We investigate an optimal growth portfolio problem with contingent convertible bonds (CoCos). As the conversion risk in CoCos is closely associated with the issuer's capital structure and the stock price at conversion, we model both equity and credit risk to frame this optimisation problem. This study aims to answer two questions that (i) how investors should optimally allocate their financial wealth between a CoCo and a risk-free bond; and (ii) which approach – investing in a CoCo or in a stock issued by the same bank – could result in higher expected returns. First, we derive the dynamic of a coupon-paying CoCo price under a reduced-form approach. We then decompose the problem into pre- and post-conversion regimes to obtain closed-form optimal strategies. A comparative simulation leads us to conclude that, under various market conditions, investing in a CoCo with a risk-free bond provides a higher expected growth than investing in stock.