Individual and collective stock dynamics: intra-day seasonalities

We establish several new stylized facts concerning the intra-day seasonalities of stock dynamics. Beyond the well-known U-shaped pattern of the volatility, we find that the average correlation between stocks increases throughout the day, leading to a smaller relative dispersion between stocks. Somewhat paradoxically, the kurtosis (a measure of volatility surprises) reaches a minimum at the open of the market, when the volatility is at its peak. We confirm that the dispersion kurtosis is a markedly decreasing function of the index return. This means that during large market swings, the idiosyncratic component of the stock dynamics becomes sub-dominant. In a nutshell, the early hours of trading are dominated by idiosyncratic or sector-specific effects with little surprises, whereas the influence of the market factor increases throughout the day, and surprises become more frequent.