Trends, reversion, and critical phenomena in financial markets

Schmidhuber, Christoph

doi:10.1016/j.physa.2020.125642

Please use this identifier to cite or link to this item: https://doi.org/10.21256/zhaw-21531

Publication type:	Article in scientific journal
Type of review:	Peer review (publication)
Title:	Trends, reversion, and critical phenomena in financial markets
Authors:	Schmidhuber, Christoph
et. al:	No
DOI:	10.1016/j.physa.2020.125642 10.21256/zhaw-21531
Published in:	Physica A: Statistical Mechanics and its Applications
Volume(Issue):	566
Issue:	125642
Issue Date:	2021
Publisher / Ed. Institution:	Elsevier
ISSN:	0378-4371 1873-2119
Language:	English
Subjects:	Trend following; Mean reversion; Future market; Market efficiency; Critical phenomenon; Social network
Subject (DDC):	332: Financial economics
Abstract:	Financial markets across all asset classes are known to exhibit trends, which have been exploited by traders for decades. However, a closer look at the data reveals that those trends tend to revert when they become too strong. Here, we empirically measure the interplay between trends and reversion in detail, based on 30 years of daily futures prices for equity indices, interest rates, currencies and commodities. We find that trends tend to revert before they become statistically significant. Our key observation is that tomorrow's expected return follows a cubic polynomial of today's trend strength. The positive linear term of this polynomial represents trend persistence, while its negative cubic term represents trend reversal. Their precise coe fficients determine the critical trend strength, beyond which trends tend to revert. These coefficients are small but statistically highly significant, if decades of data for many different markets are combined. We confirm this by bootstrapping and out-of-sample testing. Moreover, we find that these coefficients are universal across asset classes and have a universal scaling behavior, as the trend's time horizon runs from a few days to several years. We also measure the rate, at which trends have become less persistent, as markets have become more effi cient over the decades. Our empirical results point towards a potential deep analogy between financial markets and critical phenomena. In this analogy, the trend strength plays the role of an order parameter, whose dynamics is described by a Langevin equation. The cubic polynomial is the derivative of a quartic potential, which plays the role of the energy. This supports the conjecture that financial markets can be modeled as statistical mechanical systems near criticality, whose microscopic constituents are Buy/Sell orders.
URI:	https://digitalcollection.zhaw.ch/handle/11475/21531
Fulltext version:	Published version
License (according to publishing contract):	CC BY 4.0: Attribution 4.0 International
Departement:	School of Engineering
Organisational Unit:	Institute of Data Analysis and Process Design (IDP)
Appears in collections:	Publikationen School of Engineering

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Schmidhuber, C. (2021). Trends, reversion, and critical phenomena in financial markets. Physica A: Statistical Mechanics and Its Applications, 566(125642). https://doi.org/10.1016/j.physa.2020.125642

Schmidhuber, C. (2021) ‘Trends, reversion, and critical phenomena in financial markets’, Physica A: Statistical Mechanics and its Applications, 566(125642). Available at: https://doi.org/10.1016/j.physa.2020.125642.

C. Schmidhuber, “Trends, reversion, and critical phenomena in financial markets,” Physica A: Statistical Mechanics and its Applications, vol. 566, no. 125642, 2021, doi: 10.1016/j.physa.2020.125642.

SCHMIDHUBER, Christoph, 2021. Trends, reversion, and critical phenomena in financial markets. Physica A: Statistical Mechanics and its Applications. 2021. Bd. 566, Nr. 125642. DOI 10.1016/j.physa.2020.125642

Schmidhuber, Christoph. 2021. “Trends, Reversion, and Critical Phenomena in Financial Markets.” Physica A: Statistical Mechanics and Its Applications 566 (125642). https://doi.org/10.1016/j.physa.2020.125642.

Schmidhuber, Christoph. “Trends, Reversion, and Critical Phenomena in Financial Markets.” Physica A: Statistical Mechanics and Its Applications, vol. 566, no. 125642, 2021, https://doi.org/10.1016/j.physa.2020.125642.