leaves (or enters) the portfolio. The moment you pull $40,000 out during a down year, you sell shares at a low price, and those shares never get to participate in the recovery. The math doesn’t care that the average is the same.

Retiree 1 vs Retiree 2, Year by Year

Here is the 60/40 portfolio. “Fwd” is the real 2000 start. “Rev” is the same returns in reverse.

Three things jump out.

First, after 10 years Retiree 1 has $790,476 and Retiree 2 has $1,485,836. The first decade set the final gap: Retiree 1 had 53% of Retiree 2’s balance at year 10 and 52% at year 25.

Second, the 60/40 geometric return over the first 10 years was 2.93% per year for Retiree 1 and 8.04% for Retiree 2. Same 25-year average, a 5.11-point gap in the first decade.

Third, look at the withdrawal rate. In year 11, Retiree 1’s $51,325 withdrawal is 6.49% of the balance. For Retiree 2 it is 3.45%. The “4% rule” was never a fixed percentage of the current balance. It is 4% of the starting balance, adjusted for inflation. When the balance drops, that fixed dollar amount becomes a bigger and bigger bite.

Retiree 1 pulled out $1,337,405 across 25 years and still has $1,173,055 left in nominal dollars. That is a survivable outcome. The 60/40 mix, plus 2009 to 2021 being a long bull run, rescued it. Retiree 1 survived, but from year 9 onward they had about half of Retiree 2’s balance.

Same Test, 100% Stocks

If you run all stocks, the gap gets ugly. The S&P 500 alone had a 9.25% arithmetic and 7.62% geometric average over those 25 years, in both orders. With zero withdrawals both end at $6,273,650.

With the $40,000 inflation-adjusted withdrawal:

The 2000 retiree in all stocks is down to $436,391 after a decade, and the year-11 withdrawal is 11.76% of the portfolio. The reversed retiree is sitting on $2,533,849 and withdrawing 2.03%. Neither runs out in this window, but one is down to $183,734 and the other is up to $3,786,530.

The Classic Test: 1966 vs 1982

The 25-year 2000 window is a recent example. The textbook example is the 1966 retiree.

William Bengen’s 1994 paper, “Determining Withdrawal Rates Using Historical Data” in the Journal of Financial Planning, is where the 4% rule comes from. In his data, the mid-to-late-1960s starts set the worst case, and 1966 is the one people cite most.

I reran that comparison with the Damodaran data: $1,000,000, a 60/40 mix, a $40,000 first withdrawal raised by actual CPI-U each year, and a 30-year window. Damodaran’s data and my timing choices differ from Bengen’s, so my results will not match his exactly. These are the numbers from my script.

In this dataset the 1966 retiree runs out of money in 1991, in year 26. That does not contradict Bengen. In his data, a 4% withdrawal lasted at least 33 years for every start year, 1966 included. My setup takes each withdrawal at the start of the year and uses 10-year Treasuries instead of the intermediate-term Treasuries Bengen used. With the same Damodaran data and end-of-year withdrawals, the 1966 retiree makes it to year 32 before running out. The 1982 retiree ends year 30 with $12,869,047, and their year-30 withdrawal is $93,268.

Here is what makes 1966 interesting. The 60/40 portfolio compounded at 9.67% per year over those 30 years, nominal. The 1982 portfolio compounded at 10.70%. The gap is about one point a year, and the order of returns and inflation did the rest. Inflation compounded at 5.73% per year during the first 10 years for the 1966 retiree and 3.91% for the 1982 retiree. In year 10 the 1966 retiree withdrew $65,283 from a balance of $751,584, an 8.7% withdrawal rate. The inflation-adjusted schedule would have called for $188,302 in year 30. The balance never recovered, because the early years gave it nothing to grow from.

I also ran every 30-year window from 1928 through 1996 on the same setup (69 start years). Four failed: the 1965, 1966, 1968, and 1969 starts. They all fall within five years (1967 survived with $756,415 left), which is the sequence risk story at scale: a bad stretch hurts every retiree whose first decade overlaps it.

Does This Apply While You’re Still Saving?

Yes, but it works in reverse. When you add money every year, an early crash helps you, because you buy cheaply and ride the recovery with a larger share count.

I ran a saver putting $20,000 at the start of each year into the S&P 500, over the same 25 years. In the real order (2000 start) they end with $2,457,011. In reverse order they end with $1,034,843. Same contributions of $500,000. Same average return. The saver wants the bad years first. The retiree wants them last.

This is also why the real danger zone is the few years on either side of your retirement date. Your balance is at its peak, so a crash costs the most, and you stop buying and start selling at the same moment.

What to Do About It

Simulations are fun. Here are four fixes that actually move the number, kept short.

1. Hold a cash or bond buffer. One to three years of expenses outside stocks lets you skip selling equities in a short downturn, and you refill it after the recovery. A long downturn can outlast it: 2000 to 2002 was three straight down years. A rebalanced 60/40 portfolio already does some of this, because it sells bonds after a stock crash.
2. Spend flexibly. Cutting withdrawals in a down year cuts the damage. In the 100% stock case above, the year-11 withdrawal hit 11.76% of the portfolio because the dollar amount stayed fixed on a shrinking pile. Guardrail rules that trim spending when the portfolio falls deserve their own post, and they will get one.
3. Work a bit longer, or earn a bit. One or two extra years, or $15,000 a year of part-time income during the first decade, hits exactly the window that matters most.
4. Consider a rising equity glidepath. Michael Kitces and Wade Pfau’s 2013 research found that starting retirement with a lower stock allocation and raising it over time can improve outcomes in bad-sequence scenarios, compared to a constant allocation. It runs against the usual “get more conservative as you age” advice, so read the paper before you copy it.

The Short Version

Averages lie when money moves. Two portfolios with identical returns can end $1,081,899 apart (that is the 60/40 gap between $2,254,954 and $1,173,055), and the cause is which decade the bad years landed in. The first 10 years of retirement carry most of the weight. Run your own plan against a bad-first-decade scenario before you trust a single average return, because your 2 AM self will not enjoy finding out in year 8.

Common Questions

Does sequence of returns risk matter if I’m still working?

Yes, but the direction flips. While you contribute, an early crash helps, because you buy shares cheaply. A crash in the last years before retirement hurts most, because your balance is largest then. In the 2000 to 2024 test, a $20,000-a-year saver ended with $2,457,011 in the real order versus $1,034,843 reversed.

What is sequence of returns risk in simple terms?

Sequence of returns risk is the risk that bad market years arrive early in retirement, while you are withdrawing money. With zero withdrawals, any order of the same returns gives the same ending balance. With withdrawals, early losses force you to sell low and leave less to recover.

Is sequence of returns risk the reason for the 4% rule?

The 4% rule exists because of sequence risk. Bengen’s 1994 study tested historical retirement start dates and set the safe withdrawal rate by the worst starting points. The 1966 start is the classic example: it lasted past 30 years at 4% in Bengen’s data, but ran out in 1991 in my 60/40 test with start-of-year withdrawals.

How long does sequence risk last?

Sequence risk matters most in the first 10 years of retirement. In the 2000 retiree test, the portfolio was already down to $790,476 after year 10 versus $1,485,836 for the reversed order. After that decade the gap mostly just compounds.

Related Reading

• The 4% Rule: Does It Still Hold?
• Bonds: When to Actually Add Them
• Your FIRE Number: How to Calculate It
• Coast FIRE: The Lazy Path to FI
• Asset Allocation by Age: A Practical Guide