The Need for Precision in an Uncertain World – SWR Series Part 46

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: No.

Raj: What?

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?

Karsten: Yup!

Raj: And that makes him an expert?

Karsten: I guess…?

Raj: Did he stay at the Holiday Inn Express last night, too?

Source: YouTube, Holiday Inn Express

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!

Final Net Worth: 30 years of withdrawals, 75/25 portfolio, 4% p.a. withdrawals.

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.

Final Net Worth: 30 years of withdrawals, 75/25 portfolio, 3% vs. 4% vs. 5% annual withdrawals.

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!

75/25 Portfolio, 60-year horizon. Main results from a safe withdrawal rate analysis.

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”!

Final Net Worth: 30 years of withdrawals, 75/25 portfolio, 4% p.a. withdrawals. Conditional on the initial Shiller 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!

Final Net Worth: 30 years of withdrawals, 75/25 portfolio, 4% p.a. withdrawals. Conditional on the initial Shiller CAPE.

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!

Conclusion

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!

Retirement Uncertainty: Don’t pile on sloppiness risk to all the others!

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

104 thoughts on “The Need for Precision in an Uncertain World – SWR Series Part 46

  1. I’m a big believer in this statement : “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”

    In my career, I’ve educated direct reports and students that we need focus on the variables that we can control to minimize the variation on the variables that we cannot control.

    I really appreciate your blog and while I don’t understand 100% of the technical pieces, I appreciate the logical approach. I’m using your Google sheet as one piece of information to help with my planning and projections. If you’re ever up for another case study – I’m in.

    Thanks for continuing to contribute while you enjoy your retirement.

  2. Great article as always! Do you have a tool that would simulate a lost decade? In your series 28 toolbox, we can enter a fix amount for the next 10yr. Would you have one that we can use Historical data. I have run many simulation but it’s really hard to pull the trigger as with the Cape rate we are in, and next ten years of uncertainty it’s really hard to figure it out. I agree, the fear of running out of money is really there!

    1. In the US we had a lost 1.7 decades: 1965-1982. Returns flat until 1973 and then down and lot of volatility.
      The Google Sheet has a case study tab where you can model the performance of a withdrawal strategy for any starting point.

      1. If you ever run out of ideas or topics, I for one, would be very excited to read a blog post by you regarding how we could have weathered, using hindsight, the 1965 to 1982 period.

        To be clear, we may never have another 1965 to 1982. So this is just a hindsight what-if exercise. Not some sort of Prepper’s Guide to The Apocalypse. Because the next financial crisis after 2020 most likely will look, feel, and behave very differently from the past financial crises.

  3. Karsten,

    Great stuff as always. I am 55 and planning to retire next year. I have calculated a 6% withdrawal rate until age 70, then social security kicks in and my withdrawl rate goes down to 3%. Am I missing anything?

    Thanks,

    Randy

  4. Excellent graphs that visually map out the percentages! I will be borrowing these for my yearly financial review with my wife, with the idea of explaining that “honey, we are all good and 2022 is the year”. Thanks!

  5. I can’t remember who said it first: making predictions is hard especially, when they are about the future.

  6. Speaking of withdrawals, I have experienced withdrawals recently without my usual Prof. ERN fix. Thanks for supplying my need after a well deserved absence with your family. Once again I greatly appreciate your analyzes and thoughtful explanations. The US Currency states “In God We Trust”. My own personal retirement analysis with your Withdrawal Series states “In Prof ERN I Trust”.

  7. An excellent post Big ERN! The only thing I would add is the necessity to stay flexible on ones retirement journey. The notion that retires should be “static” in their income expectations died with the defined benefit plans. Relying on ones own self-directed nest egg calls for developing a withdrawal based on sound reasoning to be sure but if things are not panning out surly we aren’t lemmings that just march into the world of cat food and cardboard box shelters. Stay flexible my friends and enjoy!

  8. I can think of two specific caveats for the otherwise excellent quant analysis:

    1. As you apply conditional situations, the sample size decreases significantly. That’s probably fine when grouping by CAPE, but I expect that CAPE > 20 + SPX high didn’t occur too many times. It’s absolutely useful to consider, but a disclaimer on sample size could be helpful there, as the true shape of the distribution may not be well-known.

    2. Overfitting. I think this is mitigated by running all the way back to 1870 (vs. Portfolio Charts’s starting in the 1970s – a shame because I really like his visualizations), but it is more of a concern when you run into low n from above.

    Again, I don’t think either discount the need for quality simulations, but they are worth pointing out when applicable.

    1. 1: Not really true. SPX at ATH and CAPE>20 are correlated. About 7.4% of the observations fall into this bucket. I think it’s neither too narrow nor too broad to calibrate today’s SWR to the 7.4% most overvalued historical cohorts.

      2: I think the sweet spot is 1926-current. Include more data than 1970-current but ignore the crazy 1871-19205 data. Results will not change much. Especially if you target failsafe rates: they all normally occur in 1929 and 1965-68 anyway. Doesn’t matter how much data you have before 1926.

  9. This was a great piece, Karsten. I enjoyed reading it because I understood much better than your Ph.D. level analysis. It would be great to read an executive summary for normal people after each quant presentation. If you ran by your wife, I’m sure she will be able to tell you if it’s a ‘go’ or ‘no go’ with readers.

    Right now I fall under # 2, but my fear is holding back due to my analysis-paralysis (like you lay out in # 3).
    I was more certain of FIRE in 1-2 years when we had $2M with $75k expenses 4 years ago. NW has almost doubled, but I’m now also projecting much higher expenses due to buying ACA insurance (at least $30k/year for 4?). $110-125k all in on $4M for a family with kids at home (college ed in 5-6 years) doesn’t sound as having much of margin of safety when we live in the pandemic environment, horrendous debt, very elevated Shiller CAPE, and inflation to top all off. 50 years of future when I don’t know about next year is a heck of pressure to live with. Financial conservatism is holding me back.

    1. @S&M, it’s funny how projected expenses creep up, especially for those of us with kids. I hear some of my thoughts in your comment. We have continued to move the goal posts over time, which can be frustrating. My advice is to keep going until you feel comfortable, and know that at some point (for us 3.25%) it’s plenty. Run the scenarios and figure out what is right for your gut, and then do it again in six months or a year. There will be a number. Other piece of advice is to, if you can, reduce your work as you get closer to that number. Trying to race to the number is tough, and you might find a longer runway can allow you to enjoy your kids more and allow you to experiment for what post-FIRE life will look like, at lower risk than simply mic dropping it at work one day. We are not quite there yet, but the past couple of years unwinding and working less has allowed for what I think will be a better transition for us.

      1. In German there’s a saying:
        “small kids small worries, big kids big worries.”
        And expenses as well, I guess. Yes, couldn’t agree more. Once the kid(s) get(s) older, you might feel to help with college, grad school, wedding, house down payment. And then start over when the grand kids come. I expect to scale up our expenses mid-term!

    2. @S&M, are you sure you’ll need to pay 30K for ACA? Not sure of your household income but if it’s below around 100K (for a family of 4) you should qualify for premium tax credits. I’m single, and haven’t tried to run numbers for a family, so take this with grains of salt 🙂

      1. In WA State, it’s about $900/m for a basic plan, but then with substantial out of pocket risk.

        Alternatively, Medishare has a plan for $400/m with a $10k annual deductible and 100% coverage after that.

        1. Being in WA and recently retired, I’d be curious on your mental model of how you approached ACA choices. If it’s generally useful it would be a cool article; if not and you’re comfortable, I would appreciate a DM.

          Thanks!

          1. Others have written about it. Right now, our income is well past the threshold, so I’m not even considering any alternatives to our current Medishare plan. Will let you know if that changes! 🙂

    3. I’m assuming you haven’t looked at what ACA will be after subsidies? Its currently capped at 8.5% of taxable income and retirees usually have much lower AGI’s compared to their annual spending. With a paid off house, its pretty easy easy to get the costs to around $10k/year or less on that kind of budget. The cap is scheduled to end but a lot of people think it will be extended. Even if it reverts back to old rules, a family of 5 with an AGI of $124k would still have silver plans capped at 9.8% of income at the worst.
      Even without subsidies, if you have a large HSA ($50k+) and are healthy, the bronze plans for family that cover the best hospital in my state are only $1100/mo. with $6k OOPmax per person.

    4. Understand. But with $120k in budget and $4m portfolio you seem to be in a good position. Have you plugged in the numbers in the Google Sheet?
      Really depends on the supplemental cash flows. Might be tight when planning to pay rack rate at Ivy League schools. Seems very safe when sending the kids to a good state school.

  10. Deeper analysis and thoughtful reasoning with an eye toward pracitical personal finance is why I love this blog. Because of this, Big ERN delivers unique value and stands above the massive crowd of other bloggers that tend to say similar things but without the deeper reasoning and understanding. If I want basic personal finance, I’ll read Money magazine and be done with it.

  11. I appreciate your in-depth analysis! Though I have to admit some of it goes right over my head. But then again I do not always sleep at a Holiday Inn Express the night before I read your blog.

    Your writings gave me the confidence to retire 2 years ago at 54 and I thank you for that. But I will look you up in 30 years if I am flat broke and busted. HAHAHA

    Thank you, SWR 2.575633% give or take the recent Amazon order.

  12. Wow…if I’m understanding correctly, the data is showing that a 4% withdrawal rate faces a roughly FIFTY-FIFTY CHANCE OF FAILURE in the current environment where CAPE>20! Worse yet, stocks could crash by almost 50% and STILL have a CAPE above 20! I’m glad I’m planning on a 3.0% SWR in my imminent retirement, at least for the first few years, thanks to your previous articles in this series. (As an aside, I particularly enjoyed your discussion of uncertainties, since that’s what I deal with all day long in my career of static timing analysis in IC chip design.)

    1. Historically it is. 48.84% of the cohorts ran out with a 4% WR under the elevated CAPE+S&P all-time high conditioning. Quite scary.

      But: over 60 years you will likely get some supplemental income later in retirement (SocSec, pensions).

      But it’s still scary how a small change in the SWR compounds into large tail probabilities!

      1. How would this change considering that interest rates are also close to 0? And if someone didn’t qualify for SS or pensions (due to being in a country that doesn’t have social welfare)?

        It feels like due to super high CAPE, plus zero percent interest, plus no future cash flows except from own work/businesses, that we’re already in Japanification mode of lower SWR?

        1. to add to my comment – it’s the yield collapse across asset classes that concerns me most. It makes that a larger component of the withdrawal will need to be principal as opposed to the cash flow generated from assets. Therefore any form of cash flows are most welcome during the retirement phase.

        2. Looks scary doesn’t it? Well, the market has done well and it raises the risk that more people will get hit by the “turkey fallacy”
          I think that by calibrating your SWR to the previous worst-case scenarios (1929, 1968) should be sufficient as a hedge.

          If you don’t have any supplemental cash flows, then you use whatever the sheet comes up when setting the flows to zero.

          I don’t see a Japan scenario (yet). We still have growth unlike Japan since the 1990s

  13. I think you’re being a little hard on poor Mr. Money Mustache. While of course all your points (as usual) are perfectly mathematically sound, a bare-bones introduction to the Trinity Study is extremely valuable to those who are new to investing and/or withdrawing. And while it’s easy to make fun of people naively adopting a 4% WR, naively adopting a 3% WR is quite safe as you’ve proven – not everybody can or wants to doctoral-level research of safe withdrawal rates.

    The gap between a 4% WR and a 3% WR isn’t very significant in terms of extra time spent working (assuming a reasonably high savings rate), so honestly for 99% of people (who are far, far away from FI) setting your sights on 4% is as reasonable a goal as 3%. Once you hit the former getting to the latter should be quite quick.

    Finally, the differences between safe withdrawal rates strikes me as a smaller risk than divorce, or some popular examples of people applying the 4% rule to portfolios composed of 50% TSLA and FB.

    I suppose critiquing the 4% strategy is becoming more important and more and more people become aware of these ideas, and the Safe Withdrawal Series is by far the best resource I’ve come across, so thank you for all your work!

    1. Oh, who said I was talking about MMM? There are many retired computer dudes in the Holiday Inn expert crowd! 😉

      Yeah, but I agree: going from 25x to 30x or even 33.33x doesn’t take much longer.

      Divorce is indeed a big risk. It belongs into the idiosyncratic bucket and might be the biggest and most common financial risk. Haven’t written about it, but it would be a nice topic in a future post.

  14. I’ll second Eduardo’s comment about going through Karsten withdrawal in your absence. 😀 I look forward to these posts. The SWR Toolbox is driving my SWR selection and thus my FI number, and I am grateful to you for providing well-researched specificity in a hand-wavy world.

  15. Karsten,

    I got my fix today. Thank you.

    Indeed, the future is will not be anything like the past. Almost all SWR work, analysis and MC simulations are completed using the US historical returns and for good reason – it is a robust data set. But this reliance adds model uncertainty! In my opinion, this data set itself has an upward bias. No economy has performed like the US in the past 100-150 years. This was the time of the modern, hyper-productive industrial and financial revolution. I can only assume that this 4 std dev “event” will not repeat and conclude that the 4% SWR is too aggressive / high. I would love to hear your take on this.

    Kudos to you and yours for your efforts to educate and elucidate us on the multitude of issues. I am a fan.

    1. Yes, that’s a great point. But also keep in mind that the U.S. has overcome some major challenges. 1907 panic. WW1, 1920/21 small depression, 1930s Great Depression, WW2, Beat the USSR, dot com crash, global financial crisis, etc.

      I agree that the future looks somehow dim, but maybe it’s just the average of all the other disasters we’re experienced before.

      But I agree: the U.S. was spared of a a near-total-loss as in a lot of European countries or Japan during/after WW2. We had it pretty good here! 🙂

    2. It’s hard to see it from the inside, but US culture prioritizes the accumulation of wealth over most other things we give lip service about being valuable. We are willing to breathe toxic heavy metals with every breath because the alternative is higher electric bills or lost coal mining jobs. We tolerate six to ten robo-spam calls a day because to outlaw telemarketing might infringe upon the rights of telemarketers to make money. When we debate going to war, one consideration is how war spending helped the economy out of the depression in the 1940s (firsthand witness here, 1991 and 2001-2). During an acute housing shortage when zoning rules have basically outlawed high-rises in pricey metro areas, we prioritize the rights of homeowners in those areas to set rules that allow them to profit off of newer entrants. Our healthcare system is organized to benefit profit-making companies, unlike any other industrialized democracy, and we adamantly defend it on principle despite the horrible outcomes we endure. Today, we are facing a pandemic that will probably kill a million of us and disable tens of millions, and even faced with the risk of death or lifelong symptoms we are insistent that airlines, restaurants, cruise ships, and other super-spreading venues open so their stock holders don’t lose money. Life is cheap here.

      It is this money-centric culture that powered the world’s best stock market returns over the past century and a half, and to say such a culture is going to suddenly change would be a radical statement. Technology may change quickly, but cultural values survive for centuries at a time. I predict the US market will continue to outperform family-centric cultures like Italy, leisurely cultures like Spain or France, or collective-good focused cultures like Japan or China for at least a couple more generations.

      1. You bring up a whole laundry list of societal ills. Some of them are certainly valid (sadly), some of them are exaggerated.
        But: I’m not sure what they have to do with the specific topic here, i.e., uncertainties in retirement.

        Also, I’d rather be rich and live in a not-that-perfect society than be poor and live in that same not-so-perfect society.

        Also, I have visited some “not-money-centric countries” (a.k.a. poor countries, a.k.a. third world countries) and people there burn their trash or just dump it in the river. I prefer the clean air and water in Washington State. In fact, if you believe that lives are not worth much here in the U.S. you should go to some third-world countries.

        Also, I pray for the US to keep the enemies of freedom at bay. The world will be a better and freer place!

        God Bless America, the best country ever! (not perfect, but the best among all the imperfect places)

  16. Welcome back and thanks for another great post!

    I was wondering if there’s a way to use your Google Simulation sheet to run analyses of concepts from your “Lower risk through leverage” article.

    In that article you suggested the following ideal mix from a max SWR perspective for a stock/leveraged bond portfolio: “Probably the most elegant way to implement a sample portfolio of about 80% equities and 120% bonds would be to hold the entire equity portion in physicals (e.g. Stocks, ETFs, mutual funds), another 18% in bond funds and the remaining 102% bond futures. The 2% leftover cash is more than enough for the margin on Treasury futures.” Can portfolios such as this one be modeled in the Google Simulation sheet?

    When employing a stock/leveraged bond portfolio such as the one described above, should the bond futures be held in a taxable Interactive Brokers account, or would that be ill-advised from a tax perspective? After retiring, I plan to hold my regular bond funds in my tax-deferred account, but I don’t know where the Treasury futures should ideally be held. Unfortunately I live in a high-tax state and have limited tax-deferred space in my portfolio.

    1. Leveraged strategies like 80/120 are great for a buy and hold investor but for retiree who’s withdrawing every year, they will lower your SWR in most cases. For instance, having 120% bonds in your portfolio during the 1960’s and 1970’s inflation era would have been disastrous.

      An easy way to model it with ERN’s withdrawal toolbox is just to plug in 80% Stocks/120% Bonds/-100% Cash. The SWR drops to 2.49% if you include all data and 3.11% if you only go back to the 1960’s compared to a 3.47%SWR for a simple 75%/25% portfolio.

    2. Excellent point!

      You certainly can do that. But to be consistent you’d have to make sure that all the weights sum up to 1.00. So, if you’re using 80% Stocks, 120% bonds you also need to use -100% cash.

      That said, you probably want to start with something less risky. 80/120/-100 may be good during accumulation, but not so much during the withdrawal phase. Maybe start with 60/90/-50.

      Also keep in mind that the 80/120/-100 allocation would have been bad during the 1970s. All the risk-parity-flavor strategies that became so popular recently, have all been optimized for post-1982 data. 🙂

  17. Good article. People tend to handle a large number of uncertainties using a naive Central Limit Theorem — i.e. all the uncertainties cancel on the average and the potential outcomes are symmetrically distributed around that average. But as your Final Net Worth chart shows, retirement outcomes are not symmetric using the 4% rule. This is a risk mitigation situation, not maximizing an average. And that gets me thinking about contingency planning. Planning for retirement contingencies (investment growth/decline, changes in life situation, etc.) is IMO more beneficial than refining our simulations.

    1. The Central Limit Theorem works great for the accumulation phase. You have some investments you start at attractive valuations, and others at unattractive valuations. Over the years it averages out. There isn’t a strong correlation between investment success and the initial CAPE when you start making regular contributions

      The CLT doesn’t work with all your risks in retirement. Because you’re not taking the AVERAGE of the risks. They all compound!

  18. Thanks
    I have two questions:
    1. What do you think a bout “Excess CAPE Yield”? according to it the market is not that expensive.
    2. Why not invest in low CAPE market like UK or at least not-that-high CAPE like Japan or Germany?

    1. Both excellent questions.

      1: The excess/relative CAPE yield over or 10y bonds is not that high. At least not as outrageous as the absolute CAPE yield. But that solves only one problem. We may not have impending doom (like 2001), but if all expected asset returns are low, it’s still not good for retirees. Could be a repeat of the 1965-1968 retirement cohorts.

      2: Thought about it. I always feel these are the countries that are cheap for a reason. Sclerotic growth like in Germany, France, Japan doesn’t bode well for equity returns.

  19. In summary, don’t FIRE and it will be much easier to live without all these concerns. Brilliant!!!

  20. Great post. Glad you’re back “on the job.” I’m wondering about the impact on SWR of an uber-high CAPE. As in 38.5. As you note, that’s much higher than 20. Other conditions remaining the same, does a 3.25 percent SWR go to 2.5 percent in this environment? 25 bps higher? lower? Would make a great column, Big ERN….

    1. 38 is certainly much higher than normal. But I think due to lower dividend payout ratios and strictier accountinf standards, a 38 today may only be comparable to a 28 CAPE 50 years ago.
      Still looking for a way to quantify this, though. If the long-term CAPE median is 15, what should we use as a “normal” CAPE today?

  21. So, Bonds always counterbalanced stocks. When one goes up the other goes down.
    It seems that is not true anymore, so what would one use to have the same effect (without having to use derivative stuff of course)?

      1. That’s what I said: It seems that is not true anymore, so what would one use to have the same effect (without having to use derivative stuff of course)?

        1. Not sure what you mean by “anymore” because the stock bond correlation was negative during the 2020 recession as well. You may FORECAST that the correlation will flip going forward, but there’s no guarantee.

  22. I’m not sure if the hypothetical conversation with Raj in this post is insulting Mr. Money Mustache (a retired software engineer blogger who also is a good writer), but that was the first person that came to mind for me. If so, definitely not cool – he’s the reason that many people have even been exposed the the concept of FIRE in the first place! If not, carry on and no complaints here.

      1. You’d be the first economist I’ve met with that philosophy. Economists make the colleagues in my department (I’m a statistician) seem cordial 🙂

        1. Every profession has its own horror stories about how crude and rude the academic community is. My older brother is a statistician and that seemed a rough community. But economists might be worse. FWIW, I always say that in 2008 I left the academic econ community to join a much more polite crowd: Wall Street. 🙂

  23. If high-CAPE environments have little long-term upside, might it make sense to sell this unlikely upside as a hedging strategy? CAPE is not factored into options pricing models, so in theory the computers are overpricing call options.

    For example, sell covered calls to increase the odds of a modest return that is more likely to be above zero than the market return? Or, use the premium received from selling those calls to hedge with puts (a collar strategy). Seems like one could narrow down their possible range of long-term returns to an acceptable WR plus a reasonable guess at inflation and detach themselves from a lot of market risk – and pay for it by selling the risk of an upside which is historically unlikely.

    It would be worthwhile to forego the icing on several good years if it meant avoiding damage from one SORR event.

    It would be very hard to model historical returns based on a derivatives-hedged portfolio. Hell, it’s hard to even find or calculate historical options/futures prices. This is not a precision-based criticism of quantitative analysis on historical data, but it is a criticism in another category – i.e. only being able to analyze unhedged portfolios. How could we model having an options-based safety net for retirement portfolios? How can we analyze for the optimum hedge?

    I’m thinking we look at today’s prices for hedging risk with a certain strategy at a certain level (e.g. the net debit for a collar with outcomes between +15% and -15%, expressed as a % of the amount hedged) and subtract that price from returns for every year in the high-CAPE historical dataset. Then, go through the historical stock dataset and change returns to the outcome that would be realized each year with that strategy (e.g. if modeling a +15%/-15% collar, find all the years with returns worse than -15% and change them to -15%, and similarly change years >+15% to +15%).

    Similarly, one buying LEAPS call options in lieu of stock could simply subtract their expected time decay from the returns dataset, and then edit any years where losses exceeded the cost of the option to simulate the call expiring worthless.

    Can you think of any problems with such adjustments as a way to model derivative-hedged portfolios? The biggest issue I can think of is that “today’s prices for hedging risk” can change a bit with implied volatility and interest rates, but to incorporate these factors, one would need to calculate options prices for each year in the historical dataset which is deeper water than my mommy allows me to swim in.

    1. I hear you. But it’s hard to time the peak. The lesson from the 1990s is that if you had sold in 1996 when the market seemed already quite expensive you would have missed a lot of eventual gains.

      I like options strategies (see my relevant posts on the topic), but I don’t particarly like the covered call strategies. I’ve had good success with put writing of OTM puts.

      Collar strategies: I don’t like them. There is a smile/smirk in the implied vol curve, so puts are vastly more expensive than calls, even with the same number of point OTM.

      One avanue I’d like to explore in a future post: Buy an ATM Call with >2 years to expiration (LEAPS). and invest the bulk of the rest of the moey in some relatively safe asset (corporate bonds, maybe a little bit of preferreds). Seems like a good downside protection, Sequence Risk insurance in retirement.

      1. I agree that with a collar strategy, one would pay for the IV “smirk”. But maybe that’s a bargain compared to the reduction in SORR? It would take a study to find out. This is why I proposed establishing the “cost” of symmetrical collars – i.e. the net debit as a percentage of assets protected – which could be subtracted from the spreadsheet returns.

        I will boldly hypothesize that the cost of the smirk on a 100% collared stock portfolio is less than the cost of holding 40% of one’s portfolio in 5 year treasuries instead of equities.

        Regarding a “calls and cash” strategy, I’m looking at that too. It would be as simple as waiting for IV to reach a historically low range and buying LEAPS calls. Would one pay more for this strategy in time decay than one would pay in smirk cost? I would think so, because the unlimited upside payoff function is more attractive than the limited upside, so it should cost more.

        1. Good point. Agree with the opprotunity cost argument of a 40% bond portfolio. I don’t have the data to simulate anything at my fingertips, though.

          The LEAPS strategy certainly sounds attractive. One could introduce a little bit of leverage to overcome the tax drag.

    2. “CAPE is not factored into options pricing models, so in theory the computers are overpricing call options.”

      While they aren’t one of the inputs in the 40+ year old Black-Scholes pricing model, market participants have much more sophisticated proprietary models than the out-of-the-box Black-Scholes model. I wouldn’t assume that you’re taking advantage of anyone if the high cape is your main justification for selling calls. The person/computer who’s buying the calls from you also knows the cape ratio is high too.

  24. It’s the beginning of the end of this once great nation and the final days of a global power. US debt will be 32 trillion after Biden spending spree. Just in perspective, the total money in circulation the world today is $37 trillion. And some wonder why bitcoin is where it is…people aren’t stupid, they know this debt is unpayable and the future of the US is like the Roman empire. China thanks!

    1. Keep in mind that the $32t in government debt have to balanced against the US household net worth: $136.9 trillion. We’ll be OK!

      But I agree with your general sentiment: USA better watch out and not let Commie/Fascist China mess with us.

      1. Lots of it is lent to U.S. citizens in their retirement and pension accounts. Also $5T of the government debt is lent to….the U.S. Federal reserve as part of their $8T balance sheet.

        If China unwound their debt it would make their currency stronger hurting their exports the dollar weak boosting our exports. Part of the reason they buy the treasuries is to artificially keep their currency low to boost exports.

        I do agree that not all debt is a good use of money and its probably not sustainable to keep growing our debt forever at this pace.

        1. That’s exactly my point, only you wrote it more eloquently. We net out the US private net worth against the US Gov debt and Americans are still fabulously rich. Something that the previous poster did not know.
          But I agree: the ballooning debt debt is something that needs to be addressed.

    1. Two observations:
      1: You’re old school. What program is that? DOS-based?
      2: Wow, that’s a high withdrawal rate. Good for you that the market gods cooperated! Pretty aggressive SWR! But that’s my point all along: 2008/9 was not a bad bear market from a Sequence Risk perspective. The recovery was really swift. Good for you! Glad this worked out so well!

      1. 2008/09 End of Year numbers wasn’t the worst of it. We actually bottomed out at $864k by the end of Feb 09.

        The SWR was not pre-determined, it was calculated post spending. But we analyzed our spending at the end of each year, compared it to the portfolio’s progress, and decided then whether or not we needed to reign in our spending in the next year or not.

        I never learned/used Dos. I started out with CPM and then moved on to Unix. 8^)

    1. Yep, decades old. I was open-source text-based called Spreadsheet Calculator or, sc for short. I have the source code so I just keep porting it over to whatever platform I happen to be using. These days that is MacOSX.

  25. Pingback: Sanguine Sojourner
  26. It seems to me a lot depends on how you look at the risk, and if you’d be willing to work in the future and what you expect to earn. If you absolutely refuse to make more money, or think the best job you can get is Walmart clerk, then 10% risk is really bad! On the other hand if you expect to end up making some money somehow over the first thirty years of retirement, even if its not necessary, but it keeps you entertained. If you’d be willing to work a real job for a few years down the road, if the investments aren’t doing well, then it seems to me it might well make sense to go for it, and evaluate as you see what happens. Maybe it’ll just be a long break between jobs, maybe not, but either way lots of free time while in good shape, and if you need to work you’ll come at it fresh. I’d expect most early retirees can make an average wage and not spend all of it, so they should be investing while stocks are really cheap? As a rough set of rules I’m imagining something like if you drop below 80% of your original investment in the first 10 years, you get a real job as soon as possible and take no withdrawals until you’ve rebuilt to 90% or even 100%? of the original amount, at which point you attempt the retirement again. I know you did some models of flexibility, but I didn’t see anything nearly that extreme? Certainly you risk working too much the second time around, but in the case you don’t have an issue you make out better since you wasted less time working, you’ve also shifted some work to a time where equity prices are discounted.

    1. First: if you have an opportunity to make money and you enjoy it, you should have already factored it into your SWR analysis. The fact that you haven’t probably means that you consider it a burden. Or an embarrassment to go back to work when you announced everywhere that you FIRE’d.

      Also: I have already simulated a work flexibility rule you describe, where you start working part-time if your portfolio drops below a certain threshold. See Part 23.
      The problem with that work flexibility rule: You might go back to work for 10+ or even 20+ years. You might also get false alarms, i.e., go back to work when eventually it turns out it wasn’t even necessary.
      All those are failures. Not as catastrophic as running out of money, but failures nevertheless.

      1. Certainly they’re all failures to a degree, though working an extra year at something you don’t like because precision says you need the money, when you could have winged it and ended up not needing to work anyway is also a failure. Even doing lots more calculations than you could have gotten away with is a failure of a sort, if you don’t like that sort of thing, its work after all. I’d seen part 23, but wondered about jobs that pay more than minimum wage, I’d imagine if you got back to a job where you save 50% again, you’d fairly quickly rebuild the portfolio and it’d be less than 10 years? Maybe I should actually try that in your spread sheets rather than just asking though.
        As for adding it into the SWR calculation I think its kind of hard to be precise here at least for myself, if I quit tomorrow, I’ll probably want to work after a few months off, but will my ideal job be part time tutoring for $20k, or some software thing that pays $250k? Neither is particularly unreasonable. One way to do it I suppose is simply say I’m not entirely retired, but I’m also pretty unwilling to work on anything I don’t really like. You seem happy with your choices, so you’ve succeeded so far in the most important way, but I’m curious, did you factor the part time things your doing into your plans?

        1. Too many people confuse retiring (ie, no longer working a job for $$) and financial independence. Go for FI! Then you can work or not, whichever makes you happier.

        2. “quickly rebuild the portfolio and it’d be less than 10 years?”

          Less than 10 years is still unpleasant. I think 5 years and even 3 years of going back to work is unpleasant enough that it justifies working another year in my old cushy corporate job.

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