Sequence of Returns Risk, Explained

After reading this you will understand why two retirees with the same average return can end up with wildly different outcomes, and how to read the survival rate a historical cohort test reports for your own plan.

What sequence risk is, and one hook example

Once you retire and start spending from a portfolio, the order in which returns arrive changes your outcome. This is sequence of returns risk. While you were saving, order did not matter much: a bad year early followed by a good year late gives the same ending balance as the reverse, because you are only adding money. Once you withdraw, that symmetry breaks. A loss in year one shrinks the base that every later gain has to work on, and the withdrawal you took that year is gone for good.

Here is the hook. Suppose you retire with $1,000,000, withdraw $40,000 a year, and face two sequences that both average about the same return over 30 years. Retiree A meets a deep bear market in years one to three (think 1929 or 1966). Retiree B meets the same bear market in years 28 to 30. Retiree B barely notices: by then the portfolio has grown large and the losses hit a big base. Retiree A may run out of money entirely. Same average, opposite fate.

The tool at /finance/sequence-of-returns/ replays your plan through every actual US starting year since 1928. Each cohort gets the real S&P 500 total returns, 10-year Treasury returns and CPI inflation that followed it. The result is not a guess about the future; it is a count of how your rules would have fared against the past.

When to use a historical cohort test

Use it when you have a fixed withdrawal rule and want to know how fragile it is to bad timing. The classic question is the one Bengen asked in 1994: does a 4% inflation-adjusted withdrawal survive 30 years? This tool recreates that experiment across all cohorts.

It is the right tool when your plan is roughly "withdraw a set percentage of my starting balance, adjust for inflation, hold a fixed stock and bond mix, rebalance yearly." It is less useful if your real plan is flexible: cutting spending in bad years, working part time, or annuitising part of the portfolio. Those behaviors change the failure math entirely and are not modelled here.

A historical test tells you what happened, not the full range of what could happen. US markets from 1928 to 2023 were the best-performing of any major economy that century. A country whose worst cohort still survived does not prove your worst case is survivable. Read the survival rate as a floor on optimism, not a guarantee.

The mechanics, year by year

The model is a simple loop. Let B_t be the portfolio balance at the start of year t (before the withdrawal), W_t the withdrawal, r_t the blended portfolio return that year, and f the annual fee. Withdrawals come out first, then the remainder grows.

B_{t+1} = (B_t - W_t) \cdot (1 + r_t - f)

Here r_t is the rebalanced blend of the two assets: if your stock allocation is s (as a fraction), then r_t = s \cdot r_t^{stock} + (1-s) \cdot r_t^{bond}, using that year's real historical stock and Treasury returns. The fee f is subtracted from the return, so a 0.2% fee on a 10% year leaves 9.8%.

The withdrawal itself depends on your inflation setting. With inflation adjustment on, the first year's withdrawal is W_1 = \text{rate} \times B_1, and each later year scales by that cohort's cumulative CPI:

W_t = W_1 \cdot \prod_{k=1}^{t-1} (1 + i_k)

where i_k is the inflation rate in year k. If adjustment is off, W_t = W_1 for every year: the dollar amount stays fixed and its purchasing power erodes. A cohort fails the first year the balance cannot cover the scheduled withdrawal, that is when B_t \lt W_t.

A worked example with the demo numbers

Reproducing the 4% rule across cohorts

The demo uses the defaults: start $1,000,000, withdrawal rate 4%, withdrawals rising with inflation, 30-year retirement, 75% stocks and 25% Treasuries, 0.2% fee. First-year withdrawal is $40,000. Take the 1966 cohort, one of the hardest US starts on record because of the stagflation that followed.

Year 1 balance is $1,000,000. Withdraw $40,000 at the start, leaving $960,000 invested.
1966 was a losing year for the blend. Suppose the blended return net of fees was about -5%. The balance ends the year near $912,000.
Inflation in 1966 ran near 3%, so year 2's withdrawal rises to about $41,200. You withdraw that from a smaller base.
The late 1960s and 1970s stacked weak real returns and high inflation. Each year the rising withdrawal ate a larger share of a shrinking, inflation-battered portfolio.
By the mid-1970s the compounding damage was severe. In Bengen's original 4% study the 1966 cohort was the marginal case that a 4% rule just barely survived over 30 years at a stock-heavy mix. Small changes in fees or allocation can tip it into failure.

Run the same rules starting in 1975 instead, and the story inverts. The late 1970s recovery and the long 1980s and 1990s bull market build such a cushion that the portfolio often ends larger, in real terms, than it started. Same rule, same 4%, opposite outcome, driven entirely by the starting year.

The 1966 cohort draws down steadily and finishes near zero. A 1975 start (not shown on the same line here) would climb well above its starting value. The difference is timing, not average return.

Reading the survival rate and the spread

The tool reports three things worth understanding.

Survival rate: The share of historical starting years whose portfolio never hit zero before the retirement length ended. A 100% survival rate means every cohort made it; 90% means one in ten failed. With about 66 possible 30-year cohorts in a 1928 to 2023 dataset, one failed cohort moves the rate by roughly 1.5 points.
Terminal spread: The worst, median and best ending balances, all in starting-year purchasing power. A wide spread is the signal of sequence risk: it means your outcome depends heavily on which year you happened to retire.
Failure timing: Which years failed and when they ran dry. Failures clustered around 1929, 1937, 1966 and 1973 tell you the risk is early bear markets, not average returns.

Do not read a 96% survival rate as "96% safe." It means 4% of past cohorts failed and the future could be worse than any of them. Look at the worst-case terminal value too: a plan that "survives" by ending with $3,000 real is not the same as one that ends with $800,000.

Explore how the withdrawal rate reshapes survival

The single most instructive parameter is the withdrawal rate. Small increases do not just lower balances; they push whole clusters of cohorts across the failure line at once.

Common mistakes

The first mistake is confusing average return with safe withdrawal rate. A portfolio can average 7% a year and still fail at a 5% withdrawal if the bad years come first. The tool exists precisely because the average hides the ordering.

The second is ignoring fees. A 0.2% fee looks trivial, but over 30 years of withdrawals it compounds against you every year on a base already shrinking. Bump the fee from 0.2% to 1.0% and marginal cohorts that survived will start failing. Try it and watch the survival rate drop.

The third is treating the fixed-withdrawal setting as equivalent to the inflation-adjusted one. A fixed $40,000 looks safer on paper because the dollar amount never rises, but at 3% inflation its purchasing power halves in about 23 years. The plan "survives" while quietly starving you.

The fourth is over-reading a 100% survival rate on 66 cohorts. Sixty-six overlapping histories from one unusually successful country is a small, correlated sample. It is evidence, not proof.

Related tools

This tool stress-tests a plan you already have. To build the plan first, the Retirement Savings Calculator estimates the balance you will reach and the income it supports, and the FIRE Calculator finds your target number and time to independence. If you want to see depletion under inflating withdrawals in a single deterministic path, use How Long Will My Money Last?. The Coast FIRE Calculator shows the savings that grow to retirement on their own. To compare against a guaranteed income stream, the Annuity Payout Calculator gives the monthly payout a lump sum can sustain, and the Annuity Value Calculator values a stream of payments. For a broader picture that varies career, house and family over 1,000 simulated lives, see the Financial Life Simulator.

Frequently asked questions

Is the 4% rule safe?

In the US historical record, 4% inflation-adjusted withdrawals from a stock-heavy portfolio survived every 30-year cohort in Bengen's study, including the 1966 start. That is where the rule comes from. It is not a law of nature. It rests on US returns that led the world last century, and a 30-year horizon. Retire for 40 years or hold higher fees and the safe rate drops.

Why does the order of returns matter if the average is the same?

Because withdrawals interact with the balance. A 20% loss in year one on a $1,000,000 portfolio, right after a $40,000 withdrawal, costs you $192,000. The same 20% loss in year 30 on a portfolio that has grown to $2,000,000 costs more in dollars but is followed by no more withdrawals to compound the damage. Early losses are locked in by every withdrawal that follows.

Should I hold more stocks to raise my survival rate?

Higher stock allocations raised historical survival rates up to a point because the growth outran inflation, but they also widen the spread of outcomes and deepen early crashes. The tool lets you compare mixes directly. This is educational output, not advice; a qualified adviser can weigh it against your own situation.

What does "in starting-year purchasing power" mean?

All balances and terminal values are shown in the dollars of your retirement's first year. A $1,000,000 terminal value in 1996 dollars for a 1966 retiree is stated after removing 30 years of inflation, so you can compare it fairly to the starting $1,000,000.

Why do failures cluster around 1929, 1966 and 1973?

Those starts combined an early market decline with weak or inflation-eroded returns in the following decade. 1929 hit the Depression; 1966 and 1973 hit stagflation, where high inflation raised the withdrawal while real returns stayed flat. The combination is the worst case for sequence risk.

Try it yourself in the tool