Ebook Convertible bond arbitrage
Convertible bonds were first issued in the United States in the nineteenth century. A simple convertible bond is a relatively straightforward security. It is simply a regular corporate bond, paying a fixed coupon, with security, maturing at a certain date with an additional feature allowing it to be converted into a fixed number of the issuer’s common stock. According to Calamos (2003) this convertible clause was first added to fixed income investments to increase the attractiveness of investing in rail roads of what was then the emerging economy of the United States.
Convertible bonds have grown in complexity and are now issued with features such as put options, call protection, ratchet clauses, step up coupons and floating coupons. Perhaps due to this complexity relatively few individual or institutional investors incorporate convertible into their portfolios. It has been estimated that hedge funds account for seventy percent of the demand for new convertible issues and eighty percent of convertible transactions (see Barkley (2001) and McGee (2003)).
While the overall market for convertible bonds has been growing to an estimated $351.9 billion by the end of December 2003 (BIS, 2004) the hedge fund industry has also been growing at a phenomenal rate. Initially investors were interested in large global/macro hedge funds and the majority of the funds went into these strategies. Fung and Hsieh (2000a) estimate that in 1997 twenty seven large hedge funds accounted for at least one third of the assets managed by the industry. However, since the bursting of the dotcom bubble, perhaps due to a reduction in appetite for risk, investors have been increasingly interested in lower volatility non-directional arbitrage strategies. According to Tremont Advisors, convertible arbitrage total market value grew from just $768m in 1994 to $25.6bn in 2002, an astonishing growth rate of 50% on average per annum.
The literature on securities arbitrage dates back more than seventy years. Weinstein (1931) has been credited as being the first to document securities arbitrage. He provides a discussion of how, shortly after the advent of rights, warrants and convertibles in the 1860’s arbitrage was born. Although the hedges described by Weinstein lack mathematical precision they appear to have been reasonably successful. Thorp and Kassouf’s (1967) seminal work, valuing convertible bonds by dividing them into fixed income and equity option components, was the first to provide a mathematical approach to appraising the relative under or over valuation of convertible securities. The strategies described by Thorp and Kassouf (1967) provide the foundation for the modern day convertible bond arbitrageur.
Academic literature on dynamic trading strategies has generally focused on modelling the relationship between the returns of hedge funds which follow such strategies and the asset markets and contingent claims on those assets in which hedge funds operate (see Fung and Hsieh (1997), Liang (1999), Schneeweis and Spurgin (1998), Capocci and Hübner (2004) and Agarwal and Naik (2004)). The difficulty with these studies it that the use of hedge fund returns to define the characteristics of a strategy introduces biases as discussed in Fung and Hsieh (2000b). Fung and Hsieh (2001) circumvent these biases by constructing portfolios of look back straddles on various assets which intuitively fit the return characteristics of a trend follower and document a strong correlation between the returns of their portfolios and the returns to trend following commodity trading advisors. Fung and Hsieh (2002) follow a similar methodology to provide evidence of convergence trading in several fixed income strategies. This paper follows Mitchell and Pulvino’s (2001) influential study of merger arbitrage, in attempting to recreate an arbitrageur’s portfolio.
Rather than using combinations of derivatives which you would expect to intuitively share the characteristics of a trading strategy’s returns we create a convertible arbitrage portfolio by combining financial instruments in a manner akin to that ascribed to practitioners who operate that strategy. The portfolio is created by matching long positions in convertible bonds, with short positions in the issuer’s equity to create a delta neutral hedged convertible bond position which captures income and volatility. We then combine the delta neutral hedged positions into two convertible bond arbitrage portfolios, one equally weighted, the other weighted by market capitalisation of the convertible issuers’ equity. To confirm that our portfolios have the characteristics of a convertible bond arbitrageur we compare the returns of the convertible bond arbitrage portfolio and the returns from two indices of convertible arbitrage hedge funds in a variety of market conditions.
We also examine the relationship between convertible bond arbitrage and a traditional buy and hold equity portfolio, highlighting the non-linear relationship between daily convertible bond arbitrage returns and daily equity returns. In severe market downturns convertible arbitrage exhibits negative returns. We also find evidence that in severe market upturns the daily returns from our equally weighted convertible bond arbitrage portfolio are negatively related to equities. In effect the returns to convertible bond arbitrage are akin to writing naked out of the money put and call options. Although this is not the first study to document the put option like feature in convertible arbitrage returns1 it is the first to document the negative correlation between daily convertible bond arbitrage and equity market returns in extreme up markets. This negative correlation is explained by the long volatility nature of convertible bond arbitrage. In extreme up markets implied volatility generally decreases having a negative effect on portfolio returns. This is an important finding for any investor considering adding a convertible bond arbitrage fund to an existing buy and hold long only equity portfolio.
The remainder of the paper is organised as follows. In section 2, we identify some potential explanations for the high returns of convertible bond arbitrage. In section 3, we describe a typical convertible bond arbitrage position and provide a thorough description of how our portfolio is constructed. In section 4, we compare the returns of the convertible bond arbitrage portfolio with the returns of two convertible arbitrage hedge fund indices and some market factors. In section 5, we present the results from examining the relationship between convertible bond arbitrage and a traditional buy and hold equity portfolio. Section 6 concludes the paper.
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