“Life has afforded me many pleasurable activities, such as enjoying a fine meal, walking with Mrs. Markowitz on new fallen snow on the path through the woods near our home, flying kites with one or more grandchildren, listening to music, especially J.S. Bach, and the like. But no activity sustains my interest as long as does struggling with some technical or philosophical problem, sometimes alone, sometimes with colleagues.” – Harry Markowitz, Nobel Laureate 

This is Markowitz, someone that enjoys those little pleasures that make life worthy, but that needs intricate theoretical and practical issues to feed his outstanding intellect.

The goal of this blog is to help the process of levelling the playing field between investment professionals and the average citizen. We believe that financial literacy should go beyond the basics of personal finance and reach areas such as Portfolio management. In our quest to satisfy our mission, we believe that Harry Markowitz can help us, a lot!

Why Markowitz? 

As I already mentioned in past posts The Eternal Rivalry in Portfolio Management, or Yes We Can… Diversify!, Harry Markowitz is the father of Modern Portfolio Theory (MPT).

Before Markowitz, institutional investors didn’t have a quantitative method to allocate their funds. Portfolio Manager’s would meet and talk about their personal views on the markets and come to an agreement on how should they deploy their funds.

Markowitz changed the game, with his paper “Portfolio Selection,” started a movement that Peter L. Bernstein coined as “Capital Ideas,” in his book “Capital Ideas: The Improbable Origins Of Modern Wall Street.” This movement begun with Harry Markowitz and his modern Portfolio Theory, and continued with corporate finance and market’s behavior’s views of Franco Modigliani and Merton Miller, capital asset pricing model (CAPM) developed by William Sharpe and Jack Treynor, Efficient Market hypothesis by Eugene Fama and Kenneth French, and the option pricing model of Fischer Black, Myron Scholes and Robert C. Merton. (Don’t worry we will learn about all of them in this series ;)!)

Before these researchers started focusing on the financial markets, the scholar community completely disregarded the stock-market, and deemed it as unworthy of their time. Milton Friedman , who sat on Markowitz’s dissertation committee, clearly expressed the bigotries of the current economic thought towards the financial markets when he told Markowitz the following: “ Harry I don’t see anything wrong with the math here, but you have a problem. This isn’t a dissertation about economics. It’s not math, it’s not even business administration.” Friedman was right, it was something completely new (excuse me Louis Bachelier), proven by the fact that the paper “Portfolio Selection,” published in the Journal of Finance in March 1952, had a bibliography of three works.

This is why we say that Markowitz is the father of Portfolio Theory and the initiator of a movement that changed the course of financial theory history.

What is Modern Portfolio Theory?

Let me explain one more time what Modern Portfolio Theory is:

Markowitz illustrates how the process of selecting a portfolio may be divided in two stages. The first stage is the forecasting step. It starts with the observation of all the available securities and ends with a set of beliefs about the future performance of these securities. Well, this first part of the portfolio selection process is not the one that Modern Portfolio Theory tackles. MPT takes on the second stage in the portfolio selection process, the one that starts with the relevant beliefs about future performances and ends with an optimized efficient portfolio.

This means that MPT doesn’t try to forecast the future values of any security, but given some expected values, it provides the proper portfolio allocation.

How does it do it? By maximizing the expected return for a particular amount of Risk, or minimizing the risk for a given expected return. MPT relies in the following two “facts”

• We are all profit maximizers – Given the possibility, we will always try to make the highest amount of profit available.

• We are all risk averse – We always try to minimize risk

How does diversification play any role in this theory? Markowitz believes that assets should be evaluated not only for their individual characteristics, but for the effect on the portfolio as a whole. Why would an asset that has a high expected return be worse for a portfolio than one that has a lower expected return? The answer is correlation. The following is a portion of the Yes We Can… Diversify! post:

“…And then in 1952 Harry Markowitz shook the world of finance. Markowitz demonstrated, in an elegant mathematical way, how diversification really works. Imagine that in the universe of available companies you have one that produces ice creams and another one that produces winter clothing. Each of these companies represents a risky investment because depending on the weather, a stimulus that cannot be predicted, the companies will perform better or worse. However, as Markowitz explain, if the investor holds the two companies at the same time the portfolio created will have less risk than any of the two assets by themselves. Why? Due to correlation. If we are graced with good weather the ice-cream company will have a solid performance while the winter clothing will under perform (the inverse will happen in the opposite situation).

Markowitz took this idea further; he thought that if this worked for two assets it should be scalable to the whole universe of available securities. If we apply the above mentioned idea to the whole universe of assets and represent it on a graph in which the X-axis = Risk (measured as volatility) and Y-axis = Return of the security, we get a curve that represents the portfolios that can be created, in which the level of return is the maximum possible for a specific level of risk. All the portfolios that lay below this curve are not efficient, this is because another combination of the existing assets would maximize the level of return for a particular level of risk. All the portfolios that lay above the curve are unattainable, because there is not a possible combination that would offer a better return for the given level of risk. The following graph illustrates the concept (known as the efficient frontier):

An important point that Markowitz likes to make is that due to the market (also known as systematic) risk, which is the risk of experiencing a loss due to factors that affect the financial market as a whole, diversification cannot reduce risk to 0. The variance of the portfolio will go to the average covariance between the assets that form the portfolio. He calls this phenomenon the law of the average covariance.

We can explain it with an example that he gives. Imagine that all securities in the S&P500 have the same standard deviation, and that they all have correlations between themselves of 0.25, just for the sake of simplicity. Due to the calculations that give us the variance of a portfolio we know that the variance would approach (0.25 * the value of the variance of each individual stock). So the volatility of the portfolio would approach (0.5 * the value of the standard deviation of each individual stock). What does this mean? It means that a infinitely diversified portfolio would have a risk that is only 50% lower than the one of a single individual stock in the S&P500. How can we further decrease the risk? By adding other asset classes to the mix!

How did Markowitz do it?

Harry Markowitz is the paradigm of a Renaissance man. Not only his interests span from music, mathematics, programming, literature, economics, he is also an expert in a few of them.

• He created and commercialized a general-purpose programming language designed for large discrete event simulations.

• Sparse matrix Methods (Sparse Matrix are used to solve large systems of simultaneous equations in which most coefficients are zero).

• Creator of Modern Portfolio Theory

He actually received the John von Neumann Theory Prize (from the former Operations Research Society of America, now known as the Institute for Operations Research and the Management Sciences, INFORMS) for these very same contributions mentioned.

Markowitz developed an interest for the known and the unknown at quite an early stage of his life. He writes the following in his “Trains of thought” published in the American Economist in 1993

Until I was thirteen or fourteen I read comic books and “The Shadow” mystery magazines then, I read (I cannot remember why) Darwin’s Origin of Species. I was especially fascinated with how Darwin marshalled his facts, argued his case and considered possible objections. Subsequently I read popular accounts of physics and astronomy, from the high school library, and original accounts by philosophers, purchased from wonderful big, old, musty used book stores then in downtown Chicago.

The philosopher who impressed me most, who became “my” philosopher, was David Hume. He argued that even though we release a ball a thousand times and each time it falls to the floor, we are not thereby provided proof with certainty that the ball will drop when released a thousand-and-first time.

When he graduated from high school he went to University of Chicago for both undergraduate and graduate school. There, Markowitz took the two years Bachelor’s program in which he especially enjoyed the discussions about philosophers in a course named OII: Observation, Interpretation and Integration. When he finished the Bachelor’s degree and had to choose an upper division he decided to study economics, in particular Markowitz had his eye in “Economics of Uncertainty.” Becoming an economist was not a childhood dream for Markowitz, as he explains in his small Biography for NobelPrize.org. However, when you mix an individual so interested in knowledge with an undeveloped body of thought such as economics, and especially finance, magic is ought to happen!

Markowitz tells the story of how he decided the topic of his dissertation due to chance. When the moment came to decide in which area of economics will he perform his dissertation on, he went to his tutor’s, Professor Marschak, office. However, professor Marschak was busy at that particular moment so Markowitz sat in front of his office and started to talk with a stockbroker that was also waiting to meet the professor. When Markowitz told the stockbroker that he didn’t have a clue in what he should do his research, the stockbroker suggested that he should do it in the possibility of applying mathematical methods to the stock market. This made sense to Markowitz who, fixated with knowledge and uncertainty, saw a vast ocean to explore under his nose!

Since Marschak supported the idea but wasn’t familiarized with the appropriate literature, he sent young Markowitz to talk to Professor Marshall Ketchum who provided him with a reading list with the most important thoughts on financial theory and practice of that time.

MPT was born

Markowitz its quite the story teller, so, I will let him explain all of you how the basic ideas of portfolio theory came to his brilliant head (extract from Nobelprize.org):

The basic concepts of portfolio theory came to me one afternoon in the library while reading John Burr Williams’s Theory of Investment Value. Williams proposed that the value of a stock should equal the present value of its future dividends. Since future dividends are uncertain, I interpreted Williams’s proposal to be to value a stock by its expected future dividends. But if the investor were only interested in expected values of securities, he or she would only be interested in the expected value of the portfolio; and to maximize the expected value of a portfolio one need invest only in a single security. This, I knew, was not the way investors did or should act. Investors diversify because they are concerned with risk as well as return. Variance came to mind as a measure of risk. The fact that portfolio variance depended on security covariances added to the plausibility of the approach. Since there were two criteria, risk and return, it was natural to assume that investors selected from the set of Pareto optimal risk-return combinations.

 And the rest, as they usually say, is history!

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