Sign up  |  Log in

OAS and Z spread

Hi all,

I’m having trouble grasping the z spread and OAS spreads clearly. It seems that a z-spread > OAS means that the issuer has a call option. My confusion is that wouldn’t the lower OAS mean that the bond is discounted at a lower rate, thus a higher present value than without the call option. Why would somebody be willing to pay more when there is a call option? 

Thanks in advance and let me know if my explanation needs any clarification. 

Make the most of your CFA exam prep in one weekend! Join renowned instructors, Peter Olinto, Darren Degraaf & David Hetherington in May for a live, two-day CFA intensive final review class.

You’re mixing up the spreads: the Z-spread applies to the value of the bond with the option included; the OAS applies to the value of the bond with the option removed.  Thus, a higher Z-spread than OAS would say that the price of a callable bond is lower than the price of an identical, noncallable bond.

OAS, as you know, abbreviates Option-Adjusted Spread.  The “option-adjusted” part of that phrase means “adjusted for the value of the option”; i.e., with the value of the option removed: it’s the spread that applies to a bond without the option in question.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

I just wanna say this question is one of the most confusing in curriculum at all.

Is there any mnemonics to remember all this?

carbolic wrote:
I just wanna say this question is one of the most confusing in curriculum at all.

Is there any mnemonics to remember all this?

If you want merely a mnemonic, perhaps you could use something like this:

  • Callable bond: lower price than a noncallable, lower OAS than Z-spread
  • Putable bond: higher price than a nonputable, higher OAS than Z-spread

However, I, for one, would prefer understanding why this is true, rather than simply memorizing it.  Furthermore, the understanding isn’t all that difficult.

See my post above for why it’s true.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

                              Price                                                                         Suggestion to Mnemonic

Callable           lower                   compared to noncallable          CLeaN

Putable            lower                    compared to nonputable          PLaiN

                                                                                               Suggestion to Mnemonic

Callable           lower   OAS than Z-spread                      CLOsed

Putable            lower   OAS than Z-spread                      PLOsed

Magician, it makes sense.

Putable bond is more expensive because it gives the bond holder the right to sell, thus an advantage to the bond holder, thus a higher OAS than Z Spread. If we remove this option, the bond holder does not have this benefit, thus the price of the bond drops and yields go up (higher OAS). If we include this option, the spread is lower (price is higher) because the option is an advantage to the bond holder.

The Doobs

doobsmeister wrote:
Magician, it makes sense.

Good to hear.

doobsmeister wrote:
Putable bond is more expensive because it gives the bond holder the right to sell, thus an advantage to the bond holder, thus a higher OAS than Z Spread. If we remove this option, the bond holder does not have this benefit, thus the price of the bond drops and yields go up (higher OAS). If we include this option, the spread is lower (price is higher) because the option is an advantage to the bond holder.

Yup.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

S2000magician wrote:

You’re mixing up the spreads: the Z-spread applies to the value of the bond with the option included; the OAS applies to the value of the bond with the option removed.  Thus, a higher Z-spread than OAS would say that the price of a callable bond is lower than the price of an identical, noncallable bond.

OAS, as you know, abbreviates Option-Adjusted Spread.  The “option-adjusted” part of that phrase means “adjusted for the value of the option”; i.e., with the value of the option removed: it’s the spread that applies to a bond without the option in question.

You’re a saviour. Couldnt have understood this better. The mnemonics is the icing. Thank you.

You’re too kind.

It’s my pleasure.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

S2000magician wrote:

You’re mixing up the spreads: the Z-spread applies to the value of the bond with the option included; the OAS applies to the value of the bond with the option removed.  Thus, a higher Z-spread than OAS would say that the price of a callable bond is lower than the price of an identical, noncallable bond.

OAS, as you know, abbreviates Option-Adjusted Spread.  The “option-adjusted” part of that phrase means “adjusted for the value of the option”; i.e., with the value of the option removed: it’s the spread that applies to a bond without the option in question.

To help me engrain this: magician, if most investors are using arbitrage-free valuations, have you experienced that most OAS spreads, all else fixed, are roughly equal? Or, do the different methods of modeling short-term rates cause an OAS spread dispersion?

clangerh wrote:
S2000magician wrote:
You’re mixing up the spreads: the Z-spread applies to the value of the bond with the option included; the OAS applies to the value of the bond with the option removed.  Thus, a higher Z-spread than OAS would say that the price of a callable bond is lower than the price of an identical, noncallable bond.

OAS, as you know, abbreviates Option-Adjusted Spread.  The “option-adjusted” part of that phrase means “adjusted for the value of the option”; i.e., with the value of the option removed: it’s the spread that applies to a bond without the option in question.

To help me engrain this: magician, if most investors are using arbitrage-free valuations, have you experienced that most OAS spreads, all else fixed, are roughly equal? Or, do the different methods of modeling short-term rates cause an OAS spread dispersion?

I spent the bulk of my time at PIMCO developing prepayment models for mortgage-backed securities.  The objective was to determine for ourselves the correct OAS, rather than rely on OAS estimates from outside sources (e.g., Bloomberg).  Ultimately, our numbers sometimes came very close to those from outside sources, and sometimes differed substantially (especially for CMO tranches).

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

Appreciate you sharing–really cool to hear.

S2000magician wrote:

You’re mixing up the spreads: the Z-spread applies to the value of the bond with the option included; the OAS applies to the value of the bond with the option removed.  Thus, a higher Z-spread than OAS would say that the price of a callable bond is lower than the price of an identical, noncallable bond.

OAS, as you know, abbreviates Option-Adjusted Spread.  The “option-adjusted” part of that phrase means “adjusted for the value of the option”; i.e., with the value of the option removed: it’s the spread that applies to a bond without the option in question.

Great explanation. I was refreshing my memory and I think many people are tripped up about this (judging by the number of posts on this topic) because Schweser’s explanation makes it sound as though the Z spread does not capture the option cost with this sentence, “While the Z spread is based on the on-the-spot rate curve instead of a single YTM benchmark, it still does not consider embedded option features.

Then when it talks about OAS next, we might think that the OAS is the one that captures embedded option features and, therefore, the OAS must be higher than the Z spread in order to make the callable bond trade at a lower value.

pheonixza wrote:

S2000magician wrote:

You’re mixing up the spreads: the Z-spread applies to the value of the bond with the option included; the OAS applies to the value of the bond with the option removed.  Thus, a higher Z-spread than OAS would say that the price of a callable bond is lower than the price of an identical, noncallable bond.

OAS, as you know, abbreviates Option-Adjusted Spread.  The “option-adjusted” part of that phrase means “adjusted for the value of the option”; i.e., with the value of the option removed: it’s the spread that applies to a bond without the option in question.

Great explanation. I was refreshing my memory and I think many people are tripped up about this (judging by the number of posts on this topic) because Schweser’s explanation makes it sound as though the Z spread does not capture the option cost with this sentence, “While the Z spread is based on the on-the-spot rate curve instead of a single YTM benchmark, it still does not consider embedded option features.

Then when it talks about OAS next, we might think that the OAS is the one that captures embedded option features and, therefore, the OAS must be higher than the Z spread in order to make the callable bond trade at a lower value.

Yeah I can see how that’s confusing.  The missing part (I think) is that the market price already factors in an option cost.  That is, the market will price a callable lower than an option free bond.  From there, Z spreads are added when rates follow the forwards, which will never consider the option being exercised (realistically, clients would never buy callables structured in such a way that the bond is expected to be called when rates follow the forwards).  OAS is calculated using Monte Carlo simulations, by taking lots and lots of potential rates paths and adding the spread just as in the Z spread case.  However, with random rates paths you would inevitably come across many paths where the bond gets called.  That is why the CFA explanation is true and makes sense, but you have to dig in a little bit.

By the way, the above intuition isn’t entirely correct for MBS (because even along the forwards there’s a certain expectation for prepayments), but the general intuition is similar and really the curriculum doesn’t treat MBS deeply enough to care about this nuance.