I am confused about question 20 on page 595 of the Equity/Fixed Income book. The question has to do with whether at yield levels close to a bond’s coupon rate, the price of an option-free bond will be higher than an otherwise identical callable or putable bond.
The CFAI answer says: yes, an option-free bond will have a higher price than an otherwise identical callable bond; and no, an option free-bond will not have a higher price than an otherwise identical putable bond.
My thinking for choosing “no” to both callable or putable – since if the yields are close to the bond’s coupon, there’s no motivation for the issuer to call, or for the buyer to put, therefore wouldn’t the prices for the callable and putable bond be the same as for the otherwise identical option-free bond?
_ Always _. (If they’re extremely out-of-the-money that value may be negligibly positive, but it’s still positive.)
Because options have value, the owner of the option has to pay for that option.
If a bond has an embedded call option, the issuer owns the option and therefore has to pay for it. There are broadly two ways he can do this: pay a higher coupon on the bond, or sell the bond for a lower price.
If a bond has an embedded put option, the bondholder owns the option and therefore has to pay for it. There are broadly two ways he can do this: accept a lower coupon on the bond, or pay a higher price for it.
So, if you have three bonds with the same maturity, coupon, and all other risks, one without any embedded options, one with an embedded call option, and one with an embedded put option, the callable will sell at the lowest price, the option-free’s price will be in the middle, and the putable will sell at the highest price.