March 2, 2021
A while ago I wrote about the challenge of designing pre-retirement equity/bond glidepaths (“What’s wrong with Target Date Funds?“). In a nutshell, the main weakness of Target Date Funds (TDFs) for folks planning an early retirement is that if you have a short horizon and a large savings rate then the “industry standard” TDF is probably useless. 10 years before retirement, the TDF has likely shifted too far out of equities, likely below 70%!
The problem is that the traditional glidepaths are calibrated to the traditional retiree (who would have guessed???) with a sizable nest egg ten years away from retirement. In that case, you want to hedge against the possibility of a bear market so close to retirement from which you might have trouble recovering due to the relatively small contributions of “only” 10-15% of your income. But people planning early retirement with a small initial net worth and a massive 50+% savings rates should clearly take more risk to get their portfolio off the ground.
In any case, back then I mentioned that I had some additional material about glidepaths toward retirement for the FIRE community, to be published at a later date, which is today!
Why is this post part of the Safe Withdrawal Rate Series? First, today’s post is a natural extension of the FIRE glidepath posts (Part 19, Part 20) in this series. Moreover, the majority of readers of the series are not necessarily retired yet. Many seek guidance during the last few years before retirement. In fact, one of the most frequent questions I have been getting is that people who are almost retired and still holding 100% equities wonder how they are supposed to transition to a less aggressive allocation, say 75% stocks and 25% bonds at the start of retirement. Should you do a gradual transition? Or keep the allocation at 100% equities and then rapidly (cold-turkey?) shift to a more cautious allocation upon retirement?
My usual response: It depends on your parameters and constraints. You can certainly maintain your 100% equity allocation much longer than the traditional TDFs would make you believe. If you are “flexible” with your retirement date you can even keep the equity weight at 100% until you retire. If you are really set on a specific date and want to hedge the downside risk, you probably want to gradually shift there over the last few years. So, let’s take a look at my findings…
- I assume the investor is 10 years away from retirement. (a 5-year version follows below)
- He/She saves $1 every month for 120 months at the beginning of each month. Contributions are adjusted for inflation. You can scale this up to your desired savings level if you want. All the calculations and optimization results are independent of the scaling. If a glidepath is “optimal” (in a sense defined below) for a $1 monthly contribution, it will be optimal for $1,000 or $2,000 or $12,345 monthly savings.
- I consider actual historical stock/bond returns (01/1871-12/2020) and also Monte-Carlo-simulated returns, that mimic the same number of months and force the average returns and the variance-covariance matrix to match the historical ones.
There are a “gazillion” different equity/bond asset allocation paths because if we have 120 months and we allow equity weights anywhere between 0% and 100%, say, in 5% steps, we’d have 21^120 different combinations of equity weights. To cut down the number of possible paths, I propose the following: Every glidepath is characterized by only three parameters: The equity weight in months 1, 60, and 120. For the months in between, I simply do a linear interpolation of the three base weights. Moreover, I constrain the equity weights to be:
- In month 1: between 60% and 100% in 5% steps (9 possible values)
- In month 61: between 50% and 100% in 5% steps (11 possible values)
- In month 120: between 40% and 100% in 5% steps (13 possible values)
That gives me 9x11x13=1,287 different glidepaths. If I further constrain the equity weights to be (weakly) monotonically decreasing, i.e., W1≥W61≥W120, I’m left with 408 different glidepaths.
This gives me quite a bit of flexibility in the shape of glidepaths. The path can be flat, even at 100% throughout. Or it can be a straight line down or a concave or convex shape, see below:
When people ask me what is “the optimal glidepath” I always respond: it depends on what objective function we try to maximize. One investor might be comfortable taking on a lot of risk and is happy with maximizing the average final net worth after 10 years, not worried about the variation around the mean. Maybe because this investor has a lot of flexibility in the retirement date could just work a little bit longer if the market tanks right at the 10-year mark. Another investor might be really inflexible and wants to hedge against the risk of retiring at the bottom of a recession. And then there’s everything in between.
I simulate the performance of the glidepath for each historical starting point and the Monte Carlo simulations. Then I calculate the objective function in several different ways:
- The mean over all simulations (i.e., simulation start dates).
- A concave (risk-averse) utility function U(x)=[x^(1-γ)-1]/(1-γ), i.e., of the type CRRA (constant relative risk aversion), with a curvature parameter γ. (and note that for γ=1, the CRRA formula simply reduces to the natural logarithm)
- The minimum, i.e., we maximize the failsafe. (this would boil down to a CRRA utility function with γ=∞)
And then simply pick the glidepath that maximizes that utility function. Note that each objective will obviously give you a different “optimal” glidepath.
A few more words on the CRRA parameter
What kind of γ parameter in a CRRA utility function is “appropriate”? Well, for γ=0 we’re back to caring only about the mean (risk-neutral) and at γ sufficiently high we’re back to worrying only about the minimum/fail-safe. What is a reasonable γ parameter, then? Here’s one way to gauge this. Imagine you’re offered the following gamble: a coin flip determines your final portfolio value: $500,000 for heads and $1,500,000 for tails. And one other version, imagine you can get 5 different portfolios: $500k, $750k, $1m, $1.25m, and $1.5m, each with 20% probability.
What is the “utility” or the “value” of this gamble to you under different risk-aversion parameters? I always like to calculate not just the expected utility but also the “certainty equivalent value” by transforming the expected utility value back into dollars through [(1-γ)U+1]^(1/(1-γ)). This tells you the value of the gamble if someone offered you one fixed and risk-free payout. Clearly, for γ=0, it’s $1,000,000, because you value that gamble at the expected value. For a few other values of γ, please see the table below.
- Personally, if I had to imagine I’m starting with $0 again and I’m given the gambles over the different payoffs at a future date, I’d probably be happy with a certain payoff of somewhere around $750k-$800 in the coin toss gamble and $800k to $900k over the 5-ways. It looks like, I’m a γ=2-kinda-guy.
- When I researched glidepath design, years ago when I still worked in the industry, I found that the glidepaths commonly used in the industry TDFs, look like they’ve been calibrated to a traditional retiree (40-45 years accumulation phase) and to maximize a CRRA utility function over the final Net Worth with a γ=3.5.
- A γ=5 seems overly risk-averse. You’d have to be crazy risk-averse to accept less than $600k to get out of a $500k/$1.5m coin toss gamble.
- So, for my simulations here, I’ll be using γ=2 to model a moderately risk-averse early retirement planner with some flexibility and a baseline γ=3.5 as the typical CRRA parameter of a traditional retiree with less flexibility.
A word of caution about the CRRA utility functions
I already foresee people complaining that the risk aversion is off because many readers would value the gamble at an amount much closer to the $1m expected value. And they are completely correct! For example, if you already have $5m in the bank and someone offers you the $500k/$1.5m coin flip gamble you’d have to be crazy risk-averse to accept a certain payment of only $750k. But to do the calculation right you can’t apply the CRRA utility function to the gamble only. It has to be applied to the total final net worth numbers ($5.5m and $6.5m in this case) and then with a γ=2 you get a certainty equivalent of about $5,958,000. So, the coin toss gamble is worth $958k to you, just a notch below the expected value.
As always, I will look at optimal glidepaths not just over the entire history but also slice and dice the data to see how much of a difference it makes when we face very elevated equity valuations. This would also give us optimal glidepaths conditional on expensive equities, not just for the average FIRE investor between 1871 and 2020. Notice that we can do this analysis only in the historical data. Monte Carlo doesn’t track the CAPE over time!
So I look at two criteria:
- Valuation based on past earnings: optimize the historical glidepaths conditional on an elevated Shiller CAPE ratio. In this case, above 20. And I know, it’s actually closer to 34 right now, but historically there have been very few instances with a CAPE above 30 and people have made the case that a CAPE of 30+ today is not quite as scary as it would have been in the past, due to different accounting standards and lower dividend yields (i.e., more earnings retention and thus profit growth)
- Valuation based on past index levels: optimize the historical glidepaths conditional on the S&P 500 standing at the all-time high or within 5% of the recent all-time-high. In other words, the drawdown from the recent high is within 5%. So, if you don’t like the CAPE so much, this would be a good alternative conditioning rule.
I plot the glidepaths as four different lines (in case you can’t read the legend in the charts):
- Dark Blue = unconditional historical return data
- Light Blue = historical data, conditional on CAPE>20
- Yellow/orange = historical data, conditional on the S&P 500 within 5% of the All-Time-High
- Maroon = Monte Carlo simulations
And each chart has four subplots for the four different initial net worth levels: 0, 50x, 100x, and 200x monthly contributions.
Let’s start with the objective function with no risk aversion, where the investor cares only about the mean of the final net worth. Not surprisingly, the optimal glidepath under those objective function assumptions is to pretty much stick with 100% equities right until you retire. The only exception: for a very high initial net worth (200x) and high CAPE ratio you’d stay at 95% for ten years, see the chart below:
How about CRRA γ=2? See the chart below!
- Quite intriguingly, even for this assumption, you end up with 100% equities throughout the accumulation phase for both the unconditional historical data and Monte Carlo.
- When you factor in expensive equities (CAPE>20) you’d start with 100% equities for the first 5 years if you have a zero initial net worth, but then walk it down to 50%. And with higher net worth starting points you indeed start with 60%-70% initial equities.
- Conditional on the S&P being at or within 5% of an All-Time-High you’ll still keep 100% equities for 5 years, for all initial Net Worth numbers between 0-200x. And even between years 5 and 10 you only walk it down to between 90 and 95%. Very gutsy!!!
Once we get more risk aversion (γ=3.5) we notice some action, though. We notice the typical downward-shifting glidepath, see the chart below:
- Quite intriguingly, if using (unconditional) historical returns, then for all initial Net Worth numbers between 0 and 200, you’d still keep 100% equities for the entire first 5 years and then shift to 80% over the final 5 years.
- Conditional on a CAPE>20 you start a lot more conservatively and then shift all the way down to 40% upon retirement!
- Conditional on the drawdown less than 5% below the recent All-Time-High, you still keep equities at 100% for the first 5 years and net worth levels under 100x. But then shift down to 50% upon retirement.
- The Monte-Carlo results are much more conservative than the unconditional historical glidepaths. Even more conservative than the DD<5% paths!
And finally, let’s look at the most conservative objective function, the failsafe:
- Quite amazingly, the unconditional historical GPs and those conditional on an equity drawdown <5% are very little changed compared to the γ=3.5 assumption. You keep the equity weight at 100% for the first half!
- Conditional on a CAPE>20 you start with a very aggressive equity weight but then also walk it down very aggressively!
- The Monte-Carlo glidepaths are now much more conservative. You’d still start at 100% equities when the initial net worth is zero. But for all the other initial portfolio values you start between 60-70% and then walk down to 40%.
A quick note about Monte Carlo vs. Historical Return Simulations:
Notice that universally, the Monte Carlo Glidepaths are more conservative than the ones derived from unconditional historical return data. Sometimes the MC glidepaths (unconditional, by definition) look roughly as conservative as the glidepaths based on historical data conditional on expensive equities!
As I mentioned previously, Monte Carlo has the weakness that it doesn’t generate the mean reversion observed in the data. One bad bear market 5 years before your retirement and Monte Carlo will have a hard time ever recovering from that loss. In contrast, looking at actual equity return data, you will often observe a bounce coming out of a bear market (think 2009 or most recently in 2020!) and that is highly unlikely in a no-memory random walk!
Of course, one way around the pure random walk assumption would be to draw “blocks” of actual historical data. But if you have a 10-year horizon and you draw blocks of data long enough to preserve the mean-reversion observed in the data you’ll need blocks of roughly 10 years, so the block-Monte-Carlo is equivalent to historical return simulations! 🙂
The role of initial equity valuations
What I found quite surprising is that when the initial net worth is zero you’ll still start with a very aggressive equity allocation (100%) and keep it there for at least the first half of the accumulation phase, regardless of the equity valuation. That’s true even for risk-averse investors with a CRRA γ=3.5 (and even really crazy risk-averse investors with γ=5, results not displayed here, though, for brevity). So, I always tell people that even when stocks are expensive, it may still be a great time to invest in stocks. Even your entire portfolio.
I have shared this anecdote multiple times before: I got two major pay hikes in my life that triggered a major boost in my savings and investing. Once graduating with my Ph.D. in 2000 and once moving from the Federal Reserve to the private sector in 2008. Each time sounded like a bad time to jack up my investing (2000 bubble, 2008/9 Global Financial Crisis). But since the market tanked right after I accelerated my investing and I kept investing through the bear market, I was underwater with my investments only really briefly and then participated generously in the subsequent bull markets.
Notice how this is completely different from the equity valuations challenge that retirees face. If you start withdrawing money and the market tanks right after that, you face the negative side of Sequence Risk! As I outlined in Part 14, the Sequence Risk that hurts the retiree will aid the new investor and vice versa. The retiree keeps withdrawing through the bear market which will hamper the recovery of the portfolio. In contrast, the saver will contribute through the bear market which will accelerate the portfolio recovery once the next bull market starts. Thus, retirees and investors are always on the opposite side of the Sequence Risk headache. So, my warning about expensive equity valuations is targeted mostly at retirees. If you just start on your path to FIRE, by all means, you should be much more relaxed about equity valuations!
What about a 5-year horizon?
As promised, here’s the same simulation output when using a 60-month horizon. Now the kink point in the middle is at the 30-month mark. As starting capital levels, I use 100x, 150x, 200x, and 250x monthly savings. That’s because 5 years before retirement you should already have a sizable initial portfolio.
Moreover, to be consistent with the 10-year glidepath equity weight constraints, I use 50%/45%/40% as the lower bounds for the equity weight at the beginning/midpoint/endpoint. In other words, the 50% lower bound in month 1 corresponds to the 50% lower bound at the midpoint in the 10-year horizon simulations.
So, here’s the first chart, maximize the mean final value: All glidepaths stay at 100% throughout!
For γ=2: Still very aggressive, except for the high-CAPE conditioning.
For γ=3.5: Everything looks more like a traditional glidepath, shifting down to 40-70% final equity weight at the beginning of retirement.
And the Failsafe: Monte Carlo and CAPE>20 rules are very conservative. The other two rules start quite aggressively. But the endpoint is always 40% for all the initial Net Worth numbers!
Just for the record, I like to point out a few limitations in today’s analysis:
I don’t factor in taxes. If you plan to keep 100% equities until retirement and go “cold turkey” and lower your equity share to 75% upon retirement to hedge against sequence risk in retirement, you should consider the tax consequences. Most of us will have plenty of wiggle room to shift assets in tax-advantaged accounts (401k, IRA, Roth, etc.) and perform the shift without any tax consequences. If you have only taxable accounts, you probably can’t just yank 25% of your equity holdings and shift them to bonds all at once. That might take some planning ahead of time and would require contributions and equity dividend payments to shift to bonds over the last few years before retirement.
2: Bellman’s Principle of Optimality
My optimization calculations here still solve “only” for one fixed glidepath that will stay in place no matter what asset returns you experience over time. For the mathematical purists (and I’m one of them) that’s not the “true” optimal path. Quite the opposite, a truly optimal path would allow you to respond to the stochastic returns and portfolio values over time and then regularly reoptimize the glidepath. In other words, you’d have a “path-dependent” glidepath. See the section on the “Principle of Optimality” in my post last year for more details. Well, allowing for path-dependency would create a level of complexity a bit above what’s appropriate for a personal finance blog post. I have done the more advanced calculations (dynamic programming, Bellman Equation, optimizing via backward induction; my math honchos will know what I’m talking about) but that would be more appropriate for a separate post or even an academic paper.
That said, I was amazed that the efficiency loss from the constrained maximization wasn’t that significant. If you start with the 10-year version of the GP and then maybe reoptimize once more when you hit the 5-year mark to whatever is the constrained optimal GP at that point for your net worth level at that time, you will get pretty close to the final expected utility under the truly optimal GP that satisfies the Bellman Principle.
3: Combined accumulation/decumulation glidepaths
Today’s analysis is purely for the accumulation phase. It could be desirable to perform a combined accumulation/decumulation glidepath for the last few years of saving and the first few years before retirement. I can certainly “hack” my MATLAB code to do exactly that: simply assume that during the first 5 years you contribute $1 each month and in the final five years you withdraw $1 and then maximize a utility function over the final net worth. I’d likely get a glidepath that looks exactly like Kitces’ bond tent, at least qualitatively.
The only problem: the withdrawal amount should depend on your net worth at the start of retirement, which is unknown now. We can certainly assume that the withdrawal amount is, say, 4% annualized or one-third of a percent monthly of that (unknown) month 60 net worth. But we’d now have (at least) two outcomes over which to maximize our objective/utility function: 1) the withdrawal amount and 2) the final net worth. One could certainly define a “period utility function” for every month, likely again a CRRA-type function, and then compute the discounted sum over all dates(as is standard in dynamic macroeconomics). But it gets a bit messy and the scope of that analysis is a bit beyond the blog post here today, which is already pushing the limit in terms of word count. Maybe I will look into that in a future post. But as I said above, all of the pre-planned glidepaths run afoul with the Bellman Principle of Optimality anyway. So, it isn’t even very troublesome to run the glidepath optimizations in stages. And then I would argue that running a separate analysis somewhat mimics the path-dependency and re-optimization along the way in a truly dynamically optimal mathematical setup. So, nothing is really gained from doing a combined accumulation/decumulation glidepath.
To answer the question from the post title:
It’s not crazy at all to keep 100% equities right until you retire!
At least if you’re planning an early retirement with 1) high contribution rates and 2) some flexibility about your retirement date. The 100% equities throughout would certainly be defensible if you find yourself in the middle of a bear market a few years before retirement. Then just keep the 100% equities and ride the subsequent bull market until you retire!
Even if you apply some more risk aversion, you will certainly still start with a 100% equity allocation, but you’d likely walk that down over the last 5 or at least 2.5 years before retirement. Also quite intriguing is that the high initial equity weight is defensible even when considering that the S&P 500 is at or close to its all-time-high.
So, for all of the folks out there who regularly make fun of me as the über-conservative retirement blogger and call me the Grinch of the FIRE movement, you all should take a positive and uplifting message away from today’s post: Before retirement, I certainly endorse a very gutsy and high-risk approach to investing. Only when you get close to retirement you want to take it down a notch and walk down the equity portion to well below 100%. And when retired you definitely want to lower the withdrawal rate when equities are expensive!
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!
Title picture credit: Pixabay.com