Capturing Convertible Volatility: Assessing the Rationale behind Convertible Bond Arbitrage with Implied Volatility

Abstract

Over the past decades, convertible securities have emerged as an innovative asset class for a wide range of investors. When they initially surfaced in the 1950s, convertible bonds pertained to only a small segment of the market, and few traders would consider investing in these instruments, which they saw as overly complex. Today, fixed income, equity and arbitrage investors look to convertibles as a primary portion of their portfolios. Numerous international hedge funds and asset managers invest solely in convertible bonds for their unique and flexible nature. The allure behind convertib le securities is the fact that they possess the benefits of both equity and debt instruments. Essentially, convertibles are a straight corporate bond with an embedded call option on the underlying equity. The debt component of the bond provides a bond floor that protects the value of the convertible if the underlying equity underperforms. However, because the bond carries an equity call option, if the underlying stock appreciates past a trigger price, the bonds can be converted into stock, taking advantage of any potential upside. Therefore, issuers can look at convertibles as an offensive play on debt or a defensive play on equity. This work helps pinpoint the advantages that issuers enjoy when choosing convertibles over debt or equity financing. In conclusion, the literature review sketches out the major characteristics of convertible bonds. It elaborates on their features, their structure and their trading patterns. It classifies convertibles based on secondary market performance, and shows the relationship between premium and parity. It outlines who issues convertible bonds, and gives rationale behind their decisions. The review also explains how convertibles are prices, where they are issued and how the process moves toward final syndication. The manual fleshes out who exactly purchases convertible bonds and the various strategies they implement to survive in fluid market conditions. Particularly, the literature review analytically expands on the concepts of convertible arbitrage hedging and capturing volatility. The recent growth and importance of arbitrage funds on the convertible bond universe served as the real motivation behind this research and the hypothesis it sought to prove in the ensuing quantitative section. Arbitrage funds have come to dominate the world of convertible bonds. These funds obsess over the technical aspects of an investment, always looking for a discount. They care little for the underlying growth potential of a company. Over the past ten years, these funds have driven down the pricing on convertible bonds to historically low levels as investors, looking only at technical data, seek out cheap convertibles with low implied volatilities relative to their underlying equity volatility. The literature review lays out the process of how arbitrage investors establish a hedged position. By assuming a long position in the convertible bonds and simultaneously borrowing stock to short the underlying company, they can earn a risk-free rate of return by continuously gamma trading. At this rate of return, arbitrageurs would most likely suffer overall losses on fees associated with leveraging and borrowing stock. This begs the question: why assume the plethora of risks inherent in convertibles if a treasury bill could reap the same return? As a result, investors must believe that implied volatility described in the terms of the convertible is lower, on average, than the actual volatility of the stock.