Remembering Harry Markowitz

Thomas Idzorek: Hi, I'm Tom Idzorek. I'm the Chief Investment Officer for the retirement area of Morningstar Investment Management. I'm joined by my colleague, Paul Kaplan, today. Unfortunately, last week, the father of the modern portfolio theory, Harry Markowitz, passed away. My belief is that there are a few people on earth that have the deep knowledge that Paul has around what is modern portfolio theory. And I'm going to be able to interview Paul around Harry Markowitz and his contributions to investing. Paul, I know that you've written a book, the Frontiers of Modern Asset Allocation. In your book, it contains an interview with Sam Savage and Harry Markowitz. And I thought for the people that might not quite remember what is modern portfolio theory, that might be a good place for us to start off with Harry's contribution.

What is Modern Portfolio Theory?  

Paul Kaplan: Yes, Tom. So, this is the book, Frontiers of Modern Asset Allocation, published in 2012. And I'm going to start really at the beginning of the interview where Harry Markowitz talks about how he figured out modern portfolio theory.

He says this – the magic moment, the moment of epiphany happened while I was reading John Burr Williams' theory of investment value. I was looking into the possibility of doing a PhD dissertation at the University of Chicago, applying mathematical, statistical, or econometric techniques to stock market investment problems. I was working off a reading list a professor of finance had supplied. I'd already read Graham and Dodd's Security Analysis. I read Wiesenberger's Investment Companies. And I was reading Theory of Investment Value. Williams asserted that the value of a stock should be the present value, the discounted value of future dividends. Because future dividends are not certain, he said that you should use the expected value of future dividends. Now, I knew that if you were maximizing an expected value, the way you would do that would be to put all your money into just one stock. That didn't make sense. People do diversify. You can see it in Wiesenberger's Investment Companies and Their Portfolios. They diversify because they are worried about risk, as well as seeking return. So, I postulated that investors were interested in expected return and standard deviation. I drew a trade-off curve like economists always do. And so, that afternoon in the Business School Library at the University of Chicago, I came up with the first efficient frontier. Williams asserted that with sufficient diversification, risk would disappear. You would receive expected value. But risk only disappears with diversification if you have uncorrelated risk. And of course, markets are not uncorrelated. So, that was when and how the moment of epiphany happened.

Markowitz on Finetti's Work

Idzorek: All right. The efficient frontier, pretty magical stuff changing investing as we know it. In the early 2000s, in a journal article, it was revealed that a different researcher, an Italian researcher, Bruno de Finetti, had actually invented or had written an article that, I guess, previewed a number of elements that are part of mean variance optimization. I guess, what was Markowitz's reaction to that and what did he think about that?

Kaplan: Yeah. So, in this interview, the next question I asked was about that, about the contribution of de Finetti and how he thought about that. So, here's what he said.

The historical significance was nil because the importance of de Finetti's work was not understood. If it had any impact at all, it was among Italian actuaries. It was a response to the problem of optimum reinsurance, so it was an actuary thing. I do not believe that it ever got into the American actuary literature, and it certainly didn't get into the financial literature. So, it was a dead end, not because it deserved to be a dead end, but that was, in fact, its historical destiny. In terms of the merits of de Finetti's contributions, it turns out that he correctly posed the problem of mean variance. He understood that you had to take into account the correlations. Williams didn't understand that something happened differently when you diversify among correlated risk. De Finetti did. He was able to solve the problem of tracing out mean variance efficient frontiers assuming uncorrelated risk. He would have liked to solve it using correlated risk, but he couldn't solve that one. As I explain in my paper, de Finetti had some conjectures about what the solution must be, and at least one of the conjectures was wrong. So, he gets a gold star for posing the problem, and I get a gold star for solving it.

Idzorek: Again, I think, it's hard to imagine the giant change in investing that Markowitz and mean variance optimization brought to us. Often, maybe when we're talking about regulations or misguided ways of thinking about investments, I hear you use the phrase, they're thinking in a pre-Markowitz world. Can you maybe elaborate on what are the shortcomings of the pre-Markowitz world that moved us, let's say, out of the prudent man or perhaps the prudent person thinking into this enlightened world?

Kaplan: Yes. Before the modern portfolio theory, the fiduciary was expected to select securities from a list of securities that have basically been approved in some way and each security was held up on its own to either be appropriate or not appropriate. What Markowitz said was it's the whole portfolio that matters. Just as in the passage I just read where he was talking about the correlations, the correlated risks, the fact that each security is risk but that you can reduce risk through correlation, and you can trace out an efficient frontier and pick out what the right portfolio is for a given investor.

That Time Milton Friedman Gave Markowitz a Hard Time 

Idzorek: Now, as you would – I don't recall the exact date. I think it was in 2019, both you and I and another one of our colleagues, Ryan Murphy, we traveled down to San Diego or more specifically, La Jolla and we were able to meet with Harry Markowitz and he tells a number of wonderful stories and again, I think some of the stories related to what he was at the University of Chicago receiving or on the cusp of receiving his PhD and Milton Friedman was on his dissertation committee and he tells kind of an entertaining story. I was thinking the audience might like to hear that.

Kaplan: Yeah. It's a classic Markowitz story. I cannot give the whole story justice. I'll just say a few things about it. So, Milton Friedman was on Markowitz's PhD dissertation committee. Markowitz went in there and he was feeling pretty confident. I heard in another interview he said that he felt that not even Milton Friedman would be able to find a problem in his dissertation. So, he goes in there and of course, Milton Friedman starts saying things like, Harry, this is not economics. We cannot give you a PhD in economics. This is not mathematics. We cannot give you a PhD in mathematics. and it kind of goes on and on like that for a while until eventually someone says, Harry, this is not literature. We cannot give you a PhD in literature. So, then they ask him to leave the room. And he goes and he waits, and Milton Friedman kind of pops his head out and says, congratulations, Dr. Markowitz.

Now, an interesting thing to note that pretty much what Milton Friedman and I guess the other ones were saying, they were kind of just giving him a hard time. The fact is, when you get to the point of defending your dissertation and as I went through that process many years ago at Northwestern University, it's more of a celebration than a defense. It's like everything you've written, your dissertation committee has read it. They're familiar with everything in it. They've approved everything in it. So, your defense is just really kind of a ritual where you go through, and you explain it and you answer questions and things like that. But rarely would anything ever show up at that stage where they'd say, oh no, we can't give you a PhD.

Idzorek: Well, again, I want to pick up on this idea that Milton Friedman is giving Markowitz a hard time around, this isn't really economics or economics as they've known it. The Nobel Prize committee, they always talk about when they awarded Markowitz the prize, they tried to summarize what did he contribute. And they have a statement and it's always in what I kind of call Nobel speak for his work in financial economics. And I believe that's kind of a newer term, financial economics is different than economics, I was curious as to what is the difference between economics and financial economics? And should we think of Harry Markowitz also as, say, the father of financial economics?

Kaplan: Okay. Well, first of all, financial economics, as the name suggests, it's just a branch of economics. It's just as much economics as labor economics or monetary economics or any other specialty within economics. So, fundamentally, it's a specialty in economics. It deals with problems of uncertainty and time, and it applies them in a financial context or an investment context as Harry Markowitz did. Now, was he the first in financial economics? Strictly speaking, no. But he did launch the modern era of financial economics. Because I would say one of the greatest economists before Markowitz was Irving Fisher. And Irving Fisher, he did pathbreaking work in what we now call financial economics in the early 20th century.

The Difference Between Modern Portfolio Theory and the Capital Asset Pricing Model 

Idzorek: So, back in 1990, when Markowitz ended up getting the Nobel Prize, it also went to two others, one of which was Bill Sharpe, and Bill Sharpe was receiving the Nobel Prize for his work on the capital asset pricing model that was done with Jan Mossin, Lintner, Jack Treynor, et cetera. And so, my belief is that for a number of practitioners, they begin to infuse or fail to separate out modern portfolio theory, mean variance optimization of Markowitz and the capital asset pricing model. And my belief is that somewhat has irked Markowitz over the years. I guess, what is the distinction between modern portfolio theory and the capital asset pricing model?

Kaplan: Yeah. Well, the distinction between those two is, we have to go back to something – the history of economics in general, which is the notion of the difference between what's called normative economics and positive economics. Now, that terminology, I believe, was coined by, I guess, a latter 19th century economist, maybe early 20th, I'm not really sure, John Neville Keynes, who was the father of the famous John Maynard Keynes. And anyway, so I believe he came up with that terminology and Milton Friedman adopted it as well. In fact, Milton Friedman has a book called Essays in Positive Economics.

So, normative economics is basically – it's prescriptive. It's telling you how you ought to behave. Markowitz is telling you how you ought to behave as an investor. You ought to own a mean variance efficient portfolio on the efficient frontier, but you need to pick the one that's at the right level of risk with your level of risk aversion. And there again, we see risk aversion, a concept straight out of economics, the concept of risk aversion, and the concept of the trade-off, as Markowitz himself talked about, straight from economics.

Now, the capital asset pricing model, or the CAPM, is what we call, is an example of positive economics. It's a model that's meant to describe how the world works. It uses a technique in economics – we use this technique called equilibrium model, where we basically say supply equals demand across everything. And so, in this case, supply equals demand across securities. And that's what the CAPM is about. So, again, the modern portfolio theory of Markowitz is a normative theory. It is meant to be proscriptive, whereas the CAPM is positive economics. It's meant to be descriptive.

Some Criticisms of Capital Asset Pricing Models are Misunderstood 

Idzorek: Now, there's a number of criticisms, I think, that are, let's say, appropriate criticisms of the capital asset pricing model that people sometimes inadvertently – or they're misunderstood, and they end up attacking modern portfolio theory. I guess, a criticism of modern portfolio theory and mean variance optimization in general is the notion that returns are not necessarily normally distributed. Does that, in some way, make mean variance optimization inadequate? And I believe this is something that really – this kind of criticism really irked Markowitz, and I think he addressed it, but I guess I would hope that you could elaborate on that.

Kaplan: Yeah. Actually, I'm going to go back to the interview. I'm going to read exactly what he said. But he refers to this as the great confusion. And actually, some years ago, I wrote an article in the Morningstar magazine called The Great Confusion, where I kind of lay out what Markowitz was saying. So, let's turn to that. First of all, he's going to refer to a very critical paper he published in 1979 with Haim Levy, and this was a continuation of work that he did back in 1959. So, that's kind of how far back these ideas go.

He says, the work that I did with Levy that was published in 1979 in The American Economic Review, called "Approximating Expected Utility by a Function of Mean and Variance," is an amplification of ideas that I already published in my 1959 book. I never ever assumed that probability distributions were normal. I never justified mean- variance analysis in terms of probability distributions being normal. 

So, he is very adamant there that he never assumed normality.

He says, my basic assumption is that you act under uncertainty to maximize expected utility. In fact, I was a student of Sam's father – that was Leonard Savage – and he convinced me, as well as half the rest of the world, that the way to act under uncertainty is to maximize expected utility using probability beliefs where there weren't any objective probabilities. So, how do I get off peddling mean-variance analysis when I believe in expected utility? An illustration of what I believe is given in chapter six of my 1959 book, where I recommend maximizing expected logarithm of one-plus-return if you're in for the long run. I have a table showing various levels of return, the log utility of that return, and the value of a simple quadratic approximation.

Between a 30% or 40% loss and a 40% or 50% gain on the portfolio as a whole, the quadratic approximation is very close to the log utility. So, the expected value of the one has to be close to the expected value of the other, as long as we're talking about portfolios that rarely lose much more than 30% or 40% or gain much more than 40% or 50%. Of course, the expected value of the quadratic is a function of mean and variance. So, for the 9 or 10 securities that I had available for my illustrative mean-variance analysis, I show that not only does the approximation look good in the table, but, in fact, if you knew the mean and variance, you could guess the expected utility quite well. What Levy and I did was to do that same experiment using historical returns on investment companies and a variety of utility functions. We confirmed that if your probability distribution is not too spread out, and the annual returns on investment companies turn out to be not too spread out, then if you know mean and variance, you can guess expected utility quite well.

About 'The Utility of Wealth' 

Idzorek: Excellent. Back in 1952, Markowitz, I think he thought of that as one of his banner years. That was the year that portfolio selection came out, which is, of course, what he's most well known for. One of his other papers that I think had a big influence on the behavioral side was The Utility of Wealth. I think Markowitz was extremely proud of this paper. My understanding is that Danny Kahneman, Amos Tversky, the creators of prospect theory, actually sometimes think of Harry Markowitz as being the grandfather of behavioral finance. Again, I know when I think about Harry Markowitz, I'm typically thinking classical finance and modern classical finance, but not behavioral finance. I guess I'm wondering if you could talk a little bit about that paper, The Utility of Wealth, and also thinking about how that may could be merged, if you will, with modern portfolio theory.

Kaplan: Well, it is interesting that Harry Markowitz is, simultaneously, the father of modern portfolio theory and the grandfather of behavioral finance. Behavioral finance is not an area I've done a whole lot of work in myself. But my understanding of prospect theory from Kahneman and Tversky is that, first of all, as classical utility theory, as Markowitz was referring to in what I just read, the assumption is that the investor cares about the total level of wealth as a whole. But in prospect theory, they said, no, that's not the way people behave. People have some kind of reference amount. And that basically, if you have more than the reference amount of wealth, you're risk averse, but if you have less, you're actually risk seeking. So, this provides an explanation about why the same person would both buy a lottery ticket and insurance at the same time. So, this is contrary to, let's say, the neoclassical economics, of which, of course, modern portfolio theory is part of.

So, this leads to, like just a very different way of modeling investor behavior. I think it's just more of an attempt to model how people actually behave versus how they should behave. But now this brings us to an interesting point back to normative economics versus positive economics. I think behavioral economics may be a great positive theory. So, why should we study the theory of rational behavior? Well, one reason is because, let's say, you're a financial planner, you have clients who, of course, they tend to behave in this kind of irrational way, then it seems that as a financial planner, things that you would want to do is to try to nudge them towards being more rational. So, we still need a model of rational behavior, even if people left to their own devices are irrational, because it should seem that a goal of financial planning should be to help people, move people towards rationality. 

Idzorek: Excellent. Going back to our trip to San Diego and to meet with Markowitz, one of the things that came through there was he was extremely proud of his new four-volume series he was producing. I guess, if he were here, I think he would want us to be able to plug that to the audience. I guess, can you tell us a little bit about his four-volume book?

Kaplan: Well, first of all, I have volumes one and two inscribed by Markowitz himself. He wrote me a personal inscription on those two books. I definitely would highly recommend them. They really, really do get – I mean, the names of the books are – Risk-Return Analysis: The Theory and Practice of Rational Investing. That's what, like I was just talking about, it's so important to understand rational, what is rational investing. And the first volume is the single period model. It basically expands on the work that he did with Haim Levy back in 1979 about what is the justification for mean-variance analysis in terms of expected utility theory. The second volume, which is a much more difficult read, is about investing over time. So, there, he is getting into things which now fall into more of the area of financial planning, which is not just how I should hold my portfolio today, but how I should behave rationally across time as you go through your life cycle.

Idzorek: Yeah. And my understanding is, volume four, I don't know that it's ever been printed. I guess, we'll have to hope that maybe that will be something that comes forth.

Kaplan: Yeah. But volumes one and two, certainly plenty to get into there.

There was More to Markowitz Than You Might Think

Idzorek: I guess, before we conclude, is there anything that I haven't asked about modern portfolio theory, the work of Harry Markowitz that you think is worth noting?

 Kaplan: Yeah. I think what's worth noting about Harry Markowitz is that he wasn't just a financial economist. There were two other areas at least that he made enormous contributions to. One was in a very special area of mathematics called sparse matrices. This is where you have a table of numbers and almost everything is zero except for a few. Well, he worked out the math about how to work with those. The other is actually in computer science. Harry Markowitz invented his own programming language. It's called SIMSCRIPT. It is still used to this day. It's gone through a number of different versions of it. But it just shows you what a broad range of interests and talents he had, everything from modern portfolio theory, to behavioral finance, to mathematics, to computer programming, he covered a pretty wide set of areas.

Idzorek: Well, great. Thank you so much for sharing your insights. We really appreciate it.

Kaplan: Thank you.

Idzorek: Thank you.