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Abstract We present an adjusted method for calculating the eigenvalues of a time-dependent return correlation matrix in a moving window. First, we compare the normalized maximum eigenvalue time series of the market-adjusted return correlation matrix to that of the logarithmic return correlation matrix on an 18-year dataset of 310 S&P 500-listed stocks for small and large window or memory sizes. We observe that the resulting new eigenvalue time series is more stationary than the time series obtained without the adjustment. Second, we perform this analysis while sweeping the window size τ ∈ { 5 , ... , 100 } ∪ { 500 } in order to examine the dependence on the choice of window size. This approach demonstrates the multi-modality of the eigenvalue distributions. We find that the three dimensional distribution of the eigenvalue time series for our market-adjusted return is significantly more stationary than that produced by classic method. Finally, our model offers an approximate polarization domain characterized by a smooth L-shaped strip. The polarization with large amplitude is revealed, while there is persistence in agreement of individual stock returns' movement with market with small amplitude most of the time. Highlights • We present an adjusted method for the eigenvalues of a time-dependent correlation matrix. • We use the correlation matrix on an 18-year data set of 310 S&P 500-listed stocks. • We obtain more stationary eigenvalue time series via market-adjusted return. • Co-movement and polarization of financial variables are important. • We find an approximate polarization domain, characterized by a smooth L-shaped strip. [ABSTRACT FROM AUTHOR]

Over the last 23 years, the U.S. Securities and Exchange Commission has required over 34,000 companies to file over 165,000 annual reports. These reports, the so-called 'Form 10-Ks,' contain a characterization of a company's financial performance and its risks, including the regulatory environment in which a company operates. In this paper, we analyze over 4.5 million references to U.S. Federal Acts and Agencies contained within these reports to measure the regulatory ecosystem, in which companies are organisms inhabiting a regulatory environment. While individuals across the political, economic, and academic world frequently refer to trends in this regulatory ecosystem, far less attention has been paid to supporting such claims with large-scale, longitudinal data. In this paper, in addition to positing a model of regulatory ecosystems, we document an increase in the regulatory energy per filing, i.e., a warming 'temperature.' We also find that the diversity of the regulatory ecosystem has been increasing over the past two decades. These findings support the claim that regulatory activity and complexity are increasing, and this framework contributes an important step towards improving academic and policy discussions around legal complexity and regulation. [ABSTRACT FROM AUTHOR]