Monday, February 27, 2012

Joe Tomlinson’s “A Utility-Based Approach to Evaluating Investment Strategies”

Joe Tomlinson has written a very worthwhile article in the February 2012 Journal of Financial Planning called, “A Utility-Based Approach to Evaluating Investment Strategies.” He will visit GRIPS on March 15 to present this research and subsequent advances he has made to it.
An area of research that I am getting more and more interested in relates to developing tools to analyze how to find the best allocation for a retiree’s investment portfolio combined with single-premium immediate annuities (SPIAs), deferred annuities, and variable annuities with guaranteed benefit riders. This combines asset allocation with product allocation (as Moshe Milevsky calls the framework for choosing among different types of annuities).
How to analyze the appropriate asset allocation and product allocation? There are two basic ways. Are innovations for the framework to evaluate retirement income strategies best guided by using various criteria and risk metrics (such as failure probability or value of bequests) which allow direct retiree decisions for evaluating tradeoffs related to spending and bequests, or should the framework specifically incorporate the formal mathematical concepts of utility maximization to help guide retiree choices, perhaps under the recognition that the human mind is not equipped for making decisions among abstract and uncertain tradeoffs?
First let me give a brief answer to that. I think both approaches are useful and mutually reinforcing. Retirees should be free to choose as they wish to find the proper balance among competing tradeoffs. Most retirees will not be happy letting their decisions be guided by an indecipherable black box. They will want to feel they are empowered to make decisions. But with utility, their decisions can also be “double checked” to make sure they sufficiently understood the task of choosing among abstract and uncertain possibilities and found something matching a reasonable set of preferences.
In this article, Joe Tomlinson makes an important contribution. The article actually considers both approaches at the same time. Table 1 shows results for risk metrics (I’d like to come up with a better term for this – any ideas?), while Table 2 shows results for utility analysis.
He considers an inflation-adjusted SPIA with a payout rate of 5.05%, and he assumes that this matches the retiree’s desired spending. He also considers other strategies which combine stocks, bonds, and partial annuitization in varying ways. In later research, perhaps he can work more toward finding an optimal withdrawal rate as well.
In Table 1, he shows how the different strategies perform across 1,000 Monte Carlo simulations based on the average value of the bequest left at death, the probability that the strategy failed to provide wealth for one’s whole life, and the average amount of the losses in the cases of failure assuming that one could have kept spending into a hole.
In Table 2, he considers the matter of utility. He explained very well about the intuition for why he does this: “The problem is that three different variables need to be brought into the decision. This naturally leads to the question of whether a more informative decision tool could be developed by combining the measures. To do this we need to shift our focus from pure financial outcomes to the fuzzier concept of the satisfaction associated with those outcomes. We need to develop a utility measure.”
He uses a loss aversion utility function, in which running out of wealth has a stronger negative impact on utility than the positive utility experienced by leaving a bequest. This approach makes a lot of sense, and it can also be thought of more simply as a way to judge how important leaving a bequest is, compared to not running out of funds. Defining parameters for utility functions can be complicated, but Joe Tomlinson also describes a small survey he conducted to get a better idea about the degree in which losses hurt worse than parallel gains.
What he finds is a stark cut off: 100% stocks are preferred by someone who is not so hurt by losses and/or is more interested to leave a bequest. Meanwhile, 100% annuitization is preferred by someone who feels great pain by running out of wealth and/or is otherwise not interested to leave a bequest.
The article is quite accessible, and it includes lots of interesting gems, such as his discussion of the danger of bond ladders with uncertain lifespans, the role of the equity premium in driving the results, and his ideas for how to make guaranteed benefit riders that would be more worthwhile (“could be very useful if it became available in a low-cost, index-funds version, with an inflation guarantee, but without the commission loads and the charges for active management.”). I hear that, and hope we get there one of these days!


  1. Thanks for pointing to this superb article.
    Along the risk aversion line, the 2007 survey by AARP "What Now? How Retirees Manage Money to Make it last through Retirement around p 18 seems to confirm 5:1 or higher ratios in most cases. see Sadly, in Canada we do not even have inflation-indexed annuities.

    1. Thank you for sharing the link. I read Peter Benedik's Retirement Action, and it seems to be a reoccuring meme for him to have to always add that the financial products he is discussing are not available in Canada. I'm sorry to hear that, though it does seem that not many people actually want to buy inflation-adjusted SPIAs.

  2. Wade –

    Thanks for this blog post on Joe Tomlinson’s superb article.

    When I saw the word utility in the title of Mr. Tomlinson's article, I shuddered. I thought of the way the high priests of investment “education” have mis-used that term to train past and present generations of financial students, advisors, and even professors in diversion from the investment purpose.

    Of course, an investment’s utility is the dollar purchasing power it delivers for the investor’s needs and goals -- or assessed for the future, its probabilities for such delivery. Yet all the way from Markowitz to Sharpe to Bodie’s BKM textbook, used today for investment “education” at our universities and in our training of “fiduciaries,” investment selection has been and is taught according to a notion of “utility” that does not even address an investment’s utility. The notion of utility they teach does not address the investor’s needs and goals. It omits dollars, years, and effects of compounding along the way. Thus has the whole community of students, professors, and credentialed investment advisors been mis-trained. And even today, such mis-training continues.

    It was such a pleasure to find that Mr. Tomlinson departs from the teachings of those high priests, and instead uses the term utility to mean an investment’s utility –- its delivery of dollar purchasing power needed or desired by the investor, or its probabilities of doing so. While there is much more about how Mr. Tomlinson applies this approach that deserves discussion and praise, this feature alone is so important, it deserves the spotlight on its own.

    Mr. Tomlinson towers above the aforementioned high priests of investment “education.”

    Dick Purcell

    1. Dick,

      Thanks for the comment and the re-tweets. In case you didn't match the names together, Joe also makes comments here and the two of you interacted before. I will be sure he gets your comment. His article has been well received in many quarters. Even the hard-to-please Bob Veres gave it high praise:,-2012.html

    2. Dick,

      Also, please have a look at the article I wrote with Michael Finke and Duncan Williams in the new JFP and give your honest opinion. Did we work in the same spirit as Joe, or do you think it is a step backward?

      Best wishes, Wade

    3. Wade –-

      In answer to your question, I have a two-part answer: same spirit followed by step backward.

      I think your article in the new JFP lays out decision considerations very much in the spirit of Joe Tomlinson’s approach –- most fundamentally, your addressing of tradeoff between shortfall risk and withdrawal rate, with the analysis considering longevity probabilities, allocations, perhaps a guaranteed income source . . . I think that’s a very valuable contribution.

      Something about it that’s of special interest to me is that, while your investor example is from the wealthier minority that this whole field of study seems to be developed for, I think your article’s approach has applicability for the neglected majority of the population with less wealth. I think that’s worth a LOT!

      There is however one aspect of the article that troubles me: introduction and use of the so-called “coefficient of risk aversion.” I did not see any description of how that measure is to be determined for an investor, but I saw enough to set me aflame: what appears to be acceptance of that measure’s method of determination and use in portfolio theory.

      In my opinion, our duty is to do the very best we can to INFORM the investor of consequences of alternatives, for her choice –- inform her BEFORE her choice, so she can make an INFORMED CHOICE. I mean the consequences for which she invests, which she understands -– dollar purchasing power for her future needs and goals. This is INFORMED choice.

      The way it is done in portfolio theory is the opposite: Somehow conjuring the investor’s choice of a tradeoff between two misleadingly labeled technical measures she does not understand, before the consequences of her choice or alternatives are revealed or determined, enabling the mathematician to use her uninformed choice to pretend to calculate an optimum and its consequences. This is UNinformed choice.

      In the math at the end of the article, under the references, it appears that the “coefficient of risk aversion” is used as an input for calculation of consequences, which means the critical decision was somehow made before the consequences were revealed or calculated –- the UNinformed approach.

      So I like your article very much up to the point where the “coefficient of risk aversion” is introduced –- and very much dislike the latter part based on that factor. I would prefer that the latter part of the article be devoted to informing the investor of dollar-probability consequences of alternatives so she can make an informed choice.

      Dick Purcell

    4. Dick,

      Thanks. I hope you don't mind, as I took the liberty of moving your comment over to:

      and responding to it there.


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