Ever hear of the FIRE (Financial Independence, Retire Early) movement? Then you will know about the 4% rule. Many interpret this rule as follows: Once you can cover yearly expenses with 4% of an investment portfolio, then you are financially independent and don’t need a job anymore. This interpretation is wrong.
The “4% rule” is not a guarantee, it is a statistical finding based on (some) historical records for US stocks, bonds and inflation. It is quite easy to reproduce this finding, and get an understanding of its limitations, using a spreadsheet.
To start, you need annual returns for US stocks and bonds, as well as annual inflation rates. I was able to find data going back to 1871 fairly easily. Two sources for this data are Yale Professor Robert Schiller’s website and the “Simba” spreadsheet from the Bogleheads forum. There are many others.
The concept for the spreadsheet is pretty simple. Calculate the end of year (EOY) balance of a portfolio by adding (or subtracting) the yearly investment return. Then take out planned living expenses for the following year, after adjusting for inflation. The mechanization is a little tricky because a new long-term investing scenario begins each year in the data range. I started as shown below, with 152 rows and 152 columns for the portfolio balance calculations.
EOY balance formulas go into around 11,500 cells (152*152*1/2). Fortunately, there are lots of shortcuts and auto-population features in Excel. I don’t know about Google Sheets, but it probably has similar tools.
Here is what I did in Excel.
After poking around on the internet, I learned how to auto-populate cells along a diagonal using the Identity Matrix function MUNIT. On a blank worksheet, generate both a horizontal and vertical sequence of numbers out to 152. Select that 152 by 152 area (using the numbers as a measuring tool). With the area highlighted, type “=MUNIT(152)” into the formula bar. Instead of hitting “enter” after inputting the formula, hit “CTRL+Shift+Enter”.
This generates an identity matrix with “1” on the diagonal and “0” everywhere else. The contents of the cells are actually formulas instead of numbers. To turn them into numbers, make a copy of that area and paste over it with the Paste/Values option. Then get rid of all of the “0s” using the Find/Replace feature.
Next, replace all of the “1s” on the diagonal with some arbitrary number (I used -56789). Now cut and paste the identity matrix with -56789 on the diagonal and blanks everywhere else into the simulation spreadsheet. Use the Find/Replace feature again to substitute the desired formula for the arbitrary numbers as shown below.
At this point, I started to think about an approach for the EOY balance formulas. I decided it would be easier if I generated yearly expenses separately. So, I made a copy of my worksheet, called it “expenses” and linked it to the main spreadsheet by copying the starting withdrawal amount from there. Then I modified the diagonal entries with the Find/Replace feature as before. I also cleared out unneeded content and generated the inflation-adjusted expenses formula with appropriate relative and absolute cell references.
Back on the main worksheet, I replaced the previous column of inflation data with the return rates of the mixed stock/bonds portfolio. Then I generated the EOY balance formula.
To complete the simulation, I first filled in the formulas on the expenses worksheet. Then the EOY balance formulas on the main worksheet, since they needed those expenses. Both of these are manual click and drag operations, but go pretty quick.
The original research (from the 1990’s) that postulated the 4% rule looked at 30-year retirement periods. I decided to add a row along the top of the spreadsheet with a copy of EOY balances after 30 years, which are along a diagonal starting at cell F39. I thought I could put the next diagonal entry into the adjacent cell and click and drag to the right to auto-populate the rest of the data. This did not work in Excel.
Instead I had to use the “INDIRECT(ADDRESS(row#,column#))” command. I leave it to you to deduce its workings. Here is a hint: Excel equates the column heading letter “F” to the number “6”. I also added a formula to count the negative 30-year EOY balances.
The spreadsheet is finished, now it is time for some research!
There are two highlighted input cells, “Withdrawal Rate” and “Percent Stocks”, initially 4% and 50%. If you slightly increase the Withdrawal Rate to 4.1%, “Negative Balances” will change from 0 to 2. So, given a 50% allocation to stocks, the highest safe withdrawal rate (no negative 30-year balances) is 4%. Repeating this iterative technique at various stock allocation percentages generates the following data and chart.
Hence the 4% rule! …
Given a stock allocation between 50% and 75%, and 30 year retirement periods.
Which leads us to the main limitation of the 4% rule as it applies to the FIRE-movement community. They have much longer timelines, which we can also simulate with our spreadsheet.
Let’s say you want your money to last until age 95. At age 65, you need 30 years of coverage, so the chart implies a 4% maximum Safe Withdrawal Rate (SWR). If you want to retire at age 50 with 45 years of coverage, your SWR is 3.6% (10 percent less). At age 35 and 60 years of coverage, your SWR is 3.5%.
All these curves have plateaus which might lead to the conclusion that once you get to a certain % stock allocation, you don’t get any additional benefit with more stocks. That depends on the interpretation of the underlying data, to which we have access and therefore can draw our own conclusions. In the previous chart, I highlighted two points on the 30-year curve. These are the first % stock allocations on either side of the plateau where the 4% rule fails.
The first point is a 45% stock allocation. Here is what the underlying year-by-year data looks like (this is a view of the spreadsheet at 24% magnification).
Red columns represent where the money runs out. I superimposed the 30-year line as well as a 45-year line.
The single failure cycle is a retirement that begins in 1966, which represents a failure rate of less than 1%. However, I decided to create an additional “nervous cycles” metric, for time-periods with failures before or close to the 45-year line. Almost a third of the cycles are in that category. In contrast, here is what happens on the other side of the 30-year SWR plateau, at an 80% stock allocation.
Same failure rate but substantially fewer “nervous cycles”.
The most conservative SWR curve possible from our simulation is where no portfolio withdrawal failures occur (no red anywhere in the 24% magnification spreadsheet view). The yellow line below depicts this.
Managers of charitable endowments would probably want to be somewhere on or below this bottom line. More stocks mean more funded programs each year. This also means more risk of a large yearly loss, which might question your strategy among the trustees (and your position).
What about the FIRE community? I think anyone who wants to retire (or work less) before age 55 should stick to this lower line. As far as stock allocation, it’s the changing slope of this line (and how much $ they need) that might help them decide. Definitely at least 40% stocks, which is where the highest slope ends, providing a 2.8% SWR. Probably not more than 65% stocks, providing a 3.3% SWR.
Does this mean the 4% rule is incorrect? Or that it was once correct and is now outdated? Not at all. The charts created by our simulation are mostly based on cycles starting in the mid-1960s and earlier. This means the 1990s analyses findings were basically the same. It has always just been about interpretation. That said, the underlying data still has many limitations that should temper any conclusions. For example, 123 annual cycles are not a lot.
Another concern with the 4% rule I often hear brought up is home-country bias. The US stock market is often portrayed as an over-performing outlier compared to other countries. It’s not easy to find data from other countries that goes back very far. I tried but didn’t get enough to make good spreadsheet comparisons (very few 30-year cycles).
I did find some articles on the internet from authors (e.g. Wade Pfau) summarizing what they say was reasonably good data. From these sources I approximated 30-year SWR curves for a few other countries.
Canada, the UK and the US are quite similar, Canada with slightly higher SWR curve and the UK slightly worse.
There are several countries with really low SWRs. My 30,000 foot interpretation of this data is:
- Countries with wars fought on their own soil (including civil wars) do poorly
- Countries ruled by fascists or dictators, even for a short time, do poorly
Hopefully the US can avoid these things for the next few decades.
December 2022