We decompose, within an ARCH framework, the daily volatility of stocks into overnight and intraday contributions. We find, as perhaps expected, that the overnight and intraday returns behave completely differently. For example, while past intraday returns affect equally the future intraday and overnight volatilities, past overnight returns have a weak effect on future intraday volatilities (except for the very next one) but impact substantially future overnight volatilities. The exogenous component of overnight volatilities is found to be close to zero, which means that the lion’s share of overnight volatility comes from feedback effects. The residual kurtosis of returns is small for intraday returns but infinite for overnight returns. We provide a plausible interpretation for these findings, and show that our IntraDay/Overnight model significantly outperforms the standard ARCH framework based on daily returns for Out-of-Sample predictions.