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.
Highlights
Ángel Sánchez-GraneroEconophysics is the study of socioeconomic complex systems by means of techniques and methodologies developed to study multi-particle physical systems by physicists and other scientists
In this paper we present and discuss some interesting and novel results related with the stationarity properties of signed, multi-scale returns of the optimal trader
The methodology used in this work is empirical and consists of a data analysis of the entropy of returns distributions generated by two kind of traders, i.e., algorithms that operate on data records of the above mentioned financial markets
Summary
Econophysics is the study of socioeconomic complex systems by means of techniques and methodologies developed to study multi-particle physical systems by physicists and other scientists. Considering the extreme simplicity and intrinsic interest of this system, which allows all participants to possess the same information on market prices, by using real data from four financial indices, DJIA, DAX, IPC and Nikkei, we simulate in the most straightforward possible way the “trading” activity of 1000 noise, non informed traders involved in “bucket shop” trading and one optimal, rational, fully informed trader. We present in Section 4.1.2, a short study on stationarity properties of this random variable
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