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Mandelbrot Market-Model and Momentum

Last Updated on 10 February, 2024 by Rejaul Karim

In the research paper “Mandelbrot Market-Model and Momentum” by Wilhelm Berghorn and Sascha Otto, Mandelbrot’s contributions to finance, such as critiquing early stochastic process models and the oversimplification of the efficient markets hypothesis, are thoroughly examined.

With a focus on fractal markets and the exploration of fractional Brownian motion, his theories have inspired further exploration into the scaling behavior of trends using wavelets. This text delves into Mandelbrot’s vision of fractal markets, examining the fractal characteristics of trends and their relationship with the momentum effect.

In doing so, the study presents the Mandelbrot Market-Model as an explanation for the heavily debated momentum effect in literature. This model reveals a wilder risk side of markets due to trend structures as opposed to classical models, ultimately supporting Mandelbrot’s assertion of the nonexistence of efficient markets.

Abstract Of Paper

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.

Original paper – Download PDF

Here you can download the PDF and original paper of Mandelbrot Market-Model and Momentum.

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Wilhelm Berghorn
Mandelbrot Asset Management GmbH

Sascha Otto


In conclusion, the research paper “Mandelbrot Market-Model and Momentum” by Wilhelm Berghorn and Sascha Otto highlights the valuable contributions of Mandelbrot to finance, especially in critiquing early stochastic process models and the efficient markets hypothesis.

The study emphasizes Mandelbrot’s view of fractal markets and their wild nature, revisiting his vision through the use of wavelets to analyze the scaling behavior of trends. The momentum effect, a topic previously debated in literature, is shown to be modeled by the Mandelbrot Market-Model. With this model, the risk side of markets demonstrates an increased wildness due to trend structures, unlike their classical counterparts.

Ultimately, Berghorn and Otto’s study reinforces Mandelbrot’s long-held conviction that truly efficient markets do not exist, asserting the continued relevance of his theories in today’s complex financial landscape.

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What are the key contributions of Mandelbrot to the field of finance, as highlighted in the research paper?

The research paper underscores Mandelbrot’s critique of early stochastic process models and the oversimplification of the efficient markets hypothesis. It emphasizes his vision of fractal markets, suggesting that they are more intricate and unpredictable than classical theories suggest. Mandelbrot’s work on fractional Brownian motion and multi-fractal asset models is explored as a means to understand market behavior beyond traditional models.

How does the Mandelbrot Market-Model explain the momentum effect, and what role do fractal trends and wavelets play in this explanation?

The study delves into the Mandelbrot Market-Model as an explanation for the momentum effect in financial markets. It posits that the scaling behavior of trends, analyzed through wavelets, is the fundamental cause of the momentum effect. By examining the fractal characteristics of trends and their connection with momentum, the model reveals a more volatile risk side of markets compared to classical models. This challenges conventional notions of market efficiency.

What is the significance of the study’s conclusion regarding the nonexistence of truly efficient markets, and how does it reinforce Mandelbrot’s theories in today’s financial landscape?

The study’s conclusion reinforces Mandelbrot’s belief that truly efficient markets do not exist. The Mandelbrot Market-Model, by exposing the heightened unpredictability of markets due to fractal trend structures, questions the classical concept of market efficiency. In the context of the contemporary financial landscape, the research highlights the ongoing relevance of Mandelbrot’s theories, advocating for a reevaluation of traditional models in light of a more nuanced understanding of market dynamics.

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