Friday, September 20, 2013

You Can't Control When You're Born... Revisiting Sequence of Returns Risk

My aim is to put together some thoughts based on reading Dirk Cotton’s recent posts on sequence of returns risk at his “The Retirement Cafe” blog, William Bernstein’s excellent e-book The Ages of the Investor, as well as some of the issues I discussed in my article on “safe savings rates” and a follow-up about "getting on track for retirement" from a few years back.

Dirk Cotton clarifies that sequence of returns risk is something which can apply both in pre-retirement and post-retirement. Two investors may enjoy the same average return on the investments in their portfolio, but may still experience very different outcomes if they experience a different sequence for when these returns arrive. This can impact both those who are saving and contributing to their portfolio over time, and those who are withdrawing a constant stream of cash flows from their portfolio during retirement.

Let’s illustrate this in a simplified world to make this vulnerability very clear and prominent. Americans are a very self-reliant people who believe if you work hard and do what you are supposed to be doing, then things are going to work out. So let's consider some hypothetical individuals who are doing everything absolutely right (based on our state of knowledge) with regard to their retirement planning. When retirement is still 30 years off in the horizon, they begin saving 15% of their salary at the end of each year.

In our simplified world, these folks don’t have to worry about health risks, disability, or economic shocks to Main Street which might cause them to lose their jobs. They are able to continue work over the subsequent 30 years earning a constant inflation-adjusted salary.

As well, unlike in real life, there is no uncertainty with regard to investing. There is risk, but this risk is understood.  Each year the market provides a 7% real return on average, but the actual return is going to fluctuate around this real return with a standard deviation of 20%. So while one does not know what the year-by-year returns will be, they do know that returns will fluctuate around 7%, and with 30 years of returns the average (arithmetic) return each investor earned over their career will be somewhere close to 7%. Their wealth will not compound at this rate, as with volatility a given percentage drop in the portfolio requires a larger percentage gain to get back to where they started, and the math shows that the compounded growth they can expect for their portfolio is 5% (7% - 0.5 * (20%)^2).

So these folks play by the rules, do everything right, don’t experience any health or unemployment issues, and understand the underlying return process that affect their portfolios. Saving 15% at the end of each year and with wealth compounding at 5%, they fully expect to reach retirement with a portfolio equal to 10 times their salary.

Where do they actually end up?

The following figure shows a Monte Carlo simulation of a time series chart for 151 hypothetical investors who work and save for 30 years and get 30 years of market returns, but who differ only in which 30 year period they worked and saved in this 180 year simulated historical time frame. 
Though they could expect wealth equal to 10x their salary, the outcomes ranged from a minimum of 2.98x to a maximum of 27.7x. The median accumulation was 9.9x and the mean was higher at 11x. These are very different outcomes for people who otherwise behaved exactly the same. What’s more, we see cases like how 10 years after the person retired with 27.7x, the subsequent retiree only had 8.7x. This is despite the fact that 20 years of their respective careers overlapped. What’s more, the person retiring only one year later than the fellow with 27.7x only had 17x their salary. This despite the fact that 29 years of their 30-year careers overlapped with one another. With William Bernstein’s idea of waterfalls, some of those folks with the lower wealth accumulations  might have just missed their chance to reach their wealth target after 30 years, and might find that they don’t get to where they had hoped to be with even 50 or 60 years of work.
This is sequence of returns risk! People are more vulnerable to the returns experienced when their portfolios are larger because a given percentage change has a bigger impact on absolute wealth. A big portfolio drop at the end could possibly wipe out all of the portfolio gains from the first 25 years of one’s career. 

The problem also applies in retirement, perhaps even more strongly, if retirees are using a constant inflation-adjusted withdrawal strategy. With compounded returns of 5%, a retiree could expect to withdraw 6.2% of their retirement date assets, adjust this for inflation, and have their wealth last for precisely 30 years. But again, the actual maximum sustainable withdrawal rates experienced vary greatly over time due to the sequence of returns risk as illustrated below. For these 151 retirees, the actual maximum sustainable withdrawal rates experienced over 30-years ranged anywhere from 1.9% to 10.9% for reasons beyond one's control reflected simply by the luck of when they retired.

These hypothetical folks were all very hardworking and industrious, but they experienced very different outcomes based on the very random factor of when they were born and which years comprised their working period and retirement period. As Dirk Cotton notes, sequence of returns risk is a risk which is not rewarded by the markets and which individuals cannot diversify away on their own.

So what are the solutions? Here are some ideas:

  • First, as a society, let’s hold on to our defined-benefit pensions, including Social Security. Ideas to convert some of Social Security to defined-contribution could be dangerous on a societal level. Defined-benefit pensions are essentially a separate asset class which all investors should find very valuable to diversify into. Their most prominent characteristic of relevance here is that they allow for risk-sharing between different birth cohorts which eliminates some of the sequence of returns risk stemming from the uncontrollable factor of when one is born. Everyone can get the same benefit from the same work effort regardless of what their individual wealth accumulations might have been with their individual sequence of returns. The problems we have with defined-benefit pensions come from politicians and businesses overpromising on what is feasible, and so they should be adjusted... not eliminated. 

  • A point that Dirk Cotton emphasizes is that sequence of returns risk in retirement comes from strategies to withdraw a constant inflation-adjusted amount. There is no sequence of returns risk for someone using a constant percentage of remaining portfolio withdrawal strategy. A lot of research (including some of my own) has now shown that a constant inflation-adjusted spending strategy from a volatile portfolio is just about the most inefficient way to approach retirement. Someone can’t expect constant spending from volatile portfolio. Those who want upside (and, thus, volatility) should be flexible with their spending and should make adjustments.

  • Alternatively, sequence of returns risk is a function of volatility. Spending could be kept constant if the portfolio is de-risked. To really get constant spending, one should be looking to hold fixed income assets to maturity or use risk-pooling assets like annuities. The inefficiencies of a constant spending strategy using volatile assets may be explained because of the added sequence of returns risk which offers no reward to investors.
  • Other approaches which reduce the downside risk (volatility in the undesired direction) could also be considered. Financial derivatives can be used to put a floor on how low a portfolio may fall by giving up some of the upside potential for the portfolio. Another possibility is a stand-alone living benefit rider like those offered by Aria Solution's with the RetireOne program, which can be applied to portfolios of mutual funds and ETFs. They behave like income guarantee riders for variable annuities in that they provide the potential to annuitize and get a guaranteed income stream from a portfolio's high watermark level.
  • Another approach which Michael Kitces and I have offered in a new article discussed in last Saturday’s New York Times (and which we will both have specific blog posts about next week) is to use a rising equity glidepath in retirement with an even lower than typically recommended (at least in the safe withdrawal rate research literature) equity allocation at the start of retirement. This reduces vulnerability to early retirement stock market declines which cause the most harm to retirees. 
  • A final idea is to consider is my "safe saving rate" approach which focuses on using a consistent savings strategy and eliminates the need to worry about wealth accumulations and withdrawal rates. This strategy works better if there is a tendency for mean reversion in the markets, which we have observed historically with regard to the cyclically-adjusted price earnings ratio. Low sustainable withdrawal rates tend to follow bull markets, and high sustainable withdrawal rates tend to follow bear markets, and by linking pre- and post- retirement together the mean reversion cancels out some of the sequence of returns risk.


  1. It would seem, therefore, that the approach of using a strategy to switch into (out of) investments in secular bull (bear) markets would help reduce sequence risk. While you may not get out (in) at exactly the top (bottom), you would capture most of the benefit of avoiding long downtrends while still being invested during uptrends -- even though you are in cash (low yields) during downtrends and may have to draw on capital for annual withdrawals.

    I know all the arguments against doing this. But, has anyone looked at this strategy using the analysis you discussed?

    1. Hi, yes, Michael Kitces and I have both independently looked at how valuation-based asset allocation strategies could potentially impact retirement withdrawals. I had an article about it in the April 2012 Journal of Financial Planning:

      Safe Withdrawal Rates, Savings Rates, and Valuation-Based Asset Allocation

  2. Wade
    I love the reference to when you are born and sequence risk. Hindsight is wonderful and when we can look back on someone's life we can see whether or not they had a good sequence of returns (and even a good average return).
    The issue is that in the planning stage, it is hard to determine what will be achieved. There is some value from using valuations to improve market timing, but these are not always reliable. Remember Greenspan called the equity market top Five years too early. As some of Kitces work shows, the first five years in retirement can do a lot of the damage through sequence risk.
    One point that really should be reinforced by sequence risk is that risky assets are risky. FULL STOP. In the real world there are cash flows and you can't assume that you can get the 30 year average return by investing for 30 years. This does not mean that risky assets should be avoided. far from it, optimally they are part of the mix. But they cannot be used to overcome low savings or aim for higher spending simply by going for growth. Sometimes it will work and sometimes it won't. If you try it you have to be prepared for the outcome it the strategy fails, no matter what your time horizon is.

    1. Aaron, Thanks. Yes, stocks are risky and this risk becomes heightened in retirement due to the disproportionate impact that the first few years of returns plays on the entire retirement outcome (using a constant spending strategy).

  3. Wade, great post as usual. With the idea that a constant inflation-adjusted spending strategy is a terrible idea for most retirees, is there a variable spending approach that you have found yourself gravitating toward?

    I've been modelling, based on historic data and not monte carlo, the Guyton-Klinger Method and Hebeler's Autopilot method over at It seems like these methods do a great job at preserving your portfolio during market swings, while giving retirees the possibility of higher withdrawal rates during good times (all without affecting the success rate much).

    As you said, it seems most prudent to be flexible in your spending, but I wonder if a "dynamic" structured methodology would be best.

    1. Bo, Thanks for writing.

      Being able to reduce spending whenever the portfolio drops can be helpful, and so there is a lot of value in having a dynamic spending strategy.

      About what the optimal dynamic strategy is, though, I'm still not confident about what to suggest. Everytime I try to program something about it, I keep coming back to the idea that any optimal rules are very reliant on the underlying asset market return assumptions, and are also divorced from what people's actual spending goals are and how low they are willing to let their spending drop. So I'm still working on this.

      Nonetheless, from what I've seen done thus far, I think David Blanchett's "mortality-updating constant probability of failure" is the most reasonable approach, and in a new article in this month's Journal of Financial Planning, he is bring his approach to the masses by developing a single equation that can estimate the process pretty well.

  4. Thanks for another thoughtful post, Wade.

    A recent brief by Wei Sun and Anthony Webb of the Center for Retirement Research suggested a retirement draw-down strategy consisting of a portfolio's interest and dividends, plus the IRS Required Minimum Distribution rate times the portfolio value, approached an optimal strategy. Have you had a chance to examine this concept, and, if so, what are your thoughts?

    1. Benjamin Graham,

      Thanks. I did write just briefly about that article here:

      I've also investigated the basic IRS RMD strategy as well and found it works fine though is a bit conservative (that's why Sun and Webb add the interest and dividends), for someone willing to accept that volatility in their annual spending.

      “Optimal Withdrawal Strategy for Retirement-Income Portfolios,” by the Morningstar team David Blanchett, Maciej Kowara, and Peng Chen also have positive things to say about the RMD strategy. You can read about that here.

      The RMD strategy would reduce sequence of returns risk, though not fully. Only a constant percentage strategy can fully eliminate sequence of returns risk.

  5. i'm a dummy i dont understand the chart

  6. My only comment is your reference to maintaining defined benefit pensions. That is wishful thinking and is not realistic anymore. While such pensions if properly maintained would be a boon to retirees it puts the onus on the employer to make the investments and pension promises that can support such pensions. The humans in business who would make such investments and promises even if well meaning are subject to error. The error once made is out of the control of the retiree. then what?

  7. If I reduce my stock exposure gradually closer to retirement and move more into bonds; liquidate my total portfolio at retirement and buy a SPIA would I still be affected by the Sequence of returns?

    1. Hi, anything that reduces portfolio volatility when the portfolio the largest reduces this sequence risk, so the answer to your question is yes. But it probably wouldn't be a good idea to annuitize all of your assets!

  8. 1) Does the Monte Carlo model you have used adjust for the mean reversion / time diversification effect? Your paper with Blanchett and Finke shows that it matters a lot. Would the graph look the same if you simply used the available historical data?
    2) More and more research (e.g. go have a look at EDHEC Risk Institute is revealing that market cap index proxies for "stocks" are in fact quite inefficient. Taking a lot of the volatility risk out of the equity asset class would dampen the sequence of returns risk considerably.

    1. Thanks for the feedback. About your questions:

      1) No, this is a simple i.i.d. Monte Carlo. You are right that mean reversion would mute some of the sequences risk. That is the point I'm trying to make with the safe savings rates idea.

      2) I'm familiar with some of the low volatility investing work, but I haven't had a chance to study it closely yet. One of my colleagues has written about low-beta portfolios in a standard one-year accumulation type environment, but when we made an initial attempt to apply his data to retirement distribution, nothing interesting was coming out. There didn't seem to be any difference between high and low beta when it came to withdrawal rates, which is surprising.