Trend Momentum II: Driving Forces of Low Volatility and Momentum

46 Pages Posted: 13 Feb 2018

See all articles by Wilhelm Berghorn

Wilhelm Berghorn

Mandelbrot Asset Management GmbH

Markus Vogl


Martin T. Schulz

University of Applied Sciences Aschaffenburg

Sascha Otto

Die Sparkasse Bremen AG

Date Written: February 8, 2018


In discussions and critiques on the validity of the Efficient Market Hypothesis, there are two important research focuses: statistical analyses showing that the basic assumption of statistical independence in price series is violated and empirical findings that show that significant market anomalies exist. In this work, we combine both viewpoints by analyzing two important mathematical factor anomalies: low volatility and momentum. By applying an explicit trend model, we show that both anomalies require trending. Additionally, we show that the trend model used exhibits log-normal trend characteristics. Furthermore, the model allows us to describe how low volatility uses implicitly asymmetric trend characteristics while momentum directly exploits trends. Using Mandelbrot’s model of fractional Brownian Motions, we can finally link statistical analyses (measuring the Hurst exponent and persistence in returns) to the empirically observed momentum factor. Experimentally, the Hurst exponent in itself allows for a momentum strategy, and it can also be utilized to significantly improve low volatility strategies. In contrast to Mandelbrot’s approach, we offer a non-stationary view that allows us to describe both investment strategies using the trend model.

Keywords: Momentum Effect, Low Volatility Effect, Efficient Market Theory, Mandelbrot, Fractional Brownian Motion

JEL Classification: G11, G12

Suggested Citation

Berghorn, Wilhelm and Vogl, Markus and Schulz, Martin and Otto, Sascha, Trend Momentum II: Driving Forces of Low Volatility and Momentum (February 8, 2018). Available at SSRN: or

Wilhelm Berghorn (Contact Author)

Mandelbrot Asset Management GmbH ( email )

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


Markus Vogl

Vogl-Datascience ( email )

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

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