Realized volatility underestimates the variance of daily stock index returns by an average of 14 percent. This is documented for a wide range of international stock indices, using the fact that the average of realized volatility and that of squared returns should be the same over longer time horizons. It is shown that the magnitude of this bias cannot be explained by market microstructure noise. Instead, it can be attributed to correlation between the continuous components of intraday returns and correlation between jumps and previous/subsequent continuous price movements.