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Beating the market? A mathematical puzzle for market efficiency

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: https://doi.org/10.1007/s10203-021-00361-8

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Official URL: Volltext

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Project information

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

Abstract in another language

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
Refereed: Yes
Additional notes: This is the online first article.
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
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions
Research Institutions > Research Centres
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Result of work at the UBT: Yes
DDC Subjects: 300 Social sciences > 330 Economics
500 Science > 510 Mathematics
Date Deposited: 16 Nov 2021 13:04
Last Modified: 01 Aug 2022 07:41
URI: https://eref.uni-bayreuth.de/id/eprint/67847

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