Background Note | HBS Case Collection | January 2008

Convertible Arbitrage

by Joshua Coval and Erik Stafford

Abstract

The goal of this simulation is to understand how convertible bonds can be viewed as a portfolio of simpler securities and to introduce an over-the-counter market. The convertible bonds that are available during the simulation are at-the-money and in-the-money so that changing credit risk exposure is not much of an issue. A convertible bond can be viewed as a simple coupon paying corporate bond plus a conversion option. A bond pricing model discounts the promised payments at a rate that compensates for time, risk, and expected loss (maturity matched Treasury yield plus a credit rating matched yield spread). The conversion option can be valued using the Black-Scholes call option pricing formula. The key is to recognize that each conversion option (one per bond) is equivalent to several equity call options (the conversion ratio determines how many equity options are implicit in each bond).

Keywords: Bonds; Investment Portfolio; Price; Risk Management; Mathematical Methods;

Citation:

Coval, Joshua, and Erik Stafford. "Convertible Arbitrage." Harvard Business School Background Note 208-116, January 2008.