Convertible Bond Arbitrage: Strategy Mechanics and Performance Evidence
Summary
The document explains convertible bond arbitrage as buying a convertible bond while shorting the issuer’s stock to create a delta-hedged, long-volatility position. The strategy seeks to benefit when realized volatility exceeds the bond’s implied volatility, after accounting for coupons, dividends, and financing costs. Dynamic hedging adjusts the stock short as the share price moves.
It cites a replication study by Hitchinson and Gallagher that reported lower returns and higher volatility and kurtosis than convertible-arbitrage hedge-fund indices. This raises the possibility that hedge funds use more complex approaches than the basic strategy. The question seeks research on strategies built from sophisticated convertible-bond pricing models, including those incorporating credit default swap prices. The only additional lead is Andrew Lo’s analysis of convertible-bond strategy performance over a historical sample; it does not establish the profitability of any particular model-based arbitrage strategy.
Key ideas
- Convertible bond arbitrage pairs a long convertible bond with a short position in the underlying stock.
- Dynamic rehedging targets the convertible’s embedded long-volatility exposure.
- Returns depend on realized versus implied volatility and on coupons, dividends, and interest rates.
- A cited replication performed worse on return and risk measures than the referenced hedge-fund indices.
- Pricing-model sophistication does not by itself demonstrate profitable trading performance.
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Full text
# What research is available on the performance of convertible bond arbitrage models? # What research is available on the performance of convertible bond arbitrage models? 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. ## Answer by Ram Ahluwalia (score 1) https://quant.stackexchange.com/a/1550 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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.