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Subject 8. Valuation and Analysis of Convertible Bonds PDF Download
Defining Features of Convertible Bonds

Convertible bonds are bonds that can be converted into common stock. The option allows investors to convert the bond in the issuer's equity or in stocks of some other issuer (in the latter case, the bond is called exchangeable).

Suppose you can buy a 10%, 15-year bond today for $90 that can be converted into 10 shares. The value of a comparable straight is $84. Market price of stock = $5; no dividends.

Conversion ratio = number or shares that investors receive upon conversion (10).

Conversion price = market price of the convertible bond / conversion ratio (90 / 10 = $9). It can be viewed as a break-even price: once the actual market price of the stock rises above the market conversion price, any further stock price increase is certain to increase the value of the convertible bond by at least the same percentage.

The conversion price is referred to as "initial conversion price." It is adjusted in case of corporate actions, such as stock splits, bonus share issuances, and rights and warrants issuances.

Convertible bondholders may receive compensation when the issuer pays dividends to its common shareholders, and they may be given the opportunity to either put their bonds or convert their bonds into shares earlier and at more advantageous terms in the case of a change of control.

For example, a convertible bond can be putable. There are two types of put embedded in convertible securities:

  • Hard put - investors have the right to exchange their bonds for cash.
  • Soft put - when a put is exercised, the issuer may choose whether to pay cash for the bonds or to exchange these securities for common stocks or debt.

A convertible bond can be callable with a lockout period. If the underlying share price increases above the conversion price, or the interest rates decline significantly, a forced conversion may occur - bondholders will be forced to convert their bonds into shares, before the bond is called by the issuer. This attributes caps the capital appreciation potential of a convertible bond.

Analysis of a Convertible Bond

Continue with the example above.

Conversion value = market price of stock x conversion ratio (5 x 10 = 50).

Straight value = Value of the same bond with call and put options, but without the conversion option ($84). The value acts as a floor for the convertible security's price.

Note that the straight value at some future date is unknown: the value will change as market interest rates change or if the issuer's credit quality changes.

The minimum price of a convertible bond is the greater of its conversion value and its straight value.

Market conversion price = convertible bond price / conversion ratio ($90/10 = $9)

Market conversion premium per share = market conversion price - current market price = 9 - 5 = $4 per share. An investor who purchases a convertible bond rather than the underlying stock, effectively pays a premium over the current market price of the stock. The market conversion premium per share can be seen as the price of a call option.

Market conversion premium ratio = market conversion premium per share / market price of common stock = $4 / $5 = 80%.

Premium over straight value = market price of convertible bond / straight value - 1 = ($90/$84) - 1 = 7.14%. The greater the premium over straight value, the less attractive the convertible bond. This is an imperfect indicator of downside risk, since the straight value itself is subject to changes when interest rates change.

Valuation of a Convertible Bond

The arbitrage-free framework can be used to value convertible bonds, including callable and putable ones. Each component can be valued separately.

Convertible bond value = straight value + value of the call option on the stock

Convertible bonds are usually callable:

Callable convertible bond value = straight value + value of the call option on the stock - value of the call option on the bond

Suppose that the callable bond is also putable. Therefore, convertible bonds' value consists of the following components:

Convertible bond value = straight Value + value of the call option on the stock - value of the call option on the bond + value of put options on the convertible - Value of call options on the convertible

Risk-Return Characteristics of a Convertible Bond

The risk-return characteristics of a convertible bond depend on the underlying share price relative to the conversion price.

  • When the underlying share price is well below the conversion price, the convertible bond becomes a "busted convertible" which exhibits mostly bond risk-return characteristics.
  • When the underlying share price is well above the conversion price, the convertible bond exhibits mostly stock risk-return characteristics.
  • In between these two extremes, the convertible bond trades like a hybrid instrument.

Assume that the straight value remain constant:

  • The downside risk is reduced: If stock price falls, returns on convertible bonds exceed those of the stock.
  • When stock price rises, the bond will under-perform because of the conversion premium.
  • If the stock remains stable, return on the bond may exceed the stock return due to the coupon payments from the bond.

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