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?