#### Regression Towards The Mean Versus Efficient Market Hypothesis via CSInvesting

**H. Francis Bush,**

Virginia Military Institute

**Michael D. Canning,**

Virginia Military Institute

**Abstract**

This study investigates the dominance of the statistical phenomenon, regression towards the means, against the market efficiency of capital markets. Using Fortune Magazine’s ranking of America’s most admired companies to distinguish positive from negative firms, and using the Standard and Poor Index as a surrogate for market, the authors demonstrated that: (1) a portfolio of least admired forms will outperform a portfolio of most admired firms, (2) a portfolio of most admired firms will outperform the market, and (3) a portfolio of least admired firms will outperform the market.

### Regression Towards The Mean Versus Efficient Market Hypothesis – Introduction

Statistics play an important role as a research tool as evidenced by its use in many areas in business and science. Regression towards the mean is a concept in probability and statistics. It essentially means that, if left alone, an observation that is distant from the mean will, over time, move back toward the mean. If this is the case, then the mean of a sample of stocks that are outperforming the mean population of stocks should begin to decline towards the population mean. On the other hand, the mean of a sample of stocks that are performing below the population mean should rise towards the mean of the population. Regression towards the mean can only occur when the linear relationship between the items is not perfect.

In the capital market, each portfolio of stocks can be considered a sample. Consequently, if regression towards the mean holds true, the mean return on a portfolio of above average firms will fall towards the population mean, producing a return on the portfolio below that of the market. A portfolio of under-performing stocks, however, will act in just the opposite way. The return on such a portfolio should provide a return above the market.

The hypothesis that will be tested in this research project is that the portfolio of under-performing stocks will give a higher return on investment than the high-performing portfolio. The mean return of the high-performing portfolio will fall towards the mean return of the population of stocks, and the mean return of the low-performing portfolio will rise towards the mean return of the population stocks. The research will not be conducted simply to determine that regression towards the mean exists; regression towards the mean has been observed since Sir Francis Galton coined the term in 1875. Rather its practical application in the field of investing will be tested.

The remainder of the paper is organized as follows. The second section will give a literary review of various subjects pertinent to the research. The third section will then show the methodology used. The fourth section will give results from the data collection, which will be displayed and explained. The final section will draw conclusions, as well as describe limitations and areas for future research.

### Literature Review

Portfolio management is the act of controlling the allocation of assets so that an optimal return on investment is accrued over a period of time. It is not just a single, solitary act, but rather a dynamic process under which conditions of markets, interest rates, the investor’s goals and skills, and many other factors are constantly monitored to ensure that the portfolio of assets is as profitable as possible. Although stocks, on average, make up nearly one-fifth of an individual’s net worth, only twenty percent of individuals actually decide in which securities to invest. The portfolios in this research consist of only stocks. The portfolio management strategies described will involve only the stocks.

The goal of investing is to make, or at the very least, preserve money. This applies to every individual or institutional investor. How much, how often, and for how long are the ultimate questions that separate investors from one another. An investor must ask these questions before making any sort of substantial investment. The profits or gains made from investing are called return on investment (ROI). ROI is a tool that enables individuals to effectively analyze the success of an investment. ROI is calculated by the following formula:

ROI number is the percentage of the original investment that has been gained back by the investor. In order to make an above average ROI, the investor must have a strategy which is better than the majority of investors. Otherwise, only market returns will be gained. Depending on the type of investment one makes, a high ROI may be returned in a short period of time, or a low ROI may be returned over a long period of time. The ultimate goal of investing is to obtain a strong ROI over a long period of time.

Maginn and Tuttle (1983) developed a flow chart (See Figure 1.) describing the process of developing a portfolio management strategy. First, investors must choose a fundamental strategy for investing. Choosing a strategy is one of the most important decisions to the investor, much more so than simply choosing in which stocks to invest, since the overall strategy for investing will determine which stocks to buy, sell, and when to buy and sell. This philosophy can change over time to fit investors’ needs more suitably, or can be left alone if they are satisfied with their return on investment. Deciding which strategy to use can be difficult and confusing for investors, especially if they have very limited access to resources and information.

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