In last Thursday’s blog we looked at the concepts of alpha and beta in terms of maximizing portfolio returns while minimizing risk. Those concepts are an integral part of a larger subject known as *Modern Portfolio Theory*, or MPT. This theory determines how investors should allocate their holdings to achieve a specified return with the least amount of risk. Since my knowledge of MPT is minimal, I thought I’d turn over today’s blog to Professor Pat, a colleague of mine who is well acquainted with MPT and uses it to allocate his own investment portfolio. For the record, Pat is not technically a professor in the usual sense of the word. He doesn’t teach MPT on the university level but his knowledge on the subject is so vast that he probably could. I’m using the term here in its second definition as one who professes or instructs. So, without further ado, I’ll let Professor Pat take it away and perhaps we’ll all learn something from his elegant discourse.

**Modern Portfolio Theory (MPT): The Background**

Thanks, Dr. K, for letting me present the ideas behind MPT. Since this is such a large subject, I’m going to split it up into several segments. Today, I want to describe the theory in general and its importance to you, the investor. In subsequent columns, I’ll present concrete strategies using results **that have not been published anywhere** that you can easily implement in constructing your own investment portfolio.

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 derived 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. [Note from Dr. K: The math used in MPT is quite hairy and is beyond the scope of this discussion. For those of you who are mathematically inclined, you can research this further. Wikipedia gives a good overview of the math used in MPT. Good luck!)

An investment portfolio consists of various asset classes, some of which appreciate and some of which may depreciate within any specified time interval. The rate of change, or volatility, in the value of each class varies as well. Some investments move up and down together, some move up when others move down, while others are completely uncorrelated to each other. 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 one another.

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. (More on that later.) 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.

**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 input 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 bracket range for the desired return. One standard deviation represents approximately 68% of the values around the 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 a range from -1.7% to +21.7%. (10% +/- 11.7%) The normal distribution also tells us that about 95% of the time the return will be the average return plus or minus two standard deviations, or between -13.4% to 33.4% in this example. 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.

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 quarterly rebalancing to preserve the correct allocations following increases or decreases in the value 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!

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