What is the Safe Withdrawal Rate and how safe is our model?

If you have done some research into the topic of FIRE (Financial Independence, Retire Early) you have for sure stumbled on the idea of Safe withdrawal rate (SWR). 


According to Wikipedia, the "Safe withdrawal rate is defined as the quantity of money, expressed as a percentage of the initial investment, which can be withdrawn per year for a given quantity of time, including adjustments for inflation, and not lead to portfolio failure; failure being defined as a 95% probability of depletion to zero at any time within the specified period".


Now, in our simplified model we have already encountered the withdrawal rate, as it is simply the difference between the expected return on investment (6%) and the inflation rate (1.85%), that is 4.15%.


How does the withdrawal rate connect to the other elements of the model? 

  • Higher expected returns will lead to higher withdrawal rate and viceversa
  • Lower expected inflation will lead to higher withdrawal rate and viceversa

Many people within the FIRE community consider 4% as a Safe withdrawal rate. The source of this claim is originally a paper written by W. Bengen in 1994. He considered the historical returns of US stocks and US bonds (50:50 Portfolio allocation) and saw that a withdrawal rate of 4% would guarantee at least 35 years of cash flows (adjusted by inflation). In 1998 another paper (commonly referred to as Trinity Study - from the name of the University) confirmed the finding. 


We have in our model 4.15% and the study recommends 4% - not too far off! Seems good - it is very nice to see this validated by researches! 

First of all, a difference of 0.15% in a time horizon of 30 years and more is not at all small but can lead to significant differences. 

Second of all, there are some conditions in the current market that were different in the time series used in the studies and this should lead us to be a bit more cautious. There is a great series in the blog earlyretirementnow that explains that in details. 

Later on, I will also talk more about both studies - what are the underlying assumptions and what are the results more in details.  


Coming back to our example, let´s do some stress testing and assume that the Compounded Annual Growth Rate (CAGR) in the first 5 years after we achieved our goal (and are enjoying our well deserved cash flows) is still 6% but the market had a rough patch at the beginning, returning less than 6% or in some cases even declining. 

In blue, we have the assumption from our model - a 6% growth every year. In Scenario 1, after the first year of 6% growth, the market was flat and then slighltly negative. Then it recovered quickly. In Scenario 2, the market was flat for the first 3 years before showing any growth at all. The CAGR in all 3 scenario is 6% - which is in line with our assumption. So, are we safe then?

Well, not exactly, as we can see from the graph below that shows the capital in Year 5.

Between the model and Scenario 1 we see a difference of around 10K Euro - which is 1.2% lower than our model. In Scenario 2 the difference gets much bigger - 64K or 7.7% lower than the model. 

This is excluding inflation - which we kept the same in all 3 scenario. 

So, despite having exactly the same CAGR between Year 1 and 5, different series of returns can impact more or less substantially our capital. This is intuitive if you think about it: since we are withdrawing every year a certain amout of money, if the market is doing poorly at the beginning, there is just less money left when the recovery kicks in. 

This is known as Sequence of Returns Risk (or Sequence Risk) and is a potential killer for the capital we accumulated in a time horizon much faster than what we would expect. 

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