What is FIRE?
If you haven’t heard of this term, FIRE means Financial Independent Retire Early. This has become one of the most, if not the most, popular topic in casual small talks. Even for those who just started their career, they are already planning ahead about their life without work, including me.
What is the 4% rule?
It was based on a research report at 1998, which says that if one only spends 4% of their savings per year, there is a very high (98+%) chance that one won’t deplete all his or her savings within 30 years. This then becomes the rule of thumb for whoever wants to retire early.
For more details, please refer to Table 1. in the report, which compares different ratio combinations between stocks and bonds, different payout periods, and different withdraw rate per year.
What is the 25x rule?
Based on the 4% rule, it then can be concluded that one could start the retirement life as long as he or she accumulates 25 times of their annual expenses.
My thoughts about FIRE
Different from most of the optimistic voices, I have totally opposite thoughts on this topic. I would like to have my analysis from different perspectives as below.
Concern I: Stock market is at all-time-high now
It is very common to hear someone talks about the high-return but low-risk investment in ETF, such as SPY. Some people even claim the return could be as high as 7% to 10% per year. This might be true when we now look back the average stock return in the last 20 years. However, one should remember that the stock market is at the all-time-high now. It is very likely we are going to experience a U-shape stock drops and rises, and the average stock return might be a lot lower.
In my opinion, the fairer stock return estimate should be either head-to-head, toe-to-toe, or median-to-median comparison. Let’s again take SPY as an example and calculate the median-to-median stock return. From 2002 to 2008, the median stock price is around 123. From 2008 (the crush) to today, the median stock price is around 260. It means that the average return per year is around 3.4% only. On the other hand, if we calculate the head-to-head return, the ratio between stock prices is around 2.87 (or 
), which means the average return per year is around 3.32%.
Concern II: Tax rate needs to be taken into account
If the above calculation scares you already, please notice that we haven’t even considered the tax rate yet. The federal long-term tax rate varies between 15% to 20%, and the California income tax rate might be around 8% to 10%. In other words, there is almost another 30% cut on top of the annual stock return rate.
Concern III: Inflation rate needs to be taken into account
Based on different sources, there are different inflation rate estimates in each country. Here, I am only going to take the one with most consensuses, which is 3%.
Summary
By just adding up all the above concerns, we already see a very depressing fact – retiring early is a lot harder than people might have imagined. Let’s do a rough calculation first and then have a more detailed one later.
Lazy Estimation
Assuming that we all-in the stock market and ignore the bond market, which is usually less recommended risk-wise but gives higher return, the average annual return rate is at 3.4%. After 30% tax deduction, the real return rate drops to around 2.38%. Then we take 3% inflation rate into account. At the end, it shows us the savings actually shrinks 0.62% per year. From here, we can already tell that 4% rule or 25x rule doesn’t apply anymore.
Fine Estimation
Alright, now let’s do a more detailed calculation based on different annual return rates and different remaining lifespans. Assuming that the amount of the initial saving is 
, the remaining lifespan is 
, the annual average spending is 
(even though the realistic spending could vary a lot from years to years), the annual return rate is 
, the tax rate is 
, and the inflation rate is 
.
We can write down the formula for remaining savings as 
after 
year, where 
, or 
after multiple years. The latter formula can later to reorganized as 
. If we then assume that all the money is precisely depleted by the end of the remaining years, we have the following derivations.
![\begin{align*} 0 &= x \cdot m^{k} - c \cdot m - \cdots - c \cdot m^{k} \\ 0 &= x \cdot m^{k} - c \cdot m \cdot \frac{1 - m^k}{1 - m} \\ \frac{x}{c} &= \frac{1 - m^{k}}{m^{k-1} \cdot (1 - m)} \\ &= \frac{1 - \left( \frac{1 + r \cdot (1 - t)}{1 + \pi} \right)^{k}}{\left( \frac{1 + r \cdot (1 - t)}{1 + \pi} \right)^{k-1} \cdot \left[ 1 - \left( \frac{1 + r \cdot (1 - t)}{1 + \pi} \right) \right]}\end{align*}](https://www.hogansung.com/wp-content/ql-cache/quicklatex.com-c182fb7f569a4ecfdddf25ad3f61c3b2_l3.png "Rendered by QuickLaTeX.com")
With excel or spreadsheet, a parameterized table can be easily calculated as below, where the cell value represents the multiplier of annual expenses, i.e. 
.
| Retirement Age | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | |
|---|---|---|---|---|---|---|---|---|---|
| Remaining Years | 50 | 45 | 40 | 35 | 30 | 25 | 20 | 15 | |
| Interest Rate | 3.00% | 62.49 | 54.94 | 47.71 | 40.79 | 34.17 | 27.83 | 21.77 | 15.96 |
| 3.40% | 58.19 | 51.55 | 45.11 | 38.86 | 32.79 | 26.90 | 21.19 | 15.65 | |
| 4.00% | 52.46 | 46.98 | 41.56 | 36.18 | 30.86 | 25.59 | 20.37 | 15.21 | |
| 7.00% | 33.07 | 30.96 | 28.63 | 26.09 | 23.30 | 20.25 | 16.91 | 13.24 | |
| 10.00% | 22.77 | 21.93 | 20.92 | 19.70 | 18.22 | 16.43 | 14.26 | 11.64 | |
What does it imply?
From the fine estimation, we see even more despairing results. Under the most-likely scenario, i.e. 
annual return rate, if one wants to retire at the early 40s, one needs to save 45x of the annual expenses. This is almost 2x of what were told!
I once made a very rough estimation of what the annual expenses would be like for a four-people family. It was about 54k for house rents, 36k for food, 5k for clothes, 15k for commute, and 35k for travel, which summed up to 140k per year. That is to say, if I am going to retire at age 40, I need to have 6.3m in my savings.. It sounds ridiculous, doesn’t it?