A convertible bond is a hybrid financial instrument that incorporates features of a bond (fixed income security) and an equity claim (usually common stock). In most instances the convertible can be exchanged, at the holder's option, for the common shares of the corporation issuing the convertible. The conversion value, or stock value, is the market value of the common shares for which the convertible can be exchanged. The bond value or floor price is the market value of an equivalent bond that does not include a conversion feature. The market price of a convertible will be the conversion value or the bond value, whichever is higher, plus a premium. The purpose of this paper is to develop and test a model which estimates the premium. The premium estimated is defined as the difference between the market price of the convertible and the bond value or conversion value, whichever is larger. No consideration will be given to convertible preferreds.

Some recent empirical studies have concluded that the common stock investor can virtually eliminate diversifiable risk with a portfolio that contains a “small” number of separate common stock issues [5, 6, 10, 11, 13]. The conclusion has several important implications. One of the inherent limitations of a portfolio manager is his inability to evaluate an infinite number of securities. The seriousness of this problem is directly related to the risks associated with a “small” portfolio. The economic function of a mutual fund industry is to provide diversification and professional management. If it is assured that a “small” portfolio can virtually eliminate diversifiable risk, the necessity of these functions may be questioned. In addition, the strategy of concentration may be less “risky” than is commonly supposed. Finally, the modern portfolio models generally assume that portfolio additions are costless.