Portfolio Theory and Practice

The holy grail of professional investment management is the construction of efficient portfolios. Professor Harry Markowitz won the 1990 Nobel Prize in Economic Sciences for groundbreaking work on the theory of portfolio allocation under uncertainty. Markowitz’s 1952 seminal paper entitled “Portfolio Selection” and later 1959 book Portfolio Selection: Efficient Diversification of Investments laid the foundation for modern portfolio investment. His main contribution was that diversification can reduce the risk of a portfolio of different assets without decreasing its return. This innovation enables a manager to increase the return per unit risk of a portfolio. What investor does not want lower risk, all else the same? In this respect, diversification provides (in his words) a “free lunch” for investors. In this chapter, we review how diversification can decrease investment risk. Using diversification, Markowitz developed the mean-variance investment parabola. The parabola is mathematically derived using the returns on assets, their total risks, and the correlations of returns between assets. Importantly, the upper boundary of this parabola is the efficient frontier with portfolios that earn the highest rate of return for each level of total risk. Investors should seek portfolios on the efficient frontier based on their risk preference. No portfolios exist above the efficient frontier. Portfolios below the efficient frontier are inefficient in that they have lower return per unit risk and therefore are not desired (except by short sellers seeking to profit on their falling prices and returns). Professional investment managers seek efficient portfolios to earn alpha. Alpha is a measure of manager skill that says that an investment portfolio outperformed a chosen benchmark portfolio, the average performance of some group of managers, or specific competitor investment firms. Clearly, if a manager can construct efficient portfolios, they can earn positive alpha, benefit their clients, and outperform other investment managers. The big question is: How can an investment manager build efficient portfolios? One answer is to use the mathematical and statistical methods developed by Markowitz. Unfortunately, after many years since his publications, researchers and practitioners have been unable to successfully choose stocks (for example) to build efficient portfolios. One problem ironically lies in the math of efficient portfolios. It is necessary to use sophisticated statistical techniques that cause difficulties in the estimation of efficient portfolios. A second and even larger problem is that efficient portfolios constructed using historical data do not stay efficient in the next period. That is, ex post efficient portfolios from past data are not ex ante efficient in the future. The reason is that risk is not controlled. In this book, unlike so many before who keep trying to make the mathematics of efficient portfolios work, we take a different approach. We employ asset pricing methods to control risk and thereby ensure better ex ante performance for efficient portfolios in the future. To do this, our focus will be on the ZCAPM, a new asset pricing model published in a recent book by Kolari et al. (A new capital asset pricing model: Theory and evidence. Palgrave Macmillan, New York, 2021). The ZCAPM is derived from the mean-variance investment parabola of Markowitz. It turns out that the investment parabola has an architecture that is determined by risks measured in the ZCAPM. Using these risks, a manager can choose assets to construct relatively efficient portfolios; alternatively, any portfolio within the parabola can be constructed if desired. We demonstrate these new portfolio methods in this book. We next review the pioneering work of Markowitz. Key concepts and notations important to later chapters are introduced. Subsequently, we discuss potential statistical problems in building efficient portfolios. Given these problems, we review new insights about the mean-variance investment parabola—importantly, these insights motivate our new approach for finding efficient portfolios. We overview intuitive concepts about controlling risk in portfolios using an asset pricing model. The forthcoming chapters provide the stepping stones for building efficient portfolios. To demonstrate our investment approach, we document U.S. stock market evidence spanning over 50 years. Our results convincingly show that efficient portfolios can be constructed by controlling risk. Hence, we advocate that investment managers utilize our risk control methods to boost portfolio performance.