Modern Portfolio Theory (MPT) is a theory for how investors can construct portfolios of assets to achieve their goals in terms of desired returns and acceptable risk. Previous to the development of this theory, investors focused on choosing a collection of individual assets with the best stand-alone risk and return characteristics without regarding the relationship between these assets. Rather than focus on selecting individual securities, MPT considers portfolios of securities and examines the return and risk of these portfolios. The theory was introduced by Nobel-prize winner Harry Markowitz in 1952.
The MPT has been heavily criticized recently. We believe that this criticism is valid in many cases. Some of these criticisms stem from assumptions of the MPT which have been shown to not be generally valid. Some of these assumptions include:
Returns are normally distributed.
The market is efficient (we’ll discuss this issue later).
Costs, taxes, and transaction fees are ignored in the model.
Cumulatively the MPT critics argues that these assumptions are so fundamental to the mathematics of the model that the results are not meaningful since these assumptions are not valid. Despite these valid points of criticism, the model has introduced some key concepts into investing which we believe are valuable and contribute to the creation of a successful long-term portfolio. These concepts are: the value of diversification and the existence of an efficient frontier of investment portfolios. We’ll spend some time on these two concepts and leave it to the reader to do more research on MPT if he desires. Additionally, we’ll discuss another important theory, called Market Efficiency, and discuss its implications for the development of an investment strategy.
Markowitz used a mathematical analysis of diversification to illustrate the value of making investment decisions based on portfolios rather than individual assets. The key insight was that the behavior of the assets in relation to one another will have an impact on the overall performance characteristics of the portfolio. Investors will typically judge the performance of a portfolio based on two measures: return and variance. The variance is a measure of the volatility of the returns of an asset. An asset with low variance will always deliver very similar returns while high variance will cause the returns to fluctuate greatly on a period-to-period basis. A general principle in investing is that you must sacrifice return to get low variance (and vice-versa). An example would be U.S. Treasuries which have lower mean returns than stocks but have much less variance.
For a portfolio, the mean return will simply be the weighted average of the returns of each of the component assets. Thus, if you have a portfolio of 50% bonds with a mean return of 4% and 50% stocks with a mean return of 8%, then the mean return of your portfolio will be 6%. However, the calculation of the variance of the portfolio includes terms which represent the correlation (or covariance) of the individual assets to one another.
Diversification can actually produce a portfolio with lower variance than the simple weighted average of the variances of each of the component assets. By diversification, we mean the construction of a portfolio from assets which are not perfectly correlated. With proper diversification, it is possible to reduce the variance (or risk) of a portfolio while not sacrificing the expected return.
To achieve this goal of reduced portfolio variance while not sacrificing mean return, you want select assets that have identical or similar mean returns but are uncorrelated or negatively correlated. With this approach, you can create an overall portfolio with similar return and lower variance than the best performing asset in your portfolio. This is the power of diversification.
In general, the concept of diversification is applied to two areas when investors construct portfolios. First, it is applied within asset classes. For instance, the investor may want to invest in large cap U.S. equities. Since the investor is not a professional, he may not be able to determine which individual stocks have the highest rates of return or lowest variances. They may all look the same from his standpoint. However, since the stocks represent companies in different business sectors, they will not all be highly correlated. Thus, he can choose a collection of these stocks and benefit from diversification. The collection will have the mean return of an average individual stock but will have a much lower variance thanks to the power of diversification. Thus, it is much less risky to hold the portfolio of S&P 500 stocks instead of just holding one stock.
Secondly, the concept of diversification is applied between asset classes. Now, let’s assume that our investor purchases all the S&P 500 stocks. We can think of this as one asset with a given expected mean return and variance. Now, he may choose to add another asset to the portfolio such as a U.S. Treasury bond. This new asset will also have an expected mean return and variance. As we mentioned before, U.S. Treasuries have historically had lower mean returns than the S&P 500 but have much less variance. Additionally, let’s assume that they are completely uncorrelated. Now, the investor will be giving up some mean return by adding the Treasuries to his portfolio but will definitely reduce his variance. In practice, it usually turns out that adding a small amount of an uncorrelated asset can lead to a decent sized reduction in variance while only causing a small decrease in expected return. This tradeoff may be acceptable to many investors.
To illustrate, let’s use an example taken from "The Intelligent Asset Allocator" by William Bernstein. There are two assets: stocks and bonds. In any period, the stocks are equally likely to return either +30% or -10% (a geometric mean return of 8%) while bonds are equally likely to return either +10% or 0% (a mean return of 5%). We can see by the volatility of the possible returns that the stocks have higher variance. The stocks and bonds are completely uncorrelated. Now, we want to compare portfolios consisting of various percentages of these stocks and bonds from 100% stocks to 100% bonds. Let’s plot these portfolios with mean return on the y-axis and standard deviation of returns on the x-axis.