Safe Withdrawal Rates  Part 1: The Basics
The study of safe withdrawal rates helps answer two crucial questions about retirement savings and planning:

How much money do we need to save for retirement?

How do we make sure that our savings last throughout our retirement?
Of course, these two questions are related. If we save too little, then it will be a struggle to stretch our savings out during retirement. On the other hand, mismanagement and excessive early spending could deplete even a seemingly large nest egg. Proper planning will help us figure out what savings rate we need to hit our targets and know when we are financially ready to retire.
To get started answering these questions, we first need to have some estimate of what our expenses will be after retirement. This itself can be tough to figure out. In the end, this is highly personal and will vary for each individual. Moreover, expenses might change throughout retirement, sometimes dramatically so. In order to make any progress, we’ll have to make some simplifying assumptions.
You may have heard of the 4% rule, which says that you can safely take out 4% of your original savings every year, with adjustments for inflation. For example, if you retire in 2020 with $1 million dollars in your portfolio, then the first year you withdraw $40,000. Every year after, you convert $40,000 in 2020 dollars into the current year to adjust for inflation and then withdraw the adjusted amount.
But is this really safe? Well, it depends. The rule relies on certain assumptions. Unfortunately there is lot of misunderstanding about this on reddit and financial independence blogs! To clear this confusion up, let me explain a little bit more about where this rule comes from.
Origins of the 4% Rule: Bengen and the Trinity Study
The 4% rule is an example of a constant withdrawal rate strategy. As the name suggests, with these strategies we withdraw the same amount every year (adjusting for inflation).
The pioneering study on constant withdrawal rates, and the origin of the 4% rule, is a paper called “Determining Withdrawal Rates Using Historical Data” by William P. Bengen. The paper derives the 4% rule in a very intuitive way. Bengen took historical returns for stocks and intermediateterm treasuries from 1926 through 1992. For each year in that range, he calculated how long a retiree’s portfolio would last if they were to start retirement in that year and use a constant withdrawal rate of x%. He then considered what happened with different initial splits between stocks and treasuries, and assumed the portfolio would be rebalanced after each year to maintain this initial asset allocation. By varying x%, and seeing how long portfolios survived in different start years, he was able to estimate how “safe” different withdrawal amounts would be.
In particular, he found that with a 4% withdrawal rate and a 5050 split between stocks and treasures, the portfolio would last at least 30 years for every possible starting year. Higher percentage withdrawal rates had cases where the portfolio did not last a full 30 years. Based on this, Bengen suggested that 4% would be a safe amount to withdraw using this asset allocation for the kinds of clients he advised. 4% turned out to be similarly safe even with asset allocations with a larger percentage of stocks (he considered up to 75%).
A later study by Cooley, Hubbard, and Walz in 1998 also analyzed constant withdrawal rates. This study is often called the Trinity Study, because the authors were affiliated with Trinity University. They applied a similar methodology as Bengen, but used corporate bonds in place of treasuries. Withdrawals were modeled as happening on a monthly basis, instead of once per year, which is more realistic. They also recommended 4% as being reasonably safe. However, possibly because they used corporate bonds instead of intermediateterm treasuries, they found that even the 4% rule failed in about 5% of the starting years with a 5050 stock/bond split. This went down to a 2% failure rate with a 7525 split. For whatever reason, the Trinity Study is often thought of as the origin of the 4% rule, even though Bengen’s work was published earlier.
Below, I show a table of results for success rates for different withdrawal percentages and asset splits, calculated following the same monthly withdrawal pattern as in the Trinity Study, and using corporate bonds. The data source contains returns up through 2015:
Withdrawal % (inflation adjusted)  

3.00  3.25  3.50  3.75  4.00  4.25  4.50  4.75  5.00  
0% stocks  15 years  100%  100%  100%  100%  100%  100%  100%  100%  100%  
30 years  85%  74%  51%  46%  41%  36%  34%  31%  30%  
45 years  28%  24%  20%  15%  11%  7%  4%  0%  0%  
25% stocks  15 years  100%  100%  100%  100%  100%  100%  100%  100%  100%  
30 years  100%  100%  100%  95%  82%  62%  52%  48%  36%  
45 years  85%  67%  52%  30%  22%  20%  17%  17%  11%  
50% stocks  15 years  100%  100%  100%  100%  100%  100%  100%  100%  100%  
30 years  100%  100%  100%  100%  97%  90%  84%  80%  70%  
45 years  100%  100%  96%  89%  80%  63%  52%  41%  33%  
75% stocks  15 years  100%  100%  100%  100%  100%  100%  100%  100%  100%  
30 years  100%  100%  100%  100%  98%  95%  90%  89%  79%  
45 years  100%  100%  100%  98%  91%  87%  78%  67%  63%  
100% stocks  15 years  100%  100%  100%  100%  100%  100%  100%  100%  100%  
30 years  100%  100%  100%  100%  98%  95%  89%  87%  80%  
45 years  100%  100%  100%  98%  91%  87%  83%  74%  74% 
_{ (Note: in this table, withdrawal amounts are inflationadjusted annually, but withdrawals happen monthly. That means in years of high inflation, purchasing power decreases toward the end of the year.) }
What conclusions can we draw from this table?

If stock percentages are too low, the 4% rule and higher does quite poorly over a 30 year retirement, and terribly with a 45 year retirement.

With a longer retirement (45 years), failure rates for the 4% rule start to rise dramatically. Even with a 75%+ stock portfolio, we still get a failure rate of 9%.

A 3.5% withdrawal rate with at least 50% stock allocation does well even for a long retirement.
How robust is the 4% Rule?
The safety of the 4% rule relies on a number of assumptions. Depending on your circumstances, it may not be conservative enough. Consider the following:

Will future performance be similar to historical results? As we’ve seen, the 4% rule is based on an analysis of historical returns. So, its applicability depends on whether future performance of stock and bond markets is similar to these historical results. Of course, the historical records we’re considering involved some pretty terrible moments in financial history (Great Depression and Recession, and the high inflation of the 1970s).

Are your asset classes similar? Many analyses of withdrawal rates use generic terms like “stocks” and “bonds”, as I did above. But there are different indices of stocks and bonds with different characteristics. As mentioned above, the Trinity study used corporate bonds, while Bengen used treasuries, resulting in different suggested success rates for the 4% rule. Moreover, the calculations in many of these discussions only consider domestic stock/bond splits, but there are other asset classes too, like REITs, international stocks, and so on.

How long will your retirement be? If you are retiring early, the 30 year period that is often the focus of analyses like the Trinity study might not be long enough. The table above shows that the longer the retirement duration, the more conservative the withdrawal rate should be.

What does success mean to you? In the table above, “success” means that the retiree is able to withdraw the appropriate amount every month. In other words, if every withdrawal succeeded but at the end the portfolio was only worth $1, that would count as a success. However, many people would find it rather nervewracking to watch the portfolio drop closer and closer to $0, especially since we can only estimate the duration of our retirement.

Is your retirement start date random? A success rate of 95% in the table above does not mean a retiree will have a 95% probability of success with those numbers. Even settings aside all the caveats and issues above, the moment you retire is unlikely to be independent of the status of the economy and market at the time. If the market goes through cyclical booms and busts, then a person trying to hit a certain networth before retiring early might be more likely to reach their goal when the market is doing well. If such booms tend to precede busts, then this retiree might do worse on average than the suggested success rate.
Conclusion
The 4% rule is popular for a reason: it is simple to understand and apply. But despite its simplicity, it is often misunderstood. Moreover, it is based on certain assumptions that may not be appropriate for a retiree’s circumstances. In future blog posts, I will return to some of these issues and see how we can try to take them into account.