Why Should We Invest in CoCos Than Stocks? An Optimal Growth Portfolio Approach

This study investigates an optimal growth portfolio problem with contingent convertible bonds (CoCos). As the conversion risk with CoCos is closely associated with the issuer's capital structure and the stock price at conversion, modelling both equity and credit risk is carried out to frame this optimisation problem. We aim to answer the following questions: (i) how should investors optimally allocate their financial wealth in CoCos and risk-free bonds; and (ii) whether investing in CoCos or stocks issued by the same bank could result in higher expected returns. Therefore, we first derive the dynamics of a coupon-paying CoCo bond price under a reduced-form approach by assuming that the conversion intensity is a function of the coupon rate and the issuer's stock price. We then decompose the problem into pre- and post-conversion regimes to obtain closed-form optimal strategies. A comparative simulation between the inclusion of CoCos and stocks in a portfolio finally leads us to conclude that investing in CoCos and risk-free bonds provides higher expected returns than stocks and risk-free bonds under various market conditions.