Pricing contingent convertibles with idiosyncratic risk

We consider capital structure including equity, straight bonds (SBs), and contingent convertibles (CoCos) for nonfinancial firms. We price equity and CoCos by a utility-based method. We show that benefits from issuing CoCos increase dramatically with idiosyncratic risk and risk aversion. The firm value is concave in CoCos' conversion ratio and the optimal conversion ratio increases with risk aversion and idiosyncratic risk. If risk aversion is sufficiently high, shareholders' risk-shifting incentives disappear, and the firm issues less CoCos and equity and more SBs as idiosyncratic risk rises. The higher the idiosyncratic risk or risk aversion, the higher the leverage.