A FIRE Number Targeter Using Monte Carlo Simulations

I spent last Saturday and Sunday putting together a spreadsheet to help me determine my FIRE number, which is the amount of money you have to accumulate to be fully Financially Independent and Retire Early from the invested returns alone. (If you’re new to the concept of early retirement, here is a post that explains the idea.) This post will describe the basics of how to use this spreadsheet, and my next post explains how it works.

Overview

The standard way of finding your FIRE number is the ‘4% rule’, which is the result of the Trinity study. The authors of that study determined that shooting for a 4% withdrawal rate (or in other words, making sure that your nest egg is at least 25x your yearly expenses), will nearly always guarantee that you wouldn’t run out of funds over any 30-year time period in history. However while the 4% rule is a good rule of thumb, the Trinity study lacks a lot of considerations that are relevant to someone pursuing FIRE:

  • A 30 year time horizon is not nearly long enough. 50-90 year time horizons are more realistic.
  • There is no consideration for earning money in retirement.
  • There is no consideration for variability in spending.
  • There is no consideration for adjusting spending to market behavior.
  • There is no consideration for lifestyle inflation.
  • Social security is completely ignored.
  • Only one asset allocation strategy is looked at (75% stocks/25% bonds).
  • The study relies solely on historical returns. This is ok for its 30-year spans of market behavior, but there are not enough 80-year spans in history to build up an accurate picture of potential scenarios for us. This is also a weakness of the popular tool FIREcalc. We need a predictive model.

So I decided that I needed a way to address these considerations, and the result is this Excel spreadsheet. It uses Monte Carlo analysis to run 1000 test cases of a lifetime of financial performance. I am releasing it under the Creative Commons BY-SA license, which basically means that you are more than welcome to use it for anything, tear it apart, and post it anywhere, as long as you credit here as the source. You can download the spreadsheet here from google drive, and note that you’ll have to enable content to run it.

Inputs

Open up the spreadsheet and this is what you see. The cells you need to edit are the light yellow ones on the left. All values here are in current year dollars, and will be adjusted for inflation as the years go on so that purchasing power stays constant.

The analysis inputs on the left, the calculated results in the center, and the processed results on the right.

The analysis inputs on the left, the calculated results in the center, and the processed results on the right.

For the basic inputs, fill in your current age and the age you want to hit FIRE. Your minimum expenses are your basic housing, food, hygiene, medical, and transportation expenses, and this is the value that below which the simulation considers the outcome a failure. Your target spending is how much you want to spend each year, and the spending variability is how much your actual spending may vary on either side of that. Your average yearly side income is how much you expect to make in retirement, and that has variability as well. Finally, your acceptable chance of success is how sure you want to be that this will all work out in the end. No strategy is absolutely 100% successful, but if you are cautious enough, there are many scenarios that will give you 99.9% success. Personally I’m more of a risk taker and am shooting for around 75-80%.

The investment allocations section is fairly straightforward. I built in several asset allocation strategies: ‘Fixed Ratios’, ‘Age in Bonds‘, ‘Age-10 in Bonds’, and ‘Age-20 in Bonds’. There is also a ‘Custom’ option for which you’ll need to fill out the values for manually in the ‘Scratch Calcs’ tab of the spreadsheet.

Below this we find the option to include social security payouts. You can estimate your yearly social security payout using this government tool, and feel free to be as pessimistic as you like in guessing whether social security will be around by the time you hit the official ‘retirement age’.

Your spending correlation to market is a variable that lets you adjust your spending to how the market is doing. So if the market is having a bad year and your correlation is 50%, you will be making moderate adjustments to lower your spending accordingly. This value can range between -100% and +100%, where negative numbers mean that your spending increases if the market is down (for whatever reason).

Lifestyle inflation is bad. But you can account for it here as well.

And finally at the bottom we have simulation inputs that define what starting values we want to run the simulation for. Because we are only running 1000 test cases, a step size less than 0.25% is essentially worthless because it will get lost in the statistical noise.

Simulation inputs.

That’s it for inputs! If you want to use the spreadsheet as-is, just hit the ‘Recalculate Results’ button and let it chug away. It will take about a minute to run.

Reading the Results

As the spreadsheet works away, you will start to see the middle table fill up with results. These are the raw outputs from the simulation, and give the success rates for different time horizons (by default I chose 20, 40, and 100 years), for different starting sizes of your investment portfolio.

If you want time horizons others than those listed, you can change where the cells in the ‘Table to Calculate On’ in the ‘Scratch Calcs’ tab of the spreadsheet are pointing to.

Table of raw results.

These raw results are then graphed and compared to your acceptable chance of success, to give you your recommended target net worth, both in current year dollars and in the inflation-adjusted dollars of your starting retirement age. You can see in the graph the success curve as a function of time horizon and starting withdrawal rate. Note that these curves are slightly noisy (ie not smooth), which is a result of the statistical variation that is inherent to Monte Carlo simulations.

Processed results that give you your personal recommendation.

And that’s everything! If you’re interested in how these work or if you want to modify or extend this simulation, check out the post on how the internals of the simulation works. Otherwise, I hope this is a useful tool for you in planning for your own future, and let me know if it helped you in determining your own FIRE number.

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