I'm not sure if it's in the classic Hull's book (J C Hull - Futures, Options and Other Derivatives), but here is one.
J-P. Bouchaud and M. Potters,
Theory of Financial Risks
(Cambridge University Press, 2001)
Beware: it's written by Theoretical Physics Ph.Ds, so some heavy math is involved
In brief - if a drunk man travels n steps, (say, take n as the number of market "days" for a drunk stock like IBM) he will travel, on average, Sqrt(n) distance, assuming "efficient" (gaussian) market, and n^H, where H is the Hurst exponent, in case of non-gaussian fluctuations with Hurst exponent H.
H=1/2 means ordinary diffusion (drunk man) Gaussian process, or efficient market.
Typically for the market H>1/2 (say, 0.6-0.7)
So in general fluctuations tend to take the drunk guy further than they ordinarily would, which means a trend.
Sorry about the late reply - Just didn't have the references Handy
"Fat tails", or crashes, still occur very rarely, so that the Fed could "doctor" them for a while. But they do occur nevertheless, and it's a normal market. |
