How to Build a Portfolio

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This article is intended for the educated layman. It was written as part of a continuing series of articles on a variety of investment topics.  To view all the articles in this series, click on “More by the same author” in the left margin.


Homo sum, humani nihil a me alienum puto.1
Terence


Why Think Like an Economist?

Robert Benchley observed that “There may be said to be two classes of people in the world; those who constantly divide the people of the world into two classes, andthose who do not.” Accordingly, C. P. Snow, the English novelist and physicist, stirred up a cloud of dark sentiment back in 1959 with his thesis that there was a cleavage in Anglo-American intellectual society into two cultures, the literary and the scientific. The dust has since largely settled, and if the sciences now face hostility (as I think they do), that comes from elsewhere than the literary elite.2 All the same, I sense a corresponding cultural division and incomprehension between, on the one hand, those at ease with economic theorizing and, on the other, those inclined toward the hard sciences and, even more, the humanities.

Having been formally educated in both of the latter, when I first came to economics I saw a system of gross simplifications with pretentious scientistic claims to explanatory power over the variegation of human experience. Economists’ reduction of human behavior to a few variables, ignoring all the complexity of what has happened and does happen in the real world of human experience and action, seemed just wrong, almost as perverse as a belief in the effectiveness of occult forces. Ludicrous and sometimes terrible historical conclusions have followed from treating humanity as the object of a simple engineering project.

But as time passed, I began to appreciate the practicality and even the occasional elegance of economic generalizations. How different are their simplifications, after all, from a broad historical narrative of causes and effects, like the story of Britain’s many provocations leading to the American Revolution? Or from the idealizations of classical physics, in which bodies continue in motion until a force is applied? Once the sketch, the outline, the model exists, complications and refinements can then be added, to bring it closer to the reality that we observe. Without their abstractions and sweeping generalizations, economics would be just accounting, history would be one damn thing after another, and physics would be random startling impacts. That’s not to say that economic theories and models are necessarily valid or useful or that any of their predictions can ever approach the accuracy and precision of those created by the physical sciences, but we can debate their premises and judge them by their fruitfulness and by their proximity to reality once the complexities are layered on.

Perhaps you are more comfortable with economic reasoning than I was at first. Even Snow conceded that some of his readers were justifiably offended at his suggestion they were necessarily in one camp or the other. But I suspect that some of my readers find economics to be inhumane (and some schools of economic ideology do their best to sustain and justify that perception).

Still, even if you have been comfortable with my account of the economics of investing up until now, this particular essay may try your tolerance of economic reasoning, because it bolts together investing concepts in a way that does resemble an engineering project.

Bringing it all together

This is the first of a culminating set of three essays, in which I will combine the core ideas presented in my preceding essays into a comprehensive description of how to put together a portfolio. In this one, I’ll explain what is often called Modern Portfolio Theory. Those earlier essays may have seemed to meander, but their course was deliberately plotted to get us here. They developed and linked the four key concepts for constructing the theory:

Return
Risk
Diversification or, as a mathematician would say, “Correlation” (of returns)
Risk Tolerance

Everything else, like my discussion of market efficiency, was commentary and qualification.

Many, perhaps most investment managers do not, as they go about their work, think much about Modern Portfolio Theory. It’s no longer modern, having been set forth by Harry Markowitz (1927- ) in his 1955 doctoral dissertation at the University of Chicago. In some quarters of the investing community, it has been so deeply absorbed into the culture that practitioners follow its precepts without invoking its name. (I don’t believe I once heard the expression “Modern Portfolio Theory” when I was a business school student in the mid-1980s at the University of Chicago, its fons et origo.) Yet at the same time, it’s been knocked about for decades by investment practitioners who think that it is a useless guide to action and an inadequate explanation of how investing works. Yes, there are professional investment advisors who are as ill at ease with economic reasoning as are some laymen.

I hope to convince you, however, both that it is true, and that it is the only way to think about constructing a portfolio. Of course, you don’t have to think to construct a portfolio: You can create one without thinking about it. That is, you just buy and sell individual investments without regard to how the pieces fit together. There’s very little more I can say to illuminate that mode of operation, at least as it pertains to portfolios.

The gist of modern portfolio theory

If I express the gist of Modern Portfolio Theory in words rather than equations, as the textbooks do, its truth should be, if not obvious, at least immediately comprehensible:

  1. For any given level of investment risk, a portfolio can have multiple possible returns, resulting from combining its constituent investments in differing proportions (if there are more than two investments).
  2. At any given level of investment risk, a rational investor would like to get the greatest possible return from his portfolio.
  3. There are infinitely many levels of investment risk. (This is true in theory, though as a practical matter, no one cares about, let alone can measure, infinitesimal distinctions between levels of risk.)
  4. Out of those infinitely many, the investor should choose the particular pairing of risk and greatest possible return that accords with her degree of risk tolerance.

That’s all there is. I could reword this in terms of lowest possible risk for a given level of return, and it would amount to the same thing. Frankly, I don’t see how anyone could quarrel with these four propositions; they seem to me to be nearly inarguable. If you’re prepared to argue, I hope to convince you shortly that you’re likely laboring under a misconception. Note that the theory does not invoke the concept of market efficiency. There is no logical or historical dependency of Modern Portfolio Theory on the Efficient Markets Hypothesis. (On the contrary: both dependencies run the other way. 3) But in the public mind, the two are jumbled together, because they’re usually introduced in the same books and magazine articles.

How could a theory that combines a set of propositions so close to obvious win its creator a Nobel Prize? That’s because the definition of investment risk on which it depends was far from obvious, its definition of risk tolerance was little known, and by making a number of critical assumptions, Markowitz was able to elaborate the theory into mathematical models of investments that are usable and testable. These models, in turn, have deepened our understanding of observable investment behavior and thereby become fundamental to modern financial economics. Most important, they have insinuated themselves inextricably yet often unobtrusively into financial practice (and not just in the sphere of investment advice).

The theory, or rather, the models that embody it, runs into difficulty in practice, in large part because the values of all four of its constituent variables are unknown. We can observe historic investment returns and apply the theory to them, but that’s not useful, and it’s comparatively uninteresting. When we invest, we invest for the future.  Investing is an active, not a contemplative pursuit. For the purpose of portfolio construction, we therefore want to know future returns, future risks, and the future interaction of investments (for diversification). Risk tolerance is a little different, in that we want to know the investor’s risk tolerance in the present, but as I showed in my previous essay, we can’t measure that at all well, either. There is the further difficulty that the theory’s identification of risk with the volatility of returns, while in some ways an advance on earlier definitions of investment risk—unlike the earlier definitions, volatility is a consistent measure across all investments and can characterize both individual investments and groups of investments—is not up to the task of defining the risk of true disaster in the investment markets, as we have lately experienced it.

Modeling portfolios

To explore modern portfolio theory further, I’m going to present in outline the original simple mathematical model that Markowitz created as a precise realization of the theory. It requires three assumptions: First, that investment risk is completely defined by the volatility of returns; second, that we do know future returns, risks, and diversification behavior, as well as the investor’s current risk tolerance; and third, that the investor can’t buy investments with borrowed money (as when someone buys a stock on margin). The first assumption makes the mathematics tractable. No, I’m not going to write equations—you can engross yourself in a finance textbook if you want to learn those—but from the mathematics follow the simple drawings that I’ll present. Keep in mind that the simplified—not to say simplistic—definition of risk as volatility (and only volatility) ramifies through both the description of diversification and the definition of risk tolerance. The third assumption isn’t important; it merely keeps things simple for the purpose of this introduction. The model can easily be enhanced to take into account borrowing.

As I did in my previous essay, I’m going to state values for the volatility of returns without explaining what it means to talk of the value of volatility. Take it from me that I’m using the universal definition of statisticians.4

1. “I am a human being, and I consider nothing that is human to be foreign to me.” This is, or at least in earlier centuries was, one of the most popular quotations from Roman antiquity.

2. Especially as l’Affaire Sokal recedes into history.

3. If you’re wondering what the logical dependency is, recall from an earlier essay that market efficiency implies that risk is appropriately reflected in an investment’s price. And efficiency is a statistical phenomenon, since for any single investment viewed in isolation, it’s quite possible that the price does not reflect true value, including risk. But to evaluate investment risk in a statistical way, we have to consider the risk of a collection of investments, that is, a portfolio. Granted, there were intimations of the Efficient Market Hypothesis long before Modern Portfolio Theory existed, most notably in the work of Louis Bachelier (1900).

4. When I write “volatility,” I mean specifically standard deviation or, what is nearly the same, variance of returns; I’m disregarding statistical measures of the ways that the patterns of returns can deviate from the bell curve, like skewness and kurtosis. The implicit point is that, without knowledge of what statisticians call the higher moments or, even better, the actual shape of the distribution, we misestimate risk. It’s a mistake to attribute to Markowitz a naïve belief that volatility alone summarized investment risk. As I note below, in his book based on the thesis, Markowitz began exploring the use of downside semivariance of returns in place of variance to try to get at the drawback of unrealistically assuming a bell-shaped distribution of returns.