Fractal Markets, Frontiers, and Factors

66 Pages Posted: 10 Oct 2019

See all articles by Wilhelm Berghorn

Wilhelm Berghorn

Mandelbrot Asset Management GmbH

Martin T. Schulz

University of Applied Sciences Aschaffenburg

Sascha Otto

Die Sparkasse Bremen AG

Date Written: September 26, 2019

Abstract

In this work we develop an alternative view to the modern finance theory that essentially suggests equilibria in efficient markets by taking a risk-based view of asset returns in stock markets. Based on a mathematical analysis of stock market data using multi-scale approaches, we will alternatively describe markets and factors as trend-based fractal processes and analyze well-known factor premiums, which leads to a return-based view of markets and a model of investors reacting to market environments. We conclude that markets could be viewed alternatively as fractal, non-stationary and, at most, asymptotically efficient.

Keywords: Momentum Effect, Low Volatility Effect, Value Effect, Size Effect, Efficient Market Theory, Mandelbrot, Fractional Brownian Motion, Fractal Markets

JEL Classification: G11, G12

Suggested Citation

Berghorn, Wilhelm and Schulz, Martin and Otto, Sascha, Fractal Markets, Frontiers, and Factors (September 26, 2019). Available at SSRN: https://ssrn.com/abstract=3463151 or http://dx.doi.org/10.2139/ssrn.3463151

Wilhelm Berghorn (Contact Author)

Mandelbrot Asset Management GmbH ( email )

Helmut-Lederer-Straße 19 20
Erlangen, 91056
Germany
‭+49 9131 9303725 (Phone)
+49 9131 9303724‬ (Fax)

HOME PAGE: http://mandelbrot.de

Martin Schulz

University of Applied Sciences Aschaffenburg ( email )

United States

Sascha Otto

Die Sparkasse Bremen AG ( email )

Am Brill 1-3
Bremen, ‭+49 421 1793542 28195
Germany

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