Among mezzanine securities, convertible bonds are the most frequently issued products in the domestic and foreign security markets. However, the mezzanine market in Korea is developed mainly as a private placement market, which is difficult for individual investors to approach. Related products have been released recently, but the minimum subscription is high, and with no published convertible bond index, this type of investment is difficult to evaluate and its performance hard to measure. In this study, we confirm that the characteristics of the convertible bond index as an investment product are similar to those of the stock price index, using correlation and chaos analyses (e.g., Hurst exponent analysis), correlation dimension analysis, and maximum Lyapunov exponent analysis based on the global convertible bond index. At the same time, we establish an investment strategy based on the rough set theory and find that the convertible bond index, unlike the stock index, has a defensive tendency in the downside market. This research contributes to the development of the convertible bond index in the domestic market and the design of financial products based on this index.