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## Predators and the prey in the Dow 30

Ecosystems exhibit cyclical changes and inhabitants adapt or perish. That’s true whether you’re talking about ones populated by wild animals or financial instruments. Regardless of the venue, the inhabitants compete for a finite supply of resources.

The basic ideas of the predator-prey relationships that define these competitions were established by Vito Volterra, a mathematician at the University of Rome, and Alfred J. Lotka, a physicist at Johns Hopkins University. The Volterra-Lotka system of equations are the accepted norm for explaining this process.

This work was further extended to the stock market in Theodore Modis’ An S-Shaped Trail to Wall Street. Modis developed a mathematical model for measuring competition among stocks within an index.

The competition is similar to the predator-prey relationships first outlined by Volterra and Lotka.

However, as with all theories, they are much more useful when paired with application. To put the findings of Modis to the test, we can construct working models in an Excel spreadsheet. With that, we can better outline some of the ideas and expand on the results from the original.

COMPETING IN KIND

While technical analysis looks at price, volume and open interest, the competition model of the markets looks at the total dollar value traded. For example, every day, minute by minute, a finite dollar amount is traded in the Dow Jones Industrial Average Index (DJIA). The 30 stocks that make up the DJIA must compete for these funds.

Just like the rabbits in the original predator-prey model competing for the grass while the foxes compete for the rabbits, the dominant species changes as time passes. The rabbits will eat all the grass and ultimately die off from a lack of food supply. Foxes will die off from a lack of rabbits to eat. With a reduced rabbit population, the grass grows back. When the grass grows back the rabbits multiply from the new fresh food supply. The foxes get fat again from having more rabbits to eat. And on and on the cycle continues.

The process is similar in the markets with different stocks enjoying their fat days while others languish and, in some cases, even die out or exit the index.

To construct the competition model in Excel, the first input into the worksheet will be the price and volume data for the 30 stocks that make up the DJIA. For each security, the price is multiplied by the volume to give a total dollar value traded for each security.

The next step is to calculate the competition factor for each security. This is done in a number of steps. The first factor, “X,” is derived from dividing the volume of each security by the total volume of all 30 securities. The second factor, “Y,” is derived from dividing the dollar value of each security by the total dollar value of all 30 securities.

The last step in the process is to complete the calculation for the competition value of each security. The formula for this is:

Competitiveness = Square Root ((volume) ^2+ (value) ^2),

with both volume and value expressed as percentages of the DJIA totals.

The completed worksheet will now look something like what’s shown in “Building your worksheet” (below).

GETTING VISUAL

The last step in the process to make the spreadsheet useful will be to create the charts. For this project, bubble style charts work well. Bubble charts are a standard chart type available in Excel and other spreadsheet applications. The data points for each bubble in the chart correspond to:

• X value = “X” factor

• Y value = “Y” factor

• Bubble size = “Competitiveness” factor

The X-axis (share volume) indicates the direction of increasing competitiveness. The more the security falls along to the right of this axis, the larger the bubble size of the security. These securities are consuming a greater share of the resources in their financial ecosystem, the DJIA index.

The Y-axis (dollar value) indicates the direction of increasing price. These securities are growing in price as opposed to those that are consuming too much and not providing the investor with sufficient return.

It’s illustrative to review the

competition charts of the 30 Dow stocks for December 2004, 2005 and 2006. For comparison, we also can look at a relative price performance chart for Exxon Mobil (XOM), Microsoft (MSFT), Intel (INTC) and Pfizer (PFE) for the same period. This offers graphic perspective on how price and competition for resources evolve through time.

At the end of 2004 Microsoft, Pfizer and Intel were moving along the axis that indicates an increase in competition for resources, and Exxon Mobil was just starting to emerge from the pack along the axis that indicates an increase in price (see “Few rise higher,” below).

In 2005 a similar pattern for these same securities can be identified with Exxon Mobil continuing to move up on the axis of increasing price. Microsoft, Pfizer and Intel were continuing to be the major consumers of available dollar resources (see “Breaking out,” below).

At the end of 2006, Exxon Mobil had moved well up along the axis of increasing price and along the competition axis. Meanwhile, the other three securities continued to consume a significant portion of resources (see “New blood rising,” below).

This is indicated in how they moved along the competition axis but did not continue moving up significantly on the price axis. Also, at this time, it can be noted that Citigroup (C) has begun to rise along the price and competition axis.

“Relative return” (below) shows how this all played out in the markets.

Understanding the dynamics of competition for market dollars (resources) is a valuable tool for traders to analyze. This spreadsheet-based model dispels the idea that in the securities markets the largest consumer of investors’ dollars will reward them through the long term.

This model will assist the investor with identifying securities that may have the best potential for moving up the price and competition axis vs. securities that just move along the competition axis or price axis alone.

Ron McEwan is currently employed with the U.S. Treasury Department. E-mail him at rmac@juno.com.