Indian Convertible Bonds with Unspecified Terms: A Valuation Model

Indian convertible bonds have two peculiar features that make them possibly unique in the world: a) the bonds are compulsorily converted into equity without any option, and b) the conversion terms are not specified at the time of issue but are left to be determined subsequently by the Controller of Capital Issues (CCI) who is the government functionary regulating capital issues in India. An naïve model would say that the market simply forms and estimate of the likely conversion terms and then values the bond as if these terms were prespecified. However, the empirical investigation reported in a companion paper, Barua, Madhavan and Varma (1991) convincingly rejects the naïve model and makes a more sophisticated model necessary. In this paper, we use the general theory of derivative securities (Cox, Ingersoll and Ross, 1985) to obtain a closed form expression for the value of the Indian convertible bond. The testable implications derived from our model are in sharp contrast to those of the naïve model and are consistent with the empirical results in Barua, Madhavan and Varma (1991). Though the valuation formula contains an unobservable state variable, the crucial functional parameters of the pricing relationship can be estimated, allowing the investor to measure and manage his risk. We derive the hedge ratios which an investor needs to control his risk exposure. An investor in Indian convertibles cannot, however, protect himself from both sources of risk (firm value risk and conversion ratio risk) with a single hedge ratio. This is an important difference between the Indian convertible and the ordinary convertible bond.