Callable and Putable Bonds

Question

Hi all, in need of some help with regards to callable and putable bonds.

At the beginning of Elan's Lecture Video 47 (Level II) - Valuing Bonds with Embedded Options, Peter Olinto gives a brief refresher on callable and putable bonds. He starts off by saying that the yield (or return) on a callable bond is given by the familiar formula:

( Price at end of period - Price at beginning of period + Coupons ) / Price at beginning of period = Yield

And since the price at the end of period is capped due to the call option, you’ll end up with a lower overall return (or yield) when compared to an option-free bond. Therefore, your OAS will be less than your Z-spread.

But then he says that since the call option reduces the initial value of the bond, the initial yield will be higher than an otherwise option-free bond, as compensation for bearing the call risk.

So as you can see, these seem like contradictory statements. Any thoughts?

vincentt · Answer

no worries @DollarsToDonuts‌ i'm glad it helped.

vincentt · Answer

Let's compare 2 exactly similar bonds side by side and the only difference is one with embedded call option.

Higher Initial Yield:
Since the issuer were given the option to call the bond, the issuer have to compensate the bondholder with extra yield. That is why a similar bond without call option would have a lower yield (higher price than the one with with a call option).
Price of Callable bond = Price of Option free bond - Option Cost
By purchasing a bond with call option at a lower price, assuming it did not hit the exercise price, the bond with a call option will produce a higher yield than a similar bond without the call.

Lower Overall Return:
As I/R falls the bond price will increase but the increase in price will 'slow down' as it gets closer to the exercise price. Whereas the price of a similar bond without a call option will continue to increase.