Wednesday, December 14, 2011

Financial Physics: "Power laws in finance"

From The Physics of Finance:
My latest column in Bloomberg looks very briefly at some of the basic mathematical patterns we know about in finance. Science has a long tradition of putting data and observation first. Look very carefully at what needs to be explained -- mathematical patterns that show up consistently in the data -- and then try to build simple models able to reproduce those patterns in a natural way.

This path has great promise in economic finance, although it hasn't been pursued very far until recently. My Bloomberg column gives a sketch of what is going on, but I'd like to give a few more details here and some links.

The patterns we find in finance are statistical regularities -- broad statistical patterns which show up in all markets studied, with an impressive similarity across markets in different countries and for markets in different instruments. The first regularity is the distribution of returns over various time intervals, which has been found generically to have broad power law tails -- "fat tails" -- implying that large fluctuations up or down are much more likely than they would be if markets fluctuated in keeping with normal Gaussian statistics. Anyone who read The Black Swan knows this.

This pattern has been established in a number of studies over the past 15 years or so, mostly by physicist Eugene Stanley of Boston University and colleagues. This paper from 1999 is perhaps the most notable, as it used enormous volumes of historical data to establish the fat tailed pattern for returns over times ranging from one minute up to about 4 days. One of the most powerful things about this approach is that it doesn't begin with any far reaching assumptions about human behaviour, the structure of financial markets or anything else, but only asks -- are there patterns in the data?...MORE
Trust but verify. From a 2010 post:

"WARNING: Physics Envy May Be Hazardous To Your Wealth!"

From the abstract at Physics arXive:
...The quantitative aspirations of economists and financial analysts have for many years been based on the belief that it should be possible to build models of economic systems - and financial markets in particular - that are as predictive as those in physics.

While this perspective has led to a number of important breakthroughs in economics, "physics envy" has also created a false sense of mathematical precision in some cases. We speculate on the origins of physics envy, and then describe an alternate perspective of economic behavior based on a new taxonomy of uncertainty.

We illustrate the relevance of this taxonomy with two concrete examples: the classical harmonic oscillator with some new twists that make physics look more like economics, and a quantitative equity market-neutral strategy. We conclude by offering a new interpretation of tail events, proposing an "uncertainty checklist" with which our taxonomy can be implemented, and considering the role that quants played in the current financial crisis...
HT: Improbable Research