Z spread vs zero vol OAS

[shanlane]

Hello,

The assigned reading seemed to make a distinction between these two concepts, but in the notes the Z spread is often used in lieu of the zero vol OAS. Is there a difference between these two concepts? If so, what is it? Are there times when both mean the same thing?

Also, the idea that the OAS decreases as vol increases is a bit confusing. It seems like as the volatility increases, the option would be worth more. In this case, the MBS holder would be short this option and the bond would be worth less. If the bond is worth less, wouldn't the spread be higher? I am probably overlooking something very simple, but if you could point me in the right direction that would be great.

Thanks!

Shannon

 

[David Harper CFA FRM]

Hi Shannon,

Yes, I think there is a theoretical difference: the Z spread is the spread added to the Treasury's (risk free) theoretical spot rate curve; while the zero-volatility OAS spread adds to a single Treasury spot rate interest rate path, which could be different in the same way we can decide to assume a risk free zero rate curve different than the one we observe (the former is an objective property we can infer from the market; the latter could vary as a design choice in treating the single path as a special case of the MCS). So the difference can be in the "spread above what?" The Z-spread implies a spread above an objective Treasury zero; a zero-volatility OAS implies, per a model, that we might utilize a subjective variant on the same. I do agree the Valuation MBS chapter opens the door to the difference, but the reading also uses "zero volatility" in the Z-spread chapter, as a synonym, so it is really indecisive on the difference IMO. Further, Fabozzi (like the CFA) generally treats them as synonyms; e.g.,

"Zero-Volatility Spread The zero volatility spread or Z-spread is a measure of the spread that the investor would realize over the entire Treasury spot rate curve if the bond is held to maturity. It is not a spread off one point on the Treasury yield curve, as is the nominal spread. The Z-spread, also called the static spread, is calculated as the spread that will make the present value of the cash flows from the non-Treasury bond, when discounted at the Treasury spot rate plus the spread, equal to the non-Treasury bond’s price. A trial-and-error procedure is required to determine the Z-spread ... Why is the spread referred to as ‘‘option adjusted’’? Because the security’s embedded option can change the cash flows; the value of the security should take this change of cash flow into account. Note that the Z-spread doesn’t do this — it ignores the fact that interest ate changes can affect the cash flows. In essence, it assumes that interest rate volatility is zero. This is why the Z-spread is also referred to as the zero-volatility OAS." -- page 141 then 147 , Fabozzi Fixed Income, 2nd Edition

So, I thought about this a lot, but for our (FRM) purposes, I decided to go with: Z-spread = zero-volatility OAS spread.

Your second point is great, it comes up a lot, it's very confusing. I *think* the first key is to realize all of the following spreads are inferred from the current price: yield (YTM), Z-spread, OAS.
The relationship is: option cost = Z-vol OAS - OAS; the term on the left is not found directly, it's just the difference between the two terms on the right, themselves inferred from market prices (much like we infer implied volatility from traded option prices).

It might be more useful, from the perspective your question, to view the relationship as: OAS + option cost = Z spread; where higher option cost will increase the Z spread

Okay, so imagine I sell you a vanilla bond (no options), you will pay a price of $90 and the implied Z-spread (~ nominal yield; not the same just close) = OAS = 6%.

Now, assume exact same bond, and the same Treasury zero curve, but assume I switch to a mortgage bond with the prepayment risk (option).
You will no pay less (the difference is your compensation for writing me an option), so maybe you you now will pay $86 where: OAS = 6% + 1% option cost = Z-spread of 7% ~= nominal spread of 7%. The OAS is inferred from the lower price.
i.e., figure you are going to re-price the bond to ensure you keep an "effective" 6% (the OAS is your best guess at the yield if the prepayments happen per your interest rate model), in both scenarios, your "net net" yield is 6.0%, but now there is a nonzero option cost, so this means the Z-spread (and the nominal spread) need to increase to compensate you for the option you are writing.

It's not exactly cause-effect like that, but if we view the price as function of discounting the Z-spread/nominal spread, and the OAS as lower "implied yield" after we incorporate losses due to prepayment, then we can see how: higher interest rate volatility --> increase option cost -> increases the Z-spread (~ nominal) --> decreases bond price

I hope that helps, thanks!

 

[shanlane]

Thank you. I think I get the idea of OAS a lot better now, but the idea that it gets smaller as volatility increases is still a mystery. As you said, when volatility increases the option cost would certainly increase, as would the Z spread, and therefore the price of the bond would decrease. I have read in a few different places (including here in Fabozzi) that as the vol increases the OAS decreases and I cannot make that make sense no matter how hard I try Any suggestions?

Thanks again!

Shannon

 

[David Harper CFA FRM]

Hi Shannon,

I have a real tough time with the exact same thing. I think the best cure, at least for myself (not that i've yet mastered it), is a better understanding of what the OAS is.

Let's say I want to sell you a mortgage and we can agree on the cash flows under a baseline prepayment schedule. Although the cash flows dwindle over time, i'm selling you an expected future cash flow. The nominal yield-to-maturity, the worst, prices this bond by discounting all cash flows at the same rate.

Instead, I offer $90, and you take the Treasury spot curve and you figure out the spread of X basis points, that if added to each rate Treasury rate, discounts the cash flows to a price of $90; e.g., if the 1-ear Treasury is 1.0% and the 2.0 year Treasury is 2.0%, you arrive a Z-spread of 80 basis points because you discount the cash flows to a PV of $90 if you use 1%+80 bps, 2%+80 bps, .... (you've improved on the YTM, which discounted all cash flows as the same rate)

Now, we have agreed with each other that my $90 mortgage buys you a Z-spread of 80 bps. But that discounts a single future path of cash flows (including expected prepayments).

What if you know that interest rates are going to jump in volatility, and even you know they will go down? Do you think your spread is really 80 bps? No, because you know that prepayments will be greater (worse for you) than the single series anticipates. OAS gives you spread to that is more "real" or "effective" to you b/c it averages into the spread the impact of these unanticipated but possible prepayments (i.e., the exercise of option) by incorporating them as alternate realities in a MCS

So, as your expectation of interest rate volatility increases, you (the buyer) are getting less and less for the same $90 as you can anticipate more prepayments. With no volatility, you expected to earn a Z-spread of 90 bps, but as volatility increases, after you factor in the *probability* of greater prepayments, your more realistic spread is the OAS. It's lower because the MCS isn't just using our one single "path" of expected cash flows, it is exploring many, including the paths with a lot of prepayments that lower your yield. In short:

Z-spread (if we assume one series of future cash flows) = OAS (if we assume many series, including the high prepayments due to rate volatility) + option cost (merely inferred, the difference)

Thanks, I hope that helps, b/c it helps me to think about too!

 

[shanlane]

PLEASE forgive me for this additional follow-up but I think the critical point that I am missing is exactly why the OAS is going down. Does all of this analysis mean that the price of the security, along with the z spread would be staying constant? If so, your argument makes perfect sense, but it seems like if the vol of inerest rates increases, the option would be worth more so the z spread would (or could) just increase as OAS stays exactly the same and the price of the security would be even less. Mybe I am just thinking about it too much.

I understand completely if you cannot spend any more time on this with me, but if you could point to a reading that discusses the mechanics of all of this it would be greatly appreciated.

Thanks,

Shannon

 

[David Harper CFA FRM]

Hi Shannon,

Sure, I don't have better readings than Fabozzi on this (I checked my other fixed income, but none cover it like Fabozzi; I got a little boost in my understanding from Fabozzis MBS Text, which had a chapter assigned to the FRM last year. But was replaced by the more recent Fabozzi MBS ... it's a similar coverage such that my best text on this topic happens to be the MBS that is already assigned).

What you say is sort of TRUE: "it seems like if the vol of inerest rates increases, the option would be worth more so the z spread would (or could) just increase as OAS stays exactly the same and the price of the security would be even less"

The thing is, the OAS isn't a market rate that's the same for everybody. You are correct: if the MBS has a seller and a price, and both you and I are interested buyers, the MBS can have a Z-spread (per the scheduled cash flows and, assuming we perceive the same zero rate term structure, we would perceive the same Z-spread) but, because the OAS is computed by our respective MCS models and its assumptions, we can perceive different OAS spreads (and different options costs). So if interest rate volatility goes up, you are CORRECT: we would expect the bond price to go down and the yield to go up, and similarly the Z-spread would go up. And both of our option costs increase, as our OAS decreases, but we will likely compute different OAS spreads because it falls out of our MCS model. I hope that helps! Thanks,

 

[shanlane]

Certainly does.

Thanks again!

Shannon