Trinity study
The Trinity study, formally known as "Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable," is a seminal 1998 research paper in personal finance authored by Philip L. Cooley, Carl M. Hubbard, and Daniel T. Walz, all professors of finance at Trinity University in San Antonio, Texas.[1] Published in the February 1998 issue of the AAII Journal, the study uses historical U.S. market data from 1926 to 1995 to evaluate the sustainability of various withdrawal rates from retirement portfolios composed of large-cap stocks (S&P 500) and long-term corporate bonds over retirement periods of 15, 20, 25, and 30 years.[1] It defines portfolio "success" as maintaining a positive balance at the end of the period after monthly withdrawals, with or without annual inflation adjustments, and examines asset allocations ranging from 100% stocks to 100% bonds in 25% increments.[1] The methodology simulates rolling historical periods using annual data from Ibbotson Associates to approximate monthly withdrawals at the beginning of each month, applying constant initial withdrawal rates from 3% to 12% of the starting portfolio value, with annual adjustments for inflation using the Consumer Price Index where applicable, assuming no taxes or fees for simplicity.[1] This approach allows calculation of "success rates"—the percentage of historical 30-year periods (for example) in which the portfolio does not deplete—across different allocations, providing probabilistic guidance for retirees on safe spending without relying on future market predictions.[1] Key findings highlight the importance of equity exposure for longevity: for a 30-year horizon without inflation adjustments, a 4% withdrawal rate achieved near-100% success across all stock-bond mixes from 1926–1995, while a 7% rate succeeded in 100% of cases for a 50/50 allocation.[1] With inflation adjustments, success rates drop significantly, but a 4% rate still yielded 95% success for 100% stocks and 98% for a 75/25 stock-bond mix, underscoring the need for at least 50% equities to support inflation-protected withdrawals over three decades.[1] Shorter horizons (e.g., 15 years) tolerated higher rates, with 7% succeeding 100% of the time even in bond-heavy portfolios, but the study emphasized conservatism for longer retirements.[1] The Trinity study has profoundly influenced retirement planning, popularizing the "4% rule"—withdrawing 4% of the initial portfolio annually, adjusted for inflation—as a benchmark for sustainable spending, though it builds on earlier work like William Bengen's 1994 analysis.[2] Its results have been updated multiple times to incorporate post-1995 data, such as a 2011 revision showing 4% success rates holding at 95–100% through 2009 for 30-year periods with 50–75% stocks.[3] Recent simulations as of 2024-2025, incorporating data up to 2024, continue to validate high success rates for the 4% rule across various allocations.[4] Despite criticisms for assuming static allocations and historical patterns, it remains a foundational reference in financial independence and retirement literature, informing tools like FIRE calculators.[2]Background and Context
Origins and Authors
The Trinity study was authored by Philip L. Cooley, Carl M. Hubbard, and Daniel T. Walz, all professors of finance in the Department of Business Administration at Trinity University in San Antonio, Texas.[1] Their collaborative research emphasized academic rigor in personal finance, leveraging the university's resources to analyze retirement planning challenges empirically.[1] The study was published in 1998 under the title "Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable" in the AAII Journal, volume 20, issue 2 (February), pages 16–21.[1] This publication appeared through the American Association of Individual Investors (AAII), a nonprofit organization dedicated to investor education, providing a platform for accessible yet scholarly insights into portfolio management.[5] The primary motivation for the study stemmed from the growing reliance on defined-contribution retirement plans, such as 401(k)s, which shifted responsibility for savings sustainability onto individuals without clear empirical guidelines.[1] At the time, financial advice on withdrawal rates varied widely—from conservative dividend yields around 3% to more aggressive strategies up to 7% involving principal invasion—often based on anecdotal or rule-of-thumb approaches lacking rigorous historical validation.[1] The authors sought to address retirees' dilemmas in balancing withdrawal needs against the risk of portfolio depletion, while considering factors like personal risk tolerance and long-term goals such as estate planning, thereby providing a data-driven foundation for informed decision-making.[1] This work built briefly on prior analysis by financial planner William Bengen, who in 1994 identified a 4% safe withdrawal rate through historical simulations.[6]Relation to Prior Research
The Trinity study built directly upon foundational work in retirement withdrawal research, particularly William P. Bengen's 1994 article "Determining Withdrawal Rates Using Historical Data," published in the Journal of Financial Planning. Bengen analyzed historical market data from 1926 to 1992 to identify sustainable withdrawal rates, proposing a 4% initial withdrawal rate—adjusted annually for inflation—as safe for a 30-year retirement horizon, specifically for portfolios allocated 50% to 75% in stocks with the remainder in bonds. This approach emphasized the "safemax" withdrawal rate, defined as the highest rate that would have preserved a portfolio through the worst historical scenarios without depletion.[6] Broader influences from early 1990s financial literature also shaped the study's context, including growing discussions on portfolio depletion risks amid volatile markets and longevity concerns. Key among these were analyses by Ibbotson Associates, whose yearbooks provided standardized long-term return data for stocks and bonds, enabling rigorous backtesting of retirement scenarios and highlighting the interplay between asset returns, inflation, and spending sustainability.[1] These resources underscored the limitations of relying solely on average historical returns, as sequence-of-returns risk could accelerate portfolio exhaustion during early retirement downturns.[7] The 1998 Trinity study advanced Bengen's framework by expanding the scope of tested variables and providing probabilistic outcomes rather than singular safe rates. It incorporated more recent data through 1995 from Ibbotson Associates, examined a wider range of asset allocations from 0% to 100% stocks in 25% increments, and evaluated withdrawal periods up to 30 years with inflation adjustments, thereby confirming the 4% rate's viability across diverse conditions while quantifying success probabilities.[1][8] This systematic approach addressed prior gaps, such as the absence of comprehensive tables detailing success rates for varying withdrawal scenarios and allocations, offering financial planners a more nuanced tool for assessing retirement sustainability.[6]Methodology
Historical Data and Backtesting Approach
The Trinity study relied on historical annual total returns data sourced from the Ibbotson Associates' Stocks, Bonds, Bills, and Inflation: 1996 Yearbook.[1] This dataset provided comprehensive records of U.S. stock market performance, represented by the Standard & Poor's 500 index, and long-term high-grade corporate bonds, spanning from 1926 to 1995—a total of 70 years.[1] The analysis focused on overlapping rolling periods within this timeframe, such as 41 sequences for 30-year horizons (from 1926–1955 through 1966–1995) and shorter durations of 15, 20, and 25 years, to simulate various retirement lengths.[1] The backtesting employed a deterministic historical simulation framework, initiating each withdrawal sequence at the start of every calendar year in the dataset.[1] Portfolio values were calculated annually by first subtracting the inflation-adjusted withdrawal amount from the beginning balance, then applying the year's total return to the remaining balance.[1] This retrospective method examined actual past market sequences without incorporating Monte Carlo simulations or forward-looking projections, ensuring the evaluation was grounded solely in observed historical outcomes.[1] A portfolio was deemed successful if its ending balance remained positive after the full specified period (15, 20, 25, or 30 years); otherwise, it was classified as a failure if depleted prior to the end.[1] Withdrawals were adjusted each year for inflation using the Consumer Price Index for All Urban Consumers (CPI-U), increasing the prior year's amount by the annual CPI-U change to maintain purchasing power.[1] This approach extended the methodology pioneered by William Bengen in his 1994 analysis, which similarly drew on Ibbotson data for safe withdrawal rate determinations.[1][9]Portfolio Allocations and Withdrawal Parameters
The Trinity study examined fixed portfolio allocations consisting of large-cap U.S. stocks, represented by the S&P 500 index, and long-term high-grade corporate bonds.[1] The specific mixes tested were 0%, 25%, 50%, 75%, and 100% in stocks, with the remainder allocated to bonds; these allocations were maintained through the simulation period using historical annual returns, implying annual rebalancing to preserve the target proportions.[1] Withdrawal rates were evaluated from 3% to 12% of the initial portfolio value, in 1% increments, with the starting portfolio assumed to be $1 million for illustrative purposes to scale the dollar amounts.[1] These initial withdrawals were then held constant in nominal terms for the non-inflation-adjusted scenarios or adjusted annually for inflation in the other variants.[1] The study assessed retirement time horizons of 15, 20, 25, and 30 years to reflect varying lengths of post-retirement periods.[1] For each horizon, simulations considered both level withdrawals, which remained fixed in dollar terms without adjustment for changes in purchasing power, and inflation-adjusted withdrawals to simulate constant real spending needs.[1] Inflation adjustments were made using the Consumer Price Index (CPI), increasing the withdrawal amount each year by the observed inflation rate or decreasing it in cases of deflation.[1] Withdrawals were modeled as occurring annually at the beginning of each year, with the withdrawal amount subtracted from the beginning balance before the portfolio earned its historical return for the period to determine the ending balance.[1] The analysis incorporated several simplifying assumptions, including no taxes, transaction costs, or investment fees, and excluded any additional contributions to the portfolio during the retirement phase; it also presumed constant spending requirements without behavioral modifications by the retiree.[1]Original Findings
Success Rates Across Withdrawal Rates
The Trinity study evaluated portfolio success rates for inflation-adjusted withdrawals over a 30-year retirement horizon using historical U.S. market data from 1926 to 1995, defining success as the percentage of historical 30-year rolling periods in which the portfolio did not deplete to zero before the end of the period.[1] For a balanced 50/50 stock-bond allocation, success rates were 100% at a 3% initial withdrawal rate, 95% at 4%, 76% at 5%, and 51% at 6%, with rates falling to 17% or lower for 7% and above.[1] In a more stock-heavy 75/25 stock-bond mix, these figures improved slightly to 100% at 3%, 98% at 4%, 83% at 5%, 68% at 6%, and 49% at 7%.[1]| Withdrawal Rate | 50/50 Success Rate (30 Years) | 75/25 Success Rate (30 Years) |
|---|---|---|
| 3% | 100% | 100% |
| 4% | 95% | 98% |
| 5% | 76% | 83% |
| 6% | 51% | 68% |
| 7% | 17% | 49% |