## Executive Summary

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. My feeling is that the statistical computations should be used to arrive at a tentative set of means and standard deviations.and the judgment of practical menon 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.Judgment should then be used in increasing or decreasing some of these means and standard deviationsOne 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].

.” – Harry Markwotz, “Portfolio Selection”, Journal of Finance, Vol 7, No 1, Mar 1952. (Emphases mine)I believe that better methods, which take into account more information, can be found

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?