# CFA Sample Exam Question

Question is: At yield levels that are high relative to the bond’s coupon rate, is the price of the option free bond higher than the price of an otherwise identical ---------------Callable-------------------Puttable A--------------No--------------------------No B-------------No--------------------------Yes C-------------Yes-----------------------No D-------------Yes-----------------------Yes The correct answer was C? I understand how the price cannot exceed the price of the puttable bond (i answered A.) but i cannot get why the price of the option free bond will be greater than the price of the callable bond. At high yields the price of the option free should be the same as the callable bond right? What am i missing?

I think it’s like this: Callable Bond = Option-free Bond - Call Putable Bond = Option-free Bond + Put Therefore: Option-free Bond > Callable Bond Option-free Bond < Putable Bond Is the price of the option free bond higher than Callable? Yes Is the price of the option free bond higher than Putable? No, it is lower.

True, but at higher yields the price should be the same for a callable and option free bond, since it is not likely to be called right?

CB = OFB - CV PB = OFB + PV At High yield value of CV approaches 0 CB ~ OFB (OFB being a bit higher) CB < OFB At High yield value of PV is high PB > OFB so answer is YES for CB and NO for PB

Thanks guys! My confusion was that i was thinking in terms of the yeidl curve where it shows negative convexity for callable bonds at low yield. I forgot to factor in the fact that even if it has +ve convexity at high yeilds the price has to be a little lower.

sv, i think the CFAI looks at it strictly from the formula point of view in which case the call option itself is not worth as much as the option-free bond, the combination of which make a complete callable bond. hope that helps. thats how i see it atleast.

The put provides an option to the investor to force the issuer to redeem the bond, protecting the investor against downside risk. Since this has value to investors, they will prefer a bond with a put to a bond without a put. This heightened demand for the bond with the put will make its price increase relative to the option-free bond. The call allows the issuer to redeem the issue at its option. Investors don’t like this because it complicates modeling, increases reinvestment risk, etc. So investors will prefer an option-free bond to a callable bond. The lower demand for callable bonds relative to option free bonds will result in their price being lower than option-free bonds. Thus, C is the answer. From the perspective of the investor, the best case is the putable bond, the second best is an option free bond and the worst case is the callable bond. Prices will reflect this. I believe the information about the coupon and yield rates is a distraction.

I think, even if the yield is high, the call would still have some time value, so the call wouldn’t be worth 0 unless it’s expired.

chebychev said it perfectly. All that other information is a distraction.

Basically increase in interest rates - call premiums go up increase in interest rates - put premiums go down. so plug into the formulas and … bingo.

I think like that since call option(from derivatives) always has some value (time value) , even if option is way out-of-money, so call option > 0, making callable bond always less than option-free bond.

so if yields are LOW then would the following be true ? Option-Free Bond > Callable Bond Option-Free Bond > Putable Bond

No. Regardless of yield-coupon relationships, the following holds with respect to prices (all else being equal): putable > option-free > callable

niraj_a Wrote: ------------------------------------------------------- > so if yields are LOW then would the following be > true ? > > Option-Free Bond > Callable Bond > Option-Free Bond > Putable Bond Nope

i gotcha now. thx ppl.