The diversity index and investment portfolios

August 1, 2012

The diversity index is a concept that PWL has borrowed from the field of ecology. In 1949, statistician Edward H. Simpson developed a simple formula to measure the diversity of species. This formula was later applied in economics as a tool to measure the diversity of industries, which helped antitrust regulators answer questions like “Is Microsoft so large, relative to its industry, that it can control prices?” The more concentrated an industry is, the more likely it is that prices won’t be set competitively, at the lowest possible price.

Concentration also has a toxic effect on an investment portfolio. For example, during the 2008 financial crisis, investors who had the misfortune of having holdings heavily weighted in one or several of the companies that went into bankruptcy or reorganization would basically have lost that part of their capital forever. This is what happened with now-bankrupt firms such as Bear Stearns and Lehman Brothers. Several other companies, like Citigroup, Fannie Mae and AIG, are still in business (after being recapitalized by the U.S. government) but their value dropped over 95% during the crash and they will likely never fully recover because of permanent damage.

This is where the diversity index comes in. It helps measure portfolio diversification and avoid the dangers of concentration. Indeed, the number of securities in a portfolio can grossly overstate its level of diversification. For example, let’s take an imaginary Portfolio #1, which holds 100 stocks, the largest representing 99% of its value and the remaining 1% being evenly distributed among the 99 other stocks.

The following formula allows us to adjust the number of securities according to the more or less wide distribution of the invested capital:

Diversity Index = 1 / SUM (Security Weight)2

The diversity index of Portfolio #1 is 1.02 stocks. So, despite its apparent diversification, Portfolio #1 is basically a one-stock portfolio.

Now let’s look at Portfolio #2, a portfolio of 100 equally weighted stocks. 

This time, the diversity index is exactly 100 stocks, which means that this portfolio’s number of securities accurately reflects its diversification.

To illustrate this concept more concretely, we have calculated the diversity index of four well-known market indices and of a typical PWL portfolio. The results are given below. 

In conclusion, the diversity index provides an excellent indication of a portfolio’s robustness. In our view, an investor whose portfolio consists of a handful of securities is taking excessive and uncompensated risks. In contrast, PWL portfolios generally have an extremely high diversity index, which eliminates these uncompensated risks and provides higher expected returns.



Raymond Kerzérho

Chairman of the Investment Committee
and Director of Research
PWL Capital Inc.