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Beating the market? A mathematical puzzle for market efficiency.

DOI zum Zitieren der Version auf EPub Bayreuth:
URN to cite this document: urn:nbn:de:bvb:703-epub-6075-8

Title data

Baumann, Michael Heinrich:
Beating the market? A mathematical puzzle for market efficiency.
In: Decisions in Economics and Finance. Vol. 45 (2022) . - pp. 279-325.
ISSN 1129-6569
DOI der Verlagsversion:

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Project information

Project financing: Bundesministerium für Bildung und Forschung
Open Access funding enabled and organized by Projekt DEAL.


The efficient market hypothesis is highly discussed in economic literature. In its strongest form, it states that there are no price trends. When weakening the non-trending assumption to arbitrary short, small, and fully unknown trends, we mathematically prove for a specific class of control-based trading strategies positive expected gains. These strategies are model free, i.e., a trader neither has to think about predictable patterns nor has to estimate market parameters such as the trend’s sign like momentum traders have to do. That means, since the trader does not have to know any trend, even trends too small to find are enough to beat the market. Adjustments for risk and comparisons with buy-and-hold strategies do not satisfactorily solve the problem. In detail, we generalize results from the literature on control-based trading strategies to market settings without specific model assumptions, but with time-varying parameters in discrete and continuous time. We give closed-form formulae for the expected gain as well as the gain’s variance and generalize control-based trading rules to a setting where older information counts less. In addition, we perform an exemplary backtesting study taking transaction costs and bid-ask spreads into account and still observe - on average - positive gains.

Further data

Item Type: Article in a journal
Additional notes (visible to public): A Correction to this article was published on 06 July 2023:
Keywords: Technical analysis; Efficient market hypothesis; Robust positive expectation property; Simultaneously long short trading; Control-based trading strategies
Subject classification: Mathematics Subject Classification: 91G10; 91G99; 91B70
JEL Classification: C02; G11; G14
DDC Subjects: 300 Social sciences > 330 Economics
500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions > Central research institutes > Bayreuth Research Center for Modeling and Simulation - MODUS
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Profile Fields
Profile Fields > Advanced Fields
Research Institutions
Research Institutions > Central research institutes
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-6075-8
Date Deposited: 25 Mar 2022 08:51
Last Modified: 28 Jul 2023 05:39


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