Simulating convertible bond arbitrage portfolios

Abstract

The recent growth in interest in convertible bond arbitrage (CBA) has predominantly come from the hedge fund industry. Past empirical evidence has shown that a CBA strategy generates positive monthly abnormal risk-adjusted returns. However, these studies have focused on hedge fund returns which exhibit instant history bias, selection bias, survivorship bias and smoothing. This article replicates the core underlying CBA strategy to generate an equally weighted and market capitalization daily CBA return series free of these biases, for the period 1990 through 2002. These daily series also capture important short-run price dynamics that previous studies have ignored.

Acknowledgements

We are grateful to SunGard Trading and Risk Systems for providing Monis Convertibles XL convertible bond analysis software and convertible bond terms and conditions. We thank an anonymous reviewer for helpful comments and suggestions.

Notes

¹Fung and Hsieh (2001) and Mitchell and Pulvino (2001) follow a similar methodology to provide evidence of the risks in the trend following and merger arbitrage strategies.

²These models can be loosely classified as Sharpe (1992) asset class factor models following Sharpe's (1992) article on asset allocation, management style and performance evaluation.

³Some convertible arbitrage funds hold credit default swaps to hedge credit risk, however these hedges are likely to be imprecise.

⁴The arbitrageur may also hedge credit risk using credit derivatives, although these instruments are a relatively recent development. The short equity position partially hedges credit risk, as generally, if an issuer's credit quality declines this will also have a negative effect on the issuer's equity.

⁵It should be noted that the profitability of a long volatility strategy is dependent on the path followed by the stock price and how it is hedged. It is possible to have positive returns from a position even if actual volatility over the life of the position is less than implied volatility at the set up of the position and vice versa.

⁶For a detailed description of the different strategies employed by convertible arbitrageurs, see Calamos (2003).

⁷There are a large number of variants in the GARCH family including IGARCH, A-GARCH, NA-GARCH, V-GARCH, Thr.-GARCH, GJR-GARCH, E-GARCH and NGARCH. Empirical evidence on their relative performance is mixed (see Poon and Granger (2003) for a comprehensive review). As none of the variants consistently outperform, GARCH(1,1) is used in this study.

⁸For some equities in the sample five years, historic data were unavailable. In this situation, volatility was forecast using available data, restricted to a minimum of 1 year. Only equities with a minimum of 1 year of historical data were included in the original sample.

⁹As discussed earlier, due to transaction costs, an arbitrageur would not normally rebalance each hedge daily. However to avoid making ad hoc decisions on the timing of the hedge, we rebalance the portfolio daily and also exclude transaction costs.

¹⁰In 1990, 66 new positions were added, of which 55 were listed prior to 1990.

¹¹To ensure the level of leverage is not an important factor in our results, we apply alternative levels of leverage to the portfolio from zero to five times. Results were not materially different than for the one times equity portfolio and are available from the authors.

¹²Ineichen (2000) notes that 1994 was not a good year for convertible arbitrage characterized by rising US interest rates.

¹³The VIX index is an equity volatility index calculated by the Chicago Board Option Exchange. It is calculated by taking a weighted average of the implied volatilities of 8 30-day call and put options to provide an estimate of equity market volatility.

¹⁴Correlation coefficients were estimated for the entire sample period 1990–2002 for all variables excluding the CSFB data. There was no change in the sign or significance of any of the coefficients.

¹⁵We are grateful to an anonymous reviewer for this suggestion.

¹⁶For details on the construction of SMB and HML, see Fama and French (1992, 1993).

¹⁷The return on the DataStream Index of high yield corporate bonds is specified rather than the return on the composite portfolio from Ibbotson and Associates used by Fama and French (1993) due to its unavailability.

¹⁸The return on the DataStream Index of long-term government bonds is specified rather than the return on the monthly long-term government bond return from Ibbotson and Associates used by Fama and French (1993) due to its unavailability.

¹⁹The return on the DataStream Index of short-term government bonds is specified rather than the one-month treasury bill rate used by Fama and French (1993).

²⁰Scholes and Williams (1977) and Dimson (1979) amongst others show that betas of securities that trade less (more) frequently than the index used as the market proxy are downward (upward) biased.

²¹Data on SMB and HML were provided by Kenneth French.

²²With the exception of the market capitalization weighted portfolio in the appreciation equity markets sub-sample.