Friday, November 20, 2015

Uncertainty Denial

Joe Tomlinson wrote an excellent piece at Advisor Perspectives last week entitled, “The Most Critical Planning Assumption – and How to Choose It.” The piece is primarily a warning to advisers who rely on a single estimate of future market returns for retirement plans, or who use planning software that limits them to a single estimate, but there is a lot of good insight in the piece for all of us.

The assumption Joe has in mind is the equity risk premium, or ERP, but to simplify the explanation, I’ll substitute a related and more familiar term, the expected market return.

We need to estimate future market returns and volatility to make a number of calculations, including how much we need to save, how much we can spend each year, and what an ideal asset allocation would be. We may also use this estimate of future returns and volatility to determine how much to allocate to a floor portfolio. If we think future equity returns will be quite high, we’ll probably feel less need for a large floor portfolio and vice versa.

Since so many plan parameters are dependent upon this estimate of market returns and volatility, Joe rightly calls it the most critical assumption. (I think there's a strong argument that life expectancy is the most critical assumption, but I'm sure Joe and I agree it's best to assume a long life.)

The issue Joe describes is that there isn’t a single spending rate, savings rate, asset allocation and floor allocation that are optimal across the broad range of possible returns suggested by such a mean and standard deviation. Picking the optimal parameters from the average (and most likely) scenario may be wildly incorrect if your retirement ends up significantly better or worse than the average case you predicted.

Plan results are very sensitive to the market return and volatility assumptions. A small change in a plan's market return assumption can make a large difference in what we calculate as optimal spending rates and asset allocations. The error in our estimate of future market returns gets magnified.

"Pretending we can accurately predict a critical assumption like future market returns is dangerous overconfidence. "
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Tomlinson provides an example using Professor Aswath Damodaran’s estimated ERP of 6.25% with a standard error of 2.32% for the period 1928-2014. He assumes a 65-year old retiree with a 4% spending rate and $1M savings portfolio at retirement. He finds that depending upon where the returns actually fall within that broad range of potential outcomes, a retiree would have a portfolio failure rate ranging from 2% to 42%, a median bequest of $127,000 to $2M, and an optimal stock allocation ranging from 10% to 90%.

I ran those estimates through Moshe Milevsky's formula for lifetime probability of ruin (download PDF) and found 95th percentile sustainable withdrawal rates ranging from 2.35% to 8.5%. Here's a chart with data from the Tomlinson piece and my own SWR calculations.

Source: data from the Tomlinson post plus author's calculations.
To quote Joe's post, a completely forthcoming (though, likely unacceptable) discussion with a client should go something like this:
Your results will be heavily dependent on the extra return of stocks over bonds. Unfortunately, we have limited statistical evidence and don’t know what to expect. The best I can do is tell you that I’m 95% confident that you can expect a bequest in the $100,000 to $2 million range and that the probability of plan failure is somewhere between 2% and 40%. For an asset allocation recommendation, it could be anything from 10% to 90% stocks.
I actually believe Joe is optimistic about our prospects here because even if we could accurately predict future returns with a relatively small variance (we can’t) we need to consider sequence of returns risk when we save to or spend from a volatile portfolio. Sequence risk is unpredictable and an unfortunate sequence of returns can ruin even a good average return. We need to know the return, the variance and the sequence of those returns.

The gist of Joe's post is that retirement plans entail a great deal of uncertainty and that pretending we can accurately predict a critical assumption like future market returns is dangerous overconfidence. (Please read his column – I don't do it justice.)

We tend to think that the estimates of our optimal asset allocation, floor allocation, safe spending rate and required savings can only be as good as our estimate of future market returns. I think it's correct that they won't be more predictable. The problem is that our plans are highly sensitive to market return assumptions, so those optimal parameter estimates can actually be a lot less predictable than our market return estimate.

Generally speaking, I think most of us understand that retirement finance, and investing in particular, is risky, but I also think we are overconfident in our ability to manage that risk. We pretend that we can accurately (or accurately enough) predict future market returns. Many of us seem to believe we know whether we will live long lives. We believe we can identify a precise sustainable withdrawal rate when that rate is a function of both the rate of return we can't predict and how long we will live, also unpredictable. We believe we can avoid stock market risk by simply holding stocks a very long time.

This is overconfidence. There are ways to manage this financial risk but even if we do the best job possible there will still be much uncertainty.

You're likely overconfident when you think, "I'm really not sure what my investments will return in the future, but I probably oughta' tweak my asset allocation by 5%."

Next post, I'll suggest an approach to accept and plan for this uncertainty in 100% Certain That We're Not Sure.


  1. I also read Joe's AP column with interest.

    Expectations are predictions ... and predictions are hard, especially about the future! (side bar: info on origins of the quote ).

    Nobody can predict the future. Expected returns are all over the map - as Joe's article suggest. Monte Carlo does produce a range of outcomes ... so does one do Monte Carlo sims on the results of the Monte Carlo?

    So the question always circles back to what data does one use as inputs to future projections? While recognizing that any projection is a prediction? And predictions are often wrong ... so what degree of error should one want?

    More importantly, dynamic updating takes the uncertainty of a 29 year period (simply a number pulled for example), and incorporates the facts of the last year, to estimate the uncertainty of a 28 year period, and then for a 27 year period, etc etc until death makes uncertainty a moot point.

    There will never exist an ability to predict future returns. Markets would figure that out if it were to exist and then the markets would adjust to make the ability go away through application of various insightful strategies and counter strategies. The question should move away from implying a more perfect prediction to modeling how spending today (this year) affects spending tomorrow (future years) and what decisions really have an impact on cash flows and portfolio balances.

    As you mentioned, life expectancy (read time period), is more important than allocation. Failure rate of simulations is next. Allocation comes in third once the prior two have been evaluated.

    I look forward to your next column Dirk about managing and monitoring uncertainty.

    1. I would've bet on Yogi. Please don't tell me Nostradamus said, "It gets late early out there."

      I will always prefer dynamic updating for precisely the reason you suggest – to do otherwise is to deny ourselves useful data that has come available since the last projection.

      Accurate predictions about the future of market returns isn't on the table, but humans do a lot of useful planning despite uncertainty. I can tell you I won't recommend more accurate projections of stock returns or a more conservative estimate.

      I look forward to your comments on my next column!

      Thanks, Larry.

    2. Three unknowables:
      How the market will perform
      How long you'll live
      AND even if you knew those, how much money you'll need.

      Everyday expenses I know. Every year expenses -- property tax, auto insurance and such -- I know.

      End of life expenses for myself and wife are unknowable. LTC insurance and health insurance help mitigate the main concerns, but conceivably one of us could develop dementia and be in a nursing home for 20 years. Then we'd be forced to rely on the generosity of strangers (Medicaid).

    3. There are three unknowables:
      * Market returns
      * Date of deaths
      * How much money you'll need

      Even if I knew the market return and how long my wife and I will live, I can't know how much money we'll need.

      I know everyday expenses and every year expenses (insurance, property tax and such), but I can't know whether one of us will develop dementia and be in a nursing home for 20 years. LTC insurance and health insurance mitigate, but do not eliminate extreme end-of-life costs. If that happens, we may find ourselves relying on the kindness of strangers in the form of Medicaid.

  2. Hello Dirk
    I hope your next article separates out the essential and basic needs, thereby leaving the discretionary needs to addressed using equities and bonds. This ensures the uncertainty does not lead to tragic/catastrophic results. I too look forward to your next article.


  3. Great article. Agree with many of the points. But, when you're citing results from stochastic modelling, this would incorporate those periods where the sequence of returns was adverse? So you don't need to worry that the results don't incorporate poor sequences?

    1. Two different risks. Joe points out the risk that your actual return can be quite different from the mean of your assumptions (e.g., 1.61% vs. 6.25%).

      Sequence risk is the risk that a poor sequence of returns will wreck even a good average return.

      If you're spending from or saving to a volatile portfolio, you have both.

      Does that make sense?

      Thanks for writing.

  4. Hi Dirk
    A good write-up of a great piece by Joe. Your blog gets lots of comments here in OZ.

    Coincidentally we have just had some work done in Australia by Mike Drew and others looking at the unpredictability of the ERP. It is hosted at
    This work broadly follows the work Wade Pfau did with us on the Yin and Yang Retirement Income Philosophy. (The Retirement cafe Nov 10 2014)

    We're having a bit of fun spinning what we call here a 'chocolate wheel' (a bit like a wheel of fortune), because when you start retirement you never know just what you're going to get from the ERP.

    Aaron Minney
    Head of Retirement Income Research

    1. When I sat down in a North Carolina coffee shop after retiring a few years back and began trying to write entertaining retirement finance pieces – an oxymoron if there ever was one – I thought maybe one day they would reach "down under", but at the time I was thinking South Carolina.

      Here's a clickable link to the Mike Drew paper Aaron mentions and if you haven't seen the Yin and Yang of Retirement Income Philosophies by Wade Pfau and Challenger's Jeremy Cooper, you should really take a look. It provides a great introduction into the various approaches of the two major school of retirement income thought.

      I'm planning a few posts in the near future on uncertainty in retirement because I'm convinced most people underestimate it.

      Thanks for writing!

      (And one last thing. On behalf of UK Basketball fans everywhere, thanks for sending us Isaac Humphries. Y'all grow 'em big down there.)

  5. I enjoy your articles. You seem to find the important things to think about, and present them in logical ways.

    I've been retired for some years and have developed a rather elaborate planning spreadsheet to play with these issues (you would have to be crazy to spend the effort I've spent unless you enjoy the challenge). The reason I started was that most planning software requires a bunch of general inputs, uses them in hidden ways and returns an "answer" rather than an understanding of the issues. As you point out, the huge potential variation in results created by potential variations in investment returns can make the idea of any "plan" seem ludicrous. Any plan that offers security will probably leave unspent money (things you could have done). For those who feel foolish about missing some experiences, this creates an unsolvable dilemma-- if I try to spend the likely returns, I am not secure; if I am secure I'm not doing all the nice things I could have done.

    One possible answer is to create a retirement plan that can be maintained to an advanced age with low investment earnings, and a plan for using the possible (probable?) surplus for things that feel worthwhile (e.g., covering those frightening college costs for the next generation). If you can create a secure life that you enjoy combined with the consolation that the things you missed out on will lead to good things for your kids and grand-kids, that seems like a pretty good plan.

    1. Thanks! I enjoy writing them.

      All excellent points. Let me make a couple of comments.

      I share your experience with most planning software. I use some of it, like E$Planner, but I always end up using the results to finish with my own software. (No package ever fully meets my needs and, as you say, the algorithms are never adequately transparent.) Fortunately for me, my baccalaureate degree is in computer science, so I find this fun.

      The idea of a plan does sometimes seem ludicrous, but it's better than no plan. Humans have ways of dealing with uncertainty every day. Though we can't eliminate the uncertainty, there are ways to mitigate, insure and sometimes avoid parts of it. I think the key is to remember that retirement finance always entails a huge amount of uncertainty and to not become overconfident in our ability to predict the future.

      The "possible answer" you propose is what economists call the "life-cycle approach" and planners refer to as a "floor-and-upside" strategy. I personally think it is the way to go.

      Sounds like you have your head wrapped around retirement planning. Thanks for writing!

    2. You observe (correctly) that an uncertain plan is better than no plan. I'd like to add that creating a real plan is about more than numbers (even sophisticated numbers with ranges of possibility). It's a chance to think about what matters in your life. Others can help with the mathematical part, but you have to think through the most important stuff for yourself.