Asymmetry of price returns—Analysis and perspectives from a non-extensive statistical physics point of view

Abstract

We study how the approach grounded on non-extensive statistical physics can be applied to describe and distinguish different stages of the stock and money market development. A particular attention is given to asymmetric behavior of fat tailed distributions of positive and negative returns. A new method to measure this asymmetry is proposed. It is based on the value of the non-extensive Tsallis parameter q. The new quantifier of the relative asymmetry level between tails in terms of the Tsallis parameters q± is provided to analyze the effect of memory in data caused by nonlinear autocorrelations. The presented analysis takes into account data of separate stocks from the main developing stock market in Europe, i.e., the Warsaw Stock Exchange (WSE) in Poland and—for comparison—data from the most mature money market (Forex). It is argued that the proposed new quantifier is able to describe the stage of market development and its robustness to speculation. The main strength is put on a description and interpretation of the asymmetry between statistical properties of positive and negative returns for various stocks and for diversified time-lags Δt of data counting. The particular caution in this context is addressed to the difference between intraday and interday returns. Our search is extended to study memory effects and their dependence on the quotation frequency for similar large companies—owners of food-industrial retail supermarkets acting on both Polish and European markets (Eurocash, Jeronimo-Martins, Carrefour, Tesco)—but traded on various European stock markets of diversified economical maturity (respectively in Warsaw, Lisbon, Paris and London). The latter analysis seems to indicate quantitatively that stocks from the same economic sector traded on different markets within European Union (EU) may be a target of diversified level of speculations involved in trading independently on the true economic situation of the company. Our work thus gives indications that the statement:” where you are is more important than who you are” is true on trading markets.

The Role of Entropy in the Development of Economics

“…Moreover, calculations have demonstrated the superiority of the NCEE method over such traditional estimation techniques as Shannon entropy, the non-linear least squares, the generalized methods of moments, and the maximum likelihood approaches [ 57 ]. Non-extensive Tsallis entropy also finds a number of applications on financial markets, which includes studies concerning the distribution of return fluctuations for the Polish stock market index WIG20 [ 58 ], the origin of multifractality in the time series [ 59 ], the exchange rate return fluctuations [ 60 ], relationship between the stock market returns and corresponding trading volumes [ 61 ], the memory effect involved in returns of companies from WIG 30 index on the Warsaw Stock Exchange [ 62 ] and the asymmetry of price returns on stock and money markets [ 63 ]. Other types of entropy have also been applied to financial markets [ 64 ].…”

Quantitative approach to multifractality induced by correlations and broad distribution of data

“…In this paper we will make the similar quantitative analysis of spurious multifractality caused by different types of broad probability distribution of data including also asymmetric fat-tailed distributions. The latter ones are expected to occur in some real systems including financial ones [54,55,56,57]. It is worth to notice that in fact nonlinear effects also produce broad distribution of data what in turn influences multifractal phenomena in a way of specific feedback.…”

Efficiency of Price Movements in Futures Markets

“…Numerous early studies demonstrated market efficiency (Fama, 1970, 1991). However, others question the idea of random behaviour (Bil et al, 2017; Bouchaud & Potters, 2003; Derman & Taleb, 2005; Longin, 2016), due to nonGaussian distributions of different kinds of market data. In short, the EMH does not account for extreme movements and strong market trends.…”