## Modern Portfolio Theory Redux: An Introduction

*Today’s blog and the next few to follow are reposts of those blogs written last year on the topic of Modern Portfolio Theory, or MPT. They were written by the StockMarketCookBook’s resident academic guru, Professor Pat, but Dr. Kris has edited and updated them as needed. Since MPT is an integral part of the SMC Analyzer, we felt that including several brief tutorials on the subject would be helpful to those readers interested in learning more about the technical foundations of the Analyzer.

This week, Dr. Kris is out of town playing Aunt Kris at her nephew’s high school graduation. (Aunt Kris is proud to mention that he’s graduating at the the top of his class. Looks like he’s following in his Auntie’s footsteps proving that brains as well as modesty runs deep in the family’s bloodlines.)

We’ll be back to our regularly scheduled blogging next week. Have a safe and happy Memorial Day!

Modern Portfolio Theory (MPT): The Background
Modern Portfolio Theory (MPT) was first conceived by Harry Markowitz in 1952. For his inspiration and hard work he was awarded the 1990 Nobel Prize in Economics. Markowitz proposed that investors should be concerned not just with investment returns but also with investment risk, and put forth a strategy on how to achieve optimum performance using a mathematically determined allocation of asset classes.

MPT asserts that investors could and should balance the returns they receive on their investment portfolios with the risks those investments present. As such, and for the first time, a way to actually quantify the notion of risk was available. The new idea was that risk could be equated with volatility or the variation in returns from one time period to the next. The beauty of MPT is that it was also now possible to take this one step further and mathematically determine an optimum investment portfolio that delivers the desired long-term rate of return while simultaneously minimizing risk. The benefits of portfolio diversification in terms of risk reduction could now be mathematically derived.

Correlation and volatility
An investment portfolio consists of various asset classes (e.g., stocks, bonds), some of which appreciate and some of which may depreciate within any specified time interval. MPT uses the concepts of volatility and correlation among asset classes in its computations. Briefly, volatility is the rate of change in the value of each class. Correlation is a measure of how two asset classes move in relation to each other. For example, investments that move in tandem with each other are positively correlated; those that move in opposite directions such as stocks versus bonds are said to be negatively correlated; while those whose movements are independent of each other are said to be uncorrelated. MPT takes advantage of this fact to determine not only which investments to invest in but how much of each you should hold relative to each another.

The concept of MPT as a type of portfolio insurance
MPT can also be thought of as a type of portfolio insurance. As an investor, you hope that all of your investments will increase but you also know that this is an unrealistic expectation. MPT insures your portfolio against unreasonable losses by holding asset classes that can counteract losses in one class with gains in another. The way to achieve this is to select investment vehicles that are uncorrelated with each other. A properly diversified portfolio also includes relatively low yielding assets (like treasuries) that can be counted on to produce steady and reliable gains. An important assumption of MPT is that the future will, on average, be just like the past.

[Shameless plug: This assumption is proving to be a major drawback to MPT, especially in recent years. That’s why the addition of market timing to the MPT model not only increases potential portfolio returns but at significantly reduced risk. This is precisely the function of the SMC Analyzer*.]

MPT: The Theory
The techniques that are used in MPT to solve the optimum asset allocation problem is a branch of mathematics known as quadratic programming. There are two inputs to this program: 1. The actual historical returns of the various candidate assets input as a time series, and 2. The desired average rate of return that portfolio is expected to produce. The output of the calculations is the percentage to be ascribed to each asset class so that the entire portfolio will produce the desired return while minimizing risk. MPT quantifies that level of risk with a number called the standard deviation.

The standard deviation, denoted in statistical terms by the Greek letter σ, is a number that provides a bracketed range for the desired return. One standard deviation represents approximately 68% of the values around the expected outcome.

A basic assumption in MPT is that investment returns follow a pattern known as a normal distribution commonly found in natural processes.** Graphically, it forms a shape that looks like a bell as depicted in the illustration below. For example, if the desired annual rate of return is 10%, MPT might reveal a certain asset allocation strategy that would result in a minimum standard deviation of 11.7%. This means that approximately 68% of the time the actual return in any one year would fall in the range from -1.7% to +21.7%. (10% +/- 11.7%)

To be very confident about the exact range of one’s returns, we can again look to the normal distribution which also tells us that about 95% of the time the return the average return will be within two standard deviations of the mean, or in the above case between -13.4% to 33.4%.

The image below depicts these concepts. The dark blue region is one standard deviation,and the light blue region extends to two standard deviations. The symbol μ on the image is the average rate of return, or 10% in our example.

Investment philosophy
MPT is a useful tool for investors who prefer to remain somewhat passive in their investment activities. That is, they are not concerned with market timing. The optimum asset allocation technique tells them that they can remain comfortable with fluctuations in the market and limit their activities to monthly or even quarterly rebalancing to preserve the correct allocations following increases or decreases in the performance of individual assets held.

When we get to presenting the reality of these results, the data will confirm what everyone already knows: there is no such thing as a free lunch. That is, the higher the rate of return you wish to achieve, the more risk you have to be willing to take on. But we will see with numbers just how much more risk we’ll have to take to achieve those higher returns or how much return we need to give up to achieve more safety.

The next installment in this series will present actual results using common investment classes and will show you how to assemble a portfolio needed to achieve your desired rate of return. Stay tuned!

*For more details on MPT, take the SMC Analyzer Features Tour.

**Post-Modern Portfolio Theory (PMPT) impudently challenges this assumption, but for right now, it’s a good-enough one.