Friday, September 27, 2013

Lifetime Sequence of Returns Risk

Individuals face sequence of returns risk throughout their investing lifetimes. Though one may invest over a 60 year period, for example, the returns they experience in each of those years will have different impacts on their lifetime financial outcomes. 

This is a short blog post which picks up on the themes of my recent post about how "You Can't Control When You Are Born."

In this example, someone earns a constant inflation-adjusted salary and saves a constant percentage of this salary each year over a 30-year period. In retirement, they withdraw a constant inflation-adjusted amount over a 30-year period. The lifetime investing cycle lasts 60 years. The analysis is based on Monte Carlo simulations with 100,000 60-year periods with returns averaging 7% with a 20% standard deviation.

What the following figure shows is how much each year's return impacts the financial planning outcomes.  For the first 30 years, what we see is the percentage of the final wealth accumulation at the retirement date which can be explained by the investment return experienced in years 1-30. What we observe is that with wealth so low at the beginning, the early returns have very little impact on the final result. A given percent change in the portfolio value does not have much impact on the absolute amount of wealth accumulated at the end.  It is the returns experienced at the end of the 30-year period which have the biggest impacts on the final wealth accumulation, as this is when a given percentage change in the portfolio value has the biggest impact on absolute wealth. Individuals are especially vulnerable to these returns as they approach their retirement date.

For years 31-60, we switch from accumulation to distribution, and I am showing the impact of each year's return on the maximum sustainable withdrawal rate experienced by retirees.  The return in year 31 is the return for the first year of retirement, and the result in this first year explains more than 14% of the final outcome for retirees. Retirees are very vulnerable to what happens just after they retire. This result holds even more so in the real world when we consider how human capital plummets at the retirement date, as it becomes increasingly difficult to return to the workforce.  Sustainable withdrawal rates are disproportationately explained by what happens in the early part of retirement. The returns experienced in the last 10 years (years 51-60) have very little impact on how much one could sustainably withdraw over retirement.




And so with this figure, we can see a clear demonstration of the lifetime sequence of returns risk.

23 comments:

  1. Wade,
    Yes, this is a short post, but this is one of the best I have read in a while. It says so much with so little!
    The figure posted is a very good demonstration to clearly show the impact of individual investment/withdrawal years. Reminds me of the graphics in Bernstein's book "the age of the investor" also short, but they too tell so much. I'd love to hear more on this conversation, including implications to Asset Allocation, and the relationship with human capital.

    Great Post,
    Marlowe

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    1. Thank you Marlowe. Regarding asset allocation, the basic idea is either to reduce the stock allocation at the time when the returns have the biggest impact, or let the spending strategy in retirement be more variable in relation to what happens with the portfolio.

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  2. I like the post a lot. But I think your graphic would be better if it showed the discontinuity between year 30 and year 31 more clearly because it is showing different quantities for those two years. I'd suggest one or more of (1) placing bracketed explanations along the x-axis, one from 1 to 30 and one from 31 on; (2) placing some space on the horizontal axis between year 30 and year 31; (3) using one color for the bars from year 1 to year 30 and a different color from year 31 on; or (4) at the least, placing an obvious vertical line (perhaps red or bold) between year 30 and year 31.

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    1. Thank you. Those are good ideas. I was wondering about what to do to differentiate between pre- and post-retirement.

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    2. I'd be careful not to obscure an important point when you make a pretty curve between years 30 and 31. Assuming that's the year you retire, you have a substantial increase in risk at that point -- you no longer have a job.

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    3. It seems to me this analysis has important implications for pre-retirees, as well as retirees. I have several clients who thought they knew when they would be retiring, but were surprised by being laid off several years earlier - and never were able to get the kind of job/income they used to have - because they were in their 50s, the economy had just tanked, etc. I'm a lot more conservative with asset allocations for clients between 55 and 65 than I used to be. By that I mean a bond allocation equal to their age, but perhaps it should be more conservative.

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    4. Kathy, that is a good point. This could also be especially problematic for those who were planning to increase their savings rate a lot in their 50s after their kids had gotten through college age. The remainder of their lives could become really dependent on the impact of bad economic conditions in their 50s.

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    5. Wade, couldn't you just plot the same quantity for the first 30 years as you did for the last 30 years? That is, use the maximum sustained withdrawal rate as the explanatory target for all 60 years instead of just the final 30 years.

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    6. I couldn't use the _rate_ for all 60 years, but I could use the amount of cash flow provided by the rate with all 60 years. That's a good idea.

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  3. An interesting post Wade. It does show what Blanchett and I showed in JFP in June 2010 that sequence risk is always present. I’m trying to get my mind around the methodology. Does it measure each year as the starting point, or measure from some past point (which gets further in the past – and would thus skew the perspective)?

    Reason I ask, it doesn’t quite square with clinical experience. I would be fired by any 78 year old client, for example, if I told them not to worry about market sequences for the coming 10 to 11 years (expected longevity from Social Security table) because they have already survived the past market sequences and his exposure to sequence risk has thus gone down.

    The retiree recognizes they are just as exposed to sequence risk at 78 as they were the day they retired. The past doesn’t matter anymore, at any age. The future does. And when measured from the present, the range of possible market returns is always just as broad and uncertain as for any other given year. In other words, sequence risk is a rolling phenomenon that goes with us. We can’t out run it. And having fewer years ahead of me doesn’t change exposure to sequence risk in the present.

    Thus managing the portfolio for this ever present risk is important. Our JFP paper Nov 2011 shows that what reduces the impact of poor sequences is to retrench spending or to smooth spending by carrying forward reserves from the good years. Spending impacts portfolio balances and portfolio balances are what support future year spending. And retirees at any age, have future spending as a concern so they don’t outlive their portfolio.

    I circle back to how the impact is measured. A nice short post, however the details are needed to see points of measurement for the impact.

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    1. Larry,

      At the retirement date, I calculate the maximum sustainable withdrawal rate over each 30-year period using constant inflation-adjusted spending. Then I run 30 regressions to see the explanatory power (R^2) each year's return in the 30-year return sequence has on that withdrawal rate. The reason later returns matter less is that if the portfolio was up in early retirement, then the current withdrawal rate is lowered and with the shorter horizon, a big portfolio drop still won't derail that retirement. On the other hand, if the portfolio falls early on, then the current withdrawal rate is pushed up and even big returns later on cannot salvage things.

      With your dynamic approach, this analysis needs to be done differently. I guess we could calculate the lifetime total income provided in each simulation and run regressions of market returns on that. The importance of each year's return would be more smoothed, because you will essentially be restarting the retirement each year by calculating a new withdrawal rate each year. But early returns should still matter more, as a big return early on will help to get you on a sustainable path of more income in each subsequent year.

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    2. Yes, I see the differences in approaches. Your post here discusses an approach closer to establishing a dollar amount withdrawn at the start and then this dollar amount gets an inflation adjustment over the years (without reference to the underlying portfolio balance) if I understand you correctly.

      Our (Frank, Mitchell, Blanchett) dynamic approach doesn't make the inflation adjustment in that manner. Instead, the method use real returns (hence the inflation adjustment through that adjustment to data), recalculating the distribution period based on longevity tables and the current ages, and most importantly, reference back to the portfolio value each year.

      The profession's discussion appears to be your last sentence. Is it prudent to have the retiree's goal "more income in each subsequent year," or prudent to manage the lifetime cash flow so the retiree doesn't outlive it? It is a noble goal to say increase income each year, however not having control over the markets or underlying economy makes that goal very difficult to pull off (which gets to the point of your post about not being able to control the year you were born).

      Most people recognize their income during their working years wasn't a nice smooth constant increase either. For most people income had it's ups and downs. Retirement should be more realistically painted the same way. In practice, retrenchment of spending is rare and the income changes rare too. Your efficient frontier work may help in this area once you develop it dynamically. Great conversation!

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  4. Hi Wade,
    Quite eye-opening. Thank you for your research.

    Does your analysis assume that each distribution in retirement is from all assets in the portfolio (stocks and bonds)? If so, I'm wondering how a bucket approach or time segmentation would affect the outcome of the graph for years 31-60?

    Also, I agree with Larry in that every client of mine forgets what happened to their portfolio in the past. As soon as they receive their monthly statement, they immediately look for the account balance and they reset their brain to the new balance. If the new account balance is less than last month's, they are concerned. If the new account balance is higher than last month's, they reset their brain to how much they have in their account now and everything happening in the next month is related to that most recent balance. As Larry mentioned, sequence of returns risk is ever-present for the client. From my experience, the 80-year old client doesn't care that they got through the first five or ten years of retirement without a scratch. All they know is what they have today and they want to know what's going to happen to that money going forward. No matter what the age, a 55-, 65-, or 75-year old client will look forward, and for them, the next few years will always make the biggest impact on the sustainability of their remaining portfolio compared to the last years of their lives. This is why dynamic sustainability analysis is so important. Your chart can be used as a learning point for all clients of any age but for retired clients, no matter their age, I would point to that peak in the middle of the graph and tell them they are here, going forward the riskiest years are the ones just ahead of them. This also assumes a constrained client, not an overfunded client.

    Thanks again, Wade, for making us think! That's what it's all about.

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    1. Jim,

      Thanks for the input. If your clients do increase and decrease their spending as their situation evolves, then this diagram is over exaggerating the impact of the middle years.

      I'll be headed to the RIIA conference dinner in a couple minutes and look forward to seeing you again.

      Wade

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  5. Illuminating.

    Perhaps one way around this would be to contribute (much) more earlier on and (much) less later on in the accumulation phase and then inverse that approach when withdrawing?

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    1. Thanks.

      Yes, in principal you are right as a solution for the sequence risk. But it practice, this may be harder to do.

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  6. My understanding of sequence of returns risk is that the last 5 years of accumulation and the first 5 years of distribution are key. Your graph suggests, however, that the risk in year 1 of distribution is far higher than the risk in year 30 of accumulation. This doesn't make sense to me. The portfolio size is essentially the same and the time to death is essentially the same. I'll buy that the risk is a little higher in distribution given that you are now making withdrawals, but can the difference really be that dramatic? The only reason I can understand that it would be so different would be if you were assuming that if the market tanked in year 30 that the retiree could work a little longer.

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    1. In the set up here, the pre-retirement account (wealth accumulation) and the post-retirement outcome (sustainable withdrawal rate) are not the same. This explains the difference. I will re-do this assuming the same underlying goal of sustainable retirement income. That should remove some of the difference. There is a very real risk at retirement related to not being able to return to work, which should cause a discrete jump, but that aspect isn't part of the modeling here.

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  7. Wade,
    I too am interested in the question posed above by J. Schwartz - your retirement period analysis makes no specific assumptions about how money is take from the portfolio (such as that bonds are sold before stocks or that things are rebalanced using the distribution amount), correct? I'm interested in this because I had a client who I explained sequence risk to and his gut reaction was 'well if my stocks go down in the early years I just won't sell any of them to get the cash I need". I had no good way to counter this reaction though I know in my own gut it isn't a plan that will mitigate sequence risk. I'd be very interested to hear your thoughts on how I should help clients think past this "easy" solution.

    Sorry for the delayed post. A recent Fina Metrica email linked to it and I follow the topic of sequence risk closely.

    Thanks,
    Kay Conheady

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    1. Kay,

      Thanks for the message. As I read Jim's comment again, I realize he is asking a really good question. It's a question that I'm getting closer to being able to address, but I'm not quite there yet. What is the sequence of returns risk when you build a front-end bond ladder and only replenish that ladder in years when stocks have grown. I'm not completely sure what the answer will be, but I'll keep this question on my list of things to do.

      Wade

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    2. Hi Wade,
      Thanks for your response. Even short of doing the research you propose, my understanding is that retirees are vulnerable to sequence risk (large losses in the early years) not BECAUSE the losses presumably force them to sell stocks in a down market but WHETHER OR NOT the losses force this to happen. Kitces original research on sequence risk made no assumptions about rebalancing, did it?
      Thanks,
      Kay

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    3. Kay,
      I'm sorry for the late response.
      I'm not sure what you mean about Kitces research on sequence risk. I'm guessing you are referring to his May 2008 Kitces report. That one, along with most every article about safe withdrawal rates, assumes annual rebalancing to a pre-determined asset allocation. So the general research would usually have you reallocating toward stocks, rather than selling them, after a big stock market drop.

      Best wishes, Wade

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  8. Similar idea pesented in the Journal of Financial Planning a few years ago:

    http://www.fpanet.org/journal/CurrentIssue/TableofContents/ReturnMeasuresandDollarCostAveraging/

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