# Elan Lecture Video: Reading 47 - Valuing Bonds with Embedded Options

Hi all,

At the beginning of 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 intial value of the bond, the initial yield will be higher than an otherwise option-free bond , as compensation for bearing the call risk.

So which is it? Does a callable bond have a lower yield or a higher yield than an option free bond?

The OAS of a callable bond is (essentially) the Z-spread of the corresponding noncallable bond, and the Z-spread of a callable bond is higher than its OAS. As a higher spread means a higher yield, callables start at a higher yield than the corresponding noncallable bonds.

Whether the realized yield is higher or lower depends on when the bond is sold (or called), and at what price, and what the original price difference was. There’s not a single answer that covers all cases.

Perfect, thanks so much!

You’re welcome.