# OAS

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a) Is the option adjusted spread (OAS) the Yield WITHOUT the option?

b) Is this chart I made correct?

http://alecsobel.com/call.gif

In other words, the order of yields is:

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Here are my thoughts on the topic. Hopefully, this won’t confuse you further. Also, I tried to decipher your chart, but it has TMI, so I didn’t bother to analyze it further.

OAS accounts for the value of the option. It may be useful to imagine the formulas of callable bonds, putable bonds, and options when thinking about OAS:

P(CB) = P(NCB) - P(Option)
P(PB) = P(NPB) + P(Option)
where:
CB = Callable Bond
PB = Putable Bond
NCB = Non Callable Bond
NPB = Non Putable Bond

Notice that P(Option) can be represented as:
P(Embedded Option in Basis Points) = Z-Spread - OAS
Thus, OAS = Z-Spread - P(Embedded Option in Basis Points)

From an investor’s standpoint, for the callable bond, the option cost is POSITIVE. The option cost (to the investor) is POSITIVE because the issuer has the option to call the bond. Based on the above formula, the OAS of the callable bond will be lower because you’re subtracting the POSITIVE cost. Ultimately, the OAS will be lower than the Z-spread, and by association, lower than the nominal spread.

From an investor’s standpoint, for the putable bond, the option cost is NEGATIVE. The option cost (to the investor) is NEGATIVE because the bondholder has an advantage over the issuer. Based on the above formula, the OAS of the putable bond will be higher because you’re subtracting the NEGATIVE cost (thereby ADDING to the Z-Spread). Ultimately, the OAS will be higher than the Z-spread, and by association, higher than the nominal spread.

I typed this up hastily, so if someone sees an error/typo, please point out.

Hope this helps.

thanks for the help,

I’m confused, isn’t it the opposite?

If I invest/buy a callable bond isn’t that bad for me? The bond writer can whip it back out of my hands. Why is that positive value?

If I invest in a put-able bond isn’t that good for me? I can avoid losses.

You’re thinking in terms of the value of the ENTIRE bond! Please re-read my previous note, and try and distinguish between the cost of the entire bond and the cost of the option.

When you buy a callable bond, of course it is bad for you. So the cost to you, the investor, is positive.

When you buy a putable bond, of course it is good for you. So the cost to you, the investor, is negative. Think of it this way: you must pay extra to put the bond back on the issuer. Makes sense?

Okay I understand now! thanks so much,

It turns out my chart was correct after all.
Sorry if it had too much info.