Friday, July 11, 2014

Half Right

One way to look at retirement planning is with a spreadsheet. We make some assumptions, like 5% portfolio returns and 3% inflation and we build 30 rows representing as many years, with the same average assumptions plugged into each row.

The world doesn't actually unfold that neatly, of course. We get returns that can vary widely each year, and if you're buying and selling along the way, it isn't nearly the same thing. This variance of returns introduces sequence of returns risk when we are accumulating or spending from a volatile portfolio and the spreadsheet doesn't capture that.

Market crashes can cause wealth-destroying panic selling and high portfolio variance can increase longevity risk. The typical spreadsheet analysis doesn't account for any of that.

Most importantly, half the time your return will be more than the average and half the time it will be less, so if you assume an average return of 5%, for example, and need at least 5%, you will fail half the time. (Technically, that's the median and not the average, but I'm assuming they're pretty close in this situation.)

This chart shows a probability density function of portfolio returns with a mean of 5% and standard deviation of 11%. Your actual returns can fall anywhere along the x-axis, but most will fall somewhere close to the average return of 5% in the middle.

Your actual return could fall to the right of the average and exceed 5%, or to the left and be less than 5%. The dotted line shows the average, which tries to represent all of that data in a single number in a spreadsheet. But there's a 50/50 chance that your return will be less than 5%. A 50% chance of being wrong is more risk than a conservative retiree might want to take.

To address these problems, many planners and nearly all academics prefer to use Monte Carlo simulation, instead. Monte Carlo generates many outcomes and, unlike the spreadsheet approach, shows the distribution of outcomes, like this graph, and the probabilities of each occurring. It also simulates sequence of returns risk and creates some "market crash" scenarios.

Instead of simply using an average that we will under-perform half the time, Monte Carlo can also tell us what rates we are likely to outperform 80% or 90% of the time, for example.

Is there a way to use a spreadsheet and incorporate this volatility risk that would typically remain hidden? Wade Pfau recently published a column in Advisor Perspectives entitled "New Research on How to Choose Portfolio Return Assumptions" attempting to answer that question. I won't repeat his findings in detail — I hope you will read his analysis — but I will summarize the results.

In simplest terms, Wade performed a Monte Carlo analysis to generate a random variable with a median return of 5% (the same as the spreadsheet answer that is exceeded 50% of the time) and standard deviation of 11% and then calculated what the returns would be with more conservative assumptions, like the return that would be exceeded 90% of the time, also known as the 10th percentile.

Wade confirmed some guidelines suggested by financial planner, Daniel Flanscha, who noted that when he uses a fixed return assumption (a spreadsheet analysis), he subtracts 1.0% to 2.5% from the return during the accumulation phase and 2.5% to 4.0% from the return during the distribution phase to account for the effects of randomness.

Wade found that compared to performing Monte Carlo simulation of a retirement spending scenario with a median geometric return of 5% (arithmetic mean of 5.6%) and volatility of 11%, a return you could expect to meet or exceed 50% of the time, you could provide a reasonably conservative result, one that might be met or exceeded in 90% of cases, with a spreadsheet by using an expected return of 1.9%.

Here's our portfolio returns probability density function chart with the dotted line now showing the more conservative 10th-percentile figure of 1.9%.

There are several important take-aways from this analysis, the most important of which is that volatility costs a lot. Subtracting 1.0% to 2.5% from your return assumption during the accumulation phase and 2.5% to 4.0% from the return assumption during the retirement phase of planning eats a lot of your expected portfolio return.

Second, it shows that sequence of returns risk is greater during the spending phase than during the accumulation phase. In Wade's example scenario, you would subtract 2% during the accumulation phase, but 3.7% during the retirement spending phase. I think I showed that with my discussion of sequence of returns risk, too.

Lastly, as an anonymous commenter to the column noted, conservative stock returns start to look a lot like bond returns:
"Given the 1.9-2.5% real projected returns at the 10th percentile that you use for the example, by the time you subtract any management fees, transaction costs, and/or fund expenses, the real returns would be in the range that's quite attainable with a carefully laddered long bond-only income portfolio where the bonds are held to maturity. Even if the 50/50 portfolio at the 10th percentile might do slightly better than the bond ladder, the difference in real return might not be worth the risk. . ."
To which Wade added:
"this is an important point about how a conservative rate of return assumption starts getting close to the internal rate of return from a bond ladder. There is one important difference, however: the bond ladder will not have upside potential, while the diversified portfolio could perform better. Remember, this is a conservative return assumption."
The diversified portfolio could also perform worse; there's a 10% chance of that happening. In fact, Wade's analysis assumes that the individual earns market returns, which is a big assumption. Most don't. Underperform those stock market index returns with your own investments and you do have bond returns.

Still, there is a much better chance that you will do better than worse at the 10th percentile.

Be careful with tools other than your own spreadsheets, as well. E$Planner, for instance, used to use spreadsheet-like calculations until it began to incorporate a Monte Carlo function. Monte Carlo is still optional. (You can implement Monte Carlo simulation in a spreadsheet, just know whether or not you are.)

It was spreadsheet-like thinking that led Peter Lynch to infamously suggest that 7% should be a sustainable withdrawal rate and many people to think you can always make a profit earning an average market return that is higher than your mortgage cost.

It's half right.


  1. Thanks for always translating difficult material into understandable information Dirk. Brad

  2. Dirk: I think you have a typo in the second paragraph below the second figure. You say "Second, it shows that sequence of returns risk is greater during the accumulation stage than during the spending stage." Your numbers confirm the common observation that it is the other way around. Rick

  3. Thanks, Rick! I corrected that. I must proofread my columns at least 20 times before I hit "Publish". It is amazing what obvious errors you can overlook time and time again.

  4. Dirk, one question and one comment. I assume (looking at Wades article) that the 1.9% is a real return vs nominal return, and it would be interesting to see what the other confidence level/return combinations would be for other assets allocations other than 50/50 that Wade uses. Some retirees especially early retirees may not want to have as high an allocation as 50/50. I would assume that the real return at the 90% confidence level would fall below 1.9% with stock allocations below 50% making even more required assets. Thanks, Brad.

    1. Rather than run the numbers, I took the lazy approach and asked Wade Pfau ( Here's his response:

      "My calculations are based on the overall portfolio return and volatility. With 40% stocks, the return and volatility would both be a bit less. Overall, the results wouldn't change much for this small difference. But at any rate, the numbers should be lower than I reported because that basic explanation of the process didn't account for today's low bond yields."

      His last statement is important. Low current bond yields probably have a much more significant impact than increasing the bond allocation to 60%. As his research shows (with David Blanchett, as I recall), those rates probably leave SWR's closer to 3% than 4% at present.

  5. The approach to returns analysis where you subtract a fixed percentage from the average to come up with a conservative assumption with a high probability of success is the same approach that many structural and geotechnical engineers use for design of structures etc. The "characteristic value" of the strength is selected based on an evaluation of the probabilistic distribution (done quantitatively or qualitatively if little data is available) to put the desired frequency of strength test above the characteristic value. Similarly, factors of safety are applied to the various loads that the structure will need to endure with higher factors of safety for critical or highly variable loadings - for example the weight of concrete is well known and not variable so it would have a small factor of safety while wind loading could be highly variable and have a higher factor of safety. You can do google searches for limit state design or LRFD design (the current iteration)

    Slowly, I am seeing the financial industry starting to think about personal finance in the same way that engineers think about design. There is a reason why not many structures collapse if properly maintained, unlike the financial markets that collapse regularly.

    1. In 1969, a geotechnical engineer named Ralph Peck published a paper outlining the "Observational Method" that is now used extensively for earthwork design and construction. I think the overall approach has direct application to personal finance and retirement planning. This is basically how I am structuring our personal plan. The basic steps to this method are:

      1. Exploration sufficient to establish at least the general nature, pattern, and properties of the deposits, but not necessarily in detail.

      2. Assessment of the most probable conditions and the most unfavorable conceivable deviations from these conditions.

      3. Establishment of the design based on a working hypothesis of behavior anticipated under the most probable conditions.

      4.Selection of quantities to be observed as construction proceeds and calculation of their anticipated values on the basis of the working hypothesis.

      5.Calculation of values of the same quantities under the most unfavorable conditions compatible with the available data concerning the subsurface conditions.

      6.Selection in advance of a course of action or design modifications for foreseeable significant deviations of the observational findings from those predicted on the basis of the working hypothesis.

      7.Measurement of quantities to be observed and evaluation of actual conditions.

      8.Modification of actions or design to suit actual conditions.

      I can e-mail you a copy of the paper if you are interested. It is quite readable for a lay person.

    2. Thanks! Please email a copy to

      My reluctance to turn this blog into a civil engineering thread is surpassed by my sense that it is a quite good analogy.

    3. Although I lay no claims to any bridge-building expertise whatsoever, I suspect that the analogy falls apart with sequence of returns risk.

      In retirement planning, portfolio survivability is a function not only of keeping returns above a minimum critical level, but also of the order in which those returns occur.

      Is there a parallel in the civil engineering analogy?

    4. Dear Anon, I saw your response and this discussion is interesting but getting well beyond the scope of this blog. If you will contact me at, I would love to continue it.

    5. Sure. Be glad to.

      A simple way to think of the Safe Withdrawal Rate is that it address the worst case scenario that engineers will design for using low factors of safety, since everything is already at the worst it can be. Since we are currently at very low interest rates and stock dividend yields, it is likely that we are in a scenario where a Safe Withdrawal Rate of less than 4% is appropriate to be applied for a person retiring today. However, in the early 90s, Bengen's 4% Safe Withdrawal Rate would likely have left a lot of retirement income on the table because the likely sequence of returns would have acted for the retiree instead of against him like is likely to occur for the next decade or two.

      Comparing actual key valuation measures (Shiller's CAPE, dividend yield, interest rates) to long-term normal should be very useful and predictive of whether or not actual spending should be driven by worst case scenarios or by "normal, middle of the bell curve" scenarios. This is an area where I have seen very little published.

  6. To follow up on the engineering analogies, civil engineers also views things from both serviceability and collapse states. Something can be designed so that the structure deforms too much for it to be serviceable, even if it doesn't collapse. Personal finance is similar. Many people find out that they have retirement funded so that it won't collapse (they won't starve to death in the cold) but it won't be particularly serviceable as they won't be able to do many of the things that they want. In the end, you need to have a high factor of safety against collapse while the serviceability has more gray areas and can be viewed as a continuum where coast-benefit analyses can play a role.

    As an engineer, I use many of these concepts in my retirement planning. I have been surprised to find almost no discussion in the financial literature about this (probably because people just want A Number instead of a cloud of probabilities). It is good to see that people like you and Wade Pfau are looking at this seriously. I have always been amazed that it is the smaller practitioners instead of the big players that are doing this thinking. People like Bengen, Sharpe and you folks but almost dead silence from the JP Morgan, Wells Fargo etc.

  7. A "number" is much easier to sell. Telling people that we can't know it with any certainty is apparently far less profitable. Thanks for writing!

    1. The structures guys DO come up with a number. They back off from the cloud of uncertainty by pre-specified factors. This can give discouraging (hard to sell) results when the cloud is large. AND things still break--sometimes because the analysis fails to include critical unanticipated real-world loading conditions.

    2. I think we're all in agreement with you on that. I believe when he said that people want "a number" he was referring to the book a few years back by that title, and that number is a precise amount of money one needs to retire.

    3. Yes, I was referring to the book and lots of other sources where there is a very specific number that must be achieved before you can successfully retire. In my view, it is good to have a number as a goal, but there are too many variables with unknown inputs for an analysis to be that precise and the final decision-making needs to address the world as a cloud of probabilities instead of linear, logical events.

      Regarding engineers coming up with a single number, that is often the case. However, if you look at the documentation behind the material strengths, load inputs, code specified partial factors, you will see that there is a lot of quantitative and qualitative probabilistic thinking behind how the good engineers do it. Degrees of Belief by Steven Vick is a good book on Bayesian thinking in engineering analysis.

      One of the reasons that a structures falling down makes the news is because it is a relatively rare event. Many of the failures that you see on the news these days are because they were not maintained or were located in risky areas through zoning ordinances etc. If structure design occurred like the way the financial markets and retirement are designed, we would have a high percentage of our population living or working in tents unable to travel to other locations after their buildings and bridges fell down.

  8. This comment has been removed by a blog administrator.

  9. Thanks for the comments and references!

    Honestly, I enjoy the conversations at Wade's blog as much as fly fishing, sporting clays and afternoons at Caffe Driade. This is such a great retirement hobby.

  10. Dirk, good stuff. Two questions:
    1) I never saw an answer to previous ? re: nominal or real return?
    2) Any similar work on inflation assumptions? (seems same logic could apply)?
    Keep up the good work, er, hobby.

  11. I think I posted Wade's response yesterday, unless you're asking about a different question.

  12. I suggest that the spreadsheet approach is better than a Monte Carlo approach when the base case analysis is combined with reasonable worst case scenarios.

    Which is more conservative -- planning for sequence of returns using MCS, or planning for a one time permanent market decline of, say, 60% (or a substantial increase in inflation)? Which one better covers Nassim Taleb's unknown unknowns or Bill Bernstein's deep risk. It's true that MCS provides probabilities, but the probabilities will not cover risks that are not input into the analysis.

    Which is more practical or user friendly -- am I OK with an MCS 88.46% probability of success in meeting my goals, or can I make ends meet if the worst case occurs?

  13. I'm sticking with the same answer I've always given — you need to consider both.

  14. I am gravitating toward an approach that utilizes a 10-15 year bond ladder for the crucial first part of retirement. I would let the ladder get spent down, and not replenish it, effectively increasing the equity exposure of the portfolio over time.

    It seems to me this approach is supported by the research showing that retirees are most exposed to sequence of returns risk in the first part of retirement. It also reflects the research supporting a rising equity glide path in retirement as a way to insulate against poor stock performance early on.

    The result of the above approach should be a reduced risk of running out of money while still preserving portfolio appreciation potential.

    1. Joe, thanks for writing.

      Your approach seems reasonable to me, but maybe that's because it is essentially the one I personally use. Let me add a couple of thoughts, though.

      Strategies should be appropriate for the retiree's wealth. While this strategy feels right for me, I wouldn't recommend it for an under-saver or for someone who is extremely wealthy. In our discussions, I think we often just assume we're all talking about people who have a lot of wealth, but not an extreme amount. That is the typical financial planner's target. My target market for this blog is under-savers, so I frequently see strategies differently than most financial planners.

      Second, an observation regarding the rising equity glide path. Lower equity allocations early in the first half of retirement seem like a good idea because, as you note, SOR risk is most punishing then. But half of retirees won't live beyond the median life expectancy to see those higher allocations. For them, the strategy nets out to lower equity allocations, period.

      I think what you suggest is spot on for you, me and for other retirees in our general financial situation, but just want to point out that it isn't for everyone.

      Thanks again for your comments!

    2. Sure, I am assuming someone's circumstances are such that these strategies apply.

      With regard to the risk of premature death, I think the bigger concern is the "risk" of living a long life. I see these portfolio strategies in the same light as Social Security which, if properly managed, is a form of longevity insurance that lessens the risk of running out of money before running out of life.

    3. Joe, I agree. A long life is the biggest retirement financial risk, but that wasn't my point. I'm simply saying that, with regard to rising equity paths, roughly half of retirees won't live long enough to "make it up on the back end".

  15. Dirk, I've had this debate before, and would love to get your views.

    If the worst case scenario is worse than any result that the 100,000 MCS iterations provide, what additional benefit is derived from MCS? Sure you get % probabilities, but are those percentages more helpful than simply knowing that the further you move from worst to base case, the more likely the outcome? Why pretend this is an exact science when it is not?

  16. First, I would point out that your last sentence is precisely the discussion we were having on Wade's blog. Why argue about whether historical data or current fundamentals are the best basis for opinions about the future when there is no evidence that either is predictive? There is nothing exact or scientific about predicting the future. That is precisely my point.

    Second, I see little value to monte carlo simulation (MCS) in creating a worst-case scenario. A bad enough worst-case scenario is easy enough to imagine without help. I don't even believe MCS, as we generally use it, can accurately predict worst-case probabilities, since the models almost always assume normal distributions of market returns and stock market catastrophes are far more common than Gaussian functions would predict.

    So, if your question is truly what benefit MCS provides in defining and assigning probabilities to a worst-case scenario, I'd say very little.

    I'd also say that MCS is no better than fundamentals or historical averages at predicting the future, since those are used as MCS model assumptions.

    But if your question is what value MCS provides beyond spreadsheets, I'd answer much. It provides a far richer analysis of the problem. It provides a distribution and not just an average. It expands our relative dearth of historical stock market returns.

    It would have stopped Peter Lynch from publishing an article asserting a 7% safe withdrawal rate.

    Let me add that I use MCS for analytical studies, but rarely for developing a retirement plan for someone.

  17. Dirk, I'm a bit confused by your reply. I agree that MCS is not helpful in defining a worst-case scenario or establishing one in a retirement plan. But I'd go a step further and say it has no use or value in a retirement plan. A spreadsheet retirement plan that has a worst case and a base case also provides a "distribution and not just an average". We know that moving along the range from base case to worst case is a declining probability. Historical returns then do not matter, nor does obtaining an MCS "richer analysis of the problem". Assuming that the worst-case scenario is worse than MCS, it seems to me that adding MCS only adds unnecessary confusion.

    1. I simply don't agree that MCS has "no value" in a retirement plan. However, I did state that I generally don't use it to develop retirement plans. I use it primarily for research. I believe there is more to retirement planning than assessing the worst case scenario. The most probable cases are important, too.

  18. I am much appreciating this discussion. I note that most of the modeling you and Wade do is still assuming real bond returns that are higher than the current negative yield world we're in. I understand that the point of this discussion is the planning approach and that the assumed returns are secondary. But for a new retiree like me who is considering a TIPs ladder now, the returns are not secondary and it is very hard to accept locking in real returns over a decade or more that are negative even before the hefty bite of Federal and, in my case, high state tax rates. The answer " Put it in a Roth" is unsatisfying because everything is better in a Roth, yet in most cases it is the smallest bucket and an insufficient for a ladder. My solution, if I can call it that, is to continue to try to wait out this negative yield phase by keeping my fixed income in cash and short term funds/CDs. I have also increased my equity allocation since 2009 which of course has nicely compensated me for the negative real return on my fixed income. But I really do believe this " create a floor" makes good sense. So I feel torn: do I wait or do I build a low yield TIPs ladder now that is guaranteed NOT to keep up with inflation. Any thoughts?

  19. Barry, I think your analysis is spot on. I would caution, however, against increasing your equity allocation to offset low bond yields. That's a risky solution. It will work for you until it doesn't. Unfortunately, there isn't a good, low-risk income solution for retirees right now.

    I wouldn't lock in these rates with a bond ladder. Flooring is very expensive right now.

    You could buy a TIPs or Muni fund, depending on your income tax bracket, with a relatively short duration in addition to the cash. If you hold the fund longer than its average duration, you should make up for capital losses when interest rates rise.

    I wish I had a better answer than stick with short durations and wait, but I am not aware of one.

    Good luck and thanks for writing.

  20. I understand your warning about chasing yield in equities that can't be found in fixed income. "No free lunch!" My increasing equity allocation since 2009 more reflects that it was maybe too low before then; i.e. about 25% in 2008 and about 45% now. The greatest risk for me long term is high inflation, and I've been convinced that, besides TIPs, stocks are the best long term inflation hedge. Since everything is relative, this theoretically conservative 45% feels aggressive to a guy like me who used to play it overly safe in the world of low risk/high yield CDs and even 5% money markets. (Remember those!) As a result, I missed out on a lot of return in the 1990s, but then I also missed most of the worst in the two crashes of the 2000s, and especially 2008, that hit in those critical timing sequence years before I retired and when my savings pot was at its maximum. Does this demonstrate how smart I was? No, it demonstrates that I was a chronically good saver and that I was lucky. And I think, in the end, it's worth acknowledging that being a good saver is more important than being a good investor, and that being lucky is way more important than being smart.

  21. Barry, I received your subsequent comment. Email me at and let's set up a time to talk