APPENDIX A

Modern Portfolio Theory

Ihe efhcient market hypothesis (EMH) leads naturally to modern portfolio theory (MPT), a supposedly scientific way of explaining market behavior, quantifying risk, and outperforming the averages. This work, or parts of it, is still widely used to make investment decisions by many professional investors.

The father of modern portfolio theory is Dr. Harry Markowitz, a Nobel laureate. Markowitz framed the outline of MPT in his Ph.D. thesis in 1952. According to Markowitz, rational investors should be risk-averse. This means they should not be willing to take higher risk without receiving larger returns. Risk was defined by Markowitz, as by all subsequent efficient market researchers, in terms of short-term market fluctuations. The greater the volatility of the security or portfolio, the greater the risk. Whether this truly, or even approximately, defines risk is examined in this book.

Starting from this premise, however, Markowitz pointed out that holding different types of securities, or securities of different companies, would not significandy reduce the price movement of a portfolio.* Effective diversificadon requires securities that do not fluctuate in the same direcdon at the same time.

For each security, says Markowitz, it is necessary to establish expected return, volatility, and a covariance of return against every other

* If the direction and magnitude of the securities fluctuations were similar, the statistical term is that the stocks have a high degree of covariance. If they are dissimilar, ihey have a low degree of covariance.

security.* Witii tiiis information, lie siiowed how quadratic programming could calculate a set of optimal portfohos, which he called "efficient portfolios." An efficient portfolio would produce the highest level of return for a given level of risic. Any portfolio that produced the same return, but at a higher level of risk, would be considered inefficient. Similarly, a portfolio that produced a lower return for the same level of risk would also be considered inefficient.

The Markowitz model relies on a good understanding of statistics and an enormous number of calculations. Markowitz himself pointed this out, stating, "an analysis of 100 securities requires 100 expected returns, 100 variances and almost 5,000 covariances." Remember, well over 5,000 companies trade on the major U.S. exchanges and Nasdaq alone. In short, if investors were willing to follow this method, they would be overwhelmed by its computation.

Markowitz was a pioneer, rather than the founder of a working theory. Other academic researchers looked for ways to simphfy his complex risk-reward equations.

The Capital Asset Pricing Model-CAPM

Three researchers, Wilham Sha e, John Lintner, and Jan Mossin, working independently, simplified Markowitzs calculations. They developed the standard form of the capital asset pricing model, often referred to as the Sha e-Lintner-Mossin form of CAPM. Their major contribution was to replace Markowitzs complex calculation of risk with beta. The researchers stated that each securitys movements could

* The riskiness of a portfolio depends upon its covariance, or the extent to which asset prices move together, and not upon the average of each investment held. Thus, several risky bets may prove to be low risk as an aggregate so long as prices do not move together in the same direction.

+ , Lintner and Mossin break risk down into two distinct elements. The first is the systematic risk, or market risk (beta) outlined previously. The second element of risk is that portion of risk or volatility unique to the specific stock or other investment. This is called nonsystematic or diversifiable risk. Alpha represents the amount of return produced by a stock on average independent of the return of the market. It measures the specific component of a stocks return. Suppose, for example, the alpha is 1 % and the beta is 1.5. If the markets retum in a month was 2%, the most likely retum on the stock would be 4%. The 4% is derived as foUows: a 2% market retum with a beta of 1.5 translates into a stock return of 3% (2% x 1.5). In addition, and independent of the market, the stock tends to produce a return of 1 %. Alphas can be positive, negative or zero. These correlations, the theorists tell us, are what occur on average. In any short period of time, they can diverge from this relationship.

* This is theoretically defined as the complete universe of risky investments available for purchase, with each weighted for its share of the total market value. Since it is impossible to calculate precisely the universe of risky investments at a given point of time, it is necessary to use a proxy for this universe. As noted, the S&P 500 is frequently used, although there are certainly other choices.

+ The risk-free asset in the sense of assured rate of return is usually the 91-day treasury bill. Other important risks, such as loss of purchasing power because of inflation, arc not considered.

* These assumptions and their shortfalls are also discussed in chapter 17.

be related by its beta to a broad-based stock index such as the S&P 500, thus estabUshing a practical way to use the Markowitz model, while eliminating the tortuous calculations that came with it.

Chart A-l demonstrates MPT risk and retum measurements. The vertical axis is expected retum, while the horizontal axis indicates the risk. A key tenet of capital asset pricing theory is represented by point E. This is the expected return and the risk of the market as a whole.*

The important concept is that the market or its surtogate stock price index is seen as the optimal risk portfolio. No other combination of securities can produce a better trade-off between risk and reward. The point R T on the capital market line is the expected rate of retum on Treasury-bills, the risk-free asset, during the period under consideration.

The segment of the line from R to E indicates the various retums available through the combination of Treasury-bills and risky assets, most often stocks. The range varies from investing your portfolio entirely in 91-day T-bills, or their equivalent, to increasing the equity risk by moving right along the line to E, which is the risk of owning the S&P 500 or its equity equivalent.

In order to receive an above market retum, according to the theorists, the investor is assumed to be able to borrow at the T-bill rate (the risk free rate), and then leverage the portfoho, reinvesting the borrowed funds into the market. He can thus move along the capital market line from point E to point A. The more one borrows, of course, the greater the risk, but if the market behaves itself, the larger the retum. The concept of the capital market line has played a cmcial role in the development of modem portfolio theory (MPT).

Assumptions Underlying the Capital Asset Pricing Model

The researchers base the standard capital asset pricing model on some very dubious assumptions. Here are the top nine.*