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Trinity study
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In finance, investment advising, and retirement planning, the Trinity study is an informal name used to refer to an influential 1998 paper by three professors of finance at Trinity University in the US.[1] It is one of a category of studies that attempt to determine "safe withdrawal rates" from retirement portfolios that contain stocks and thus grow (or shrink) irregularly over time.[2]
In the original study success was primarily judged by whether portfolio lasted for the desired payout period, i.e., the investor did not run out of money during their retirement years before dying; capital preservation was not a primary goal, but the "terminal value" of portfolios was considered for those investors who may wish to leave bequests.
Study and conclusions
[edit]"The 4% Rule" refers to one of the scenarios examined by the authors. The context is one of annual withdrawals from a retirement portfolio containing a mix of stocks and bonds. The 4% refers to the portion of the portfolio withdrawn during the first year; it is assumed that the portion withdrawn in subsequent years will increase with the consumer price index (CPI) to keep pace with the cost of living. The withdrawals may exceed the income earned by the portfolio, and the total value of the portfolio may well shrink during periods when the stock market performs poorly. It is assumed that the portfolio needs to last thirty years. The withdrawal regime is deemed to have failed if the portfolio is exhausted in less than thirty years and to have succeeded if there are unspent assets at the end of the period.
The authors backtested a number of stock/bond mixes and withdrawal rates against market data compiled by Ibbotson Associates covering the period from 1925 to 1995. They examined payout periods from 15 to 30 years, and withdrawals that stayed level or increased with inflation. For level payouts, they stated that "If history is any guide for the future, then withdrawal rates of 3% and 4% are extremely unlikely to exhaust any portfolio of stocks and bonds during any of the payout periods shown in Table 1. In those cases, portfolio success seems close to being assured." For payouts increasing to keep pace with inflation, they stated that "withdrawal rates of 3% to 4% continue to produce high portfolio success rates for stock-dominated portfolios."
The authors make this qualification:
The word planning is emphasized because of the great uncertainties in the stock and bond markets. Mid-course corrections likely will be required, with the actual dollar amounts withdrawn adjusted downward or upward relative to the plan. The investor needs to keep in mind that selection of a withdrawal rate is not a matter of contract but rather a matter of planning.
Attempts have been made to study the effects of asset valuations on safe withdrawal rates and update the 4% rule and Trinity Study for longer retirements.[3]
Other studies, impact and criticisms
[edit]Other authors have made similar studies using backtested and simulated market data, and other withdrawal systems and strategies.
The Trinity study and others of its kind have been sharply criticized, e.g., by Scott et al. (2008),[2] not on their data or conclusions, but on what they see as an irrational and economically inefficient withdrawal strategy: "This rule and its variants finance a constant, non-volatile spending plan using a risky, volatile investment strategy. As a result, retirees accumulate unspent surpluses when markets outperform and face spending shortfalls when markets underperform."
Laurence Kotlikoff, advocate of the consumption smoothing theory of retirement planning, is even less kind to the 4% rule, saying that it "has no connection to economics.... economic theory says you need to adjust your spending based on the portfolio of assets you're holding. If you invest aggressively, you need to spend defensively. Notice that the 4 percent rule has no connection to the other rule—to target 85 percent of your preretirement income. The whole thing is made up out of the blue."[4]
The original Trinity study was based on data through 1995. An update of their results using data through 2009 is provided in Pfau (2010).[5] Shortly afterwards, the original authors of the Trinity Study published an updated study, also using data through 2009.[6]
The procedure for determining a safe withdrawal rate from a retirement portfolio in these studies considers only the uncertainty arising from the future returns to be earned on the investment. Another major uncertainty is the amount of spending that will be required each period to provide a given standard of living. For instance, there is a small chance each period of an emergency arising that will require a large extra withdrawal that may be comparable in size to the loss from a financial bear market. An example is major repairs to a home not covered by insurance caused by water incursion or an earthquake. The effects of such possible emergencies in addition to uncertain investment returns are considered in Pye (2010).[7] Under conditions where a 4 percent withdrawal might otherwise be reasonably sustainable, reasonable assumptions about the chances for an emergency each year and its cost reduce the withdrawal from 4 to about 3 percent.
This latter analysis also differs by using the Retrenchment Rule to determine the value of the withdrawal each period. This rule is discussed in Pye (2010) and also Pye (2012).[8] When using the Retrenchment Rule the default withdrawal each period is the prior withdrawal adjusted for inflation as in the earlier studies. There are conditions, however, when this default withdrawal is not applicable. In particular, the initial withdrawal is related to the prior standard of living of the retiree, not just the withdrawal that is reasonably sustainable. Also, the withdrawal for a period is reduced when a test indicates that such retrenchment is necessary. This occurs when the risk of running out of funds before the end of a plan has become too high given the size of the then current withdrawal and the funds that remain.
See also
[edit]References
[edit]- ^ Cooley, Philip L.; Hubbard, Carl M.; Walz, Daniel T. (1998). "Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable" (PDF). AAII Journal. 10 (3): 16–21.
- ^ a b Scott, Jason; Sharpe, William; Watson, John (11 April 2008). "The 4% Rule—At What Price?" (PDF). Stanford University. Retrieved 29 May 2018.
- ^ Jeske, Karsten (14 August 2019). "Safe Withdrawal Rate Series". Early Retirement Now. Retrieved 2020-08-26.
- ^ Fonda, Daren (2008), "The Savings Sweet Spot," SmartMoney, April, 2008, pp. 62-3 (interview with Ben Stein and Laurence Kotlikoff)
- ^ Pfau, Wade D (2010-10-29). "Trinity Study, Retirement Withdrawal Rates and the Chance for Success, Updated Through 2009". Archived from the original on 2011-07-08.
- ^ Cooley, Philip L.; Hubbard, Carl M.; Walz, Daniel T. (2011). "Portfolio Success Rates: Where to Draw the Line".
- ^ Pye, Gordon B. (November 2010). "The Effect of Emergencies on Retirement Savings and Withdrawals". Journal of Financial Planning. Vol. 23, no. 11. pp. 57–62.
- ^ Pye, Gordon B. 2012. "Retrenchment Rule"
External links
[edit]- Bengen, William P. (October 1994). "Determining Withdrawal Rates Using Historical Data" (PDF). Journal of Financial Planning: 14–24.
Trinity study
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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% |
Effects of Asset Allocation on Outcomes
In the original Trinity study, asset allocation between stocks and bonds significantly influenced portfolio success rates for sustaining inflation-adjusted withdrawals over 30-year retirement periods. Using historical data from 1926 to 1995, the authors analyzed portfolios ranging from 0% to 100% in stocks (with the remainder in bonds), applying a 4% initial withdrawal rate adjusted annually for inflation. Success was defined as the portfolio not being depleted within the 30-year horizon across rolling historical periods.[1] Stock-heavy portfolios, with 75% to 100% allocated to stocks, demonstrated the highest success rates, achieving 95% to 98% for the 4% withdrawal rate over 30 years. This superior performance stemmed from the long-term growth of equities, which historically outpaced inflation and withdrawals, allowing portfolios to recover from downturns despite higher volatility. For instance, a 100% stock portfolio succeeded in 95% of historical 30-year periods, while a 75% stock/25% bond mix reached 98%.[1] Balanced allocations around 50% stocks and 50% bonds achieved a 95% success rate at the 4% withdrawal rate for 30 years, balancing the growth potential of stocks with the stability of bonds and reducing the impact of market volatility while capturing sufficient returns to sustain withdrawals.[1] In contrast, bond-heavy portfolios with 0% to 25% stocks exhibited markedly lower success rates, ranging from 20% for 100% bonds to 71% for 25% stocks/75% bonds at the 4% rate over 30 years. Fixed-income assets struggled to keep pace with inflation over extended periods, leading to portfolio erosion even in favorable environments, as bond returns were insufficient to offset ongoing withdrawals.[1] The analysis revealed that higher equity allocations amplified short-term volatility and sequence-of-returns risk—where early market downturns could deplete principal—but ultimately enhanced long-term success probabilities due to equities' historical outperformance. The study did not incorporate diversification beyond stocks and bonds, emphasizing the dominant role of U.S. equities in driving sustainable outcomes across tested scenarios.[1]The 4% Rule
Core Principles and Calculation
The 4% rule, as derived from the Trinity study, stipulates that retirees can safely withdraw an initial amount equal to 4% of their starting portfolio balance in the first year of retirement, with subsequent annual withdrawals adjusted upward for inflation to preserve purchasing power. The Trinity study identifies withdrawal rates of 3-4% as conservative safe rates for sustaining a portfolio over 30 years, based on historical backtesting without assuming specific future growth rates.[1] This approach ensures a constant real spending level over the retirement period, rather than accommodating variable or fluctuating needs based on market performance.[1] The calculation begins with the initial withdrawal, defined as:
where is the initial portfolio value at the start of retirement. For each subsequent year , the withdrawal is adjusted for the prior year's inflation rate using the formula:
The inflation adjustment typically employs the Consumer Price Index (CPI) to reflect changes in the cost of living.[1] A portfolio is considered successful under this rule if its balance remains positive after 30 years of withdrawals.[1]
To estimate the required retirement corpus using the safe withdrawal rate, first determine the current annual expenses and adjust them for anticipated future inflation and changes in retirement lifestyle to arrive at the expected future annual expenses. The target corpus can then be calculated as the future annual expenses divided by the safe withdrawal rate (e.g., divided by 0.04 for a 4% SWR). It is important to add a buffer for unexpected costs, such as healthcare expenses.[10][11]
In practice, the 4% rule applies to 30-year retirement horizons and performs best with diversified portfolios featuring 50-75% allocation to U.S. equities, complemented by long-term high-grade corporate bonds.[1] It assumes a balanced mix of large-cap stocks (e.g., S&P 500) and fixed-income securities to mitigate volatility while capturing long-term growth.[1]
The rule's foundation rests on historical backtesting from 1926 to 1995, which demonstrated a 95% success rate across the worst-case rolling 30-year sequences for portfolios with substantial stock exposure, establishing it as a benchmark for 95% confidence in portfolio longevity.[1]