Emergence of correlations between securities at short time scales

The correlation matrix is the key element in optimal portfolio allocation and risk management. In particular, the eigenvectors of the correlation matrix corresponding to large eigenvalues can be used to identify the market mode, sectors and style factors. We investigate how these eigenvalues depend on the time scale of securities returns in the U.S. market. For this purpose, one-minute returns of the largest 533 U.S. stocks are aggregated at different time scales and used to estimate the correlation matrix and its spectral properties. We reveal the emergence of several dominant eigenvalues as the time scale increases. A simple lead–lag factor model is proposed to capture and reproduce the observed time-scale dependence of eigenvalues. Using this model, the relaxation time of the eigenvalues emergence is estimated to be around one minute for all the dominant eigenmodes, including the market mode. As a consequence, the use of five-minute returns time series for inferring correlations between stocks turns out to be a good compromise between statistical abundance of data points and well-established correlations. Our findings evidence that the underlying economic and financial mechanisms determining the correlation structure of securities depend as well on time scales.