The Ultimate Guide to Safe Withdrawal Rates – Part 22: Can the “Simple Math” make retirement more difficult?

This post has been on my mind from day one and it’s also been a topic that was requested by readers in response to previous installments in the Safe Withdrawal Rate Series (click here for Part 1):

Is the FIRE (Financial Independence Retire Early) community setting itself up for failure by making retirement conditional on having reached a certain savings target?

If we specify a certain savings target, say 25x annual expenditures, as in Mr. Money Mustache’s legendary “Simple Math” post, we are more likely to retire after an extended equity bull run. And potentially right before the next bear market. Very few savers would have reached that goal at the bottom of a bear market! Don’t believe me? Let’s look at some of the calculations from my post from a few weeks ago: The Shockingly Simple/Complicated/Random Math Behind Saving For Early Retirement. Specifically, let’s assume that every month, starting in 1871, we had sent off a new hypothetical generation on their path to FIRE. They start with zero savings, then save 50% of their income (adjusted for CPI-inflation), invest in a 100% equity portfolio and retire when they reach 25-times annual spending. Even though the starting dates are perfectly spread out, one each month, the retirement dates are not. They follow the big bull markets with extended gaps in between, see the chart below. The endogenous retirement dates are in red. Using the Mr. Money Mustache Simple Math method, you’ll mostly retire during a bull market, and often during the last part of the bull market, right before the peak and the next bear market!

Retirement dates when using a 50% savings rate, 100% equity portfolio, 25x savings target. Simulated retirement dates in red. Using the Mr. Money Mustache Method, you’ll only retire during a bull market!

How much of an impact will this have on Safe Withdrawal Rates? That’s the topic of today’s post…

Before we take a deep-dive into the numbers, let me again show why this clustering of retirement dates occurs. This is a chart from the post from a few weeks ago (slightly different assumption because of the 60% savings rate, but the intuition is the same). Two neighboring cohorts, one starting their FIRE savings path in October 1992 one in November 1992 retire over four years apart! How is that possible? Well, the first cohort just barely reached their target in the Summer of 2000 and retired exactly when the market peaked. The cohort behind it just fell short, then saw its portfolio drop to only slightly above 15x annual expenses. With the help of the additional contributions and the market recovery this cohort eventually reached the savings goal in 2004. Of course, maybe that second cohort would have retired in 2000, too, because they came so close to the savings goal. Well, it doesn’t really matter where we set the cutoff. At 25x or 24.99x or 24.9x. Some cohort, maybe the December 1992 or January 1993, would have been forced to retire after the Dot-Com bust. There will always be a clustering of new retirees in 2000, then no retirees for a while and a new cluster starting in 2004.

ShockinglyComplicatedMath Chart07
Two different start dates in October and November 1992 reach FI over four years apart!

Endogenous retirement timing vs. Safe Withdrawal Rates

Let’s see how that clustering of retirement dates messes with the Safe Withdrawal Rates and failure probabilities. Let’s plot the same cumulative S&P500 chart again (top panel). In the bottom panel is the time series of Safe Withdrawal Rates (60Y horizon with capital depletion, 80/20 portfolio). The blue line represents the SWR that would have exactly exhausted the portfolio over a 60-year horizon. (Just for the record, this requires some extrapolation of returns beyond 2017. Please check Part 1 for the simulation details.)

The effect of retiring only during bull markets: Lower Safe Withdrawal Rates!

With the red dots, I mark the SWRs that were attainable in the months when FIRE savers actually reached their goal. Just eyeballing this chart, it’s obvious that the SWRs are lower for the FIRE crowd with the endogenous retirement timing than for the retirees that would have picked a random retirement date along the blue line. The red dots always coincide with the troughs of the blue line, which occur exactly at each of the equity market peaks. But none of the peak safe withdrawal rates are ever feasible for the early retirees. That’s because they occur when the market is depressed and nobody can afford to retire, like 1932, 1949, 1982, 2002 and 2009.

Why is this important? Sometimes I read that the 4% Rule is way too conservative because one can show that for some past retirement cohorts the portfolio would have grown to some exorbitant amount after 30 years. Of course, as I have pointed out before, looking at the best possible outcomes or even the median outcomes after 30 years is not very helpful because the whole idea of calibrating the SWR is to hedge against a tail risk. To use the airport analogy again (inside joke, please listen to ChooseFI episode 35), when I budget my driving time to the airport I like to be 99% sure I catch my flight. Not 50% sure (median). And certainly not 1% sure (fastest possible driving time). Then why people look at the best possible outcomes in Safe Withdrawal exercises is completely beyond me.

But today’s research taught me that there is an additional reason to ignore the best possible outcomes. Of course, one can find examples where even with a 4% withdrawal rate the portfolio would have grown to five 5+ times its initial value (inflation-adjusted!!!) after 30 years. The only problem: that would have been the cohorts starting retirement in 1932 or 1982, at the bottom of some of the worst recessions and bear markets. Nobody following the “Simple Math” method would have ever retired back then!

Failure Rates for different equity weights

So, how much of a difference does the endogenous retirement decision make on the failure rates of different SWRs? It’s easy to compute, we just check what’s the share of the blue line and the red dots below a certain target SWR. Let’s plot the failure probabilities of two Safe Withdrawal Rates: 1) the often quoted 4% Rule and 2) the 3.25% Rule, which is what I would endorse in the absence of any future supplemental cash flows (pensions, Social Security). With that additional income, I would increase my personal SWR to 3.5%, but for the purpose of this exercise let’s assume there is no future income.

In the chart below is the failure probability in percent of the 4% Rule (blue) and the 3.25% Rule (red) as a function of the equity weight during retirement (just to be sure, for the FIRE savers, I always assume 100% equities in the accumulation phase!). The solid line is the failure probability the way it’s normally constructed, i.e., for all retirement cohorts between 1871 and 2015, while the dashed line is for the cohorts that retired when they reached their 25x savings target.

Retiring after reaching a certain savings target will increase the failure rate by several percentage points when using the 4% Rule. If the SWR is lower there is only a negligible impact from the endogenous retirement decision, at least for equity weights above 70%.

As expected, endogenous retirement timing increases the failure probabilities. But not by a lot. Somewhere around 2-4 percentage points for the 4% Rule and less than 1 percentage point for the 3.25% withdrawal rate (at least for the high equity weights). The 4% Rule becomes a little bit less appealing than it already is but not by much. The 3.25% Rule doesn’t seem to be impacted much at all! I was very surprised by those numbers. I would have thought that the endogenous retirement timing would have made more of a difference. There is certainly a noticeable and significant impact, but a few percentage points in the failure rate don’t make or break a SWR. For us personally, the 4% Rule is toast with or without endogenous retirement and the 3.25% Rate is safe either way. I guess there are (at least) two reasons for the relatively small impact:

  1. Nobody retires during the first few months after the market peak when the Safe Withdrawal Rates were still high. In that sense, the savings target actually provides some protection against retiring when the SWR is low.
  2. A lot of cohorts that just barely missed the previous market peak (e.g., August 2000) will likely retire early during the next bull market (e.g., late 2004) when equity valuations are still reasonable and SWRs are still high.

Of course, endogenous retirement timing still raises the failure probability, just not by that much!

Some caveats

Of course, not everybody follows the Mr. Money Mustache “Simple Math.” Some may have actually retired at the bottom of a bear market. Maybe by choice because they got a large cash infusion (inheritance, the sale of a business, etc.) or involuntarily because of a job loss. Some may become eligible for a generous (government) pension and can afford to retire even with a decimated portfolio. Good for you, but it’s not the norm. All I’m saying here is that if we pick a random start date for your FIRE journey, then follow the Mr. Money Mustache Simple Math Method and save until we hit 25x annual spending (or any other pre-determined spending multiple), we’re more likely to face higher failure rates in retirement.

Does the market follow a Random Walk?

Notice that none of what I wrote today should have any significance if we were to assume that financial markets follow a strict Random Walk assumption, i.e., past returns have zero influence on future returns. But the Random Walk assumption doesn’t really work with financial data. Even the heavy hitters in the passive investing world, namely, Professor Burton Malkiel (“A Random Walk Down Wall Street”) and Jack Bogle (Vanguard Founder) pointed out that expected equity returns are not exactly identical all the time because of mean-reversion of equity valuations:

“You take that 6 percent return and maybe knock it off a couple of points perhaps for a lower valuation, slightly lower valuation over a decade and you’re talking about a 4 percent nominal return on stocks.”    Jack Bogle on CNBC.


I’m not a big fan of the 4% Rule, as you may know by now. Even when calculating the failure probabilities as in the Trinity Study, a 4% withdrawal rate would have unpleasantly high failure probabilities. I’m happy to report that with endogenous retirement timing, which is more realistic for the FIRE crowd, the failure probabilities do not increase by all that much. But they still increase. Picking a lower, more conservative safe withdrawal rate is even more important for us in the FIRE crowd. We should also consider equity glidepaths (See Part 19 and Part 20), to hedge higher the higher risk of retiring right before the next bear market!

We hope you enjoyed today’s post. Please leave your comments and suggestions below and make sure you check out the other parts of this series:


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