Efficient Frontiers and Volatility Spreads of Convertible Bonds: Evidence from the Chinese Financial Market

A convertible bond is a financial instrument which can be considered as a straight bond with embedded options. As option pricing theories underwent significant advancements, theories of convertible bond valuation have correspondingly advanced. This study examines how convertible bonds improve portfolio efficiency and analyzes whether these instruments are mispriced in Chinese financial market. Efficient frontiers of both the two-asset and three-asset portfolio are depicted through simulation. The results indicate that after adding the CSI Convertible Bond Index, the performance of efficient frontier improves compared with the condition in which only the CSI 300 Index and the CSI Aggregate Bond Index are included. Using the Black-Scholes Model and the GARCH (1,1) Model, this study calculates the implied volatilities and the GARCH volatilities of 942 convertible bonds respectively and analyzes their equal-weighted spreads. Moreover, the equal-weighted spread is persistently positive over recent years, which implies that convertible bonds in China appear to be underpriced.