The use of close-to-close returns underestimates returns correlation because international stock markets have different trading hours. With the availability of 16:00 (London time) stock market series, we find dynamics of daily correlation and covariance, estimated using two non-synchroneity adjustment procedures, to be substantially different from their synchronous counterparts. Conditional correlation may have different signs depending on the model and data type used. Other findings include volatility spillover from the US to the UK (and France), and a reverse spillover which is not documented before. Also, unlike previous findings, we found the increase in daily correlation is prominent only under extremely adverse conditions when a large negative return has been registered.