The Ultimate Guide to Safe Withdrawal Rates – Part 14: Sequence of Return Risk

This is a long overdue post considering how much we’ve written about safe withdrawal rates already. Sequence of Return Risk, sometimes also called Sequence Risk, is the scourge of early retirement. Or any retirement for that matter. So, here we go, finally, we have a designated post on this topic for our Safe Withdrawal Rate series (check here to go to the first post and also make sure you download Big Ern’s SSRN working paper on the topic).

Besides, in case you haven’t heard it, yours truly, Big Ern, was asked by Jonathan and Brad at ChooseFI to be an occasional contributor to their awesome Financial Independence podcast. Specifically, I’ll be the in-house expert on everything related to safe withdrawal rates. And that’s alongside an A-plus-rated team of experts: real estate guru Coach Carson, tax expert The Wealthy Accountant, and business guru Alan Donegan from PopUp Business School! How awesome is that? Because Sequence of Return Risk is something we’ll cover in the podcast soon as part of a crowdsourced case study, I thought it would be a good time to have a go-to reference post on the topic here on our blog. So, once again, make sure you head over to the ChooseFI podcast:

-> ChooseFI Podcast <-

What is Sequence of Return Risk?

Investopedia has a nice definition:

“[s]equence-of-returns risk is the risk of receiving lower or negative returns early in a period when withdrawals are made from an individual’s underlying investments. The order or the sequence of investment returns is a primary concern for retirees who are living off the income and capital of their investments.”

In other words, if you are a buy-and-hold investor your final asset value is simply a function of the compound (geometric) average growth rate. It doesn’t matter in what order the returns came in because of the beautiful fundamental rule of mathematics: (1+x)(1+y)=(1+y)(1+x). All that arithmetic goes out the window, however, if you have additional cash flows into or out of the portfolio over time. Let’s look at a little example, see the table below. For a buy and hold investor it doesn’t matter if you get two consecutive 10% returns, or -15.00% followed by +42.35%, or +42.35% followed by -15%. They all generate a compound return of exactly +21% and the same final portfolio value of $121 for each initial $100 invested. The IRR (internal rate of return) is always 10% p.a.:

SRR Table01
The order/sequence of returns is irrelevant for buy and hold investors. But the sequence matters when there are additional cash flows throughout the investment horizon!

A retiree, however, who withdraws $10 per year (assuming the withdrawal occurs at the beginning of each year) will not be indifferent. The final portfolio value and IRR now vary depending on the sequence of returns. If you suffer a 15% loss early on you end up with less money than with steady 10% returns. The intuition is straightforward: Because you withdraw money at the bottom of the market, you experience the +42% return in a portfolio that’s already significantly reduced. You have a lower IRR because you participate less in that strong +42% return. In contrast, receiving a high return early on will ensure that you handily beat the +10%/+10% scenario.

Savers are impacted by Sequence of Return Risk, too!

Huh? Why would savers be impacted by SRR? Isn’t this something that only affects retirees? No! SRR impacts all investors who have cash flows out of the portfolio and/or into the portfolio. Let’s look again at the 2-period example above and add a third person, a saver who starts out with $0 and then invests $10 per year at the beginning of each year.

Among the three different return scenarios, the saver would greatly appreciate the -15%/+42% return pattern, see table below. The highest final value occurs when returns are low initially and then stronger in the second period. The exact opposite as for the retiree. Also look at the IRR: close to 20%, which is almost twice the IRR of the “Buy and Hold” investor. Makes perfect sense because we suffer less from the market drop early on with less money exposed to the big drop. But then we benefit from the large increase with all the principal invested. Sweet!

SRR Table02
Sequence of Return Risk: A retiree’s loss is a saver’s gain! It is literally a zero-sum game!

Also, notice something peculiar about the final portfolio values: The retiree and saver portfolio values add up to the Buy and Hold portfolio values: For example, for the +42%/-15% case: $100.40 + $20.60 = $121.00. This is not a coincidence. The cash flows of the saver and retiree add up to exactly the Buy and Hold strategy. This explains that when the retiree’s IRR lags behind the Buy and Hold Strategy, the saver’s IRR must beat the buy and hold IRR. Sequence of return risk means that there is a zero-sum game between savers and retirees! During periods when the retirees suffer from SRR, savers will benefit and boost their IRRs and it’s all thanks to SRR!

SRR Table05
Cash Flows of Retiree and Saver add up to the Buy and Hold Strategy. Sequence of Return Risk is thus a zero-sum game: A retiree’s loss is a saver’s gain!

We have benefited greatly from Sequence of Return Risk!

Yes, you heard that right. The ERN family has benefited from SRR over the last decade or so. You can probably already see where we are going with this, so let’s do the following more thorough calculation. Let’s look at monthly real equity returns from our SWR study database and simulate 10-year rolling windows of three investors:

  1. Buy and Hold for 10 years
  2. Retiree: Start with the same initial wealth as investor 1, but withdraw at a 4% p.a. initial rate and then increase the withdrawals by the rate of inflation (the standard 4% Rule)
  3. Saver: Start with $0 initial wealth but save the exact same amount that investor 2 withdraws.

Clearly, we have a zero-sum situation again: The cash flows of investors 2 and 3 add up to the buy and hold strategy because the savings and withdrawals exactly cancel out each other.

Now, let’s calculate the IRR of the 3 investors over time, see plot below. Each value plotted corresponds to the end point of a 10-year window and refers to the Buy and Hold, Retiree, and Saver IRR, respectively. It turns out that over the last 10 years (3/2007-3/2017) the IRR for the 3 investors were: 5.65% for Buy and Hold, 4.46% for the Retiree, and 10.48% for the saver. In fact, throughout much of the 2000s, the savers did better than the buy and hold investors (the green line is mostly above the blue since 2010). And the explanation is very simple: Retirees got hammered by SRR during the 2000s, compliments of two nasty drawdowns. We benefitted from the two bear markets because our cash flows were largely the mirror image of the retirees. Specifically, Big Ern started with about $0 in the year 2000 and built up the ERN family portfolio through steady contributions to retirement plans and taxable savings. Picking up stocks at bargain basement prices actually increased our IRR to levels way above the Buy and Hold IRR.

SRR Chart04
Internal Rate of Return (IRR) of three investors over 10-year rolling windows (end-point of the 10Y window on the x-axis). Despite lackluster equity returns over the last 10 years, the saver made over 10% IRR p.a.

Another way to look at the same image to better bring out the zero-sum game feature: Subtract the IRR of the Buy and Hold (the blue line) from the retiree and saver IRR, i.e., calculate the incremental IRR above the Buy and Hold investor, see chart below:

SRR Chart05
Yup, it’s a zero-sum game! Whenever the retiree underperforms the Buy and Hold investor, the Saver beats the Buy and Hold Investor!

Side note: The zero-sum feature applies only to the cash flows. The incremental IRRs don’t sum to zero for (at least) two reasons: 1) the IRR calculation is a highly non-linear affair, and 2) in this example, the saver has less money invested, on average, which explains why the magnitude of the excess IRR of the saver is much higher than that of the retiree. But you can show that the incremental IRRs will always have opposite signs.

Needless to say, occasionally, the saver will get hammered, too! For the 10-year windows that started between 1993 and 1995 and ended between 2003 and 2005, the situation is reversed: The retiree experienced the very strong returns early during the 10-year window. The saver, in contrast, participated to a much lower degree in the late-1990s equity rally but then got slammed in the 2001-2003 bear market, right when he/she had the maximum portfolio value. Murphy’s Law! That’s the dip in the green line in the early 2000s.

Just for fun, here’s also the longer time series, starting in 1900. The +5% outperformance for the saver over of the most recent 10-year window seems impressive but it’s not the highest in history. The 10-year window that ended in late 1939, of course, was even better for savers: they benefited from the steep drop in equities during 1929 and the early 1930s! Of course, in the window that started just a few years later (1932-1942) the result is reversed: As a saver you do significantly worse than the Buy and Hold investor because of the strong recovery from the stock market trough.

SRR Chart06
100+ years of Retiree vs. Saver Zero Sum Games!

One more cool plot I created: In the chart below, let’s look at how the equity market performs over the 10 years when the saver IRR either significantly beats the Buy and Hold strategy (blue bars), is about in line with the Buy and Hold strategy (green bars) and significantly lags behind the Buy and Hold strategy (maroon bars). As expected, the profile of equity returns is increasing over the 10-year window when the saver benefits from SRR. But that exactly the return profile when the retiree loses the most!

SRR Chart07
When the saver significantly beats the Buy and Hold IRR it’s because equity returns are low early on and high toward the end of the 10-year window. When the saver significantly falls behind the Buy and Hold IRR, returns tend to be high initially and low toward the end of the 10-year window!

One more thing…

One more thing occurred to me: Before doing this research, it would be easy for us to believe that in retirement we don’t have to worry about a bear market because we did quite well with our portfolio during the accumulation phase between 2000 and 2017. Despite all that market turmoil! You read this quite often in the FIRE blog community! But that’s a delusion: the retirees’ losses during that time were our gains due to the zero-sum feature we pointed out here:

The fact that we did well during 2000-2017 should actually worry us more about volatility in retirement, not less.

In any case, we have so much more material on SRR! I don’t want to go above 3,000 words in one post and it wouldn’t be fair to leave out the other fun content we still have on this topic. So, stay tuned for a part 2 next week!

Conclusion

Sequence of return risk is a symmetric risk: you can benefit from it or it can seriously harm your investment returns. It impacts both retirees and savers and the risk is exactly a zero-sum game. Sometimes the retiree loses and the saver gains, as in the 2000s, but there were many instances where this was reversed.

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

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