39 Pages Posted: 6 Jul 2015
Date Written: June 18, 2015
Mandelbrot has significantly contributed in many ways to the area of finance. He was one of the first who criticized the oversimplifications centered around the early stochastic process models of Bachelier utilizing normal distribution. In his view, markets were fractal and much wilder than classical theory suggests. Additionally, he was a profound critic of the efficient markets hypothesis. Particularly, his work of fractional Brownian motion showed that the independence claim made by that hypothesis is not valid; in addition, he proposed a multi-fractal asset model to reconcile for effects observed in the market. However, it is also known that his vision of fractal markets used fractal trends. Recently, we were able to show that the scaling behaviour of trends, as defined by a specific trend decomposition using wavelets, are the root cause for the momentum effect.
Additionally, we were able to show that these trends have fractal characteristics. In this work, we will revisit Mandelbrot’s vision of fractal markets. We will show that the momentum effect discussed heavily in literature can be modeled by the so-called Mandelbrot Market-Model. Additionally, this model shows, from the risk side, that markets are wilder because of trend structures compared with classical models. In conclusion, we derive what Mandelbrot always knew: There are no efficient markets.
Keywords: Mandelbrot, Momentum effect, Wavelets, Efficient Markets. Model, Trends
JEL Classification: G11, G12
Suggested Citation: Suggested Citation
By Andrew Ang
By Meb Faber