Came across this particular question from a certain Mock exam. Q - If the OAS on Company A’s straight bond was estimated to be 48bps, which of the following statements is most accurate? a) The OAS of callable bond will be greater than 48bps, and the OAS of the convertible bond will be less than 48bps. b) The OAS of the convertible bond will be less than 48bps, while the OAS of the putable bond will be greater than 48bps. c) The OAS of the callable, putable and convertible bond should be equal to 48bps.
I thought OAS for a callable bond is lower than for a putable bond.
But I don’t understand the correct answer.
Option adjusted spread is used to compare bonds with options vs straight bond. It’s the spread we get after removing all the options in the bond(more like ‘option removed spread’). Hence, Oas of any bond with options is going to be equal to straight bond, if not then there is mispricing. also, OAS spread= Z-spread - option cost.(+ve for call, -ve for put) straight bond will have no option cost, so therefore oas spread = z-spread.
Understood, but what does the answer mean by the OAS is the same for all three options?
According to your formula, wont a call reduce OAS vs a put that would increase OAS?
Pardon me here never really got around OAS.
Trying to understand by rewriting it in my more simple language:
OAS spread of a bond with option will equal Z spread of a straight bond?
Meaning that in order that the OAS be equal of a callable, putable and straight bond, it is their Z-spread which will not equal?
Callable bond has a Z spread > than that of a (same characteristic) straight bond, but removing the value of the call we get to its OAS spread which will equal the straight bond’s OAS (= Z)?
Same with putables only we increase the Z to get to the OAS?
Yes, you are right. Option cost is positive for call option and negative for for put option. The Z spreads for the straight bond and bonds with option is also going to be different.
Z-spread for a straight bond = Credit spread + liquidity spread Z-spread for a bond with option = Credit Spread + Liquidity spread + Option cost.
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Very clear, thanks a lot roawker.
This was a very enlightening thread, thanks to all participants!!!
I just wish the curriculum would do a better job explaining this material.
AF ftw
Okay to summarize, OAS + Option cost = Zspread Callable Z-spread > Straight bond Z-spread > Putable Z-spread
The A in OAS abbreviates “adjusted”; the way to think of it is “option removed spread”: the spread on the corresponding option-free bond.
Therefore, if two bonds have the same underlying, option-free bond, then they’ll have the same OAS, no matter the nature of their respective options.
Thanks Magician, also, wish this was made a bit more obvious in the curriculum.
Hi, everyone.
I got a trickier question for you.
Sharon Rogner, CFA is evaluating three bonds for inclusion in fixed income portfolio for one of her pension fund clients. All three bonds have a coupon rate of 3%, maturity of five years and are generally identical in every respect except that bond A is an option-free bond, bond B is callable in two years and bond C is putable in two years. Rogner computes the OAS of bond A to be 50bps using a binomial tree with an assumed interest rate volatility of 15%. If Rogner revises her estimate of interest rate volatility to 10%, the computed OAS of Bond C would most likely be:
A) higher than 50bps. B) lower than 50bps. C) equal to 50bps.
The OAS of the three bonds should be same as they are given to be identical bonds except for the embedded options (OAS is after removing the option feature and hence would not be affected by embedded options). Hence the OAS of bond C would be 50 bps absent any changes in assumed level of volatility.
When the assumed level of volatility in the tree is decreased, the value of the embedded put option would decrease and the computed value of the putable bond would also decrease. The constant spread that is now needed to force the computed value to be equal to the market price is therefore lower than before. Hence a decrease in the volatility estimate reduces the computed OAS for a putable bond.
Why will the OAS remain constant, if it’s option adjusted?
OAS of a putable bond is directly related to volatility OAS of a callable bond is inversely related to volatility. Thats why when the volatility of a putable bond drops, OAS also drops. OAS + Option cost = Z spread also OAS = Zspread - Option cost. For a put option, Volatility decrease would decrease the value of the option , in other words, the cost of the option increases. Volatility does not affect the Z spread. Holding everything else constant, the OAS drops. Not sure if this is entirely correct though (Partly sounds like BS to me). Maybe someone can confirm.
I thought that volatility does increase the Z-Spread. See the comment by roaker above. The whole reason why we have the OAS is to remove that option out of the Z-Spread, isn’t it?
Ok so Kotausi’s example there completely contradicts what we just established doesn’t it?
I would have argued that the OAS would have remained constant after the change in volatility, since the OAS is the spread we obtain after we remove the value of the option.
If I understood correctly, the OAS it is kind of comparable to correcting for inflation in the nominal interest rate, so kind of like the real rate.
If the real nterest rate is:
r=i-pi
3%=5%-2%
Now if the inflation changes to 3% AND the nominal rate changes to 6% we get the same result:
3%=6%-3%
If I understand correctly, when the interest volatility changes, this also changes the Z-Spread (because it contains the option value according to roawker’s comment above) and the option itself obviously. Since both change at the same time, I would expect the OAS to stay the same, similar to my example above.
I read that the Z spread is unaffected by volatility. But as you say, maybe the Z spread does change with volatility for a bond with an option maybe not for a straight bond.
I think that is the big question here.
The question that you posted originally and Kotausi’s question clearly seem to have to have contradicting views on this (or we are just missing something here).
Wiley notes provides credence for both interpretations:
The OAS essentially removes option risk from the z-spread
AND
_For a given bond price, the lower the interest rate volatility assumed, the lower the option cost and therefore, the higher the OAS for a callable bond given the z-spread. _
So I think the 2nd statement, assumes that there is no change in Z-Spread as a result of our change in assumptions (which makes sense, the market is not going change Z-spreads because I sit at my compute and decide to change sigma). While the first one assumes, that the market somehow used a certain assumption for volatility and included that in the Z-Spread.
I would thus conclude, that typically we should expect the OAS for bonds with options and bonds without options to be the same
But, when we start coming up with new assumptions for interest volatility the z-spreads are not going to change accordingly, thus leading to differing OAS for bonds with options compared to straight bonds.
What do you guys think?