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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29 thoughts on “The Ultimate Guide to Safe Withdrawal Rates – Part 14: Sequence of Return Risk

  1. Hello!

    Thanks for the post.

    Sequence of returns risk is eliminated by withdrawals that are proportional to the portfolio (rather than a fixed dollar amount). So, a withdrawal method of a fixed percentage, say 4% of the portfolio, or even a variable (but proportional) withdrawal method, like VPW, is not subject to sequence of return risk, in the sense that the final portfolio value is not affected by the order of the returns.

    Correct me if I am wrong.

    Liked by 1 person

    • Thanks for stopping by. SRR is most definitely not eliminated when using VPW. The IRR is lower with withdrawals than under the Buy and Hold scenario when returns are weak initially. I can address that issue in the follow-up post next week.

      Liked by 1 person

      • OK, I probably have a naive view of it. The simple case of a fixed percentage withdrawal method (say 4% of the portfolio, annually) seems behave just like buy and hold with respect to sequence of returns. Adjusting your example leads to: (-15%-4%)/(42%-4%) in one case, and with the order reversed in the other case. The resulting portfolio value is the same $111.78. That is why I think of the sequence risk as being eliminated.

        VPW behaves the same way, it just has a different percentage withdrawal each year.

        Liked by 1 person

  2. Have you heard of the “mortgage your retirement” philosophy (http://lifecycleinvesting.net/mortgage_retirement.pdf)? The idea as I understand it is to highly leverage your investments early in the accumulation phase and then slowly deleverage as your assets increase, leading to a more constant exposure to risk over time and decreasing SRR. I haven’t implemented it myself mostly because in the face of uncertainty I’d rather stick with something I understand (straight equities) but I know you’re not opposed to using leverage, so I’m curious if you have any thoughts.

    Liked by 1 person

    • Hi Kyle! Thanks for the link. This is awesome! They are correct, though there are some limitations:
      In a perfect world where you know your future path of wages it would be indeed efficient to borrow against that future stream to invest it all up front for two reasons:
      1: equities have higher returns, so you want to invest early (related to last week’s post, by the way: https://earlyretirementnow.com/2017/05/10/lump-sum-vs-dollar-cost-averaging/)
      2: You get better diversification across time as the authors very correctly point out. This eliminates or at least reduces the SRR for savers!!!

      The reasons against this method: You don’t know your future path of wage earnings and that path could be correlated with the stock market. I work in finance and my wage income is highly correlated with the stock market.
      But what I would endorse: If you’re young invest the maximum you can in stocks. Completely avoid bonds. Don’t bother paying down the mortgage faster than you have to. I could have paid off my mortgage but didn’t and one of the reasons is exactly this time-diversification argument!

      Many, many thanks for sharing this!!!

      Like

      • “The reasons against this method: You don’t know your future path of wage earnings and that path could be correlated with the stock market”

        I don’t think there’s a strong requirement to know your future wage earnings — simply knowing “I will, with a high degree of certainty, have a bigger nest egg to invest in the future than I do now” should be enough information to justify this strategy, right?

        And yeah, I’m definitely in 100% stocks. I’m comfortable with the risk because I’m 25 with a 10-year projection for financial independence. If the markets don’t work out that’s ok — I just get to work a few more years at my high-income job that I mostly enjoy!

        And on-topic for this post, I should mention that I’m very selfishly hoping for a major correction in the next couple of years — like you pointed out, your loss is my gain as an accumulator! 😛

        Liked by 1 person

  3. Very insightful, once again. Since I’m 45 days out from ER, I’m really curious to see how my strategy plays out in a market that I’m perceiving to be very high on the sequence of returns risks. I love all of these posts since they make me *think* I have set things up in a way to hedge against those risks, but part of me is thinking, am I being overconfident? I have a largish chunk of my stuff in some alternative investments which you suggested from a modeling perspective I might look at as 50 stocks/50 bonds. I’m hoping that monthly cash flow needs can come from those alternative investments and I can leave all my other 80 stocks/20 bonds alone and let dividends reinvest and even shift allocation from alternatives to stock indices as time goes on… Does that logic make sense? From a modeling perspective using the 50/50 stock bond ratio for those alternative investments, it may seem that I am being overly conservative with my allocation but this cash flow is more readily accessible to me with a higher likelihood of principal preservation in my brain at least. I haven’t dug through your blog in all it’s glory, do you have other posts on alternative investments? (of course I am about to search myself but wondering if you have anything you think is extra insightful). Jumping off this cliff is a little scary. 🙂

    Liked by 1 person

    • Yeah, modeling alternative investments is tough. If there is a steady flow of yield/income, say from rentals this might be the best way to avoid this SRR issue because you avoid selling equities at a low price.
      I personally will do a similar bucket investment strategy:
      100% equities in retirement accounts that I will not touch for about 20 years. In taxable accounts, I will run 2 alt strategies: Real Estate (through private equity funds, no posts on this topic yet). And options trading (see post here: https://earlyretirementnow.com/2016/10/05/passive-income-through-option-writing-part-2/)

      Quick question: If you plan to not touch the 80/20 portfolio for a long time, why not keep 100% equities in that bucket?

      Liked by 1 person

      • You make an excellent point and honestly I don’t think that I have quite figured exactly out how I am going to access my cash flow more than 5 years out which is why I stuck to an 80/20 rule across the board. I feel like I will be shifting allocations sometimes – like when my private equity investment reaches the 5 year mark and I can choose to get it back or re-up it another 5 years (I have only 3 years left anyway), I may decide to employ that in index funds or find something else. I haven’t explored options strategies yet though I did read that article a few weeks ago and even bookmarked it so I would come back to it (eventually) after I read through your safe withdrawal rates treatise. 🙂 I don’t feel like I don’t have enough knowledge to deploy something like that yet, but it’s something I want to start considering. I could be totally off base, but here is where I’m at – my husband should be FI in 5-7 years (we got married a year ago and I was much farther along in my process than he was!) – and we *might* not have any W-2 income at that point. If tax laws don’t change, I’ll likely think about employing the backdoor IRA conversion down the road, just to have more flexibility. I have a plan in place and have done projections but I honestly am not sure how this will all play out. By 6/30, I hope to be sitting at a safe 3% – 3.25% withdrawal rate across all asset classes which I hope will last me the next 60 years. Big picture, I have that (unless the markets drop precipitously between now and then) covered and I feel like I need to be flexible with my approach otherwise. In the meantime, I’ll keep reading your insightful analysis.

        Liked by 2 people

        • Thanks for sharing! With 3-3.25% you should be safe.
          Probably don’t touch options the way I do unless you have some deeper knowledge into the subject.
          What kind of private equity are you investing in? I do real estate through PE. Worked out pretty well so far.
          Cheers!

          Liked by 1 person

          • Real estate as well. And I have a chunk of money in Peer Street which are hard money loans and are more liquid than my PE but it’s a quasi private equity type account with lower yields since they are less risky in the risk/return continuum. I do have a fairly predictable monthly stream of cash flows which is what I wanted to dial in prior to pulling the plug. Good advice on the options though the curious part of me wants to learn more. I don’t think my early retirement stash is a good way to experiment with them.

            Liked by 1 person

          • Please correct me if I am wrong, but upon surface examination, RMDs exceed Safe Withdrawal Rates. Not being snarky, but I was reallly hoping to leave something for legacy! The only way out is to do Roth conversions in down markets and take the hits, I guess.

            I very much appreciate your thinking on these topics, as it would be – err – challenging for me to work through the variables. Needless to say, I am not an ER candidate, nor am I in Finance, lol!

            Liked by 1 person

            • Two solutions.
              First, I try to not keep that much money in tax-deferred accounts subject to RMD. If only half your money is in that kind of account you can have an RMD twice the withdrawal rate.
              Second: Even if your RMD exceeds your target withdrawal rate you don’t have to consume everything. Invest the excess in a taxable account! Leave a bequest that way! 🙂

              Like

  4. Great post. I have thought about SRR a great deal these last few years. Is it a reasonable strategy to mitigate this by using a total return approach during up markets and switching to taking just the interest and dividends from the portfolio during down markets? My portfolio is large enough to provide enough income to support me without any change in my lifestyle. Thank you.

    Liked by 1 person

    • Thanks for the comment!
      If your portfolio is large enough to only live off the dividends you certainly alleviate the SRR problem but you never eliminate it either:
      a: dividends can be cut during a recession.
      b: the IRR calculation takes into account the lower positive cash flows during the down market. So you will still have a lower IRR if the recession hits early vs. later.

      Good luck!

      Like

  5. I have never been more intimidated and excited about a concept before. But you do a great job breaking down these super technical ideas that are so critical for someone ready to pull the trigger for Early Retirement. Your Analysis of Paul’s case was awesome and ChooseFI is so lucky to have you bring these concepts to life by applying them to real life case studies 🙂

    -Jonathan
    ChooseFI

    Liked by 1 person

  6. Thanks. This is one of the things I think of when I look at current FI bloggers and their draw down numbers, especially when they sell it as “it worked for me, so it’ll work for you!” Most of them have been the beneficiaries of the markets you describe and their numbers don’t break down history like yours do. It is especially true in the first couple years after retiring because that is when it will hit you the hardest.

    To me it is similar to the “if the market takes a downturn, just go get a short term job” but they are thinking of the job market in today’s terms when it is fairly easy to find a side hussle. If the economy takes a downturn those side hustles will thin out as well.

    Liked by 1 person

  7. Thank you for replying to my post. I have been reading you for quite a while and your work is outstanding. The long series on safe withdrawal rates is the best analysis I have seen over 2 decades of trying to learn these things. I have a 60/40 stocks bonds portfolio which yields close to 100k in combined income. It has seemed to me that the IRR is not relevant, just whether I am comfortable living on the yield. I am 56 and will be fully retired in 2 years. My retirement budget is 90k per year with lots of discretionary spending. My goal has been to separate myself from any concern about the nominal value of my portfolio. Of note I am broadly diversified in index funds, not chasing yield to achieve these ends. So little is written for high net worth investors it is difficult to find competent opinions about safe withdrawal rates and strategies that are relevant to my situation. Your work has been quite helpful.

    Liked by 1 person

  8. Great post as always, ERN. Without deploying your level of financial modeling, and yet considering the currently high stock market valuations and SRR going forward, I hacked my way using a detailed calculator’s methodology and arrived at 3.27% SWR. The logic is here: http://tenfactorialrocks.com/hacking-the-retirement-calculators/

    This pretty much is in line with what your detailed studies have shown! Given the multi variable uncertainty here, I felt I should approach this a different way to convert a quirk of modern retirement calculators to our advantage. My own Occam’s Razor, if you will 😊 Glad our results agree.

    As a dividend investor, I further take this to mean that I should reinvest my current dividends above the 3.27% yield (that is, use only 3.27% out of 3.75% yield my portfolio currently has and reinvest the rest), so can stay true to my SWR.

    Like

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