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.
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