A convertible security or convertible is a hybrid security with a provision for the convertible to be exchanged for some other security. Usually, conversion is at the security holder's option, but a mandatory convertible security requires conversion, usually according to some schedule. Most convertibles are either convertible preferred stock or convertible bonds issued by a corporation and convertible to that corporation's common stock any time, at the security holder's option. These standard convertible securities are the topic of this article. Convertible securities have a par value, and their yield is quoted as a percentage of par. Each security may be converted into a fixed number of common shares. That number is the security's conversion ratio. For example, if a convertible bond's conversion ratio is 12.5, and the bond has a par value of USD 1,000, then each USD 80 of par value can be converted into a single share. This number is called the conversion price:
Convertibles routinely have an anti-dilution provision, which adjusts the conversion ratio as appropriate in the event of a stock split or stock dividend. Some convertibles have a conversion ratio that changes according to a fixed schedule. For example, a convertible bond's conversion ratio might be 12.5 for the bond's first five years and then drop to 11 after that. As is typical of hybrid securities, convertibles can be difficult to value. Further complicating valuation, convertibles may have additional embedded options or features. Many are callable after a few years of call protection. When called, holders are forced to either surrender the security for the call price or convert them. If they convert, the transaction is called a forced conversion. Some convertibles have a put feature, allowing holders to return the security to the issuer for some fraction of par value on certain dates. A convertible's investment value is what the market value of the convertible would be if it were stripped of its conversation feature. This reflects the security's future cash flows, current interest rates, the issuer's credit quality, and any other features such as put or call provisions other than the conversion option. Investment value isn't generally observable in the marketplace, but it is a useful notion that can be ascribed a value using standard bond pricing or financial engineering methodologies. A convertible's conversion value (or parity value) is the value that could be realized by immediately converting the convertible to common stock. It is easily calculated as
These notions—investment value and conversion value—are important because a convertible's market price should always exceed both quantities. Otherwise, arbitragers will step in and start accumulating the convertible, thereby driving up its market price. The two quantities are often quoted as premiums:
Obviously, both premiums should be nonnegative. Exhibit 1 illustrates how a convertible's market price depends upon the underlying stock price. Both the investment value and conversion value are plotted. The investment value is fairly flat at higher stock prices but drops off as the stock price falls. This reflects the fact that the credit quality of the issuer is likely to fall with a marked decline in the stock price. By [2], the conversion value is a simple linear function of stock price. The convertible's market price is also plotted.
Practitioners tend to distinguish between four modes of behavior of a convertible bond, depending upon the level of the underlying stock and the issuer's credit quality. Usage is hardly standardized, but we may distinguish between
modes of behavior. These are also indicated in Exhibit 1. A convertible's behavior is equity-like when its conversion value exceeds its investment value, and the bond behaves like an in-the-money option. Its value fluctuates almost directly with the underlying stock price. The convertible's behavior is hybrid- or option-like at lower stock prices where the conversion value is less than the investment value but there is still a reasonable likelihood of the stock price rising enough to make conversion attractive. In this state, the convertible exhibit's truly hybrid behavior. Its market price is sensitive to the underlying stock price, interest rates, implied volatilities and the issuer's credit quality. At still lower stock prices, the conversion option is so far out of the money that it is almost worthless. Here, the convertible is called busted. Its behavior is much like a non-convertible bond or other fixed income instrument. Its market price fluctuates with interest rates and the issuer's credit quality. Finally, if the issuer becomes financially troubled, its credit rating will fall well below investment grade and the stock price will plummet to very low levels. Here the conversion feature is all but irrelevant. The convertible is a distressed security whose market price fluctuates primarily with the credit quality of the issuer. Because convertibles can be so difficult to value, there is a perception that they are frequently mispriced in the market. Convertible arbitrage is a market neutral trading strategy that seeks to profit from such mispricings.
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