We find a nonlinear dependence between an indicator of the degree of multiscaling of log-returns time series of a stock and the average correlation of it with the other stocks traded in the same market. This result is a robust stylized fact holding for different financial markets. We investigate the relationship of this result with the stocks' capitalization and we show that a linear dependence from the logarithm of the capitalization  does not explain the observed stylized fact  .
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 .
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the relationship of this result with
this result conditional on
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on the kurtosis of stocks' log-returns in order to search for possible confounding effects. We
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and the logarithm of kurtosis
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, which we interpret as being originated from a deeper relationship