The goal of convertible bond arbitrage is to consistently make money regardless of market conditions and to do so with minimal volatility. The basic mechanics of this market neutral approach is to take simultaneous long and short positions in a convertible bond and its underlying stock. By having the appropriate hedge between long and short positions, the arbitrageur hopes to profit whether the market goes up or down. Despite a focus on absolute returns rather than beating market indices, convertible bond arbitrage strategies have outdone the S&P 500 index with significantly lower volatility over the past decade.

**A little about Convertible Bonds**

It is helpful to think of convertible bonds as consisting of two components: a traditional ("straight") bond that pays a regular coupon and an equity call option on the underlying stock. Typically, when a company issues a convertible bond, the conversion price - the effective price at which the bond is converted into the underlying shares - is at a premium (say, 15% or 25%) to the company's stock price. Companies oftentimes find convertible bonds to be an attractive source of funds because convertibles typically carry a lower coupon than comparable straight bonds. In many jurisdictions, companies also find that there is a tax advantage to issuing convertible bonds in lieu of common equity. Convertible bond investors are willing to receive lower coupon payments because convertibles contain imbedded equity call options that allow investors to convert the bonds into shares if share prices rise. In effect, the difference in yields between a convertible bond and a comparable straight bond is the price the investor must pay to have a call option on the underlying stock.

The minimum value of a convertible bond is the "investment value" of its bond component, which is the present value of future coupon payments and principal repayment from the bond. Because of this fact, a convertible bond should be worth at least as much as the value of its underlying shares. A convertible bond nears this "bond floor" when the underlying stock falls far below the conversion price and the equity option component becomes nearly worthless or far "out-of-the-money." It should be noted, however, that if the issuing company's credit quality has deteriorated, the convertible bond's minimum value will fall accordingly.

The upside of holding a convertible bond is the option to convert the bond into shares if the underlying share price rises above the issue's conversion price. As the underlying share price rises above the bond's conversion price, the convertible becomes "in-the-money." The higher the stock price, the higher the convertible bond trades; the convertible bond's maximum value is essentially the value of its underlying shares.

**How to Profit from Convertible Bond Arbitrage**

On a general level, the arbitrageur seeks to exploit mispricings between a convertible bond and its underlying stock. If a convertible is cheap relative to its underlying stock, the arbitrageur will buy the convertible and sell short the underlying shares. He will do the reverse if the convertible bond is overvalued relative to its underlying shares. How much the arbitrageur buys and sells of each security depends upon the appropriate hedge ratio.

*Hedging*

Typically, the hedge ratio is determined by the "delta" - the sensitivity of a convertible bond's price to a price change in the underlying shares. For example, a delta of 50% indicates that the convertible bond should rise or fall at half the rate of its underlying shares. Given that a convertible's minimum value is its "bond floor," while a share's minimum value is zero, theoretically the delta must always be less than 100%. As far as hedging goes, for a convertible bond with a delta of 50%, one might sell short ¥50 of stock for every ¥100 in convertibles bought if the investor thought the convertibles were undervalued. It is important to note that delta is not a constant number; it changes as the underlying share price changes. This change in delta is called "gamma." Because of gamma, an arbitrageur must adjust his delta position - the ratio of his share to convertible position - if he wishes to remain "delta neutral" as the underlying share price changes.

*Strategies*

One convertible bond arbitrage strategy is volatility trading, which is commonly attempted with convertible bonds that are "at-the-money" - when the underlying stock price is close to the bond's conversion price. Using a very simplified example where we assume a starting delta of 50% and no hedging adjustments, an arbitrageur might buy ¥100 of convertible bonds and simultaneously sell short ¥50 of the underlying stock. If the share price rises, the loss from the arbitrageur's short position in the stock should be less than his gain from the convertible bond's price appreciation. On the other hand, if the share price falls, the gains from shorting the stock should exceed the loss on the convertible bond. (Remember that the convertible cannot fall below the "bond floor.") 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. As always, though, there are risks to this strategy, including incorrect interest rate assumptions, issuer credit deterioration, stock volatility, stock borrow recall and takeover of the issuer without provisions for convertible bondholders.

Deep in-the-money convertible bonds are attractive for their income advantage. These are usually highly leveraged trades, as the proceeds from selling the underlying stock short can be used to buy more convertibles because of the high delta. High leverage is also necessary to make good returns in such situations. The arbitrageur does not need to have a directional view on the underlying share price, though he sometimes might view this as a cheap put on the stock. Risks for this strategy include unexpected dividend growth, bond recall, stock borrow recall and re-pricing of the convertible.

Deep out-of-the-money or "busted" convertible bonds can be attractive to arbitrageurs as a fixed income play. These convertibles have very little sensitivity (i.e., low delta) to changes in the underlying share price and are often mispriced because other hedge funds might have sold the convertibles regardless of credit fundamentals. However, these convertibles can be attractive because the investor receives the upside of a significant rise in the share price (a cheap call option) in addition to a bond yield equivalent to that of a straight bond. This strategy carries interest rate, stock borrow and default risk.

Some convertible bond arbitrage strategies combine the above strategies and yet others have directional biases - through their use of hedging - that allow arbitrageurs to capitalize on expected rises or falls in the underlying stock price. In short, there are numerous variations of convertible bond arbitrage strategy.