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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