Yesterday's Wall Street Journal (Friday Sept 7th) had two more articles on the August turmoil in financial markets (pay-for links here and here). In the second article, they quote Former Federal Reserve Chairman Alan Greenspan,
"The behavior in what we are observing in the last seven weeks is identical in many respects to what we saw in 1998, what we saw in the stock-market crash of 1987, I suspect what we saw in the land-boom collapse of 1837 and certainly [the bank panic of] 1907," Mr. Greenspan told a group of academic economists in Washington, D.C., last night at an event organized by the Brookings Papers on Economic Activity, an academic journal.
That's all very well, but the current crew is using "sophisticated" computer models to drive their trading. Nowhere in either article is there any discussion of these models and yet that may be the key to what's gone wrong. In any case it recalls some interesting mathematics which appear in both nature and in commerce.
Power laws versus normal and log-normal distributions
The issue is how you model markets. Small price changes occur very frequently while large price changes are very infrequently. If you plot the number of changes of a given size against the size of the change on a log-log scale, you get a straight line, at least out some distance. Conventional finance assumes this fits a log-normal curve which eventually falls off. But extensive analysis, by Benoit Mandelbrot and others, of historical price data in many markets suggests the data fits a fractal or scale-free model, i.e. follows a power law. If so, the likelihood of extreme events (like Black Monday in October 1987) has been and is being consistently underestimated.
I've written on power laws before in "Scale free networks, long tails and big bucks - or maybe not," as they are the basis of Chris Anderson's, The Long Tail.
Power laws point to big bucks for Amazon, but also to big problems for Long Term Capital Management which collapsed in 1998 as I wrote about in "Power law vs log-normal with really big bucks implications."
Are the quants using models based on log-normal or power law distributions?
A quick Google search suggests that very few even understand the issues. Ed Wright and Yves Smith seem to get it, especially in the comments to their post. But otherwise one has to wonder about the financial community...
If you'd like further information, Nigel Goldenfeld has an excellent review of Fractals and Scaling in Finance by Benoit B. Mandelbrot that he did for Physics Today back in 1998.
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