Bengen, the Trinity study, and the birth of the safe withdrawal rate

Before 1994, one question got the same wrong answer with impressive consistency: how much can I take out of my portfolio every year? "The average return, obviously." Stocks returned 10% historically, so withdraw 8%, said professional advisers with a straight face.

William Bengen, and then the Trinity study, showed why that answer ruins people, and invented the method that still organizes the whole field: replay history. This page covers what those founding papers actually established, how their method works, what was brilliant about it, and what has aged.

It is a piece of intellectual history as much as a technical one: the concepts introduced here (vintage, SAFEMAX, success rate) run through the rest of the book.

Why the "average return" answer ruins people§

The intuition "stocks make 10%, so I can withdraw 8%" makes two mistakes, and they compound.

The first is confusing the arithmetic average with the growth that actually compounds. Volatility makes a portfolio grow more slowly than its annual average (Arithmetic mean, geometric mean, and volatility drag), and inflation takes another 2 to 3 points off. The engine of a balanced portfolio is a geometric real return of 3 to 5%, not 10.

The second is deadlier. A retiree who withdraws a fixed amount sells more shares when prices are low. Two sequences with the same average then produce opposite fortunes, depending on whether the bad years land early or late (Sequence of returns risk: the retiree's real enemy). The average tells you almost nothing; the order tells you almost everything.

In the early 1990s Bengen, an MIT-trained engineer turned financial adviser, kept meeting clients who had been sold the 8% number. Rather than answer one opinion with another, he did what nobody had published. He tested it.

Bengen 1994: the vintage method§

The idea is beautifully simple. Take the annual US data since 1926: S&P stocks, intermediate government bonds, inflation (Bengen used the Ibbotson series). Invent a retiree who leaves on January 1, 1926 with a 50/50 portfolio and an initial withdrawal of, say, 4% indexed to inflation. Run the years one at a time: return, withdrawal, rebalance. Write down how long the portfolio lasts. Start over for someone leaving in 1927, then 1928, and so on: each start year is a vintage (a cohort, ERN's "retirement cohort"). Then run the whole thing again at other withdrawal rates.

The result fits in one famous chart: how long the portfolio lasted, vintage by vintage, at each rate. At 3%, every vintage clears 50 years. At 4%, the worst vintage lasts 33 years, and all of them last at least 30. At 5%, the late-1960s vintages run dry in about 20 years. At 6%, dozens of vintages fail inside 20 years.

Bengen would later name SAFEMAX the highest rate that survives every vintage over the chosen horizon: about 4.15% over 30 years at 50/50. He also picked out the three worst moments to leave: 1929 (crash and deflation), 1937, and above all 1966, which was not the worst crash but the worst combination, fifteen years of flat real markets while inflation kept inflating the withdrawals. The lesson matters more than the number: what kills a retiree is not the spectacular crash, it is long, grinding real erosion (Inflation and the withdrawal rate: the exact link).

His later papers (1996 to 2006) filled in the frame. The best allocation holds 50 to 75% stocks, because going lower lowers the safe rate: bonds alone do not stand up to inflation. Adding small caps lifts SAFEMAX, to 4.3% in 1997 with 30% of the equity sleeve in small caps, then to 4.5% in 2006 with a wider set of assets. His 2025 book goes to 4.7% with five equity styles, a lift that ERN's Part 65 credits to the pre-1981 small-cap premium rather than to diversification (Factors (Fama-French, value, momentum) in the withdrawal phase). Horizon matters too: about 4.15% over 30 years, but only about 3.5% over a very long one.

Trinity 1998: from a floor to a probability§

Four years later, three finance professors at Trinity University in Texas, Philip Cooley, Carl Hubbard and Daniel Walz, published "Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable". Same replay method, one conceptual shift: instead of the floor rate that survives everything (Bengen's SAFEMAX), they published a grid of success rates. For each combination of withdrawal rate, allocation and horizon, it gives the share of historical windows in which the portfolio ended with money left.

A slice of the grid (figures from the 2011 update, inflation-indexed withdrawals, 1926 to 2009 data):

Initial rate100% stocks, 30 years75/25, 30 years50/50, 30 years25/75, 30 years
3%100%100%100%100%
4%98%100%96%80%
5%80%82%67%31%
6%62%60%51%22%

Three lasting lessons come out of that grid.

THE TRINITY CLIFFBetween four and five percent, the floor gives wayShare of thirty-year retirements that made it, withdrawal rate by withdrawal rate0%25%50%75%100%3%4%5%6%7%8%initial withdrawal rate, indexed to inflation thereafter →the cliff100% stocks75 / 2550 / 5025 / 75past 4.50%, all equity moves backahead of the 75/25One more point of withdrawal, from 4 to 5%, costs the 75/25 twenty points of success; the point before it cost two.Recomputed in house on the Jorda-Schularick-Taylor record for the United States (annual real returns, stocks and government bonds,1872-2020), giving 120 rolling thirty-year windows. Not one number published by Trinity is reused here:the original study covers 1926-1995 and is partly nominal, while this record starts half a century earlier and stays real.A fixed withdrawal taken at the start of each year, a share of the starting capital, held in purchasing power, both legs rebalanced yearly.The deeper sample hardens the verdict: at 4%, the 75/25 fails twice in a hundred here and never in Trinity, and the 25/75fails one time in four where the text says one in five. The asymmetry is intact: too few stocks stays far more dangerous than too many.
The Trinity grid rebuilt in house, on a century and a half of American data rather than its seventy years: the share of thirty-year retirements that made it, withdrawal rate by withdrawal rate. The drop between 4 and 5% is the cliff; the spread of the curves in the lower half is the allocation asymmetry; and past 4.50%, all equity moves back ahead of the 75/25, which is the same lesson read where it surprises.

The cliff. Between 4 and 5%, success collapses. The subject is nonlinear, and that is why "just a little more" costs so much.

Allocation cuts one way. Holding too few stocks is far more dangerous than holding too many: the 25/75 fails one time in five, where the 75/25 never failed at all.

The success rate itself. Trinity is where failure probability became the common language of the field, the one every modern simulator speaks (Failure probability: reading it, choosing it, and not letting it run you).

What the founders had not seen yet§

Reading Bengen and Trinity today means admiring the method and measuring how far the field has come since. Their blind spots, each covered elsewhere in this book, map out the program of modern research.

None of this refutes them. The vintage method still stands; what widened is its inputs and its frame. Bengen has kept updating his own number, upward for the classic 65-year-old American retiree holding a more diversified portfolio, while repeating that it depends on the frame. So when you hear that "the 4% rule is dead" or that "4% is far too timid", the question to ask is the same either way: in what frame, over what horizon, with what margins?

Redo Bengen yourself§

One of the method's great teaching virtues is that anyone can redo it. The classic historical simulators, FICalc and cFIREsim first among them, replay the vintage logic on the long US indexes, one withdrawal rate at a time. A simulator that reads a real portfolio replays it on the history of your own holdings and hands down a verdict start date by start date. Either exercise is worth the hour. Watching your plan go through 1966 or 2000 makes sequence risk concrete in a way no probability does.

The essentials§

Going further§