Trinity Study

The paper, “Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable,” appeared in the AAII Journal in February 1998. Its authors taught finance at Trinity University in San Antonio, Texas, which gave the study its nickname. They set out to answer a planning question, what withdrawal rate a retiree can sustain, by replaying every overlapping stretch of US market history rather than relying on average returns, which hide the damage a bad sequence of years can do. The design:

With withdrawals held flat in dollars, rates of 3% and 4% almost never ran out in any mix or period. The picture changed once withdrawals rose with inflation, which is how most people read the study today: success rates fell sharply at middle and high rates. Starting at 3% or 4% still worked in nearly every 30-year window for stock-heavy portfolios, 5% worked in most, 6% and 7% held up only over short payouts, and anything above 7% did poorly over every horizon.

The stock and bond mix mattered in both directions. Some bonds raised success at low and middle rates: with flat withdrawals, a 50/50 portfolio matched or beat more stock-heavy ones at 7% and below. But bonds alone lacked the growth to keep up with rising withdrawals; an all-bond portfolio lasted only 20% of 30-year windows at a 4% start. The authors concluded that most retirees would likely benefit from holding at least 50% in stocks.

The table below shows the inflation-adjusted, 30-year results most often cited. The 4% rule leans on the 95%–98% figures in its 4% column.

The paper is often boiled down to “4% is safe,” but its conclusions were more nuanced and, in places, pointed the other way. For stock-dominated portfolios, the authors called 3% and 4% withdrawal rates “exceedingly conservative,” likely to leave large estates to heirs. They treated a withdrawal rate as a planning figure rather than a contract, expecting mid-course corrections up or down as markets unfolded.

They also questioned the inflation assumption later readers adopted. Raising withdrawals with the CPI every year, they argued, trades present spending for future spending, which may not suit retirees with large fixed costs or those who spend less as they age. They noted that many economists thought the CPI overstated the rise in living costs, which would make the inflation-adjusted success rates too pessimistic.

Two other conclusions hold up well. Early retirees facing long payouts should plan on lower rates. And because half of people outlive their life expectancy, it is wise to plan for a few extra years, the concern known as longevity risk.

A success rate in the Trinity tables is a count of historical windows, not a probability. The 98% for a 4% start with 75% stocks means 40 of the 41 overlapping 30-year windows between 1926 and 1995 ended with money left. Those windows share most of their years, so a handful of hard stretches, such as the Depression and the high inflation of the 1970s, decide many results at once. The method is a form of historical backtesting, with the strengths and blind spots that implies. Several other limits matter when applying the numbers today:

Bengen’s 1994 paper and the Trinity study are often cited together, and both land near 4% for 30 years, but they measured different things. Bengen used intermediate-term Treasuries for bonds and reported the worst case: the highest starting rate that lasted a minimum number of years from every start. Trinity used long-term corporate bonds and reported the share of periods that succeeded, which lets readers choose their own tolerance for failure. That difference in framing is why a safe withdrawal rate can be quoted either as a worst case or as a percentage.

In April 2011 the same authors published an update in the Journal of Financial Planning, using monthly data from January 1926 through December 2009. With inflation adjustments, a 5% start from a 75% stock portfolio succeeded in 82% of 30-year periods. They suggested that retirees who raise withdrawals with inflation plan on starting rates of 4% to 5% from portfolios at least half in stocks.