We analyze the impact of sovereign wealth fund (SWF) investments on firm values and provide evidence consistent with the tradeoff between the monitoring and lobbying benefits versus tunneling and expropriation costs of SWFs as blockholders. The data show significant positive (negative) returns to announcements of SWF investments (divestments). The returns are non-monotonic, first rising (falling) and then falling (rising) with the share sought (sold) for investments (divestments). Moreover, we find that SWFs are often active investors. Slightly more than half of the target firms experience one or more events indicative of SWF monitoring activity or influence.