Handbook example question 18.5

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Hi David,

Could you please help me with the following question?

Two comparable (same credit rating, maturity, liquidity, rate) U.S. callable corporate bonds are being
analyzed by you. The following data is available for the nominal spread over the U.S. Treasury yield curve
and Z spread and option adjusted spread relative to the U.S. Treasury spot curve
X Y
Nominal spread 145 130
Z spread 120 115
OAS 100 105
The nominal spread on the comparable option free bonds in the market is 100 basis points. Which of the
following statements is correct?
a. X is undervalued.
b. Y is undervalued.
c. X and Y both are undervalued.
d. Neither X nor Y is undervalued.
Answer: b

Why is b correct? I read the explanation on the handbook but still have no clue. Thanks a lot for any help!

 

[[email protected]]

Hi David,

Not sure if you've seen this post.... Hope you would help me with this problem. Thanks!!

 

[AG]

Simply put, the lower the option cost, the cheaper the bond is.
Option cost for X=120-100=20bp, for Y=10bp.

Also, OAS does not account for option risk. Thus, the compensation for bearing credit and liquidity risk in X is 100 bp, however, the compensation for bearing the same risk for Y is higher (105 bp). Thus Y is a better investment, and hence it should be undervalued or trading cheap.

Let me know if it explains.

 

[David Harper CFA FRM]

Ganish, thank you! David

 

[[email protected]]

Thank you for your help, Ganish!
I have a question for your first statement. The buyer of callable bonds shorts the call option. Should it be the higher the option cost, the cheaper the bond?

 

[AG]

Idcn, your question got me thinking...

The question is about the relative value, not the absolute price. In terms of absolute price, yes, the investment with a higher option cost is priced low, but then, the higher option cost reflects the higher pre payment risk cancelling out the effect of lower absolute price.

In terms of relative value however, the correct choice is the one with a lower option cost, since everything else being same, you will need a lower price to buy back the call option to make it option free and arrive at the similar set of cash flow...

Let me know if it's ok...

 

[[email protected]]

Ganish, I am a bit confused about the relative price and absolute price.

For this problem, I agree with your comments below.

Also, OAS does not account for option risk. Thus, the compensation for bearing credit and liquidity risk in X is 100 bp, however, the compensation for bearing the same risk for Y is higher (105 bp). Thus Y is a better investment, and hence it should be undervalued or trading cheap.

David, would you have more comments?