In this paper, we statistically analyze how investors distribute their trading intensity to different securities in stock markets. We find that trade allocation distributions are distinctive between investors. More importantly, the patterns of trade allocation across securities are surprisingly persistent for each investor, even when there is a turnover of securities in their portfolios. This suggests that even if investors have security-specific strategies, the securities can be replaced by others while the strategies remain. We also find that time constraints do not appear to limit investors’ activeness: the larger the set of securities an investor trades, the more frequently she trades each security on average.