July 15, 2020
Welcome back to a new installment of the Safe Withdrawal Series! If you’re a first-time reader, please check out the main landing page of the series for recommendations about how to approach the 38-part series!
I’ve been mulling over an interesting question I keep getting:
Is there a time when we can stop worrying about Sequence Risk?
In other words, when is the worst over? When are we out of the woods, so to say? A lot of people are quick throwing around numbers like 10 years. I would normally resist giving a specific time frame. The 10-year horizon indeed has some empirical validity, but I also want to point out a big logical flaw in that calculation. Nevertheless, in today’s post, I want to present three different modeling approaches to shed light on the question. And yes, I’ll also explain what the heck that Mandelbrot title picture has to do with that! 🙂 Let’s take a look…
1: Regress Safe Withdrawal Rates on realized portfolio returns
You can arrive at this 5 to 10-year figure until Sequence Risk becomes less of a problem through at least two different routes.
First, if you’re unlucky and you retire at the peak of the market right before a recession and bear market hit then it might take about 10 years to get back to the old peak again. In my post “Who’s afraid of a Bear Market?” I pointed out that a Bear Market can have a much longer destructive impact on your portfolio than the 1-2 years often quoted in the personal finance world. That’s because the portfolio doesn’t merely have to start to rise again (= end of the bear market) but your portfolio has to reach its old peak again to overcome the effects of Sequence Risk. in CPI-adjusted terms! So, instead of 1-2 years, we’re looking at much closer to 5 years for a moderate bear market and often 10+ years for the deep market events.
We can also confirm this 10-year time through a second approach – a more quantitative exercise as I proposed in Part 15 of the series: calculate the safe withdrawal rate (assume a 30-year horizon, a zero final value target and a 75/25 stock/bond portfolio) for all different starting dates between 1871 and 1990 and then regress that on the realized returns. As you can see in the table below (left panel) you get statistically significant estimates, but a relatively poor R^2. Only about one-third of the variation in the SWR is accounted for by the (geometric) average annualized portfolio return over the retirement horizon. The reason is that the returns early in retirement have a much larger impact on retirement success than the later returns. To prove that, I disentangle the average returns and split them into six 5-year windows (years 1-5, 6-10,…, 26-30) and when I run a regression of the SWR on an intercept and those 6 different subperiod returns, boom, I get a much higher R^2 and much higher beta estimates on the earlier returns. And also much higher t-stats.
Side note: The results here are slightly different from the post back in 2017, for (at least) two reasons: a slightly different time frame with additional data and a 75/25 portfolio instead of an 80/20 portfolio. Also, recall that a t-stat with an absolute value above 2 is normally considered statistically significant.
The conclusion of this exercise is that only about one-third of the variation in the Safe Withdrawal Rate is (statistically) explained by the average return over the retirement horizon, while the other two-thirds come from the sequence of returns. That’s a very powerful result: the sequence matters roughly twice as much as the average return! That’s why Sequence Risk is such a big deal; success or failure of your withdrawal strategy hinges mostly on the returns during the first ten or so years of your retirement.
So, should I now conclude that Sequence Risk is over and finished after 10 years? It looks like the first ten years pick up a majority of betas: 0.286+0.190=0.476 vs. the combined 0.282 of the remaining 20 years of beta estimates. Unfortunately, that would be a complete misinterpretation of my regression result, though. The reason is that after those ten years have passed, and I do another SWR calculation, this time of the remaining 20-year retirement horizon and I regress that SWR on the returns of the remaining 20 years I get the results in the table below, see the panel on the right.
Well, after the first ten years of returns are “water under the bridge” the next 10 years (i.e., years 11-20) of returns are now crucial in determining the success over the 20-year remainder of your retirement. So, remember the Mandelbrot picture where you can zoom in and find ever new Mandelbrot shapes? Or any other self-similar images, e.g. the Koch snowflake, etc.? That’s a bit like Sequence Risk. After the first 10 years passed, the subsequent 10 years are now the main source of Sequence Risk, even though previously they were much less important.
Thus, Sequence Risk will still be an issue even 10 years into your retirement. Strictly speaking, Sequence Risk will be around until you’re done with your withdrawals.
But maybe we should look at a different kind of calculation. Forget about readjusting the SWR after 10 years. Simply look at what kind of portfolio values I would need to see after ten years to get some reassurance that my initial 4% withdrawal plan will still work over the remainder of my retirement. Which brings us to method 2…
2: Success/Failure probabilities conditional on the 10-year portfolio value
Let’s assume we have a 30-year retirement horizon, a $1,000,000 portfolio invested in 75% stocks and 25% bonds and a 4% withdrawal rate ($3,333.33 per month) always adjusted by the CPI. If I run historical simulations with starting dates between 1871 and 1990 (and thus I use portfolio return data all the way to 2020), I get a vast variety of possible outcomes after 30 years:
- 1.8% of the cohorts completely run out of money
- An additional 5.5% end up with only about between 0 and $250,000
- But likewise, almost 50% of the cohorts more than double their initial nest egg in 30 years! The highest final net worth was over $9m, and that’s adjusted for inflation!
By how much can we cut down this vast uncertainty if we are now 10 years into our retirement? By a lot! That’s what I do in the chart below. I take all portfolio time series and I put them into different buckets depending on what range they fell into after 120 months. And then look at the probabilities of the 30-year final portfolio value conditional on falling into different buckets at the 10-year mark. And just for completeness, I also include the unconditional distribution over all the different simulations regardless of their 10-year value, see the bars on the right.
What do we find here? The 10-year portfolio value gives you a pretty good indicator on the 30-year outcomes:
- If after 10 years your portfolio has dropped by more than 50% (in CPI-adjusted terms) you can pretty much kiss “Good Bye” to the idea of vast riches at the end of your retirement. But I was positively surprised that the risk of running out of money increased from 1.8% (unconditionally) to “only” 13.9%. So even with extreme financial stress, you still have a large chance of making it for another 20 years! But chances are you will exhaust more than 50% of your initial capital. That’s fine for traditional retirees, probably not acceptable for early retirees who have to tag on another 20-30 after that initial 30-year window!
- If you’re down between 25 and 50%, you still have a 5% chance of running out. but quite surprisingly, you also had a 10%+ chance of getting all the way up to $2m at the end of the horizon!
- If your portfolio dropped only slightly, by 0-25% after 10 years, you still had a minute probability (0.6%) of running out of money. But you also face a 10%+ probability of severely depleting your portfolio (0-$250k left after 30 years).
- If you manage to preserve or even slightly grow your capital, you’re definitely out of the woods. There were no historical instances where your portfolio fell into the $1-1.25m range after 10 years and you still run out of money. Even better, there were no historical cohorts where the portfolio dropped to below $250k after another 20 years!
- And finally, if after 10 years you grow your portfolio by more than 25%, you should definitely splurge a little bit more. Or “risk” a vast overaccumulation of assets after 20 more years! 🙂
So, long story short, if after 10 years you still preserved your capital or at least 75% of it, you should be safe from completely running out of money after 30 years. But again, you still face a vast risk of where your final portfolio will eventually land. That’s due to both average future returns and – even more so – the sequence of returns!
And by the way, this is just the outcome for a generic 30-year retiree without any supplemental cash flow, another positive (pensions, Social Security) nor negative (additional health expenses, nursing home, etc. later in retirement). Everyone who’s not like this academic, generic retiree would have to do his/her own analysis!
3: Fail-safe withdrawal rates as a function of the horizon (and equity valuations)
Another way to look at the “are we out of the woods?” question is to simply calculate the fail-safe withdrawal rates as a function of the horizon. Then, calculate the capital that’s necessary to sustain that retirement horizon.
Specifically, let’s construct the following example:
- Same allocation as before: 75% stocks (S&P 500) and 25% bonds (10Y U.S. Treasury benchmark bond)
- Zero dollars final value target
- No additional cash flows
- A horizon of 60 to 720 months in 60-month steps…
For example, over a 720-month horizon, the fail-safe withdrawal rate would have been right at about 3.25%. So to sustain a $40,000 a year withdrawal, we’d need $40,000 divided by 0.0325, so it would take $1,229,000 in fail-safe capital to make it through the worst history has ever thrown at us:
One could now use this chart to get some guidance on where our portfolio value should stand 5 or 10 years into retirement to still guarantee the remainder of our retirement. But here’s the bad news: if you go from 60 years to 55 years and 50 years, the failsafe capital necessary to sustain a $40k a year withdrawal goes from $1.229m to $1.215m and $1.194m. This approach doesn’t give you much breathing room. The 50-year safe capital level is only about 3% below the 60-year number!
How about traditional retirees with a 30-year horizon? Well, thanks to the shorter horizon, you’d start with a failsafe initial capital of $1.047m over a 30-year horizon. 5 years and 10 years into retirement that’s down to $990k and $898k respectively. In other words, if after 10 years you’ve lost only less than 14% of the initial capital (adjusted for inflation!) then you should still be 100% safe.
Well, that doesn’t really sound too comforting. It means that if we lose even a bit of our initial retirement stash after 10 years, should we now be scared of running out of money? Well, the good news is that this approach is likely overly cautious and conservative. Certainly, if you lose less than a few percents you should be 100% super-safe. But it doesn’t mean that if you had lost 14.0001% after 10 years that you should be hair-on-fire scared about running out of money.
You see, the extreme market peaks that pose a severe retirement and Sequence Risk challenge occur only every 30 years or so: 1929, 1965-68, 2000 (and maybe, maybe 2020, but let’s hope not!). So, if you had the misfortune of retiring with a 60-year horizon right around a multi-decade market peak, it’s not too likely that 10 years into retirement you’re at another 1929-like market peak. So, calibrating your new 50-year retirement safe capital number to the historically worst outcomes seems wayyyy too conservative.
How do we fix this? We should factor in equity valuations! For example, if you had retired in 1965, then 10 years into retirement would put you right at the bottom of the 1975 recession and bear market. The S&P 500 was more than 30% from its peak (inflation-adjusted). Why would you then use the fail-safe withdrawal rate that’s calibrated to the extreme market peaks again?
Rather, we should factor in equity valuations! And that’s something we can easily do with the Big ERN Safe Withdrawal Rate Google Sheet. See Part 28 for more details.
Specifically, I grabbed the fail-safe SWRs, conditional on the relative equity valuation (i.e., relative to the most recent S&P 500 all-time-high). Then calculated the failsafe capital needed (=40,000/SWR) for all the different horizons and equity drawdown figures (0-50% in 10% steps) and plot the whole thing in the chart below.
Now we’re talking! If you’re 10 years into a 60-year retirement the fail-safe capital levels can be much reduced if the market is currently well below all-time-high. For example with a 30% drawdown, $899k is the safe capital level. If you’re a traditional retiree and you are 10 years into retirement, you’ll be fine with “only” $667k to sustain the remaining 20 years of $40k/year withdrawals. These are much more palatable “out of woods” targets for your portfolio on your 10th retirement anniversary!
In retirement, you’ll always face risks. The biggest concern for me personally and a lot of other retirees I know would be spending uncertainty because we’ll never know our old-age expenses, especially health and nursing home expenses until we actually get there. But even for flat, perfectly foreseeable expense patterns you will always face Sequence Risk until you’re down to your last and final withdrawal. So, we can’t really declare victory over Sequence Risk. Ever! And certainly not after only a few years into retirement.
Even if you try to answer a question like “will I know after 10 years whether I will make it?” it’s not trivial at all. It’s an inherently mathematical and quantitative issue. It’s not about whether you overcome the risk of running out money after observing 10 years’ worth of return data. It’s about what portfolio value you need to target to eliminate (or at least minimize) the risk of failure. So, general guidance that “Sequence Risk is done after 10 years” sounds like a bunch of mumbo-jumbo to me.
Ideally, I’d want to use the thought process in model 3, similar to what I proposed in Part 37 a few months ago. Whether it’s 10 months or 10 years into retirement, the mathematically and logically sound approach is to pretend it’s your first day in retirement all over again; look at your current portfolio value and your horizon but also the current equity valuations and check what’s a safe withdrawal rate now. Think of your retirement as in the movie “Groundhog Day”: every day is your first day in retirement again. And since this is your new imaginary first day in retirement again, you face a renewed Sequence of Return Risk again over the next roughly 10 years! Sorry: Sequence. Risk. Will. Not. Go. Away!
Updates 7/15, 8 a.m.:
- I wanted to but forgot to give a shoutout to Andrew Chen and his podcast and blog “Hack Your Wealth“. We talked about some of the issues of Withdrwawal rates and Sequence Risk, especially the question of “when can I stop worrying” on his podcast: Part 1 and Part 2. Also available as a Youtube video!
- Some people pointed out that today’s post seemingly contradicts the usefulness of glidepaths (see Part 19 and Part 20). I don’t think there’a a contradiction. As I’ve pointed out in the earlier posts, a GP didn’t work so well in a long, drawn-out event like the 1960s to 1980s. Also, if the market keeps going up during your first 5-10 years of retirement you might benefit from what I called an “active GP” where you don’t perform the bonds ->stocks shift until the market actually drops. Also, remember that Sequence Risk works both ways. It can hurt you and it can help you. The folks in method 2 that depleted their portfolio down to $500k after 10 years would hope for the benevolent Sequence Risk: high returns for the next 10 years because they find themselves at the bottom of a bear market. And to benefit from that (hopefully) impending rally, you’d be best positioned with 100% equities, not 75/25.
Thanks for stopping by today! 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!
Picture Credit: pixabay.com