Advanced Finance

The Updated Trinity Study Simulation

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. 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 conducted in 1998 by three professors at Trinity College, in Texas. The goal of the study was to determine a safe withdrawal rate (SWR) for potential retirees. A withdrawal rate is the “salary” that you pay yourself during retirement, by withdrawing money from your retirement nest egg. So, a safe withdrawal rate is a withdrawal rate that allows a retiree to not run out of money by the time they die.

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 (if you’re unfamiliar, check out my starter post here) frequently reference the Trinity Study and its results. 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

The study assumed that most retirees portfolios can be lumped into a few buckets, using stock/bonds ratios of 100/0, 75/25, 50/50, 25/75, and 0/100. This is fair. Most retirees’ portfolios contain a mix of stocks and bonds.

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.

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 study used actual market data from 1926 to 1995 to affect the simulated portfolios.

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% withdrawal in Year 1, and then slowly increase 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

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 Year 1 and afterwards, increased for inflation. This would have allowed that retiree to successfully live a 30-year retirement without running out of money in 95% of the 30-year periods that the study looked at.

The Wade Pfau Updated Trinity Study

Wade Pfau is a professor and PhD in Financial Planning (that’s a thing?!). He’s written some really 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 government bond data. (I’m not here to explain the difference between corporate and government bonds. But as I’ve always said, “If Wade Pfau says use government bonds, then use government bonds.” If you’re unsure what a bond is, I included a quick definition in this post about the 2008 crisis.)

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 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.

I still haven’t answered the question–will the future ~= the past? So let me ask you this: 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.

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.

Assumptions

To create my version of the updated Trinity Study, I ran a Monte Carlo simulation. I created an alternate reality (no nudists), used randomness to determine the nature 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 a few 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 (4% rule is based on 30-year retirement).
  • 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 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.

Results

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% SWR column is ravaged with low success rates. There’s nothing even close to the previous ideal of “greater than 95% chance of success.” 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 2% markets, 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% SWR column. 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). 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.

This post, like many others, was inspired by conversations with readers. If you’d like to reach out to me, you can leave a note via the Contact page, send me a Tweet (@BestInterest_JC), or find me on Reddit (u/BestInterestDotBlog).

Thanks for reading the Best Interest.

-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. I hope you enjoy my thoughts, numerical breakdowns, and general musings. 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. Jesse
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