August 5, 2021
Welcome back to another post in the Safe Withdrawal Rate Series. For a quick intro and a summary of the series, please refer to the new landing page.
People in the FIRE and personal finance blogging community – readers and fellow bloggers alike – often tell me that while they enjoy my writings here, they wonder if I haven’t gone a little too far into the rabbit hole of quantitative analysis. Why measure safe withdrawal rates down to multiple significant digits? Why do all of this careful analysis if there’s so much uncertainty? Market uncertainty, policy uncertainty, personal uncertainty, model uncertainty! Why not just wing it? I always try to give a short reply to defend my quantitative approach and out of the many different mental and written notes I’ve taken over the years I created this post for your enjoyment and for my convenience to refer to if I get this question again next week.
Specifically, I want to propose at least three reasons for being diligent and precise not despite, but precisely because of retirement uncertainties. And, by the way, I will keep today’s post relatively lean in terms of simulations and calculations, and rather try to make this more of a philosophical exercise. So, if you’re one of the quant-skeptics I hope you keep reading because I can promise you that we don’t have to get too deep into the (quant) weeds. So, let’s take a look at my top three reasons to get the math right…
1: You’ll retire with more confidence and have a more relaxed retirement!
Let’s take a look at an (imaginary) conversation with my (actual) best buddy, Raj. Just like yours truly, Raj has a Ph.D. in economics but he took the academic route and is now a full professor at a large university. He was the best man at my wedding and I always run ideas by him, especially about major decisions. It doesn’t mean that I always listen to him but I appreciate his advice. So here it goes, sometime in late 2017, early 2018, talking to my best buddy Raj about my plans to retire at the age of 44:
Karsten: Hey, Raj, guess what? I’ll quit my job and retire early!
Raj: What? Are you sure?
Karsten: Oh yes!
Raj: Have you thought this through? How confident are you that you’ll not run out of money?
Karsten: Oh, I won’t run out of money!
Raj: I’m mean you hold a Ph.D. in economics, you’re a CFA® charter-holder, so you probably did your own calculations: simulations, historical backtests, Monte Carlo Simulations, Bootstrapping methods, the whole enchilada, right?
Karsten: Oh, no, I didn’t have to do that.
Raj: Well, what did you do then?
Karsten: Oh there’s this blogger. He’s a retired software engineer. He said I’ll very likely not run out of money.
Raj: OK, so he’s a software engineer, so he obviously ran all those simulations and calculations, right?
Karsten: But he’s a great writer!
Raj: But how’s he so sure you won’t run out of money?
Karsten: Oh, he read the Trinity Study. It was written by three professors at Trinity University.
Raj: He read it?
Raj: And that makes him an expert?
Karsten: I guess…?
Raj: Did he stay at the Holiday Inn Express last night, too?
Karsten: Huh? What?
Raj: Nevermind… So, this Trinity Study shows that you won’t run out of money?
Karsten: That’s right! With a 4% withdrawal rate, you almost certainly won’t run out of money over 30 years. How amazing is that?
Raj: In 30 years your wife will be in her mid-60s.
Karsten: Uhm, yeah. I guess. We will also get Social Security! We’re just going to wing it then! But lots of historical cohorts ended up with more money after 30 years than they started with!
Raj: In nominal or real terms?
Karsten: Uhm, good question… not sure…
Raj: And that low probability of running out of money, is that an unconditional probability, or conditional on today’s expensive equity multiples and low bond yields?
Karsten: Uhm, never thought about that…
Raj: What a stupid idea! Best of luck, buddy, but don’t complain to me later that I didn’t warn you!
Of course, this conversation never took place. That’s because very early in the conversation after Raj asked me if I had done my homework, of course, I answered something along the lines of:
Karsten: Heck, yeah, I did my calculations. Do you think I would give up my six-figure job in San Francisco, title and status, window office, nice condo in the city, etc.? Without doing my homework first? Come on, you know me, right! I’m a math geek! I wrote a whole series on safe withdrawal strategies on my blog. I wrote my own Matlab code to loop over millions of different simulations. Especially, I wanted to study the impact of the initial equity valuations on my retirement safety!
That shut down Raj’s concerns. And we moved on to talk about the really important things in life: economics, finance, beer, cars, etc.
What I’m trying to convey here is that if I had never done my research, who knows, I might have never developed the confidence to pull the plug on a generally pretty sweet life in San Francisco.
A lot of my readers feel the same way. Yeah, early retirement sounds like a great lifestyle, but this is not an impulse purchase of a pair of sneakers. Before you hand in your resignation at the office you might want to do some more careful analysis. People do a lot of research before they buy a house or a car or a new dishwasher. Early retirement, i.e., foregoing 20 or more years of peak career earnings, is an even more substantial “purchase” and will necessitate a bit more analysis than hand-waving. I need a bit more assurance than “I’ll do 4% then be flexible if it doesn’t work out” and my readers seem to agree with my view.
Moreover, since I retired in June of 2018, I have already experienced two scary episodes of equity volatility: the late 2018 correction (stocks -19%) and the 2020 pandemic Bear Market (stocks -33%). I slept really well during those, knowing that my simulations showed that my withdrawal strategy would have been safe even during a repeat of the Great Depression or the 1970s/80s. It didn’t occur to us to even lower our retirement budget, much less worry about running out of money. And again, I don’t want to minimize the volatility over the last few years, but having done my homework made those episodes much easier on the nerves. Booking requests for podcasts went up in January 2019 and April 2020, so I have that strange suspicion that some folks in the “Wingit” crowd had rougher nights back then.
2: You may be able to retire earlier!
This idea wasn’t applicable to us personally, but I’ve done numerous case studies for volunteers a while ago and some of them were able to retire with a safe withdrawal rate North of 4%. Specifically, in the ten case studies I performed in 2017/2018, only three safe withdrawal rate recommendations came in at under 4% (between 3.75% and 3.90%), two were right at 4% and five were above 4% (all the way up to 6%). Likewise, in a 2019 case study for Becky and Stephen, I found that the initial fail-safe retirement budget rate was all the way up at 6.6% of their current net worth due to significant supplemental cash flows later in retirement.
Thus, some of these folks would still be working and worrying if they had relied on the naive 4% Rule. In other words, risk management goes both ways. You want to balance the risk of running out of money with the risk of working too long. Thus, quite in contrast to my (totally undeserved) public image as the “grinch” of the FIRE community, wagging my finger and warning people of the dangers of the 4% Rule, I have probably talked more people into retiring early than dissuaded them from retiring. Doing the math right can actually do that!
3: It’s the mathematically sound thing to do
3a: Avoid compounding risks!
In my professional career, I’ve dealt with a whole lot with statistics and risk management. Exactly because there is a lot of uncertainty, we had to be particularly diligent not to add even more uncertainty. I have never encountered situations where the presence of uncertainty asked for less precision and more sloppiness and hand-waving in your numerical analysis.
To drive home this point, let me first concede how uncertain retirement success has been in historical simulations. In the bar chart below I plot the final portfolio value histogram of all historical cohorts (since 1871!) if they had withdrawn 4% p.a. from their 75/25 portfolio over 30 years. The portfolio value is normalized to a $1 initial value. About 1.5% of the cohorts would have run out of money. But more than 70% of the cohorts ended up with more than they started with. There were even some cohorts that ended up with more than 7x their initial net worth! That’s a lot of uncertainty!
And I am the first to admit that running more safe withdrawal rate simulations will not reduce that uncertainty. But you know what else will not reduce the uncertainty? Winging it! In fact, winging it will just add even more uncertainty. So, let’s now assume that Mr. Wingit who doesn’t care if he has a 3% or 4% or 5% withdrawal rate – who’s counting, really?! – applies this additional uncertainty and piles it on top of the (market) uncertainty we already face.
Let’s look at how that would work out in the retirement simulations. In the histogram chart below, I plot the same chart as above but one histogram each for a 3%, 4%, and 5% withdrawal rate. Again, doing your analysis you will not eliminate risk, but adding uncertainty about how much need in retirement, 3% vs. 4% vs. 5% will broaden the spread of the final distribution even more. So, for someone who doesn’t really know or doesn’t care if his or her withdrawal rate is 3/4/5% and we assign a 1/3 probability to each of the values, we’d spread out the already vastly dispersed final asset distribution even more than the baseline 4% net worth distribution. Also notice that uncertainty about the SWR will increase the probability of tail events, especially the unpleasant ones. For example, the weighted probability of retirement bust, (0%+1.5%+19.6%)/3 = 7% is much higher than the 1.5% probability in the baseline.
To drive home this point some more, let me give you a medical analogy. Imagine a Medical Doctor, Dr. Wingit, MD, has to inject medicine into a patient. He looks up the dosage information and finds that a patient of this age and size and with this specific condition calls for a 40ml dosage. But Dr. Wingit points out that there is a lot of uncertainty about the patient’s survival chances anyway, so who really cares about the exact amount. 30ml, 40ml, 50ml, it’s all the same, right? Uhm, no it’s not. You want to be precise to not add even more uncertainty to an already volatile situation. (But just to be sure, in Part 47 I provide a few examples of retirement modeling issues where you can safely wing it!)
Statistically speaking, because uncertainty compounds, the presence of one uncertainty (over which we may have no control) doesn’t eliminate the incentives to reduce the volatility over which we do have control. Quite the opposite. You still want to minimize the uncertainties you control. Statisticians even have a joke about people who don’t understand this idea:
An airline passenger is caught carrying a bomb in his carry-on luggage. The police interview him and ask him about his motives. He responds: “The chance of a bomb on a plane has got be less than one in a million. If I already bring one with me, the chances of that second bomb must be minuscule!”
Yes, granted, the joke is mostly about another statistical misunderstanding, but the same flavor applies here. The fact that you face one risk doesn’t mean that you can be nonchalant about another additional and compounding risk!
In other words, the “precision skeptics” put forward the classical strawman argument: I never claimed that I could eliminate or even reduce market uncertainty. I simply don’t want to add to that risk!
3b: Numerical Precision of Safe Withdrawal Rates
Related again to the 3%/4%/5% issue, over the years, one of the main criticisms has been this one: why do I even pin down safe withdrawal rates to several significant digits? I can’t count the number of times I’ve heard people object “hey, 3%, 4%, or 5%, doesn’t really matter, it’s only 1% difference!” If I had a dollar for every time I rolled my eyes over that objection, I’d be – let’s see – roughly 1% richer than I already am (pun intended).
Only, people who make this objection clearly don’t understand percentage calculations (sixth grade, I believe?) because going from a 3% to a 4% and then a 5% withdrawal rate is not a 1% increase. It’s a 1 percentage point increase. Big difference! Imagine you have a $2m portfolio and you contemplate retiring with a $60,000 or $80,000 and $100,000 a year budget (=3%, 4%, and 5% of $2m, respectively), it doesn’t take a rocket scientist to figure out that going from a 3% to a 4% withdrawal rate is actually a 33.3% increase, not a 1% increase in annual spending: $60k to $80k. And an increase from $80k to $100k is a 25% jump, not a 1% jump. We may not want to go too far overboard and display a safe withdrawal rate at a higher precision than, say, 0.01% steps, because with a $2,000,000 portfolio that would mean we pin our annual retirement budget down to a $200 precision. Who can do that, really? But 1.0 percentage point steps in the withdrawal rates are way too coarse!
To drive home this point some more, let’s look at the output from my Google Safe Withdrawal Sheet below (see SWR Part 28 for more details). In the top portion of the table, I display the failure rates of different withdrawal rates. I assume a 60-year horizon and 75% stocks, 25% bonds portfolio.
I like to focus on the column that conditions on expensive equity valuations, as we currently experience! Conditional on the Shiller CAPE, a widely respected measure of the S&P 500 valuation, at greater than 20x cyclically-adjusted real earnings (actually closer to 40 while writing this), plus the S&P 500 at or close to its all-time high, notice how rapidly the failure probabilities increase if we raise the withdrawal rates in 0.25% steps: no historical failures at 3.25%, then 13% failures if we raise the withdrawal to 3.5%. Then 30% and just under 49% when we raise the withdrawal rate to 3.75% and 4.00%, respectively. I would almost prefer going in 0.10% or even 0.05% steps because the historical failure probabilities rise so rapidly!
The two reasons why such small changes in the withdrawal rate have such a large impact on the failure rates? First, let me repeat myself, a 0.25 percentage point increase implies an increase in the retirement budget by almost 8% (3.25% to 3.50% = a 7.7% increase in retirement spending). Second, what helps you in the accumulation phase – small monthly contributions accumulate to significant sums over time due to the miracle of compounding – will now hurt you in the withdrawal phase. Small changes in withdrawal amounts can make the difference between growing or maintaining or wiping out your nest egg! Hence the extreme sensitivity of retirement success to small changes in the withdrawal amounts!
We can also slice the same simulation data and compute the withdrawal rates that would have generated various failure rates in historical simulations, see the bottom panel in the same table above. For example, the historical failsafe was 3.25%, i.e., the highest withdrawal rate that would have not failed and thus created one cohort ending their retirement with exactly $0.00. Raising the withdrawal rate to 3.41% you already have a 5% failure probability. Some people might still be comfortable with that (I would not), but raising the WR by only another 0.06 percentage points already creates 10% failures, definitely not an acceptable risk.
So, all the action in this particular withdrawal simulation took place in a very narrow window of somewhere between 3.25% and 3.50%. Anyone who claims that you should not do withdrawal planning past the withdrawal rate percentage decimal point commits financial planning malpractice. I repeat myself, I would even argue that 0.25% steps are a bit too coarse.
3c: Oops, maybe we can reduce the market volatility…
One additional reason for doing a more thoughtful analysis: there is a way of reducing some of the financial market uncertainty. Unfortunately, it’s not in a way that anyone would like very much. It’s related to equity valuations. If we slice the histogram chart above and condition on different levels of the Shiller CAPE at the start of retirement, we get the chart below. Notice how the dispersion of final values is not entirely random. Quite intriguing, considering that the equity market is normally considered a nice perfect random walk. Well, it’s not exactly a random walk, as I pointed out in a “random” post a long time ago! Cohorts that started when the CAPE was low (CAPE<12, equities are cheap relative to earnings) were responsible for most of the positive outliers. Likewise, most of the failures occur in the cohorts that start retirement when the CAPE ratio is elevated. As in “today’s CAPE”!
Another way to display the same numbers: Each CAPE regime with its own histogram chart, please see below. Quite intriguingly, the standard deviation of final values is indeed lower when conditioning on a high CAPE: 1.06 vs. 1.63 unconditional. But the lower uncertainty comes from eliminating the upside and raising the probabilities of adverse outcomes, including a 5.8% risk of running out of money after 30 years. Lower uncertainty but in a bad way because you vastly reduce the prospect for large expansions of your net worth!
3d: Model Uncertainty
As a last resort, “Hail Mary Pass” argument against a rigorous withdrawal strategy, the quant skeptics will often object that “future returns can look very different from past returns!” Guess what?! I agree! In fact, my #1 criticism of the naive 4% Rule is that the ostensibly low failure probabilities are merely the unconditional probabilities averaged over the entire simulation horizon. Ignoring today’s high equity multiples will make any kind of probabilistic statements like “the 4% Rule had a 98% success rate” useless.
I always like to use the “traffic jam analogy” where you calculate the probability of a traffic jam by looking at the incidence of traffic jams at 24 different times of the day, always at the top of the hour. You notice that traffic jams always occur at 7 am, 8 am, 9 am, 4 pm, 5 pm, and 6 pm, and thus deduce that the probability of a traffic jam is 6/24=0.25=25%. But that number is useless if you already know that your commute is at 8 am, and the 25% estimate wildly underestimates the risk of a traffic jam. And if your commute is 3 am, the 25% estimate might be too high! Just like a 4% withdrawal rate might be too risky if the CAPE ratio is above 30. And the 4% rate might be way too conservative if the CAPE ratio is in the single digits, as we saw around the market bottom in the early 1930s, mid-1970s, and early 1980s!
So, I certainly addressed part of the model uncertainty issue. Of course, one could object that even when we’re accounting for the current equity valuations, future returns can still look different than in the past during comparable equity bull markets. I concede that there are various reasons to push future returns either higher thanks to artificial intelligence and other breakthrough productivity gains. Or lower due to massive debt loads in the industrialized world, social unrest, etc. I think that the positive and negative risks balance each other. Unless someone can convince me that one effect is much larger than the other, I’d be comfortable with the working assumption that we should probably just calibrate our current SWR to the historical CAPE>20 and S&P 500 at the all-time high scenarios. Not the mid-1970s!
In retirement, we face a lot of uncertainties. On my blog here I cover the market uncertainty portion in much detail. But I also studied a lot of the others. For example, I propose factoring in future Social Security payments and accounting for a “haircut” to account for future benefit cuts. I also provided a free (!) Google Simulation sheet (See Part 28 for the details), where folks can model their own idiosyncratic budget assumptions. like higher health care expenses in old age, college expenses, etc. It also has other features, like modeling spending increases of +/-x% over CPI and many other bells and whistles.
Model uncertainty? That’s a tricky one. We can and should certainly account for the possibility that future returns may not look like the past unconditional returns. I routinely do so by conditioning retirement failure rates based on equity valuations (CAPE ratio) and/or where the S&P 500 stands relative to its recent all-time high. Model uncertainty beyond that is indeed hard to wrap your head around. Maybe someone can educate me on what the future might hold!? Looking forward to discussions on that one!
Anyway, folks, we’re close to 4,000 words now and that’s enough for today. To wrap things up, the presence of uncertainties calls for more mathematical rigor not less. I like to understand and try to model the risks to make an educated decision and live confidently in retirement. I don’t want to add even more fear in the form of “sloppiness” uncertainty. I hope the quant skeptics got a better understanding of my thought process. And I hope the regular readers enjoyed today’s post as well!
Please leave your comments and suggestions below! Also, make sure you check out the other parts of the series, see here for a guide to the different parts so far!
Title picture credit: Pixabay.com