project paper (part 1)

This is the first part of a paper originally submitted to my computer science professor to fulfill a graduation requirement. It's probably a bit dry for many of our readers, but it offers a long-winded reply to the faq "so, what the hell have you been up to lately?" Lately, I've been spending a part of my copious free time re-examining the topics I researched in this paper in hopes of coding the theories into some sort of usable application.

"A person is smart. People are dumb, panicky, dangerous animals."
--Kay from Men in Black

I began my research by looking into Modern Portfolio Theory (MPT) specifically to examine whether or not the ideas behind it could be coded into a useful program. I found that the basic tenets of portfolio theory, as put forth by the two books Modern Portfolio Theory and A Random Walk Down Wall Street provide a more than adequate basis for a tool that could assist moderately experienced investors. Specifically, MPT readily translates into a tool or tools which can: a/ analyze a single stock's "risk" in relation to the overall market b/ select a particular set of stocks and analyze the overall riskiness of the portfolio, and possibly (but less likely), c/ select a stock in order to diversify an existing portfolio and thereby reduce that portfolio's risk.

As such however, MPT unfortunately provides few, if any, starting points for novice investors with no preferences for particular companies. Both books emphasize the seeming futility of attempting to analyze individual stocks. They outline a great many studies displaying that stock prices move in a random or near-random manner and preach that examining past performance cannot lead to useful predictions about future performance.

I feel that despite all this, more consideration must be paid to the selection of individual stocks. Perhaps, there is no perfect system for predicting which stocks will result in the highest returns, but there must be ways to weed out those with little to no hope of doing well in the future. By narrowing the pool of stocks to choose from, novice investors may have an easier time selecting stocks and are thereby more likely to benefit from the contributions of MPT.

I also feel that the two books are limited in the fact that they do not appear take into consideration very recent developments in online trading and information dispersal. I will continue with a more in depth description of ways to extend an MPT tool after a brief overview of the basic tenets.

Modern Portfolio Theory

The foundations of MPT lie in the belief that central criterion for investors to consider is risk. In simple terms, risk can be understood to be the probability for disappointment-- the probability that future returns will deviate from expected returns. "Investment risk... is the chance that expected security returns will not materialize an, in particular, that the securities you hold will fall in price." (Malkiel 201) This is more tangibly understood as a measure of the variability of returns.

One technique for quantifying risk is to examine the historic data of a particular stock, determine the set of monthly returns for the time period, and then calculate the standard deviation of this set. For instance, the S 500-Stock Index was found to have an average return of about 1 percent per month or about 11 percent per year with a standard deviation of about 4.5 percent per month (Malkiel 204). Given an extensive history of closing prices, which may be found at finance.yahoo.com, www.bigcharts.com and other financial websites, a script or program could easily compute the average monthly returns and the corresponding risks of individual companies.

MPT further states that by diversifying a portfolio, an investor can reduce his or her overall risk as long as the companies that comprise the portfolio do not move completely in tandem with each other. "As long as there is some lack of parallelism in the fortunes of the individual companies in the economy, diversification will always reduce risk." (Malkiel 209) Correlation coefficients can be calculated by examining the extent that companies hit their peaks and valleys at the same time. As I understand it, the mathematics are reasonably complex, but the upshot is that not even negative covariance is necessary to reduce the risks of a portfolio, "anything less that a perfect positive correlation can potentially reduce risk." (Malkiel 211) The more extensive a portfolio, the less variability in returns up to about ten stocks. At that point, adding more stocks to a portfolio does not appear to reduce risk further. The catch, however, is that there is no way to completely eliminate risk so that an investment will yield guaranteed outcomes.

It's an obvious assertion, but the reasoning behind this is that there are two types of risk associated with stocks. One is "systematic" risk, or the risks associated with the general market fluctuations. These risks stemmed from basic unpredictability of the economic movements as a whole and "the tendency for all stocks to go along with the general market, at least to some extent." (Malkiel 221) The other type of risk is called "unsystematic" risk and refers to the risks coming from the particular company being considered. Expected and unexpected contracts, new discoveries and shifts in management all contribute to a stock's unsystematic risk.

Diversification reduces the unsystematic risks particular to each of the companies but obviously reduce the risk of entering the market as a whole. Systematic risks are quantified with a measure called beta. Beta is very basically a comparison between the fluctuations of a particular stock and the fluctuations of a broad market index.

The calculation begins by assigning a beta of 1 to a broad market index, such as the S & P 500. If a stock has a beta of 2, then on average it swings twice as far as the market. If the market goes up 10 percent, the stock tends to rise 20 percent. If a stock has a beta of 0.5, it tends to be more stable than the market (it will go up or down 5 percent when the market rises or declines 10 percent). Professionals often call high-beta stocks aggressive investments and level low-beta stocks as defensive. (Malkiel 222)

What follows is that portfolios with betas equal 1 should close resemble the S & P 500 in its risks and expected returns. Investors who can stomach more volatility for greater expected returns have a method of systematically increasing the risks they take.

part 2

Part two will cover the limitations of beta as well as possible ways to extend MPT.