Characteristics of Principal Components in Stock Price Correlation

The following methods are used to analyze correlations among stock returns. 1) The meaningful part of the correlation is obtained by applying random matrix theory to the equal-time cross-correlation matrix of assets returns. 2) Null-model randomness is implemented via rotational random shuffling. 3) Principal component analysis and Helmholtz-Hodge decomposition are used to extract leading and lagging relationships among assets from the complex correlation matrix constructed from the Hilbert-transformed data set of asset returns. These methods are applied to price data for 445 assets from the S&P 500 from 2010 to 2019 (2,510 business days). Additional analysis and discussion clarify key aspects of leading and lagging relationships among business sectors in the market. Numerical investigation of these dataset reveals the possibility that leading and lagging relationships among business sectors may depend on gross market conditions.