No abstract

THE INTENT of this paper is to supplement previous studies of convertible debentures [1], [5], [13], [15] in at least two respects. One, the specific influence of the so-called bond floor upon the risk premiums associated with convertible debentures is analyzed by reference to the market model developed by Sharpe [14] and Lintner [12]. Two, the effect of involuntary terminations upon the range of possible returns from holding convertible debentures is examined by means of a simulation model. Under the market model, convertible debentures-like their underlying common shares-are regarded as components of a risky market portfolio. Such assets differ from their underlying stocks in that they may be less responsive to the vicissitudes of the market and may therefore feature smaller premiums. The essence of the bond floor in the context of the market model is that it conditions covariability with the market.Despite the highly useful insights that it affords, the market model cannot cope effectively with the changing responsiveness of convertible debentures to the market (occasioned by varying ratios of stock conversion value to straight bond value) and with the stochastic process by which convertible debentures disappear from the scene. An alternative approach of Monte Carlo simulation is thus introduced to obtain comprehensive forecasts of rates of return on convertible debentures conditional upon the simulated behavior of the underlying stock.In the treatment that follows, the conventional model is first described for purposes of contrast. The market model and its limitations are then treated. The remaining sections deal with the simulation model, its behavioral inputs, and simulation results.