Convertible Arbitrage

Calamos, of the family investment firm that specialises in convertible securities, wrote a practitioner treatment of convertible arbitrage strategies.

The instrument comes first. A convertible bond is debt that the holder may exchange for a fixed number of the issuer's shares, which makes it a bond plus an equity call option. Its value therefore depends on interest rates, on credit spread, on the share price, on the share's volatility and on the time remaining, and it can be decomposed into those components.

The arbitrage strategy exploits the fact that convertibles have historically been issued cheap relative to the value of their components, because issuers pay for the certainty of placement and because the natural buyer base is narrow. The classic trade buys the convertible and shorts a quantity of the underlying stock determined by the convertible's delta, meaning its sensitivity to the share price. This removes the directional equity exposure and leaves a position that is long volatility, since the hedge must be adjusted as the share price moves, which generates profit when the stock moves in either direction, and that earns the bond's yield less the cost of the short.

Calamos covers the practical management: delta hedging and rebalancing frequency, gamma and what it earns, the credit exposure that remains and how to hedge it with credit default swaps, interest rate exposure, the short borrow cost and recall risk, and the leverage that the strategy conventionally uses.

The risks are structural. The strategy's returns are small per unit of capital and are conventionally amplified with leverage sourced from prime brokers, which means the position depends on continued financing. In 2005 and again in 2008 convertible arbitrage funds suffered severe losses when financing was withdrawn and every participant liquidated the same positions simultaneously. The book predates the second episode.