The Ultimate Guide to Safe Withdrawal Rates – Part 15: More Thoughts on Sequence of Return Risk

Welcome back to our Safe Withdrawal Rate Series! Last week’s post on Sequence of Return Risk (SRR) got too long and I had to defer some more fun facts to this week’s post. Again, to set the stage, I can’t stress enough how important Sequence of Return Risk is for retirement savers. In fact, after doing all this research on safe withdrawal rates (start series here, and also check out our SSRN research paper) if someone asked me for the top three reasons a retirement withdrawal strategy fails I’d go with:

  1. Sequence of Return Risk,
  2. Sequence of Return Risk,
  3. and let’s not forget that pesky Sequence of Return Risk!

Huh? Isn’t that lame? Surely, low average returns throughout retirement ought to be included in that list, right? Or even top that list, right? That’s what I thought, too. Until I looked at the data! Let’s get rolling and look at some more SRR fun facts.

Low average returns are less of a problem than Sequence of Return Risk!

To see how much or how little average returns impact SWRs, let’s look at the following example of a retiree with a 30-year horizon and an 80/20 equity bond portfolio. I calculate the SWRs with the following assumptions:

  • All simulations are in real terms (CPI-adjusted withdrawals and CPI-adjusted asset returns)
  • Capital depletion (final value =$0). Results would be qualitatively similar results if I use capital preservation, which would be more applicable for early retirees with a longer than a 30-year horizon.

As a warm-up, let’s look at the table below: three case studies for different retirement starting dates. It displays the SWR that would have exactly exhausted the portfolio over 30 years, the 30-year average return of an 80/20 portfolio (0-30 years, point to point CAGR), as well as the average returns over the 5-year windows: 0-5 years, 5-10 years, … 25-30 years.

SRR Table04
Three case studies: Safe Withdrawal Rates of an 80% Stock, 20% Bond portfolio (30-year horizon, $0 final value) vs. realized real returns.

Retiring in December 1968 would have afforded you an SWR of only 3.8%. And that would have exhausted your capital over 30 years! But the average return over the 1968-1998 period would have been a staggering 6.16%. The reason why you still ran out of money after 30 years is that you had low returns early on and the strong returns, even double-digit real returns in years 15-30, came too late.

If you had retired only ten years later you would have experienced a very similar 30-year average return: 6.03%. But the SWR would have been a staggering 9.12%. The strong returns came during the first 20 years of the simulation and the weak returns during the last 10 years that cover the recessions in 2001 and 2008/9 wouldn’t hurt your SWR anymore. Also, October 1955 is an intriguing case study: Only very underwhelming average returns: 3.45% over the next 30 years, but a very healthy SWR of 5.72%.

Of course, with case studies, we can go only so far. In the chart below, let’s plot the entire SWR and average return time series. Wow, the SWR and the average return are only very slightly correlated. Even if you knew the average return of your portfolio mix over the next 30 years, you’d have a hard time pinning down an appropriate SWR. Some of the lowest 30-year returns in the late 1800 and early 1900s actually coincide with relatively decent SWRs of around 4% and as high as 7%!

SRR Chart01
The path of the Safe Withdrawal Rate has only little in common with the 30-year average return of the underlying portfolio! Note: the x-axis is the retirement start date, so it goes through March 1987!

Very interesting! There have been plenty of examples where the 30-year SWR far exceeded the 30-year rate of return. SRR is a risk that can go both ways; sometimes it helps the retiree sometimes it hurts the retiree. We knew that already from last time: the beneficiaries and losers are the savers and retirees. If the retiree benefits then the saver loses and vice versa. It’s a zero-sum game!

Some more serious SRR analysis

Let’s do some more sophisticated statistical analysis. We run two linear regressions to “predict” the SWR based on future returns. 1) knowing only the 30-year average return and 2) knowing the average returns during the six windows: 0-5 years, … , 25-30 years. Of course, “predicting” the SWR is a bit of a misnomer. Nobody knows the future returns. This is more of a thought experiment of how well you could have pinned down the SWR if you had known future returns. Or, let’s call it accounting for the SWR in hindsight, rather than predicting it.

The results are in the table below:

  • Knowing only the average returns over 30 years we get a pretty underwhelming regression fit. An R^2 of only 0.31, so knowing the 30-year return explains only 31% of the variance in the realized SWR. We already saw the poor fit/correlation from the chart above, but this is the statistical and quantitative confirmation. But note that the slope coefficient on the average return is positive and statistically significant. And for statistics wonks, yes, this is a Newey-West adjusted t-stat to account for the overlapping windows.
  • Knowing the returns in the 6 separate windows you get an almost perfect fit: close to 96% of the variation in the SWR are explained by the average returns in the 6 windows. What’s more, the slope coefficients for the different windows are very different and all extremely highly statistically significant. They may sum up to roughly the same number as in the univariate regression, but the earlier windows get a much larger slope coefficient. By weighting the 6 different time windows differently we now get an almost perfect fit. Precisely what I mean by SRR matters more than average returns: 31% of the fit is explained by the average return, an additional 64% is explained by the sequence of returns!
SRR Table03
Linear regression result: SWR on future realized returns. Knowing only the average returns over the next 30 years is not very informative (low R^2). The distribution of returns over the 30 years matters a lot more! Note: Due to overlapping windows the t-stats are Newey-West heteroskedasticity-adjusted.

If you’re unlucky you can get screwed twice by Sequence of Return Risk!

What’s even worse than getting screwed over by SRR in retirement? Very simple: first you get screwed over by SRR while saving and then again while withdrawing money in retirement. Let’s look at the following hypothetical retirement saver who starts saving $5,000 in 1959 and does so for 15 years. Then he withdraws $4,000 from the portfolio during retirement. During the last few years of the accumulation and the first few years of retirement, the 1973/4 recession hits. You get hammered twice because that’s exactly the kind of return profile that you want to avoid while saving (high return early on, low returns later) and retiring (low returns early on, high returns later).

To see how much this saver/retirement cohort lost from SRR let’s plot the actual portfolio value that’s subject to SRR and the hypothetical portfolio value had this person experienced the exact average monthly return that prevailed during those 30 years (orange line). Without SRR you would have about 25% more in your portfolio at the beginning of retirement. After 15 years of retirement, you would have seriously depleted your portfolio. Without SRR you’d be about 100% better off! So, SRR hurt you both while saving and during retirement. Bummer!

SRR Chart03
Investing $5,000 per month in an 80% Equity, 20% Bond portfolio for 15 years, then withdrawing $4,000 per month for 15 years. All values are real, CPI-adjusted numbers. Actual returns vs. experiencing the 30Y average throughout reveals that Sequence Risk can cost you both during the accumulation and retirement!

Are there ways to alleviate Sequence of Return Risk?

Last week after posting the first part of the SRR blog post, two commenters had suggestions on how to overcome or at least alleviate the SRR problem. Both of them are brilliant ideas. But only one of them works.

1: Use the Bogleheads-endorsed VPW rule.

Instead of withdrawing a fixed amount regularly, why not withdraw a certain percentage of the principal. This can be a constant percentage or the age-dependent withdrawal percentage in the VPW rule. Now, the final net worth looks like it’s independent of the order of returns:

(1-w) ∙ (1+r1) ∙ (1-w) ∙ (1+r2) = (1-w) ∙ (1+r2) ∙ (1-w) ∙ (1+r1)

Since the final net worth is the same, does that mean SRR is irrelevant for people who apply the VPW? Not really. Because the second withdrawal will now differ depending on which of the returns is larger. Imagine r1>r2. Then your second withdrawal is higher when you experience r1 first than when you experience r2 initially. So, you can’t hide from SRR. If you try to equalize the final portfolio value through VPW then SRR hits you through the withdrawal amounts! If you try to equalize the withdrawal amounts then SRR hits you in the final portfolio value. Pick your poison! The VPW has its pros (and cons) as we showed here, but it can’t eliminate SRR!

2: “Mortgage” your retirement.

For retirement savers there is one sure-fire way to avoid missing out on strong equity returns early during the accumulation phase: Borrow against your future retirement account contributions and invest the whole loot as one big lump-sum payment without further contributions in the future (i.e., use your future retirement contributions to pay down the margin loan). Sounds crazy? Two researchers from Yale found that this is a way to “diversify across time,” which is just another way of reducing SRR. As we showed last week, a lump-sum investment is not subject to SRR!

If this sounds too extreme to you, I’d have to agree. There are multiple reasons why this is not workable. For example, since I work in a very volatile industry I’d not be comfortable borrowing against future earnings. But there are ways to at least alleviate the SRR problem:

  • Hold a 100% equity portfolio early on. Don’t bother about holding any bonds.
  • Don’t bother about paying down low-interest debt when young (mortgage, low-interest student loans). Put every last dollar you can scrape together into the stock market early on. (of course, high-interest debt, especially debt with interest higher than your expected equity return should be paid down as early as possible)
  • Once you have a critical mass of equity investments, then tackle your low-interest debt.

The benefit of this method is twofold: 1) you gain from the higher expected return in equities over fixed income investments and 2) you alleviate the SRR by spreading around the equity risk more evenly across time. It’s a win-win!

We hope you enjoyed today’s post. Please leave your comments and suggestions below!

Advertisements

99 thoughts on “The Ultimate Guide to Safe Withdrawal Rates – Part 15: More Thoughts on Sequence of Return Risk

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

w

Connecting to %s