OAS > Z-Spread

This question doesn’t fit neatly into any of the forums, so Level 3 it is:

Finance theory states that the difference between a bond’s z-spread and its option adjusted spread is defined as the option cost, or the risk measured in basis points associated with a bond’s embedded option. In practice, I’ve seen it largely used as a basis for relative value.

For illustrative and reference purposes: OAS + Option Cost = Z-Spread

There is greater context here that will provide only minimal value to the question at hand. In short, I am working on a project that requires me to isolate and estimate a Non-Agency IO’s option cost for use in valuing the bond’s embedded derivative (blame the accountants).

Have any of you seen instances whereby the OAS is greater than the Z-Spread, implying a negative option cost? If so, how can you qualitatively describe what exactly a negative option cost represents… and why it could actually be negative? The magnititude (and signage (+/-)) of the option cost, in the model that I have designed, dramatically affects the component value assigned to the host contract and the embedded derivative.

If you can, please keep this in the context of Non-Agency IOs…

I read that OAS could be larger than Z-spread when the option is a put option

Remember that option value = Z-spread – OAS; if OAS is less than Z-spread, the option value (to the bondholder) is positive, and if OAS is greater than Z-spread, the option value (to the bondholder) is negative.

Put another way, if OAS is less that Z-spread, the issuer is paying the bondholder a higher yield than he would for an option-free bond; if OAS is greater than Z-spread, the issuer is paying the bondholder a lower yield than he would for an option-free bond.

Not necessarily; the option is owned by the bondholder, but it doesn’t have to be a put option. It could be a conversion option, for example. It is definitely an option that favors the bond holder.

Similarly, when the OAS is smaller than the Z-spread, we know that there’s an option that favors the issuer. It could be a call option, or a prepayment option, or any other option that is owned by the issuer.

I think we would agree (at least I hope we do) that in the case on Non-Agency IOs, the difference between the bond’s Z-spread and OAS is directly attributable to the borrower’s (mortgage holder) ability to prepay his/her mortgage in a declining interest rate environment.

That being said, if I am the holder of the bond, ie, the beneficiary of the mortgage holder’s cash flows, I have issued (in my mind) a zero-cost put option to the mortgage holder such that they have the ability to modify the contractual cash flows by prepaying either a portion of their outstanding mortgage or in full.

This ability creates uncertainty as to the stream of cash flows that the bondholder will receive. If at any point there is volatility (or the chance of it) in the future cash flow stream, as a bondholder, I would demand a risk premium to compensate me for this.

Therefore, the Z-spread that I demand would include a positive option cost such that Z-spread > OAS.

In a perfect world, the behavior of the mortgage holder is 100% predictable such that there is no volatility in future cash flow streams. (At any given date in the future, my expectation of the mortgage holders’ payment equals actual cash received.). I would think in this instance that Z-spread and OAS would converge on one another with the option cost having a limit of 0 bps.

If this unpredictability in cash flows exist, why would I, the bondholder, be willing to accept a negative option cost? How could it even be possible?

Even if the collateral was say a weighted average coupon of 10% (realizing this is extreme but using it to prove a point) and current mortgages are being issued at 3%, any mortgagors that could would have likely prepaid would have and what’s left is the junk that can’t get approved for a new mortgage due to deteriorated credit, poor payment performance, etc. While the option is technically in the money from the mortgagors perspective, they could never exercise it given the above reasons. So, why would it ever flip signs and be negative, I would think it would revert to 0.

Sorry for the long winded post but I think this is an interesting example of taking CFA material outside the perfect world of blue box examples and applying it realistically, to actual real life transactions…

First, you’re not selling a _ put _ option to the mortgage holder; you’re selling them a prepayment option (which is a variation on a call option, not a put option).

Second, these two statements sound incompatible: either it’s a zero-cost prepayment option, or else it isn’t. In fact, your second statement is correct: you’re selling them a prepayment option, and the cost is (Z-spread – OAS).

Thank you. I suppose I am less concerned over the semantics of what type of option they hold (your points are certainly appreciated), as I am over how option cost could be negative given what I have described in my last post.

My pleasure.

I’m not concerned about semantics unless it clouds one’s thinking.

Years ago I was tutoring a friend of my younger son in algebra. Whenever he meant “a times b” he would say “a to the b”, as if he were thinking of b as an exponent. It took a lot of work to get him to use the correct language, but I’m sure that it made his thinking more clear. I likened it to someone who would say, “right turn” just before turning his car to the left. It’s a dangerous practice, and one day I could imagine that person saying “right turn” and then turning right from the left-turn lane and getting broadsided by someone.

Question still stands: if the bondholder demands compensation (additional spread) for the modification of cash flows that result from the exercising of the prepayment option embedded in the security, under what circumstances could that spread turn negative such that OAS > Z-spread?

I cannot imagine any circumstances in which that would happen. Whenever the issuer holds an option, he has to pay for it, even if it’s far out-of-the-money.

Have you seen this in practice?

I have seen agency IOs trading at spreads described above. Hard to isolate one specific driver of this given that the analytics the mortgage desks put out are all based on their own pricing and cash flow assumptions, most of which the user of the analytic has little transparency into.

Also, in Fabozzi’s Bond Portfolio Management (2001), he states “There are certain securities in the MBS market that also have an option cost that is negative”. Of course, that’s the only detail he goes into on the subject.

He does say that a negative option cost means an investor is long (or has purchased) an option. I get that, since the bond holder will dictate whether or not cash flows from the security will be modified so he/she will have to pay up for this (higher price/lower yield). But this is not the case with an IO since the bondholder has not purchased the option.

Bit of a head scratcher here.

Yes, if the bondholder has an option, then the OAS could be greater than the Z-spread (negative option value). I’m not sure what sort of MBS would give rise to that.

The only thing I can think of is that since OAS is interest rate path dependent, a dealer’s estimation of short and long term volatility in rates will drive the value of the OAS and therefore the option cost. Rate volatility and anticipated paths relative to the bond’s WAC and the borrower’s propensity to repay could yield some wacky results I suppose, especially in extreme cases where we have experienced refi burnout and the WAC is greatly in excess of the prevailing mortgage rates.

Explaining this phenomenon in a vacuum might not be feasible.

Appreciate the academic back and forth.