Modern Portfolio Theory
If you live and breathe in the realm of maximizing returns on a continual basis, you are probably familiar with Warren Buffet. He is the man that everyone looks to when they think of a prominent investor. As an industrial engineer, however, there are other legends of the stock market that appeal to me. Harry Markowitz developed Modern Portfolio Theory as a tool to allow investors to base their current portfolio diversification upon the risk/return model that they individually are willing to take on.
Many argue that the stock market is unpredictable. When most people think of the stock market, the first icon that comes to mind is the Dow Jones Industrial Average. The Dow Jones Industrial Average started in 1896. Since then, it has included the top 30 US companies and has reliably trended upwards as time has progressed. General Electric is the only company that has been in the Dow Jones since inception. This is largely due to the fact that the Dow Jones has its own method of maintaining the top stocks and sorts out the companies that fall out of power while adding the new largest companies.
To avoid bias, it is better to start out with an index that encompasses a few more companies with a little less rotation, say the Wilshire 5000. By choosing the Wilshire 5000 to compare a portfolio to instead of the Dow Jones, you are comparing your portfolio to the entire market as opposed to the largest companies in the United States. The Wilshire 5000 has also arguably increased in value over time. Imagine being able to choose a portfolio of stocks out of the Wilshire 5000 that has lower risk and greater return potential than the Wilshire 5000. This is where Engineering meets reality.
Below is an excerpt from an Article that tries to model an “Efficient Index,” that discusses a few competing ways to build the best portfolio. An Efficient Index is an index comprised of stocks that is designed to meet current predefined specifications and subsequently follow a normal distribution of expected outcomes.
“In an attempt to identify what will be the minimum-variance portfolio, the authors form portfolios with the minimum variance over the trailing twenty-four months (subject to certain conditions). These portfolios are then tracked for the next quarter, and reformed. The resulting simulation has lower variance and higher return than the Wilshire 5000 in the period 1972 to 1989. The authors suggest that portfolio efficiency is possible for this behavior.” (Winston 27).
It is ideas like this that spawn from creativity and ingenuity. Here, several individuals historically built a portfolio and reallocated it based on specific criteria to see if they could beat the average market return. Since it sounds like they were to able to limit the variance while simultaneously grow the return, this indeed sounds like an approach that would attract attention for a multitude of investors.
In this theory, there is an efficient frontier design whereby you want to place your portfolio strategy on the frontier because if you do not, you are not reaching your true potential. This allows for two core ways to allocate your portfolio, the first is to maximize return with little to no risk and the second is to maximize return with as much risk as possible. Then, you need to develop your frontier that connects these two points by calculating your maximum expected return at every risk in-between the two previously mentioned. With this analysis, any investor can choose their acceptable risk level and be delivered a basket of stocks that matches up with their expectations.
By now, you should be getting a feel for how exactly this works and I think it’s acceptable to get into a few trickier specifics. Again, from a global standpoint, we are able to determine the expected portfolio return, and the risk (standard deviation) associated with this return. So, you might ask how exactly do we plan to efficiently find these stocks that meet these specifications? Markowitz himself, along with a few other authors have developed an outline listed below to do so.
“A feasible portfolio is one that meets specified constraints. A mean-variance efficient portfolio is one that provides minimum variance along feasible portfolios with a given (or greater) expected return, and maximum expected return for given (or less) variance. The expected return and variance provided by an efficient portfolio is called an efficient mean-variance (EV) combination. The set of all efficient EV combinations is called the efficient frontier” (Jacobs 586).
Thereby, using linear algebra and a matrix of stocks and the criteria related to their risk and returns, we should be able to build algorithms that identify the stocks that fit into the efficient frontier.
Everything mentioned above are works that are not of my doing, but by the doing of others. As for it’s interest to me, I plan to implement a system of fuzzy logic and neural networking logic structures to reliably pick out stocks that have historically done better than those in their same category, and categories that have done better than other categories at any given point in time with respect to the current interest rate (IR) and gross domestic product (GDP) trends. I choose these two trends because they seem to be the leading indicators of economic health in our economy.
In my system, neural networking logic would determine which aspects of a company are the most important during the IR/GDP trends are the most related to future growth. From there, fuzzy logic would determine which stocks have the best profile as well as when to buy and sell these specific stocks. I feel that if I am able to contribute in this way to the financial industry, I will be able to help very many other individuals.
My reasoning is this. Economically speaking, every transaction is mutually beneficial to both parties when the transaction is mutually agreed upon by both parties involved. If I am able to come up with a system that allocates money in a market such that more money is going to those that require it and are able to use it better than those around them I will benefit as well as them. And when we both are benefiting, our expenditures will be increasing and more people will be benefiting around us. In my system, there are no losers because there are winners, there are only people who have chosen not to take the opportunity to gain.
Right now, I am currently involved in an Operations Research project simulating the before mentioned Markowitz Modern Portfolio Theory. I feel that I need to fully understand how other similar systems work before I even begin to try and integrate fuzzy logic and neural networking into them because through the process of emulating others strategies, I will be learning how the systems work and possible troubleshooting techniques. I will say that I am not the first to contemplate and execute a strategy such as this. There are already companies out there that have launched indices that rotate their portfolios based upon specific criteria. Most of the attention is of course in the Exchange Traded Fund category because these funds are set up given specific criteria and are absolutely perfect for testing the truth behind these strategies. Claymore’s Sector Rotation Fund, (XRO) or possibly Powershares Dynamic Large Cap Portfolio, (PJF) are a good place to start looking into current and similar strategies that already exist and have been implemented.
Thanks for taking time out of your day to read my paper, I hope it was as interesting to read as it was enjoyable to write.
Glen Bradford
10/14/2007
Works Cited
Jacobs, Bruce; Levy, Kenneth; Markowitz, Harry. Portfolio Optimization with Factors, Scenerios and Realistic Short Positions. Operations Research Vol. 53. Pages 586-589. July 2005.
Winston, Kenneth. The “Efficient Index” and Prediction of Portfolio Variance. Pages 27-34. Journal of Portfolio Management. Spring 1993.
