Option adjusted spread

Hi guys, a quick question regarding OAS. I recently found a question on a mock which read:

A putable bond has an OAS of 5%. Analysts estimate that that the value of the embedded option is 1%. What is the closest estimate of the z-spread?

A. 4%

B. 5%

C. 6%

I was under the impression that the value of the embedded option=z-spread-OAS, which would make the answer C. The mock gives the answer as A, with little explanation.

Does this formula change when the bond is puttable as opposed to callable? Thanks for the help.

Since it is a putable bond the value of the option is greater than zero which means you must subtract it from the OAS of 5%.

I usually remember it as since a putable bond is a plus for the holder of the bond, they take reduced yield in favor of the right to sell it in case interest rates go higher. The opposite is true for a callable bond where the % price of the call must be added to the spread to compensate for call risk.

I’m sure a charterholder would have a much more in depth explanation for this though. Hope this helps a little!

The problem is that either the question writer was trying to be too clever, or the analysts are idiots.

When we talk about spreads and the value of options, we always do so from the viewpoint of the investor (bondholder): a Z-spread of 150bp means that the investor is earning 1.5% above the Treasury rates; an OAS of 200bps means that the investor is earning 2.0% above Treasury rates, and so on.

With that convention, the value of the put option is not 1%; it’s -1%. The investor is earning a lower spread because of the option, not a higher spread. And, lo and behold, if you use -1% in your formula (which is correct, by the way, and doesn’t change between call options and put options), you get:

Z-spread – OAS = option value

Z-spread – (5%) = -1%

Z-spread = 4%