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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 post with updated results from the Trinity Study!

I have recently talked in detail about The Trinity Study. This study researched different withdrawal rates for retirement. Although the original research was not about early retirement, it is referred a lot in the Financial Independence and Retire Early (FIRE) movement!

However, for me, there are two caveats with 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 decided to reproduce all the results of the original study. I used much more recent data from 1871 to 2019. I have also considered periods as long as 50 years. It means many more withdrawal simulations than the original study.

In this post, you will find how I did it, and all the results I have been able to gather from this data!

## The Trinity Study

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

The goal of their research paper 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 portfolio 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 with the terminal values of the portfolio.

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

### 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 will be able to 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.

I think 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 highly depend on your portfolio and how much stocks and bonds you have.

## Why did I do it again?

If the study is great, 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 make sure that the results were holding with more recent stock market behavior. So this simulation will cover returns until the end of 2019!

Secondly, the original study was only covering up to thirty years of retirement. I wanted to be sure that the portfolio can sustain withdrawals for much more 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. Overall, it was a lot of fun preparing the data for this article. And being a big geek, now I can run many simulations with the data I want.

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

## My simulation

My simulation is using monthly withdrawals. I think 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 will collect the same results as the original study: success rates without inflation, success rates with inflation, and terminal values.

## Success Rates

I am going to start the simulation with the entire data from 1871 to 2019.

In this simulation, a success rate 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. If the portfolio runs out of money before that (could be in the first year or in the nineteenth year), this is a failure.

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 directly with 20 years since I do not think anybody is going to care about a ten years 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 any 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

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 makes a major hit to our chances of success! Before inflation, an 8% withdrawal rate made some sense, now 6% is the limit. And even 6% is 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 very dangerous, with 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 allocation to stocks, withdrawal rates between 3% and 4% are very safe. Some people would even dare using 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 simulation 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 the 4% withdrawal rate that is used by most people. 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.

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

## Terminal Values

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

So let’s see what would be 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 is greater than zero, the minimum value will zero.

However, the average and median values are quite remarkable. We are going to 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. During the ten additional years, on average, your retirement money will double.

## The success rate is not everything

Now, 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 10 years
- 96% to last 50 years, but a chance of running out after 48 years

For me, the second scenario is definitely better. You do not want to have a chance of failing after only 10 years if you are planning for 50 years. But if it it fails after 48 years, you have many years to do some adaptations.

Another metric that is quite important 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 duration for each of these portfolios:

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

So what does this mean: you need a balance in your portfolio. Bonds will greatly reduce the chances of your portfolio going to zero too early on. 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 50% chance of reaching 50 years, this is gambling not planning.

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

## 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 is 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. Thanks a lot for his work! I have completed its data with the missing years using the same methodology.

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

## Conclusions

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

First of all, **the original conclusions of the paper still hold **even with much more data taken into account. And it still stands accurate up to 2019! It is great 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 not safe anymore**. 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 are very likely to 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.

### 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%, maybe. I will have to run more simulations. And this will have to wait until I get Europe and Switzerland data for more results.

Since I plan to make a few more posts like this one 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?

Now that my code is ready for computations, I plan to try to get the data for other indexes. I want to run these simulations for a European investor. First, I will try to see if I can find all the values necessary for a pure Swiss portfolio. But it is not easy to find all this information. I would also need to get the inflation data for Switzerland.

The next simulations I am going to run are going to be by only taking the most recent data of the data set. I want to see if the recent returns on the stock market are significantly different from the last 150 years.

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?