Entropy Variations of Multi-Scale Returns of Optimal and Noise Traders Engaged in “Bucket Shop Trading”

Alejandro Raúl Hernández-Montoya, Carlos Manuel Rodríguez-Martínez, Manuel Enríque Rodríguez-Achach and David Hernández-Enríquez
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Alejandro Raúl Hernández-Montoya: Instituto de Investigaciones en Inteligencia Artificial, Universidad Veracruzana, Xalapa Veracruz 91097, Mexico
Carlos Manuel Rodríguez-Martínez: Instituto de Investigaciones en Inteligencia Artificial, Universidad Veracruzana, Xalapa Veracruz 91097, Mexico
Manuel Enríque Rodríguez-Achach: Unidad Experimental Marista (UNEXMAR), Universidad Marista de Mérida, Mérida Yucatán 97300, Mexico
David Hernández-Enríquez: Instituto de Investigaciones en Inteligencia Artificial, Universidad Veracruzana, Xalapa Veracruz 91097, Mexico

Mathematics, 2022, vol. 10, issue 2, 1-20

Abstract: In this paper a comparative, coarse grained, entropy data analysis of multi-scale log-returns distribution, produced by an ideal “optimal trader” and one thousand “noise traders” performing “bucket shop” trading, by following four different financial daily indices, is presented. A sole optimal trader is assigned to each one of these four analyzed markets, DJIA, IPC, Nikkei and DAX. Distribution of differential entropies of the corresponding multi-scale log-returns of the optimal and noise traders are calculated. Kullback-Leiber distances between the different optimal traders returns distributions are also calculated and results discussed. We show that the entropy of returns distribution of optimal traders for each analyzed market indeed reaches minimum values with respect to entropy distribution of noise traders and we measure this distance in σ units for each analyzed market. We also include a discussion on stationarity of the introduced multi-scale log-returns observable. Finally, a practical application of the obtained results related with ranking markets by their entropy measure as calculated here is presented.

Keywords: financial markets; entropy; price trends; multi-scale returns; optimal trader; noise trader; market efficiency (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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