Spectral analysis of time-dependent market-adjusted return correlation matrix

Bommarito M. J., Duran A.

Physica A: Statistical Mechanics and its Applications, vol.503, pp.273-282, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 503
  • Publication Date: 2018
  • Doi Number: 10.1016/j.physa.2018.02.091
  • Journal Name: Physica A: Statistical Mechanics and its Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.273-282
  • Keywords: Market-adjusted return, Return correlation matrix, Maximum eigenvalue, Multi-modal distribution, CROSS-CORRELATIONS, NOISE, DYNAMICS
  • Istanbul Technical University Affiliated: Yes


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.

Keywords: Market-adjusted return, Return correlation matrix, Maximum eigenvalue, Multi-modal distribution