Yesterday's post was rather rushed as I was about to get on an airplane. Once on board, it occurred to me, there's another book I've read where the difference between log-normal and power law distributions is key. That's The Misbehavior of Markets by Benoit Mandelbrot & Richard Hudson. They argue modeling markets with normal distributions (in price changes, for example) is erroneous and leads economists to underestimate the likelihood of extreme events (like Black Monday in October 1987).
Put another way, small price changes occur very frequently and large price changes very infrequently. If you plot these on a log-log scale you get a straight line out some distance. Conventional finance assumes this fits a log-normal curve which eventually falls off. Mandelbrot, argues historical price data fits a fractal or scale-free model, i.e. follows a power law, meaning the likelihood of extreme events has been consistently underestimated.
Those of you in high tech in the US may have followed the accounting change which requires stock options be expensed by the company issuing them. To do this one must be able to estimate the present value of the options are the time they are granted. This is done using the Black–Scholes formula. While the authors received the 1997 Nobel prize in economics (Scholes & Merton; Black had died in 1995) and the Black-Scholes formula is now written into accounting practice, Mandelbrot argues it consistently underestimates infrequent cases of extreme price volatility.
As an interesting aside, Long Term Capital Management (LTCM), a hedge fund with Scholes & Merton on it's board, collapsed in 1998 due to a series of correlated repricing events that were extremely unlikely, but did occur in the late summer 1998. LTCM lost $4.6B.
Power laws and log normal distributions appear in many disciplines, not just networking and markets. In many cases it's hard to determine which applies. Whether Mandelbrot is correct about power laws and finance, at least we can agree -- $4.6B is big bucks!