This note presents three results closely related to Franke, Stapleton and Subrahmanyams work (11) on the role of options in an economy with non-hedgeable background risk. It first shows two necessary conditions for the existence of equilibrium when negative terminal wealth is non allowed. It then shows the impact on investors cautiousness of background risk and gives a simple proof of one main result in their work. Thirdly, it shows how investors construct their optimal sharing rules using call options.