Unexpectedly Intriguing!
24 April 2009

Just a quick aside, here's Greg Mankiw just a short while ago:

The Economix blog offers up a simulation that alleges to show a roller coaster ride "whose track charts the Dow Jones industrial average from October 2007 to March 2009."

But that can't be right. Stock prices are approximately brownian motion, which means they are everywhere continuous but nowhere differentiable. In plainer English, "continuous" means that stock prices an instant from now, or an instant ago, are close to where they are now. But "not differentiable" means that the direction they move over the next instant is not necessarily close to the the direction they were heading over the last instant. A roller coaster with that property would be quite a ride.

Since at least January 2008, stock prices moved away from approximating Brownian motion to instead follow more of a Lévy Flight. The charts below demonstrate the difference, with generic Brownian motion shown on the left and Lévy flight on the right (here's our post where we originally presented these non-stock market-related charts):

Brownian Motion Levy Flight

As for being "quite a ride," we'll agree with that, especially if you take a ride on our model of the roller coaster:

S&P 500 Average Monthly Index Value vs Trailing Year Dividends per Share, Dec-1991 thru 23 April 2009

Update 25 April 2008: Welcome Eddy Elfenbein fans!

If you think this is math geekery, you ain't seen nothin' yet! Michael F. Martin over at Broken Symmetry has also taken note of this discussion, and makes a very good note about the nature of Lévy processes while adding a whole new angle to describing how the market is behaving: an inhomogeneous Poisson processes!

But, if you're not quite ready to throw Lévy processes out with the bath water, you might consider Andrzej Palczewski's and Emilia Rudzka's Truncated Levy flights on Warsaw Stock Exchange, which argues that truncated Lévy flights can be rather simply adapted to account for the observed asymmetry in the distributions of returns in a stock exchange, which tend to not only have "fat tails" compared to a normal Gaussian distribution, they also tend to have one tail be fatter than the other.

We'll stop there since detailed technical discussions of this kind of stuff makes our own eyes glaze over....


About Political Calculations

Welcome to the blogosphere's toolchest! Here, unlike other blogs dedicated to analyzing current events, we create easy-to-use, simple tools to do the math related to them so you can get in on the action too! If you would like to learn more about these tools, or if you would like to contribute ideas to develop for this blog, please e-mail us at:

ironman at politicalcalculations.com

Thanks in advance!

Recent Posts

Stock Charts and News

Most Popular Posts
Quick Index

Site Data

This site is primarily powered by:

This page is powered by Blogger. Isn't yours?

CSS Validation

Valid CSS!

RSS Site Feed

AddThis Feed Button


The tools on this site are built using JavaScript. If you would like to learn more, one of the best free resources on the web is available at W3Schools.com.

Other Cool Resources

Blog Roll

Market Links

Useful Election Data
Charities We Support
Shopping Guides
Recommended Reading
Recently Shopped

Seeking Alpha Certified

Legal Disclaimer

Materials on this website are published by Political Calculations to provide visitors with free information and insights regarding the incentives created by the laws and policies described. However, this website is not designed for the purpose of providing legal, medical or financial advice to individuals. Visitors should not rely upon information on this website as a substitute for personal legal, medical or financial advice. While we make every effort to provide accurate website information, laws can change and inaccuracies happen despite our best efforts. If you have an individual problem, you should seek advice from a licensed professional in your state, i.e., by a competent authority with specialized knowledge who can apply it to the particular circumstances of your case.