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Under classic Modern Portfolio Theory, there is a single portfolio that is considered to have the most efficient risk/return balance for a given target return or target risk level; any portfolio which deviates from the "optimal" allocation must, by definition, either offer lower returns for a comparable level of risk, or result in higher risk for the same level of return. Accordingly, as the theory is extended, advisors should avoid making portfolio shifts that constitute tactical "bets" in particular stocks, sectors, asset classes, etc., as it must by definition result in a portfolio that is not on the efficient frontier; one that will be accepting a lower return for a given level of risk, or higher risk for a comparable return. Unfortunately, though, this perspective on MPT with respect to making tactical portfolio shifts is not accurate, for one simple reason: it is based on an invalid assumption that there is a single answer for the "right" return, volatility, and correlation assumptions that will never change over time, even though Markowitz himself didn't think that was a good way to apply his theory!

The inspiration for today's blog post stems from some of the comments discussion that arose from my blog post yesterday about the difference between being tactical and market timing. In the comment, one of my readers espoused a view that is shared very commonly in the financial planning world - the idea that since one portfolio must be the most efficient, anything that deviates from that through tactical asset allocation must be riskier.

First and foremost, it is worth pointing out that even under the classic MPT theory, a portfolio that does not lie on the efficient frontier could simply be lower return for a comparable level of risk, not necessarily higher risk (in other words, it could move "south" away from the efficient frontier; it doesn't have to move "east"). So to say the least, we should probably stop automatically referring to portfolios that don't lie on the presumed efficient frontier as being "riskier" - they could simply be lower return, or moreover they could actually be less risky, while also giving up return. We can say - at least under classic MPT - that the portfolio has a less efficient risk/return tradeoff, as that is true by definition of the efficient frontier. But portfolios not on the efficient frontier do not have to be higher risk; in fact, they can be lower.

More important, though, is to look at how the efficient frontier is determined in the first place. The efficient frontier - as well as the expected return of the portfolio, the volatility of its investment choices, and the volatility of the overall portfolio after accounting for the correlations amongst the assets - is based on the inputs that you provide to the model. In other words, the efficient frontier is only the efficient frontier because of the means, standard deviations, and correlations, that you entered as inputs into the model in order to derive the efficient frontier.

This in turn means that ultimately, your estimate of the efficient frontier is only "right" if all of your inputs into the model were accurate to begin with. Modern Portfolio Theory only tells us what the efficient frontier would be, given a series of inputs. It's still up to us to come up with those inputs. If we use the "wrong" inputs, then we could actually be wrong about what is efficient and what is not; we could misjudge a portfolio to be higher or lower risk than it actually is, or higher or lower return than it actually will be.

So in the context of the original issue - is a tactical portfolio inferior because it doesn't lie on the efficient frontier - the question really becomes: what inputs will you use to draw the efficient frontier, and whose inputs are the "right" ones!?

After all, making a tactical decision to make a portfolio shift, for example, to reduce small cap exposure and buy more large cap, in essence represents a perspective that going forward, the risk/return characteristics of small cap have become less desirable than they were, at least relative to the risk/return characteristics of large cap. In other words, if you took your current asset allocation based on MPT, and then re-ran it with a lower return and higher volatility for small cap, or a higher return and lower volatility for large cap, your MPT process would tell you "oops, the efficient frontier moved somewhere else, you need to change your allocation in order to be on the (new) efficient frontier!"

"But wait!" says the classic MPT advocate. You can't just change your inputs to Modern Portfolio Theory! You should look at long-term market history to determine the correct means, standard deviations, and correlations for your assets, and use those on an ongoing basis! However, using the long-term historical returns and volatility that have been observed in the past is not the only way to generate the inputs for MPT. In point of fact, here's what Markowitz had to say about it, when he published his original paper "Portfolio Selection" back in March of 1952!

To use the E-V rule [expected return-variance rule, or what we now call MPT] in the selection of securities we must have procedures for finding reasonable [estimates of] means and standard deviations. These procedures, I believe, should combine statistical techniques and the judgment of practical men. My feeling is that the statistical computations should be used to arrive at a tentative set of means and standard deviations. Judgment should then be used in increasing or decreasing some of these means and standard deviations on the basis of factors or nuances not taken into account by the formal computations. Using this revised set of means and standard deviations, the set of efficient E, V combinations [i.e., the efficient frontier] could be computed, the investor could select the combination he preferred, and the portfolio which gave rise to this E, V combination could be found.

One suggestion as to tentative mean and standard deviation [as inputs for MPT] is to use the observed means and standard deviations for some period of the past [i.e., using long-term historical averages]. I believe that better methods, which take into account more information, can be found." - Harry Markwotz, "Portfolio Selection", Journal of Finance, Vol 7, No 1, Mar 1952. (Emphases mine)

So there you have it. Even Markowitz, in discussing the application of his own MPT model, advocated - almost 59 years ago! - that simply using long-term historical averages (i.e., observed inputs from the past) is insufficient, and that more effective inputs should be derived using our judgment to increase or decrease those factors (i.e., making forward-looking forecasts). And to the extent that the economic and market environment changes (2008-2009 was certainly more volatile than 2003-2007!), those inputs and forecasts can and must change over time.

Which means, in the end, making tactical changes actually is the application of Modern Portfolio Theory - once you follow Markowitz's original instructions about how to use his theory, and apply your judgment to alter the means, standard deviations, and correlations based on the market environment (and any other "factors or nuances not taken into account by the formal computations). As the inputs change over time, the efficient frontier will move, and the MPT process itself will recommend tactical changes to your allocation based on the continuously updated inputs to the model!

So what do you think? How do you derive the inputs for determining your portfolio allocation? Do you allow for the possibility for those inputs to change over time? Is it possible that your portfolio is actually not efficient anymore because the efficient frontier has moved since you originally designed the portfolio?


  • http://arichlife.passionsaving.com Rob Bennett

    Michael:

    I applaud you for going even more in depth re this discussion. You are conducting important work here.

    I don't believe that the Modern Portfolio Theory can be reconciled with the challenge presented by the valuations/behavioral finance school. I appreciate the good intent of those who try to find some compromise path. But I believe that the differences here are so fundamental that all attempts at compromise will ultimately fail.

    The core question is -- Are investors rational?

    If investors are rational, the MPT really does follow, in my assessment. If not, then the MPT is gravely flawed and cannot be salvaged and we just need to give up the effort to find a compromise path.

    I'll give one illustration of what I am getting at with the aim of rooting what I am saying here in something real. The dollar value of the overvaluation in the U.S. stock market in January 2000 was $12 trillion. Just about everyone agrees that stock prices revert to the mean over 10 years or so. So we all "knew" (we obviously knew this only on one level of consciousness and not on all levels) that we were going to see a loss of $12 trillion in buying power sometime around 2010. There's your economic crisis! We don't need to look for any additional explanations!

    If investors are rational, it is impossible that stocks could ever be overvalued to the tune of $12 trillion. But that's what the numbers say.

    I think we all need to try to adopt more humble views as to what we really know and what we only believe without being entirely sure. I think that if we figure this out, it is going to take us to some truly wonderful places. But we need to let in the possibility that some things that many of us have come to believe in with great confidence are simply not so. It's not what you don't know that kills you but what you know for certain that just isn't so!

    We need a national debate on these questions, in my view. The debate needs to include not only financial planners but also economists, policymakers, journalists, and ordinary investors. My personal take is that we are going to need to go back to the roots and put even the most basic questions up for grabs. I don't see this as being even a tiny bit a bad thing. I see the upside potential here as being positively huge.

    Anyway, I do thank you again for getting people talking about this stuff. Talking frankly about the questions is the first step to getting in a position where we can begin figuring out the answers.

    Rob

    • Michael Kitces

      Rob,
      I'm not sure why these positions can't be reconciled though.

      Adjusting MPT inputs for valuation is certainly one very reasonable way to address the question of "how do you develop your inputs" - and it would lead you to portfolios that change in varying valuation environments, as a direct outcome of using MPT.

      Whether you use valuation as an influence in your investment decisions or not, you still need SOME process by which you decide how to compose a portfolio, once you have developed an outlook/forecast. The rationality of investors affects how you determine those inputs. I don't see why it invalidates MPT as a model to develop the portfolio, once you HAVE those irrationality-influenced inputs determined.

      Respectfully,
      - Michael

  • http://arichlife.passionsaving.com Rob Bennett

    Adjusting MPT inputs for valuation is certainly one very reasonable way to address the question of "how do you develop your inputs"

    Okay. I need to take back what I said. If you adjusted for valuations, I think it would all work.

    Probably what I should have said is that that is a big change, probably a bigger change that many realize when they first consider the idea.

    It's true, though, that your suggestion points to a wonderful reconciliation because it would lead to the development of a new model that would put many of the powerful insights of the MPT model to new uses. I certainly do not mean to suggest even a tiny bit that there is nothing valuable in that model. I see HUGE value in that model. We wouldn't be moving to the wonderful places which I believe we are in the process of moving to today were it not for all we have learned from the MPT model. That's the foundation for all that follows.

    I stated things poorly in that earlier post. I am grateful for your kind way of correcting me, Michael.

    Rob

  • http://www.kennethklabunde.com Kenneth Klabunde

    Great article, Michael. You and your readers may be interested in an article that appeared in the August 2010 edition of "Financial Planning" (financial-planning.com), page 41. Donna Mitchell interviewed Markowitz and reveals that Markowitz himself is a tactical investor.

    Quote: "He (Markowitz) also suggests that advisors consider shifting clients' portfolios occasionally, either because of concerns about inflation, market volatility or changes in the clients' personal circumstances. The notion that there is one optimal portfolio for every investor comes from the industry, not Markowitz..."

    If you need a copy of the article, just shoot me an email.

  • VG

    Interesting experiment for anyone to try: run a portfolio model through Morningstar, Zephyr, and any other software that has "their" institutional inputs already loaded, and notice how your projected risk/return output will are vary for each program.

    GI/GO? Maybe not, but it surely does beg the question, as you point out, of who's assumptions are correct - is it Ibbottson, Zephyr, Schiller, Siegel, Gross, Bogle, Grantham, or perhaps even Jim Cramer (ok, maybe not Cramer)??? Who's right?

    And, if we knew that, we wouldn't need this job, would we?

    Thanks for sharing your insightful thinking, Michael. You state well what so many of us fumble around with looking for the right words to express.

  • http://www.porticowealth.com Jonathan Leidy

    In other words, Michael, MPT is a construct whereby, given a particular set of assumptions, any portfolio can be "optimal." This notion is very intimidating for many professionals... Not unlike the idea that you proposed earlier this week regarding the true value of precision in financial planning cash flows. What you are asserting, and I think rightfully so, is that there is no one right answer to these questions. There is no way to truly know correlation in advance, just as there is no way to know (with 100% accuracy) a client's total future income. Which gives rise to the paradox alluded to by VG: if we knew these things, our ability to be right (and hence add the ultimate amount of value for our clients) would be certain. However, so would the extinction of our craft, as no one would need us to tell them what was already known. That is why focusing on client goals is the way we chose to approach the "unsolvable" challenge of portfolio optimization. Doing so allows you to jointly paint, with your client, a dynamic picture of your client's future. This is just another way of saying that the bad news is all of the inputs into our models are subjective. The good news is that so is each of our client's definition of success. And if we can help guide them to their own perception of financial fulfillment, recognizing that we may have started by painting a picture of a butterfly and it might turn out looking more like a horse, then we are doing our clients a great service. Very meta, I know. But so too is our undying desire as a profession to possess omnipotence.

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