It is my understanding that OAS takes into account liquidity and credit risk. Z-spread adds option premium to OAS. Here is my confusion: If you are valuing a bond with embedded options (e.g. callable bond), you add same OAS to forward rates to find an arbitrage-free present value. Why are we callin this additional spread OAS and not Z-spread? Second Confusion: Similarly, I am somewhat confused where we do spread analysis for Fixed Income securities. For example, when looking at Mortgage Back Securities (with prepayment option), why are we using OAS and not Z-spread? Thank you for your comments.

1rst: we add OAS because in the binomial tree is taking into account the fact that the callable bond will follow the ‘call rule’ and its value at certain nodes will reflect the fact that it will be called at the given interest rates… if there was no possibility that the bond will be called then z-spread would be appropriate because the cash flows would be the same and OAS = Z spread 2nd: we use OAS so that different securities (with different option costs) can be compared, and the relative credit and liquidity can be evaluated. If we use z-spread a security with an z-spread of 250 bps will appear to a security (with similar credit and liq) with a z-spread of 200 bps, however is the first security’s has a prepayment option worth 150 bps and the second security has a prepayment option worth only 50 bps then the first security will actually be overvalued relative to the second

Thanks, Marty3 but I am still confused. In several places in CFAI and kaplan the OAS as defined as the “spread with the option cost removed” But if the OAS is calculated using the tree while accounting for the call rules, how is does this NOT include the option cost?! Its certainly not the same spread as you’d get on an otherwise identical bond WITHOUT the options. If you calculate the spread on the tree and fully incorporate the call rules, how does this NOT reflect the option cost? This has been REALLY bothering me. The two treatments of the OAS seem to conflict: if z spread = OAS + cost of call option but OAS is calculated in a way that reflects the option, how does this work!?

Just as an example CMBS valuation is done with z-spread. Virtually no prepayment risks. Plain MBS valuation done with OAS using a binomial i-r- model because prepayment risk is heavy

z spread = OAS + cost of call option cost of option could be positive or negative, so the above is correct.

But if the OAS is derived using a tree that reflects the call rules, how can we say that the OAS does NOT reflect the option cost??

Say you buy a security with a coupon of 40 paid every 6 months for four years callable at 100 after two years and there is a downward sloping yield curve, the yield on a treasury with same maturity is 3% so the nominal spread is 5% and the z-spread will be greater than the nominal because of the downward sloping yield curve so lets say the z-spread is 6% However since the bond will probably be called in two years because of the the downward sloping yield curve you will receive your principal in two years and no interest. These forgone payments of interest and early return of principal have a value representing the cost of the option. When this cost is deducted from the z-spread you have the OAS spread. People say that the OAS spread “does not reflect the option cost” because it is the spread on the payments that you are expected to receive given the structure of interest rates therefore it can be used to compare a security with an option to securities with different or no options. OAS essentially represents the spread on the payments you are expected to receive while z-spread is the spread if all payments are received.

Ahh… Thanks, Marty. Seriously, this was bugging the $!#@# out of me. Is this related to what you do for a living, by chance? In other words, the OAS very much reflects the cost that the option imposes on a security. It only “does not reflect the option cost” when it is used viz benchmark that also has similar option. This way, if you compare OAS between to callable securities, any differences will likely be to non option related factors. And so, if you use the OAS viz benchmark for bond of same issuer, coupon and option characteristics, you can judge whether your particular bond is under- or overvalued. In the sense of the difference between the OAS and the z spread, the difference IS the option cost. So OAS does in fact fully reflect the fact that the cashflows from a a bond that can be called are different from an otherwise identical noncallable security. Phew.

zoya Wrote: ------------------------------------------------------- > In the sense of the difference between the OAS and > the z spread, the difference IS the option cost. > So OAS does in fact fully reflect the fact that > the cashflows from a a bond that can be called are > different from an otherwise identical noncallable > security. thats right. Think of two rate trees with all the same attributes except one is callable and one is not. The price for the non callable, less the price for the callable is the option cost. The “spread” or percentage over the callable options interest rates at every point in the tree that would make the value equal to that of the Z-Spread (market price of the non callable bond)

I got another one for you all. Question number 35, reading 54: Jokinen states: “If interest rates rise and volatility is unchanged, the value of a callable bond should decrease” Correct / incorrect? Isnt this a bit iffy tho? Interest rates rise, so bond values fall, ok. But, as interest rates rise, the (negative!) value of the call decreases, right? As the likelihood of the call being exercised decreases, yes? So how can we conclusively say that this statement is correct, as the book tells us.

zoya Wrote: ------------------------------------------------------- > I got another one for you all. > Question number 35, reading 54: > > Jokinen states: > “If interest rates rise and volatility is > unchanged, the value of a callable bond should > decrease” > > Correct / incorrect? > > Isnt this a bit iffy tho? Interest rates rise, so > bond values fall, ok. > But, as interest rates rise, the (negative!) value > of the call decreases, right? As the likelihood of > the call being exercised decreases, yes? > > So how can we conclusively say that this statement > is correct, as the book tells us. it specifically says that volatility is unchanged so it will be treated like a non-callable( even though it inst) its just coz interest rate movement will not effect the price of the call option and keeping the call option price constant the bond price will decrease… that’s how i put it together correct me if i am wrong

yep, I think YAH got that right.

I also think the call option value does decrease, but the decrease in the bond price is more than the small gain from the reduction in the call option.