Hide the chart and the price hugs value. Publish it, and the tails grow fat.

A market maker moves the price by excess demand. Fundamentalists buy what is cheap against the fundamental F; chartists buy the trend they read off the chart, r_t, with bounded positions. The shares n follow realised profit through the logit. At F the reflexive gain is μ·g·n_c; past one the fundamental cannot hold.

The Cobweb’s switching rule, moved to an asset market: traders take the strategy whose realised profit has been higher, with intensity β, fundamentalists paying a cost to know the value. Calm markets make the free trend look as good as the costly value; that is how the chartists get in.

The fourth moment against the square of the second: 3 for a Gaussian, far more when large moves come too often. With it, the autocorrelation of r near zero and of |r| decaying slowly — calm and storm come in spells — are the stylised facts of real returns.

For a tail P(|r| > x) ∝ x^−α, the mean log-excess of the k largest moves over the next one estimates 1/α. For returns of real markets Cont (2001) puts it between two and five; a Gaussian sample gives a number that keeps climbing as the sample grows.