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Updated Trinity Study Simulation–Beyond 2020

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Today we’re going to take a look at the well-known Trinity Study. For those who aren’t familiar, don’t worry. I’m going to start off by explaining what the Trinity Study is, how it was done, and how to use its results. It’s all about saving for retirement and planning for retirement.

But then I’m going to take a look at a few possible visions of the future. We’re going to create an updated Trinity Study that we can use as part of our retirement planning.

I’m also going to introduce an interesting idea. Maybe you’ve heard of it before. It’s called consumption smoothing. Bears do it, trees do it, and if retirees do it, it can improve their likelihood of retirement success.

The What: Describing the Original Trinity Study

If you’re already intimately familiar with the Trinity Study, feel free to skip down to the Wade Pfau section. Right now, we’ll introduce the original Trinity Study.

The Trinity Study was a retirement planning study published in February 1998 issue of AAII by three professors at Trinity College, in Texas. They based their work off of William Bengen’s SAFEMAX study (1994).

The goal of the study was to determine a safe withdrawal rate (SWR) for retirement accounts. A withdrawal rate is the “salary” that you pay yourself during retirement, by withdrawing money from your retirement nest egg—investment options like mutual funds, taxable accounts, tax deferred 401k, tax advantaged Roth IRA, annuities, defined benefit pensions etc. (FYI—social security funds are not part of the Trinity Study).

So, a safe withdrawal rate is a withdrawal rate that allows a retiree to not run out of money by the time they die.

SWR can also be thought of as a portfolio success rate. What’s a sustainable withdrawal rate and asset allocation that leads to retirement success?

Running out of money would be bad—not safe for one’s retirement plans. The Trinity Study aimed to provide a reliable SWR such that retirees would know how at-risk they were to run out of funds.

People in the FIRE movement frequently reference the Trinity Study when planning early retirement withdrawals. If you Google “4% Rule” or “retire with 25x your annual spending,” you’ll see what I mean.

Many FIREees directly tie their Savings Rates to the Trinity Study so they can figure out when it’s safe for them to retire.

Study Assumptions, Method, and Outcome

Asset Allocations

The study assumed that most retirees portfolios can be lumped into a few buckets. Example: a portfolio with a 75% stock allocation and 25% bond allocation. Other stock/bond allocations that were used are 100/0, 50/50, 25/75, and 0/100. This is fair way to tweak this variable. Most retirees’ portfolios contain a mix of stocks and bonds.

The study used long-term high-grade corporate bonds (both in the Trinity Study and Bengen’s original research). Corporate bond returns are typically higher but riskier than government bonds (note: as of June 2020, gov’t bond returns are about as low as possible).

The stocks were assumed to be a diverse mix of stocks from developed market countries i.e. a portfolio with returns using historical data. For example, a Vanguard or Fidelity total market index fund.

Retirement duration

The study also looked at various lengths of retirement. Some people will retire at 50 and live until 90–a 40-year retirement. Other people retire at 65 and live until 80–a 15-year retirement.

A shorter retirement might be successful even with the highest withdrawal rate. A long retirement, on the other hand, would likely have to use one of the lowest withdrawal rates.

Different Withdrawal Rates

The study authors varied their withdrawal rate variable from 3% to 10%.

A 3% withdrawal rate is likely to be more successful—you’re spending less money. But it also leads to a more meager retirement lifestyle. An 8% withdrawal rate is more opulent, but is more likely to fail.

An unfortunate side effect of spending more money? That you’ll run out.

The question, then, is “How do we find the highest withdrawal rate possible while not running out of money?”

Heart of the Trinity Study

The real heart of the study–the question being asked and answered–is:

“If a person retired in Year A, stayed retired for B years, and withdrew C% of their portfolio each year, will they run out of money using a D ratio portfolio of stocks and bonds?”

The researchers asked this important question for every single combination of Year A (from 1926 through 1995), B years of retirement (from 15 to 40, by multiples of 5), C% of SWR (from 3% up go 10%), and D ratio (mentioned above…from all stocks to all bonds).

Ostensibly, a retirement that is too long, or suffers through a bad market, or that withdraws too much money each year…that retirement could run out of money.

The withdrawal rates are test using historical data from 1926 to 1995 to affect the simulated portfolios. A 30-year retirement portfolio was tested for all 30-year rolling periods.

The creation of the 4% Rule

While there are many interesting outcomes from the Trinity Study, the main result has been nicknamed the “4% Rule.” The highlights are the 4% Rule are:

  • If you use a 4% as Year 1 initial withdrawal, and then slowly increase each year to adjust for inflation…
  • In a 50/50 stock/bond portfolio…
  • For a 30-year retirement…
  • Then you would have been “safe” for 95% of starting years in the study

So this would suggest that a retiree with $1 million dollars could reasonably expect to withdraw $40,000 (which is 4% of $1 million) in their first year and afterwards increase for inflation each year. This would have allowed that retiree to successfully live a 30-year retirement without running out of money in 95% of the rolling 30-year periods that the study looked at.

The Wade Pfau Updated Trinity Study

Wade Pfau is a professor and PhD in Financial Planning. He’s written excellent pieces on the Trinity Study, including an updated Trinity Study using data through the year 2014.

Along with the extended data set, Pfau also changed the type of bond that the study assumed. The original study used corporate bonds, but Pfau thought it was wiser to look at intermediate-term government bonds.

With this change, Pfau’s outcomes actually look more optimistic than the original study. Pfau found a 100% chance of success (instead of 95%) using the same assumptions that created the original 4% Rule. In Pfau’s update, every 30-year retiree still had money using a 50/50 stock/bond portfolio and withdrawing 4% (plus inflation) of their retirement savings each year. This is good news!

But Pfau also asks and examines a crucial question in his updated Trinity Study: will the future look like the past?

Will the future look like the past?

To call this a “million dollar question” would be an understatement.

The Trinity Studies are based on historical market data. That data was taken from a period of wild growth. In the past 100 years, our society has taken unprecedented leaps in manufacturing, technology, and information. Is it wise to assume that the future will look like that past? Will growth continue to be as positive?

The contrarian might point out that the Trinity time periods also included the Great Depression, Stagflation in the 70’s, the Dot Com bubble and the 2008 subprime crisis. So, there are some bad times in there too.

Does it make sense to analyze a scenario where everything is wonderful?

What will our retirements look like if the entire world achieves peace and harmony, enough wealth for daily lattes and avocado toast, and nobody wears clothes? Is that a question worth answering? And why are all utopias also nudist colonies?

No! That’s not a question worth examining! We don’t need to be worried about utopia.

Have you ever heard the saying, “Hope for the best, but plan for the worst?” That’s what we want to do here. We want to plan on things being tough.

We might have to choose lower withdrawal rates. If we’re right, we’ll be very thankful we planned for it.

But if we’re wrong and things are great…well, great! If I’m wrong, I’ll accept “things are great” as a consolation prize.

Just be careful–I don’t want some hairy dude too close to my avocado toast.

The Best Interest Updated Trinity Study Simulation

Riffing off of Wade Pfau, I’m unofficially addending to the Trinity Study to look at possible bleak futures.


To create my version of the updated Trinity Study, I ran Monte Carlo simulations.

I created an alternate reality (no nudists), used randomness to determine the nature and volatility of that reality, and then figured out how a retiree would fare in that reality. Then I repeated that random reality a few million times for different market returns, SWRs, etc.

Some assumptions in my analysis:

  • I looked at average annual market returns varying from 1% to 4.5%, calculated on a monthly basis. People often cite the S&P 500 having 9%-10% returns. A balanced, lower-risk portfolio might have 6%-7% returns. But remember, we’re looking at worse markets than the past. So it’s 1%to 4.5% for us.
  • Assumed that monthly portfolio returns have a standard deviation of 3%, due to mix of stocks and bonds. This is based off of historical variations from Burton Malkiel’s data sets.
  • Used a Laplace distribution to determine the “randomness” in the simulation.
  • Only looked at 30-year retirements, to keep in line with the oft-quoted result from the original Trinity Study (the 4 percent rule is based on 30-year retirement).
  • Chose various withdrawal rates using the original study as a guide
  • Assumed our investor only withdraws their money once per year. E.g. they withdraw $40K on January 1st, and live off that $40K until the following January 1st, etc.
  • Assumed an annual 3% inflation to calculate the inflation-adjusted withdrawal rate
  • (For second analysis only) Assumed a 1.5% return on cash (e.g. a high yield savings account).

Keep in mind, this took me a few hours to set up and get results. The actual Trinity authors are career academics and ran their studies like professionals. I admit than my assumptions and methodology are not as rigorous as theirs. But I think we can glean some insightful information nonetheless.

On pessimism:

A lot of people feel that my analysis is so pessimistic that it loses all integrity, that it’s worse than the worst-case scenario.

So, I want to emphasize: I’m not predicting a terrible, bleak future. I’m only asking What if? there’s a terrible, bleak future.

How might someone conservatively alter their retirement goals? How might someone’s current savings plan and savings rate be affected? Is it worth re-checking the retirement calculator?

I, like you, hope the future is as good or better than the past. So I don’t want anyone to start stockpiling precious metals because of my fictional simulation.

In the post-coronavirus investing world of zero percent interest rates, is it so crazy to think that the next few decades will have less-than-ideal returns?


Below is the summary table of results from my random simulations.

The SWR varies by column, and the average annual return varies by row.

The actual entries in the table are the percentage of simulations that created a successful retirement based on a particular combination of SWR and market return.

What sticks out? Where do we start?

To me, I immediately take a look at the 4% SWR column, because that’s what the Trinity Study has convinced us is safe.

If the market stagnates long-term, then the 4% Rule is in deep trouble.

The 4% withdrawal rate column is ravaged with low success rates. There’s nothing even close to the previous ideal of “greater than 95% chance of success.” 5% withdrawal rate and 6% withdrawal rate are non-starters.

This should make sense, though. The 4% Rule succeeds in historical environments. I’m assuming a pessimistic future, much worse than historical environments. We’d expect the 4% Rule to fail, and indeed it does. What would work instead?

If we want to achieve the “security” that the tradition 4% Rule provides, we have to look for a ~95% chance of success. In markets with 2% annual returns, that occurs using a 2.0% withdrawal rate. In 3% markets, that occurs between a 2.0% and 2.5% SWR.

Keep in mind, the traditional 4% Rule is also explained as “Save 25x your annual spending.” Which means a “2% Rule,” or 2% SWR, would equate to “Save 50x your annual spending.”

That’s a sobering difference. Do we have any other levers to pull?

Consumption smoothing

Perhaps one key idea that neither the original Trinity Study nor Pfau’s update looked at was the idea of consumption smoothing. In brief, consumption smoothing means “do more when times are good, do less when times are bad.”

To explain more, I want you to think about a tree. Here in chilly Rochester, NY (and other non-equatorial climes) trees only have leaves during the late spring, summer, and early autumn. During the long summer days, the trees absorb as much solar energy as they can. But during the winter months, days get short. It doesn’t make sense for the tree to maintain its leaves–which consumes resources–for such a short day. Therefore, the tree drops it’s leaves in the autumn and survives off the previous summer’s gathered energy.

Put another way: the tree uses surplus energy gathered during the bountiful summer in order to survive the harsh winter.

For our purposes today, consumption smoothing means “withdraw more money when the market is up, and withdraw less when the market is down.”

You know that phrase Buy low, Sell high? Well, consumption smoothing helps you emphasize the Sell high part by withdrawing more money when the market is high. It also prevents you from Selling Low too much, by withdrawing less when the markets are down. You use your extra Sell High money to “smooth out” the bad years that may come later.

Simulation with consumption smoothing

So I ran the simulation again, this time using a consumption smoothing algorithm. What did this algorithm look like? In short, I created a “Cash Reserve” in the simulation, which started at $0. After each year that the market went up, I would pull that both that year’s withdrawal (the SWR amount) and extra money to go into the Cash Reserve. But if the market went down, I used a combination of the previous years’ Cash Reserve and retirement withdrawal to fulfill that year’s spending need.

It’s just like the tree in Rochester. During good years, I’m the tree in summer. I’m getting money for this year, and money for a time when I’ll need it in the future. During bad years, I’m like the tree in winter. I’m borrowing from the good years’ reserve before tapping into my retirement account.

Consumption Smoothing Results

The results might surprise you. If you’re a FIRE zealot who understands the nuances of the 4% rule, you’ll want to understand the repercussions. Consumption smoothing reduces the chances of running out of money during retirement in a small, but very positive way.

I used the same exact assumptions as the first Monte Carlo analysis, except this time I used consumption smoothing.

So let’s take another look at the 4% withdrawal rate. It still looks bleak. Consumption saving won’t save your butt completely. But before the 4.5% market yielded a 43% success rate; now, I’m getting a 50% success rate. Small difference, but it matters. Similar small differences (~5% increases) occur all over the table.

Consumption smoothing will not make or break your retirement. You’re much better off choosing a different knob to turn.

For example, you could save more money, delay retirement longer, or reduce your SWR (e.g. reduce your spending in retirement). These all act to play around with your retirement income.

Alternatively, as this updated Trinity Study showed, a bad market is your worst enemy. You can’t control whether the market is good or bad, but wow does it make a difference.

Perhaps consumption smoothing is too inconsequential for you to pursue. But if you’re the type of person who likes to cover all their bases–and I know a lot of FIRE nerds fall into that camp–then perhaps consumption smoothing is worth considering.

Parting Thoughts about the Updated Trinity Study

At the end of the day, we don’t know what the future will look like. Today, I chose what most people would consider an overly pessimistic view. It can be scary, but as the Roman civium used to say, “praemonitus, praemunitus.” Forewarned is forearmed.

I’m not suggesting that a 2% SWR is needed. I don’t think it’s the only way forward. But I do think it’s worth the mental exercise. How prepared will you be for a pessimistic future?

There are many personal finance ideas that work this way. You can educate yourself on the objective possibilities, but the final decision really comes down to your subjective feelings about risk.

I hope today’s post brought you a new perspective, and provides you with some objective possibilities so that you can make your best financial decisions.

If you enjoyed this article and want to read more, I’d suggest checking out my Archive or Subscribing to get future articles emailed to your inbox.

This article—just like every other—is supported by readers like you.

-Jesse Cramer

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About Jesse Cramer

I’m Jesse. I’m an engineer, a new owner of an old home, and an avid reader/writer. If you’d like to comment, ask a question, or simply say hi, leave me a message here, on Twitter (@BestInterest_JC) or on Reddit (u/BestInterestDotBlog). Many of my posts have been directly influenced by my readers. It’s the most fun part of writing this blog. And as always, thanks for reading the Best Interest.
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13 thoughts on “Updated Trinity Study Simulation–Beyond 2020

  1. It’s an interesting thought experiment, but the idea that the market would suddenly yield such low returns overall – not just an individual company, but the entire market — is unlikely for a number of reasons. It would necessitate a fundamental shift in both how people consume, how businesses operate, and human nature itself. Companies will always seek profits first and foremost for their shareholders, as their charters require of any publicly traded company, so a sustained period of marginal gains is unlikely. More modest and even gains are more likely in a scenario in which a new style of public company charter is passed through legislation, in which sustainability is prized over profitability. It’s also human nature to jump on bandwagons, which is why when stocks move, they often really move, one way or another. The bitcoin bubble of late 2018 is a great example. People were borrowing money to buy bitcoin on the bubble, when it was far too late. And when it started dropping, they all sold in a panic. But lastly and most importantly, Wall Street has too much power to ever let slow growth happen. We saw that in 2018 when the markets crashed – bankers got bailouts without question, while homeowners and even some industries were left out in the cold or had to beg for bailouts. The market recovered in about two years, while employment and other measures lagged. All to say that when you invest in the index, you’re aligning your interests with the most powerful people on the planet. And they sure as heck aren’t going to let anything bad happen to the market long term.

    Could there be other factors? Sure. Climate change impacts could drastically make a massive change to how business is conducted. Although I believe the market will most likely find a way to adapt, we don’t know what that adaptation could look like. But my point is that SOMEthing will have to change in order for those low returns to become the norm. And it won’t be subtle.

    I am a big fan of planning for the most-likely, not the pessimistic worst case scenario. Pessimism taken to its extreme, would mean we would all assume the market will crash tomorrow and never recover, and we should just all keep working forever. I think for FIRE to work, we need a healthy dose of rational optimism.

    1. Hey Frugal Wheels. Thanks for the thoughtful comment. I agree with a lot of what you wrote.

      I’m certainly not planning my life around an assumed ultra-pessimistic future.

      But I do like to understand answers to “what if?” questions, and that was really my main goal here. Simply asking “what if the fundamentals change—then how would my retirement plans be forced to react?”

      Like you said, it’s a thought experiment. It’s certainly not backed up with real market data, nor am I using it in a predictive sense.

      Thanks for reading!

  2. While it has historically paid to be a market/growth bull, here’s some bearish perspective for your consideration:

    1. A lot of growth has come from additional workforce. Boomers followed by dual income households. People also used to work a higher % of their lives (i.e. expected life duration has increased more than expected retirement age).

    2. Growth has largely been fueled by debt, particularly in the US. It is unclear how much further debt can be issued given low/negative interest rates (which will need to remain low due to the huge amounts of existing debt). It is true that with lack of fixed-income options, equities may continue to froth but the actual cashflow/dividend returns will continue to decrease so you’ll need to rely on high P/Es.

    3. Taxation could take the wind out of the market’s sails to deal with the above mentioned deficit/debt issues.

    4. All of the money printing and push to repatriate manufacturing could lead to inflation rates that outpace share price growth.

    5. Demographics. While there may be a windfall of income from the death of boomers that is inherited by millennials, a lot of that will likely go to servicing debt or first-time home purchases. It’s likely taxation will take a big hit out of any passage of wealth given social security and pension funds have become unsustainable and could suffer from a very negative ‘death loop’ if the bubble in junk bonds and equities is allowed to deflate.

    Bailouts and all sorts of funny manipulation has been caused by the US Gov’t and Fed (and other governments / central banks to a lesser extend) which has inflated a massive bubble for the last decade (and arguably since the last 70s). To expect the bubble to grow another 50 years is too optimistic for me.

    1. Dave, thanks for the comment. You raise thought-provoking bearish points. How much growth is actual growth? vs, how much is either non-repeatable or gov’t magic tricks?

      Re: the bubble—your idea reminds me of the “index fund bubble.” Are you familiar with that idea?

  3. For a realistic example of a “bad” market, look at the Nikkei 225 post 1989 bubble. I actually wonder if we can rerun some of the Trinity simulations using the Nikkei (not predicting anything – the US market is significantly more diversified, but we’re starting to pull the same levers – e.g. FED purchases of bonds and possibly wading into the stock market at a later did, that the BOJ did in the 90s). Japan also got hit with the demographic problem earlier than most other western countries. So for all of the pessimists out there, it’s a troubling parallel.

    1. Pasha, thanks for reading and commenting. The Nikkei crash (and subsequent lack of growth) is certainly something to consider.

      That said, are you familiar with Richard Werner? I was listening to him speak a few weeks ago on Odd Lots podcast. He brought up some very interesting points about Japan’s issues in the 80s and 90s. It seems that Japan’s mistakes aren’t too parallel to today (at least in my understanding).

      Podcast link:

      Anyways, hope to hear more from you.


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