The Multifractal Wave

Mandelbrot framed the movement in stock prices as a “multifractal.” In his paper, A Multifractal Walk Down Wall Street, he sees “The mathematics underlying portfolio theory handles extreme situations with benign neglect: it regards large market shifts as too unlikely to matter or as impossible to take into account. Portfolio theory may indeed account for what occurs 95 percent of the time in the market. But the picture it presents does not reflect reality if one agrees that major events are part of the remaining 5 percent. A certain analogy is that of a sailor at sea. If the weather is moderate 95 percent of the time, can the mariner afford to ignore the possibility of a typhoon?” He describes the multifractal as formed by a three curve pattern repeated at smaller and smaller time scales. This generic pattern is then modified to fit drastic fluctuations in shortening or lengthening the time axis, creating a multifractal from a unifractal, where “the key step is to lengthen or shorten the horizontal time axis so that the generator pieces are either stretched or squeezed.” Unfortunately, Mandelbrot’s paper will not show you how to avoid major losses, another multifractal approach, Elliott wave, comes closer to a solution.

Different than Mandelbrot, Ralph Nelson Elliott’s Wave Principle is a multifractal analysis based on a primary trend in stock prices of a 5 up, 3 down wave pattern. Specifically, the total pattern is five waves in the trend’s general direction, and three moving away from the trend. The three waves are called corrections. The Elliott wave can then be broken into self-affine curves (waves) identical to the process Mandelbrot uses. Also different than Mandelbrot, Elliott used his analysis in actual stock markets. See the attached to learn more.