# Predators and Prey in the Dow 30: Market Activity Is Often Compared to Darwinian Principles, but Does Natural Selection Really Work in the Stock Market? We Can Find out by Examining the Dynamics among the 30 Component Stocks of the Dow Jones Industrial Average Index

By McEwan, Ronald | Modern Trader, April 2007 | Go to article overview

# Predators and Prey in the Dow 30: Market Activity Is Often Compared to Darwinian Principles, but Does Natural Selection Really Work in the Stock Market? We Can Find out by Examining the Dynamics among the 30 Component Stocks of the Dow Jones Industrial Average Index

McEwan, Ronald, Modern Trader

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" (above).

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. …

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