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Convertible Bonds

admin — Tue, 21 Apr 2009 16:48:04 +0000

Conver tible bonds are bonds issued by companies that have an embedded option that entitles the holder to exchange the bond for a predeﬁned amount of equity in the company at a speciﬁed price. In some countries conver tible bonds are referred to as debentures. The price of such a conver tible bond is given by the following:
Conver tible bond price = Straight bond price + Value of stock call option
The conversion terms for individual issues vary widely. There is nothing to stop a company issuing a bond that contains an embedded option that gives the issuer the right to force conversion. In this case the holder of the bond has effectively sold a put option on the bond:
Conver tible bond price = Straight bond price − Value of bond put option
Most equity analysts dislike having to incor porate the effects of conver tible instruments because they complicate calculations of future fully diluted earnings per share (EPS) and hence valuations. Institutional investors are likely to be able to take account of the potential dilution from the issue of new shares; this is not, however, true for most retail investors.

Putable Bonds

admin — Tue, 21 Apr 2009 10:47:26 +0000

Putable bonds are the opposite of callable bonds and entitle the holder of the bonds to sell them back to the issuer before the maturity date. This is equivalent to the issuer of the bond writing a put option:
Value of putable bond = Value of equivalent straight bond + Value of put option
The put option gives the holder of the putable bond some protection against the effects of higher yields (which may be due to upward shifts in the yield cur ve or may be due to a widening of credit spreads). If market prices fall below the put price the bondholder can exercise their option at the put price.
As the holder of the bond and the holder of the put option are the same party we can get the price of the putable bond by simply adding together the two.The effect is a form of price compression, as yields rise and the bond’s price approaches that of the put price fur ther price falls are truncated. The put price is $7500.
Putable bonds are wor th more than their vanilla equivalent and trade at higher yields to maturity. Put options on long-term bonds are potentially dangerous to issuers because their exercise is out of the control of the issuer.
Bondholders may demand such an option because of concerns about a company’s creditor thiness. The protection offered by put options is, however, limited. If credit spreads at a par ticular issuer widen this is likely to be because of speciﬁc problems or weaknesses at the issuer. In the event that bondholders seek to exercise their put option the company may not be able to honor its commitment.

Callable Bonds

admin — Mon, 20 Apr 2009 20:39:37 +0000

Some cor porate bonds are issued as callable bonds. These are bonds issued that contain an option exercisable at the discretion of the issuer to “call” or redeem the bond at a par ticular price. The exact call conditions are often more complicated than this but we will look at the case of a single call price where in the event of the issuer calling the bond it buys back all issued bonds.
This call option alters the way in which the bond’s price changes. We will use a 15-year bond with a coupon rate of 4.5% trading at $8000. The call price is $10 000, the bond’s par value. In effect while the issuer of the bond has sold a bond the buyers of the bond have also written a call option to the issuer.
(The reader should bear in mind that corporates cannot in practice issue bonds with such long terms but the longer term makes it easier to see the how the bond’s value is affected by the presence of the option.)
As yields-to-maturity fall the value of the vanilla bond rises. The position for the writer of the call option is opposite. As the bond’s price rises the writer’s losses increase. These are shown in the ﬁrst of the following two char ts.
As the holder of the bond and the writer of the call option are the same party we can get the price of the callable bond by simply adding together the two positions. The effect is a form of price truncation, as yields fall and the bond’s price approaches that of the call price fur ther price increases are truncated.
We can express this as follows:
Value of callable bond = Value of equivalent straight bond − Value of call option
The exact terms of the call option vary in terms of call price and call schedule. Some bonds are issued with a schedule of possible call dates, call price on each date and may specify a maximum percentage of the issue that can be called on each date. When comparing yields-to-maturity of callable bonds to other bonds one of two yields is used:
Yield-to-call. The yield-to-call is the yield of the bond assuming it is called at the call price at the next call date.
Yield-to-worst. The yield-to-worst is used for callable bonds with a schedule of call dates and call prices. The yield-to-worst is the yield-to-call for the call for the combination that is most disadvantageous to the holder of the bond.
Callable bonds have lower value than equivalent vanilla bonds. When issued pricing has to reﬂect the “premium” paid to the writer of the call option. Callable bonds always have lower yield-to-maturity than their vanilla equivalent.