The Econophysics Blog

This blog is dedicated to exploring the application of quantiative tools from mathematics, physics, and other natural sciences to issues in finance, economics, and the social sciences. The focus of this blog will be on tools, methodology, and logic. This blog will also occasionally delve into philosophical issues surrounding quantitative finance and quantitative social science.

Monday, February 27, 2006

Power Law and the S&P 500 Index

I just read an interesting article in The Economist discussing how some mutual funds and asset management companies are employing tactics and strategies normally associated with hedge funds: The long and the short of it. The gist of the article is that some mutual funds and asset management outfits are employing short selling strategies (often using derivatives) in order to boost the amount of return ("alpha") beyond those returns associated with the asset's co-movement with the larger market ("beta").

It's worth noting that many mutual funds and asset management companies have been using these types of strategies for years -- prior to the latest hedge fund craze -- by using instruments like 'structured notes' -- which had embedded derivatives (a 'hidden' option, swap, etc.) -- that had the characteristics (at least on the surface) of the type of securities in keeping with the stated investment objectives but had more complex, underlying relationships that could give such investments characteristics that mimicked radically different types of instruments. For example, an investment that looked like a Standard and Poor's AAA rated bond issued by a government related entity like Fannie Mae or Freddie Mac whose performance largely depended on the currency exchange rate of the Thai Baht, the Mexican Peso, etc, rather than on the American mortgage market.

What I found most interesting about the article was the graphic based on data from State Street Global Advisors. The graphic shows that the top 10% (approximately) of the stocks (by market capitalization -- i.e., market value) in the S&P 500 Index make up the vast majority of the index share weight of the S&P 500 (as you may know, the Standard and Poor's 500 Index is an index of stock where the proportions of the shares in the index are weighted on the basis of the respective market capitalization of those shares).

This type of situation is what is referred to in mathematics and physics as a 'power law.' Power laws have been gaining in popularity lately in quantitative finance circles as a possible improvement over the normal/log-normal/Gaussian paradigm of how prices and returns of investments are modeled.

In the near future, I will be writing more about power laws and what implications they might have for finance. I thought I would briefly take note of an example I found of a power law working in the securities market (and a familiar example at that).