Close Distribution Difference from Normal

Here are the actual difference from Normal for the frequency distribution of change in Ln(adjusted close prices). The y-axis corresponds to %s of the population, and the x-axis is the size of the move in Standard Deviations from the mean.

Unlike the original approach the purpose now is no longer to model this, but rather to understand it so that it can be incorporated into a fractal system.

If we assume that the markets are random (from the standpoint of the market there are random events in the industries) then the pattern here is due to investors (a feature of psychology, and interactions between markets).

There are 2 noticeable shortfalls in this chart which mean that events of –1.5 STDEV and +1.4 STDEV are far less likely than expected. The events that would have fallen into these are mostly pushed to the centre (-0.5 to +1) and to the extremes (<-2.5 and >+2.2). I explain this as follows. Small drops in the daily price (>-1.5) get bought into returning the close price to near or slightly above the open price, and likewise small daily rises in price (<1.5) suffer from profit taking causing the price to fall.

Daily moves below 1.5 lead to worry in speculators and they sell causing a larger than expected move. Once the rot sets in investors will follow and cause the fat tail.

Daily moves 1.5 lead to euphoria which seems to happen in two waves. Closing prices 3 STDEV from opening price are less likely as a second wave of euphoric buying pressure pushes the price higher. There after irrational exuberance stretches the price upwards.

This chart is for the majority of events (speculators). Another chart can be produces to study the behaviour of the extremes (investors).