In recent years, index-based insurance has been offered to smallholder farmers in the developing world to protect against common shocks such as weather shocks. Despite their attractive properties, these products have met with low demand. We consider the frequent situation where farmers are members of groups with common interests. We show that this creates strategic interactions among group members in deciding to insure that reduce the demand for insurance for two reasons. One is free riding due to positive externalities on other group members when a member chooses to insure. The other is potential coordination failure because it may not be profitable for a risk-averse member to insure if the other members do not. As a consequence, we argue that the demand for insurance against common shocks could increase if the insurance policy were sold to groups rather than to individuals.