Convertible Arbitrage Strategies

Managers pursuing a convertible arbitrage strategy purchase a convertible security such as a convertible bond or convertible preferred stock while simultaneously selling short a percentage of the issuer's stock. In some instances stock options or an index of stocks, rather than the issuer's specific stock, is sold short to hedge the equity risk. Generally the goal of the strategy is to identify relative pricing discrepancies between the convertible security and the stock of the issuer. However, convertible arbitrage managers can earn profits even when no pricing discrepancies exist by engaging in gamma trading. To execute a gamma trade, a manager identifies and purchases undervalued convertible securities and then hedges the equity exposure through short sales. Once the convertibles realize their fair value, they are sold for a profit. Gamma trading also earns profits from re-hedging the equity exposure through short sales. We will discuss gamma trading shortly.

Convertible securities are selected using bottom-up analysis, paying attention to price, interest rates, stock price, stock volatility, credit quality, conversion price and premium, bond floor, and other factors that affect the value of the convertible security. Because many convertibles are debt instruments, managers may choose to hedge credit, interest rate, or other risk factors using derivatives. Market exposure is most often kept neutral but can be net long or short, depending on the managers market outlook. Equity hedge ratios, which range from 0.2 to 0,8, are determined using the delta of the conversion option embedded in the convertible security. The hedge ratio determines the amount of stock to be sold short. Leverage ratios for convertible arbitrage strategies range from 1:1 to 5:1.

Sources of Return from a Convertible Arbitrage Strategy

Managers pursuing convertible arbitrage strategies generate returns using many different trading, hedging, and leveraging schemes. Even though the methods of generating returns take on many different technical aspects, the returns from a convertible arbitrage strategy can be traced to one of three sources: static returns, gamma trading, and pricing inefficiencies.

Static Returns

By simply holding the convertible arbitrage position (i.e., long convertible, short stock), the convertible arbitrage manager earns the static return. There are two components to the static return, both of which are related to systematic risk premia. These components include the interest or dividend income earned from holding convertible bonds or convertible preferred stock, as well as the short rebate interest earned on the proceeds from selling the issuers stock short. Generally, static returns are highest for lower credit quality convertibles with in-the-money conversion options. Since the option delta for in-the-money options is relatively high, more of the issuer's stock must be sold short to hedge the equity position. With increased short sales comes increased short rebate interest, increasing the static return. In addition, the lower credit quality increases default risk and the accompanying coupon payment to compensate the investor. Average credit ratings for bonds used in convertible arbitrage strategies range from BB to BBB.

Gamma Trading

Gamma measures the rate of change in an option's delta (hedge ratio) for a given change in the underlying stock price. Because convertible arbitrage managers hedge their equity exposure by shorting stocks using the delta hedge ratio, they are said to be long gamma (exposed to changes in the hedge ratio). As the underlying stock price rises, the option delta rises, and more short positions are needed. This implies a loss on the short position. However, the loss is more than offset by an increase in the value of the convertible. As the underlying stock price falls, the option delta fails, and fewer short positions are needed. This implies a gain on the short position. In this case, the loss in value of the convertible is less than the gain on the short position. Thus, the convertible arbitrage manager makes trading gains by re-hedging the position no matter which direction the underlying stock moves.

In addition to being long gamma, convertible arbitrage managers are long vega. In other words, they are exposed to changes in the price volatility of the stock underlying die option embedded in the convertible security. As the volatility of the stock price decreases, the embedded option value decreases, but no gain on the short position occurs. Lower volatility also translates into smaller stock price moves and less opportunity to profit from gamma trading. However, higher volatility creates more opportunities for gamma trading gains.

Pricing Inefficiencies

Like many hedge fund strategies, convertible arbitrage strategies attempt to find and exploit mispricings in the convertible securities markets. Exploiting pricing inefficiencies is the main source of alpha generated by convertible arbitrage managers. Generally, the manager searches for undervalued issues to purchase and hold until the securities reach their fair value while hedging away the systematic risk of the equity exposure. Divergence from fair value may occur either at the time of issuance, since issuers often discount the security to entice buyers, or during times of high volatility, when the market misjudges the impact of high volatility on the value of the security. In addition, managers look for securities in which the market has overestimated the credit risk of the issuer.

Convertible Arbitrage Risks

Convertible arbitrage strategies have some risks since the relationships among variables affecting convertible value are complex, requiring a carefully constructed quantitative valuation model. Also, sudden drops in the price of the hedged stock may bring about mark-to-market losses. These factors, known as model risk and mark-to-market risk, are argued by some to be a source of returns from risk premia (return as a reward for talcing on the systematic risk of complex securities), rather than pricing inefficiencies.

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