We find a nonlinear dependence between an indicator of the degree of multiscaling of log-price time series of a stock and the average correlation of the stock with respect to the other stocks traded in the same market. This result is a robust stylized fact holding for different financial markets.

We investigate this result conditional on the stocks’ capitalization and on the kurtosis of stocks’ log-returns in order to search for possible confounding effects. We show that a linear dependence with the logarithm of the capitalization and the logarithm of kurtosis does not explain the observed stylized fact, which we interpret as being originated from a deeper relationship.

R. J. Buonocore, G. Brandi, R. N. Mantegna, T. Di Matteo, On the interplay between multiscaling and stock dependence, Quantitative Finance 20(1) (2019) 133-145