The change in the cost of capital that results from a divestiture strategy can be closely approximated by a simple function of three parameters: (1) the fraction of socially conscious capital, (2) the fraction of targeted firms in the economy and (3) the return correlation between the targeted firms and the rest of the stock market. When calibrated to current data, we demonstrate that the impact on the cost of capital is too small to meaningfully affect real investment decisions. We then derive the conditions that would be required for the strategy to have a meaningful impact. We empirically corroborate our theoretical results by studying firm changes in ESG status and are unable to detect an impact of ESG divestiture strategies on the cost of capital of treated firms. Our results suggest that to have impact, instead of divesting, socially conscious investors should invest and exercise their rights of control to change corporate policy.