# callable bond price change

Team - if interest rates rise, how does the price of the callable bond rise slower than the price of a an optionless bond? confused here, at work w/out materials… thanks for your help! m

do you have schweser? They have a great picture of this. Not sure if this pic is in CFAI tesxt. It is b/c of negative convexity- you could google that too. So when rates go down, normal bonds will go up, but callable bonds are “capped” and don’t go up by much, or could even go down at a certain point, because the likelihood of the bond getting called goes up. This is bad for you the bondholder, so the value of it goes down. Does that help?

Remember, rates increase = bond value decrease. I think what you’re actually asking is when interest rates rise, why does a callable bond’s value "decrease " less than that of a straight bond. Price of Callable bond = Price of Straight Bond - Value of Call Option Lets use #s: Option Bond = \$100 Straight Bond = \$105 Value of Call = \$5 Callable / Straight / Call Option Value 100 = 105 - 5 If rates increase, the price of the straight bond decreases. At the same time, the value of the call option decreases - if rates rise, the company is borrowing at a rate lower than the current market rate, so they are less likely to prepay (a.k.a. call) the debt. Since the option less likely to be exercised, it is worth less. So lets say the straight bond declines in value \$2 and the call option declines \$1: Callable / Straight / Call Option Value 99 = 103 - 4 Since the option is now worth less to the borrower, it cushions the impact of the rate decline: the callable bond only declined \$1 (100-99) while the straight bond declines \$2 (105-103).

Also, if rates decline, callable bonds increase in value slower than straight bonds because they are more likely to be called, due to negative convexity as Andrew mentioned above. Think of the extreme…if I took out a mortgage loan at 5% that had a call (prepayment) option, and rates went to 0%, you’d bet that I would prepay all of that 5% debt and refinance at the new market rate of 0%. Same kind of idea with callable bonds…the lender (investor) has a risk of having their investment called if rates decline, so the bond is less attractive, and is priced lower than a straight bond. msr Wrote: ------------------------------------------------------- > Team - > > if interest rates rise, how does the price of the > callable bond rise slower than the price of a an > optionless bond? > > confused here, at work w/out materials… > > thanks for your help! > m

well, i was also wondering if that was a typo, thanks Thisisbrianly for the precision, i mean about the interest rise, so price decrease

excellent. thanks team m