Abstract
Stock market is a canonical example of complex systems, where a large number of interacting agents lead to joint evolution of stock returns and the collective market behavior exhibits emergent properties. However, quantifying complexity in the stock market data has been a challenging task. In this report, we explore four different measures to characterize the intrinsic complexity by evaluating structural relationship among stock returns. The first two measures are based on linear and non-linear comovement structure (accounting for contemporaneous and Granger-causal relationships), the third one is based on algorithmic complexity and the fourth one is based on spectral analysis of interacting dynamical systems. In our dataset comprising daily prices of a large number of stocks in the complete historical data of NASDAQ (1972- 2018), we see that the third and fourth measures are able to identify the largest global economic downturn in 2007-09 and associated spillovers, substantially more accurately than the first two measures. Finally, we conclude this brief research report with discussions on implications of such quantification for risk management in complex systems.
Highlights
How can complexity in financial markets be measured? financial markets are routinely thought of as complex systems, exact characterization of their embedded complexity seems non-existent, as pointed out in Brunnermeier and Oehmke [1]
In this brief research report we investigate the following question: Given the realized dynamical behavior of a system, can we find the degree of complexity embedded in the system? We note that in the case of financial markets, while interactions between economic agents can be nonlinear in nature, a complete enumeration of all such non-linearities is almost impossible
The dataset we analyze is extracted from complete historical data between 1972 and 2018 of NASDAQ (National Association of Securities Dealers Automated Quotations), which is one of the largest stock markets in the world in terms of trading volume
Summary
How can complexity in financial markets be measured? financial markets are routinely thought of as complex systems, exact characterization of their embedded complexity seems non-existent, as pointed out in Brunnermeier and Oehmke [1]. Different characterizations and underlying mechanisms have been proposed; explanations include the emergence of macroscopic properties from microscopic interactions [2, 3], the presence of power laws and/or long memory in fluctuations [4], and scaling behavior in growth rates of economic and financial entities [5], to name a few. In this brief research report we investigate the following question: Given the realized dynamical behavior of a system, can we find the degree of complexity embedded in the system? We compute each of these measures on 4-years windows and study how the measure evolves when we move the windows by 1 year (from 1972 to 2018 there are 44 such windows)
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