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The basic principles of convertible bond arbitrage have been clear at least since Thorp and Kassouf (1967). For those who are not familiar, the arbitrage entails purchasing a convertible bond and selling short the underlying stock, creating a delta neutral hedge long volatility position. Arbitrageurs profit from dynamically hedging the long volatility exposure, adding to or subtracting from the short stock position as the stock price changes. The trade generates a positive return if the actual volatility over the life of the position is greater than the implied volatility of the convertible bond, accounting for income/expenditure from the bond’s coupons, the stock’s dividends, and interest rates.

Hitchinson and Gallagher (2004) documented and replicated the original strategy and compared it to hedge fund returns. They found that their convertible bond arbitrage strategy had lower returns and higher volatility and kurtosis than either the HFRI Convertible Arbitrage Index or the CSFB Tremont Convertible Arbitrage Index. This leads me to believe that the strategies employed by the hedge funds must be considerably more advanced and sophisticated than the simple strategy first published in 1967.

More technically sophisticated models of convertible arbitrage are out there (Ayache-Forsyth-Vetzal, Tsiveriotis-Fernandes, and Brennan-Schwartz are the most popular), but most work following these models is more concerned with their estimation and their accuracy in pricing, rather than the P&L performance of a strategy based on the models.

Is anyone aware of academic or professional quality research which tests the profitability of some of the sophisticated convertible bond arbitrage models on real data? Has anyone even done any work replicating convertible arbitrage and documenting its performance in the last 8 years? I am particularly interested in strategies that incorporate CDS prices, but anything at all would be nice.

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Andrew Lo has an analysis documenting the performance of Convertible Bond strategies (see page 13 here). His purpose is to see whether various hedge fund strategies can be replicated by a portfolio of tradeable risk assets. His sample period his 1986-2005.

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Thanks for the link, but I'm looking for research on the strategy itself, not on funds that employ the strategy. In Lo's paper, convertible bond arbitrage is just one of many hedge fund strategies that he examines. He does not discuss how different variants of CB arbitrage (particularly employing the more recent models) have performed. –  Tal Fishman Aug 1 '11 at 14:19
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