Offshore investment funds are alleged to have engaged in trading behavior that is different from their onshore counterparts because they may be subject to less supervision and regulation. In particular, they may trade more intensely. They could also pursue more aggressively certain trading strategies such as positive feedback trading or herding that could contribute to a greater volatility in the market. Using a unique data set, this chapter compares the trading behavior in the Korean stock market between offshore investment funds with their onshore counterparts registered in the US and UK. There are a number of interesting findings. First, there is indeed evidence suggesting that the offshore funds trade more intensely than their onshore counterparts. Second, however, there is no evidence that the offshore funds engage in positive feedback trading. In contrast, there is strong evidence that the funds from the U.S. and U.K. do. Third, while offshore funds do herd, they do so far less than onshore funds in the U.S. or UK. Fourth, offshore funds hold less glamour stocks (e.g. stocks with high P/E) in their portfolio than funds in the U.S. or U.K. do. Moreover, flight to glamour stocks during the in-crisis period is less evident in the case of offshore funds. In sum, offshore funds are no especially worrisome monsters.