Wade Pfau, Ph.D., CFA

Modern Portfolio Theory

Before shifting into further discussion about whether these historical numbers provide the most appropriate assumptions for future market performance, it is worth understanding how to choose an asset allocation and put together an investment portfolio while assuming that these historical numbers are the right ones to use. The more basic point is that any assumptions can be used. Once a set of assumptions are agreed upon, how is an investment portfolio asset allocation determined as based on those assumptions? With efficient markets, this asset allocation decision among the available asset classes becomes the most important driver of overall portfolio returns and volatility, rather than trying to select individual securities or predict overall market movements.

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In the 1950s, Harry Markowitz created Modern Portfolio Theory (MPT), which has served as the foundation for how wealth managers build investment portfolios for their clients. Harry Markowitz won the Nobel Prize in Economics in 1990 for this work. It provides a framework for choosing an asset allocation under a specific set of assumptions that wealth managers have traditionally accepted as being a reasonable starting point for households.

His fundamental insight was to show why investments should not be treated in isolation, but rather in terms of how they contribute to the risk and return of the overall portfolio. A very volatile individual investment might help to reduce overall portfolio volatility if its price movements tend to be in the opposite direction of the rest of the portfolio. This is diversification. Prior to Markowitz, portfolio managers seemingly did not realize this on a widespread basis, as they viewed their job was to choose what they felt are the very best individual securities, with each considered on a standalone basis. In their view, diversification would only reduce the potential for outsized returns.

Modern Portfolio Theory is a single-period model. It does not reflect how households are making decisions over multiple periods of time. It also does not include any spending constraint. It is an assets-only model about how to achieve efficient diversification, or to find the best tradeoff between portfolio returns and volatility. For the inputs, a user decides on the universe of asset classes to consider, and then decides on an average arithmetic return and standard deviation for each asset class, as well as the cross correlations for returns between each of the asset classes.

While we have discussed arithmetic average returns and standard deviations, correlations have not yet come up. The correlation coefficient between two asset classes measures their degree of co-movements. It ranges from -1 (move precisely in opposite directions) to one (move precisely in the same direction). If the correlation coefficient is zero, this means that the two asset classes move independently from one another. The lower the correlation coefficient, the greater the reduction in the portfolio volatility when the two asset classes are combined. With low correlations, the volatility of the portfolio can be less than the volatility of any of its component asset classes. Exhibit 1.1 provides an example of these inputs as based on the historical returns from the Morningstar data.

Exhibit 1.1 Inputs for Calculating Modern Portfolio Theory’s Efficient Frontier as Based on US Financial Market Nominal Annual Returns, 1926–2018

Source: Own calculations from SBBI Yearbook data available from Morningstar and Ibbotson Associates.

With these historical numbers we can see that movements in small-cap and large-cap stocks are closely related, as are the movements between the different types of bonds. But stocks and bonds did not experience close movements with one another, and Treasury bill movements are mostly unrelated to the other asset classes except intermediate-term government bonds.

As a next step, Exhibit 1.2 plots the portfolio returns and volatilities for different combinations of the six asset classes as based on their return characteristics shown in Exhibit 1.1. The exhibit shows the portfolio return on the vertical axis and the portfolio volatility on the horizontal axis. Investors would like to move toward portfolios in the upper left-hand corner, all else being the same, as that direction represents portfolios with higher returns and less volatility. The dots reflect the different combinations for these asset classes. The curve that envelops them on the upper-left side is the efficient frontier. It is the asset class combinations offering the highest returns for a given volatility, or the least volatility for a given return. It only makes sense for investors to consider asset allocation combinations from the many combinations reflecting different risk-return characteristics on the efficient frontier.

Exhibit 1.2 Modern Portfolio Theory’s Efficient Frontier as Based on US Financial Market Nominal Annual Returns, 1926–2018

Modern Portfolio Theory’s Efficient Frontier as Based on US Financial Market Nominal Annual Returns, 1926–2018

Source: Own calculations from SBBI Yearbook data provided by Morningstar and Ibbotson Associates.

This is an excerpt from Wade Pfau’s book, Safety-First Retirement Planning: An Integrated Approach for a Worry-Free Retirement. (The Retirement Researcher’s Guide Series), available now on Amazon.

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