COMPARATIVE RETURNS AND RISK OF CONVERTIBLE BONDS AND THEIR UNDERLYING EQUITY, DEBT, AND OPTION VALUES IN THE POSTWAR PERIOD*

Abstract

THE OBJECTIVE of the study is to evaluate the relative return-risk performance of convertible bonds, the stock into which they are exchangeable, their straight debt value, and their conversion option value. The main emphasis is on the relative performance of the convertible bond and the stock. A subsidiary objective is to present a record of ex post yield data of 346 convertible bonds issued between 1951 and 1966. The purpose is to find out what past performance may tell us about present market conditions and what investors expect in the future. Expectations about growth, dividends, and price volatility are analyzed in a model of convertible bond premium determination. The examination of ex post yields required (1) computation of the various yields considered, (2) the development of histograms to show the distribution of yield outcomes, and (3) the computation of five statistics to measure return and risk. The mean and two types of weighted means were used to measure return, and the standard deviation and semi-standard deviation were used to measure risk. Multiple regression analysis was employed to explain convertible bond premiums by (1) the standardized theoretical value of the conversion option, (2) expected growth, (3) the dividend yield, and (4) stock price volatility. Multiple regression analysis was also used to explain the relationship between convertible bond and stock yields from which a breakeven yield was obtained. Finally, the appropriate statistics for return and risk were analyzed together on a year to year basis employing a linear model to determine whether convertible bonds or the common stock into which they are exchangeable performed better. The study shows that (1) convertible bonds are very much more like common stock than pure bonds in terms of both return and risk, (2) the similarity above was augmented by rising interest rates which served to reduce straight debt values, (3) the breakeven yield is estimated to have been approximately 8%, (4) convertible bonds outperformed common stock in more years than common stock outperformed convertible bonds,(5) the advantage of convertible bond performance increased when interest rates were relatively low and/or falling, (6) the advantage of common stock performance increased when interest rates were rising, (7) the relative performance of straight debt was particularly poor with risk-free securities yielding more as a general rule, and finally (8) the relationship between return and risk in the capital market appears to be curvilinear and concave to the origin reflecting higher required yields for increased risk taking.