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Would you like to know precisely which withdrawal rate is safe and will sustain your lifestyle for a very long time?

You will find the answer in this article with updated results from the Trinity Study! This study researched different withdrawal rates for retirement. Although the original research was not about early retirement, it is often referred to in the Financial Independence and Retire Early (FIRE) movement!

However, there are two caveats to the original study. First, they are only covering the period until 1995. And then, they are not covering more than thirty years of retirement. Thirty years is not enough for some people wanting to retire early.

Therefore, I reproduce the original study’s results with recent data, all the way to 2021! And I extended the data back to 1871. This makes for **much more data than the original study**.

I have also considered **periods as long as 50 years**. It means many more withdrawal simulations than the original study.

In this article, you will find how I did it and all the results I have gathered from this data!

## The Trinity Study

I have already talked at great length about the Trinity Study. It is an excellent research paper done by three professors from Trinity University.

Their research paper’s **goal was to see which withdrawal rates people should use to sustain a particular lifestyle** for up to 30 years. It is important to note that the original research was not about early retirement but official retirement.

They tested **the success rates of withdrawal rates from 3% to 12%**. Also, they tested portfolios with between 0% and 100% stocks by jumps of 25%.

The authors also **took inflation into account in the results**. Indeed, it is interesting to compare the results with and without inflation. Finally, they also provided the terminal values of the portfolio.

I wrote a detailed article about the Trinity Study if you want more information.

### The 4% Rule (of Thumb)

The Trinity Study is the source of the 4% Rule. This rule states that if you only withdraw 4% of your initial portfolio every year, you can sustain your lifestyle for a very long period. And your withdrawal is **adjusted for inflation every year**.

Some people believe that the original study shows that this will sustain forever. But this is not what the original research was about. They **only tested simulations for up to 30 years**.

It is better to call it **The 4% Rule of Thumb**. Because if you plan to retire very early, you will probably need a lower withdrawal rate. Moreover, your withdrawal rate will depend on your portfolio and asset allocation to stocks and bonds.

## Why did I do it again?

If the study is excellent, why did I want to redo it? I have several reasons for that.

First, I wanted to see **how this was working with recent stock market returns**. The original study was only covering years up to 1995. I wanted to have more recent data. I wanted to ensure the results were holding with more recent stock market behavior. So this simulation will cover returns until the end of 2021!

Secondly, the original study only covered up to thirty years of retirement. I wanted to **ensure that the portfolio could sustain withdrawals for extended periods**. For people retiring early, I think that 50 years is not unreasonable.

Finally, I have to admit that I like to write code. So it was **cool to write code related to this blog**. And being a big geek, now I can run many simulations with the data I want. Overall, it was a lot of fun preparing the data for this article.

Ultimately, I want to extend the Trinity Study to the European markets. It will be challenging to obtain the data. But I will try to find it for as many years as possible.

## How I redid the Trinity Study

My simulation uses** monthly withdrawals**. Most people in retirement will withdraw money monthly. It is also possible to withdraw money at the end of the year instead. But I believe that it is not common.

I have **calculated all the returns monthly**. Doing that makes the results much more accurate than doing it yearly. And the monthly withdrawal is updated with inflation every month as well. Every possible starting month in the available data is tested.

For this simulation, I have **not done any rebalancing**. For more information, I have compared different rebalancing methodologies for retirement.

Withdrawals are based on the current allocation. For instance, if your base allocation to stocks is 60%, but your current allocation is 80%, 80% of the withdrawal will be taken from stocks. I may use different withdrawal techniques in the future.

Based on this simulation, **I collected the same results as the original study**: success rates without inflation, success rates with inflation, and terminal values.

## Success Rates of the Trinity Study

I start the simulation with the entire data from 1871 to 2021.

In this simulation, success is when your portfolio does not run out of money before the end of the simulation. For instance, if we simulate for 20 years and end up with one dollar after 20 years, it is a success. This is a failure if the portfolio runs out of money before that (could be in the first year or the nineteenth year).

So, the success rate is the percentage of the months that end up with success. Obviously, the higher the success rate, the better the results are.

Let’s see what success rates we have when we ignore inflation. Let’s start with 20 years since I do not think anybody will care about a ten-year-long simulation. I will begin at a 3% withdrawal rate and go up to 12%, increasing by 1% at a time.

We can see what we already expect:

- Increasing the withdrawal rate decreases the chances of success
- Any withdrawal rate higher than 8% does not make sense in the long term, even without inflation.
- A small allocation of bonds can help with lower withdrawal rates
- Generally, a 100% stocks portfolio will perform better than the other portfolios.

Let’s see what happens when we push the simulation to 30 years.

We can see that increasing the number of years decrease the likelihood of success. It is logical since you are more likely to run out of money.

With 30 years of retirement without inflation, a 6% withdrawal rate with a significant allocation to stocks still makes a lot of sense!

## Taking Inflation into Account for retirement

But, let’s get serious. It is much better to take inflation into account in our simulation! Let’s see again with 20 years to compare the results:

As we can see, inflation causes a significant hit to our chances of success! Before inflation, an 8% withdrawal rate made some sense. Now 6% is the limit. And even 6% has a barely over 75% chance of success!

Let’s see what happens with 30 years.

We can now see that anything higher than a 6% withdrawal rate is hazardous, with a less than 75% chance to succeed even with 100% stocks.

### More withdrawal rates

Since we see that reasonable withdrawal rates are in the range of 3% to 6%, let’s try more withdrawal rates. I have simulated increments of 0.1% of withdrawal rates.

With a large stock allocation, withdrawal rates between 3% and 4% are very safe. Some people would even dare use withdrawal rates of about 4.5%. But even a portfolio with 100% stocks has only an 85% chance of success after 30 years with 4.5%.

### Longer retirement time

One of the caveats of the original study is that they stopped at 30 years. Let’s **run the same simulation again but with 40 years this time**.

After 40 years, we are starting to see lower success rates, even for most people’s 4% withdrawal rate. Unless you have 100% of stocks, your success rate will be less than 90%.

Let’s see what happens with more than 50 years.

As expected, we see lower success rates. But it is still not bad at all with reasonable withdrawal rates. A 100% allocation to stocks and a 3.5% withdrawal rate still have more than a 98% success rate. This is significantly more than I expected.

It shows that the study’s original conclusion can still hold for a much more extended period than 30 years. It is excellent news!

## Updated Terminal Values

Another interesting thing from the study was that they also **compared the terminal values of the different withdrawal rates and portfolios**.

So let’s see the terminal values of a 1000$ portfolio after 30 years. I did the simulation for a portfolio of 100% Stocks. For the sake of display, I have reduced the number of withdrawal rates.

I did not show the minimum values. Indeed, they are always zero. If the chance of failure exceeds zero, the minimum value will be zero.

However, **the average and median values are quite remarkable**. We will focus on the median since it is generally more representative than the average.

For a withdrawal rate of 3.5%, which is my current target, the median terminal value after 30 years is about 6700 dollars! Not only did your portfolio sustain your lifestyle, but it also increased six-fold! Let me repeat this. After 30 years of doing nothing but withdrawing money, you have six times more money than when you started!

The maximum values do not mean a lot. But it is crazy to see that after 30 years, you could have about 30 times more money than when you started! And this is with a 3.5% withdrawal rate!

Let’s see what happens when we extend to 40 years.

We can see that the results are comparable. However, all the values are significantly higher. The numbers are all about twice higher. On average, your retirement money will double during the ten additional years. So, even though you are not contributing any more money and living from it, your portfolio will double in 10 years. How cool does that sound?

## The success rate is not everything

There is something important with these measurements: the success rate does not tell the entire story. For instance, for you, which of these two scenarios is better:

- 98% to last 50 years, but a chance of running out after ten years
- 96% to last 50 years, but a chance of running out after 48 years

For me, the second scenario is better. You do not want to have a chance of failing after only ten years if you are planning for 50 years. But if it fails after 48 years, you have many years to make some adaptations.

So, **another quite important metric is the worst duration of a scenario**. This means after how many months can you see the first failure can happen.

For reference, here are the success rates of each portfolio for 50 years and different withdrawal rates:

And now, here are the worst durations for each of these portfolios:

If we only look at the first graph, the conclusion is that having a higher allocation to stocks is always better. But if we look at the second graph, 100% stocks is the worst one!

So what does this mean: **you need a balance in your portfolio**. Bonds will significantly reduce the chances of your portfolio going to zero too early. This does not mean that you should optimize for the highest worst duration either. Because if your highest duration is 40 years, but you have only a 50% chance of reaching 50 years, this is gambling, not planning.

So balance is essential. While stocks will increase your success, stocks are more subject to sequences of return risks.

## How to implement the Trinity Study?

Now that we have seen that the results of the Trinity Study are encouraging and would let people retire early, how should we implement it?

In theory, the Trinity Study is based on a simple concept: you can retire based on a large principal by withdrawing with a fixed withdrawal rate.

However, in practice, this means you need to accumulate a lot of money, more than what most people accumulate during their lifetime. And you need to accumulate this earlier than retirement age.

To accumulate this money is definitely not easy but it is also not complicated. First, you need to save money (as much as possible). For this, you will need to focus on your expenses and earnings.

Then, you will need to invest that money until you can retire. Once you have accumulated the proper amount through capital gains and savings, you will be financially free.

If you are interested, I have many articles on my blog about financial independence.

## How did I do it?

You can find my code and my data on Github. Everything is available to share as much as possible!

I wrote the entire program in C++. I used this programming language because it is my favorite! And it is blazing fast! I have not especially optimized my code, and it takes less than a second to generate thousands of simulations.

If you are not a coder, I also have an online FIRE calculator that can do most of the calculations presented here.

My U.S. data s based on the data made available by Big ERN in its Safe Withdrawal Rate series. It is a good dataset that has been tested several times already. Big ERN made all this available for free. I am very thankful for his work! I have completed its data with the missing years using the same methodology.

If you want to use the graphs in this article, I would ask that you cite this article as the source of the image!

## Future of the series

It was fascinating to reproduce these results. And it was very insightful as well. I have learned many things from the results. It is great to see the confirmation that the original conclusions hold for more than 50 years.

And it also shows that my current withdrawal rate (3.5%) is a safe bet. I may switch to 3.75% in the future. I will have to run more simulations.

Talking of simulations, I have run a few more simulations with the same idea:

- Trinity Study Results with Swiss Stocks
- Withdrawal rates and low-yield bonds
- When should you rebalance your portfolio?
- Does the Trinity Study work in recent years?
- How often should you withdraw money?

Since I plan to make a few more articles like these with more simulation, I would like to get your point of view on this article! Please let me know what you think in the comments below! What should I improve?.

What do you think of these results? Would you like me to run more simulations like this? Do you have ideas on what kind of simulations I should run next?

## Conclusions

With all these results, we can have several important conclusions.

First, **the paper’s original conclusions still hold **even with much more data taken into account. And it still stands accurate up to 2021! It is excellent since it shows that the 4% rule of thumb still works!

If you increase the simulation time to **more than 30 years, a 4% withdrawal rate is no longer safe**. With 50 years of retirement, you have a 90% chance of success with a 4% withdrawal rate at most. A withdrawal rate of around 3.5% would be safer for most people.

If you want real chances of success, **you will need more than 50% of your portfolio allocated to stocks**. The stocks are what allow us to fight inflation and cover the withdrawal rate year after year.

If you choose a reasonable withdrawal rate, **you will likely end up with much more money than when you started**! For instance, a 3.5% withdrawal rate over 30 years with 100% stocks would leave you about six times more money than when you started!

For information about the original study, read my detailed article about the Trinity Study.

If you want to start investing to become Financially Independent, you will be interested in my guide on how to get started in the stock market.

Great articles. A few critiques on this. With a 4% withdrawal rate giving a 90% chance of success over 50 years, that’s great but a 50 year retirement, imo, the first 5 years at maybe 3% would offset the risk and put it well above 90% over that 50 year period?

Or probably more solid would be give yourself a cash buffer, don’t withdraw anything for 2/3 years and that gives you decent leeway, all going well with the investments, to have a 50 yr retirement of 4% drawdowns

For me I’m 100% stocks but I think the main risk on being with this type of allocation is withdrawing early. Being cash backed for the first few years mitigates this, at least somewhat, if you hit a 50% loss at year 3 u need cash then yes you might need to go back2drawing board

On the other hand if you do quite well the first year or two then it might be prudent to take some off the table and give yourself another 2-5 years cash without really distrupting the ~7-10% average gain that would be gotten from following the index

Hi Chris,

You can indeed withdraw less in the few years and this will increase your chances. But then you likely need to save more. And you have to make sure you can stay below 3%.

I have an article about cash buffers, the results are the same as lowering your withdrawal rate.

Where do taxes come into this, All figures quoted are after taxes?

Taxes should be taken into account into your FI Number, so the 4% (or other WR) withdrawal should cover your taxes.

Outstanding! It will be awesome to see the same simulations/results adding leverage.

We don’t have very good historical data with leverage. However, we could assume perfect leverage and double/triple all the returns, whether up or down, and see what would happen. Would that be interesting?

Thank you for extending your analysis to the 50 years mark. Could benefit those who need to extend their withdrawal years beyond their lifetimes; to support, say, an autistic child for the rest of her life.

That’s a good point, I have never thought of that. If you are planning to support somebody else financially, you may have to support him longer than your own lifetime. This could even make simulations beyond 60 years more interesting.

Thanks for pointing that out. And good luck dealing with that situation if that’s your own.

Hi, nice material and research. I’m wondering if you can provide the math formula for the terminal value or success rate

Hi Alice,

It’s not a formula, it’s a historical simulation. I am using 150 years of historical data to do these simulations from each starting month and then do the calculations each month based on returns and inflation. The actual code is available in the article.

Hello,

Are the terminal value results adjusted for inflation as well?

Yes and no :)

So, they account for inflation in the sense that all the withdrawals accounted for inflation. But they represent the amount of money in the future.

So, if the terminal value is 1M, it may not be worth the same as 1M today.

Does that make sense?

Having moved to Switzerland 7 years ago and will never reach the 40 year max, I wonder it it’s a good idea to take a personal bank loan and pay a large sum into my pension fund? With inflation shooting up, and interests relative low and tax deductions, is it worth it?

Hi Nena,

I don’t think it’s really worth it no. Most second pillars will not return much, so you need a very cheap loan to make it worth it.

It may sometimes be worth having a loan to invest in stocks, but that’s risky.

Hi Nena, you may consider paying the maximum into a 3rd pillar account. About CHF 6’000 per year for employees. This can provide a great tax advantage if you file a tax return in Switzerland. The account should be with VIAC or comparable providers that provide 100% equity allocation with total expense ratios of about 0.50% p.a.

Great article. Thanks for Denmark😃

You are welcome :)

Thanks for sharing your work so that it benefits others.

You are welcome :)

Wonderful piece of information. I am trying to achieve financial independence & retire by mid-thirties. But, often worried about the amount one should amass in order to live a risk free life if the average life span would be 80 years.

You have got a wonderful take there taking in to account all the nitty-gritty for a FIRE lifestyle.

This website is just pure gold, chapeau to you! I’ve been reading about FIRE for some years now but most of what’s written is very US-centric. Living in Europe, all of the differences about taxes, brokers and the mutual funds vs ETFs differences made me stayed away from starting, but your articles cover basically all of the practical doubts I had and even executed already some ideas I had (like these simulations). Your articles are very possibly one of the last two things for getting started, the other one being moving to Switzerland from Italy (where everything is super complex tax-wise), which I hope happens soon thanks to work. I’d be great if you wrote an article on any differences there may be regarding taxes and other practical issues for non-swiss private investors residing in Switzerland, in contrast to swiss nationals. In any case, thank you so much your site is GREAT!

Thanks for the kind words, Ale!

Good luck getting started and moving to Switzerland.

You have a good point, I should make articles about tax at source and differences between the different permits! This goes on my list.