Discrimination of Callable Bond, Puttable Bond and Convertible Bond
　　1           Callable Bond
　　1.1          Definition
　　Callable bonds are bonds that the issuer may repurchase or call at some fixed set of prices on some fixed set of dates. The purpose is to call back the bond when the cost of issuing new debt is lower than the current coupon paid on the bond.
　　1.2          Analogy
　　Callable bond can be decomposed into a long position in a straight bond minus a call option on the bond price.
　　1.3          Negative Convexity
　　When the prevailing market yield for comparable bonds is higher than the coupon rate on the callable bond, it is unlikely that the issuer will call the issue so that the callable bond will have a similar price/yield relationship as an otherwise comparable option-free bond. As yields in the market decline, the concern is that the issuer will call the bond. The value of the embedded call option increases as yields approach the coupon rate from higher yield levels. Therefore, it reduces the price relative to an otherwise comparable option-free bond. This characteristic that price appreciation is less than price decline when rates change by a large number of basis points is called negative convexity.
　　1.4          MBS
　　Owing to changes in prepayment rates, the price/yield relationship of MBS is similar to that of the callable bond which exhibit price performance that is generically referenced as negative convexity. Since prepayments increase when rates decline, MBSs shorten in average life and duration. Conversely, when the bond market sells off, mortgage average lives and durations lengthen.
　　2           Puttable Bond
　　2.1          Definition
　　Puttable bonds are bonds that the investor has the right to put the bond back to the issuer at fixed prices on fixed dates. The purpose is to dispose of the bond when its price deteriorates.
　　2.2          Analogy
　　Puttable bond can be decomposed into a long position in a straight bond plus a put option on bond price.
　　3           Convertible Bond
　　3.1          Definition
　　Convertible bonds are bonds issued by a corporation that can be converted into equity at certain times using a predetermined exchange ratio. The purpose is to partake in the good fortunes of the company.
　　3.2          Analogy
　　Convertible bond can be decomposed into a long position in a straight bond plus a call option on stock price.
　　4           Example
　　4.1          FRM EXAM 2003-QUESTION 95
　　With any other factors remaining unchanged, which of the following statements regarding bonds is not valid?
　　a.       The price of a callable bond increases when interest rate increases.
　　b.       Issuance of a callable bond is equivalent to a short position in a straight bond plus a long call option on the bond price.
　　c.       The put feature in a puttable bond lowers its yield compared with the yield of an equivalent straight bond.
　　d.       The price of an inverse floater decreases as interest rates increase.
　　Answer: a
　　Answer b is valid because a short position in a callable bond is the same as a short position in a straight bond plus a long position in a call (the issuer can call the bond back). Answer c is valid because a put is favorable for the investor, so it lowers the yield. Answer d is valid because an inverse floater has high duration.
　　4.2          FRM EXAM 2009-QUESTION 4-16
　　From the time of issuance until the bond matures, which of the following bonds is most likely to exhibit negative convexity?
　　a.       A puttable bond
　　b.       A callable bond
　　c.       An option-free bond selling at a discount
　　d.       A zero-coupon bond
　　Answer: b
　　A callable bond is short an option, which creates negative convexity for some levels of interest rates. Regular bonds, as in answer c and d have positive convexity, as well as puttable bonds.
　　4.3          FRM EXAM 2009-QUESTION 3-20
　　What is the effect on the value of a callable convertible bond of a decrease in interest rate volatility and stock price volatility?
　　a.       An increase in value due to both interest rate volatility and stock price volatility
　　b.       An increase and decrease in value, respectively
　　c.       A decrease and increase in value, respectively
　　d.       A decrease in value due to both
　　Answer: b
　　A decrease in stock price volatility decreases the value of the equity conversion option and thus the convertible bond price. A decrease in interest rate volatility decreases the value of the interest rate call option. Because the bond investor is short the interest rate option, this increases the value of the convertible.
　　Reference:
　　1)        Bruce Tuckman, Fixed Income Securities
　　2)        Frank J. Fabozzi, The Handbook of Fixed Income Securities
　　3)        Handbook
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