Convertible Bond Arbitrage

A convertible bond arbitrage is an arbitrage strategy that aims to capitalize on mispricing between a convertible bond and its underlying stock. The strategy is generally market neutral; in other words, the arbitrageur seeks to generate consistent returns with minimal volatility regardless of market direction through a combination of long and short positions in the convertible bond and underlying stock.

A convertible bond is a hybrid security that can be converted into equity of the issuing company. It typically has a lower yield than a comparable bond that does not have a convertible option, but this is usually balanced by the fact that the convertible bondholder can convert the security into equity at a discount to the stock’s market price. If the price of the stock is expected to increase, the bondholder will exercise his option to convert his bonds into equity.

Convertible bonds are sometimes priced inefficiently relative to the price of the underlying stock. To take advantage of such price differentials, arbitrageurs will use a convertible bond arbitrage strategy. If the convertible bond is cheap or undervalued relative to the underlying stock, the arbitrageur will take a long position in the convertible bond and a simultaneous short position in the stock. In the event that the price of the stock falls in value, the arbitrageur will profit from its short position. Since the short stock position neutralizes the potential downside price move in the convertible bond, the arbitrageur captures the convertible bond yield. On the other hand, if stock prices rise instead, the bonds can be converted into stock which will be sold at the market value, resulting in a profit from the long position and ideally, compensating for any losses on its short position. Thus, the arbitrageur can make a relatively low-risk profit whether the underlying share price rises or falls without speculating as to which direction the underlying share price will move.

Conversely, if the convertible bond is overpriced relative to the underlying stock, the arbitrageur will take a short position in the convertible bond and a simultaneous long position in the underlying stock. If share prices increase, the gains from the long position should exceed the loss from the short position. If stock prices decrease instead, the loss from the long position in the equity should be less than the gain from the price fo the convertible bond.

As seen above, the basics of the convertible bond arbitrage is taking simultaneous long and short positions in a convertible bond and its underlying stock. The arbitrageur hopes to profit from any movement in the market by having the appropriate hedge between long and short positions. How much the arbitrageur buys and sells of each security depends on the appropriate hedge ratio which is determined by the delta. Delta is defined as the sensitivity of the price of a convertible bond to changes in the price of the underlying stock. Once the delta has been estimated, the arbitrageur can establish his delta position – the ratio of his share to convertible position. This position must be adjusted continuously as the delta changes following changes in the price of the underlying shares.

The price of a convertible bond is especially sensitive to changes in interest rates, the price of the underlying stock, and the issuer's credit rating. Therefore, another type of convertible bond arbitrage involves buying a convertible bond and hedging two of the three factors so as to get exposure to the third factor at an attractive price.