Fixed Income OAS questions

I’ve seen this same question or some variation pop up on nearly every mock. It asks us to pick the best bond for our client, and it seems like the answer every time is to pick the one with the highest OAS, regardless of z score or nominal spread. Is this generally the bible rule or are there execptions?

Usually you want to pick the bond with the highest OAS cause it means it’s underpriced and lowest option cost. Depending on what the problem says, you might have to look at the interest rate sensitivity.

hier OAS with LOWER option cost

What about for callable bonds Z-spread >= OAS? So, selecting the highest OAS is not always right? Also, I recall that you compare the OAS against the spread on an option-free bond, in which case you will chosse the other option-free bond if it has a higher spread>>>still have not fully wrapped my head around these concepts.

if Z-Spread > OAS in a callable Bond, you are OK. since option cost is positive then it all make sense. you pick HIGH OAS LOW OPTION COST

if Z-Spread < OAS in a callable Bond, this is impossible, since a negative option cost means a PUT which is not in a callable bond. if a callabale bond has this patern, then buy it until you ran out of money

if OAS is negative, and your benchmark is the treasurie, then you know you are undervalued since you have less risk than the risk-free curve.

You never compare OAS on a option free bond since OAS = Z-spread.

OAS negative should be overvalued, am i right?

if OAS is negative, then the option cost is to the roof.

then yes.

If there are two bonds, one is option-free with a nominal spread of 8.5%, and the other has an OAS = 8%, how do you choose between the two?

it depends on the option, is it a put or a call…

if it’s a call it’s very hard to say since one is estimated on the yield and the other one on spot. so if you dont have more comparable you cannot say…

if it’s a put, then i would go for the option free one since the put shoud give you more OAS than nominal in most cases. but as i said, comparing OAS and nominal is very disturbing since it’s yield and spot.

Z spread is evaluated on spot, just like the OAS, so it’s easier to compare them

If I then find that the option-free bond has a z-spread of 7.5%, what do I conclude?

if OAS = 8 %

then if the bond is calable it’s undervalued since the option cost is negative. because you assume that a callable bond will have a positive option cost.

if it’s putable, you can’t tell if you can’t compare it with other similar putable bond.

May be I need to review FI again, but my understanding is that if you are valuing a bond that has no options using a z-spread, then you have determined the proper spread for the bond. Now if you check another bond, and you adjust for the option, regardless of whether it’s callable or puttable, you have determined its OAS, so the option is no longer relevant. Since the OAS has been calculated using spot rates, and te z-spread is also calculated based on spot rates, you have two bonds with two spreads that can be compared directly. I don’t get why I need to worry about the option cost…I have already factored that in and got the OAS. Again, I may be off on this one.

Dreary what SS is saying that there are three types of spreads: nominal, Z, and OAS. Don’t confuse nominal with Z or use them interchangeaby (which it seems like you did)

Nominal: nobody really pays attention to in this case. Nominal is just YTM - benchmark yield. It doesn’t tell us much. YTM just gives us a single yied rate

Z spread - we must assume that each cash flow is discounted at its appropriate spot rate. If we use a binomial tree, we are assuming some volatility around those benchmark rates. However, if we discount a bond at the observed spot rates with the benchmark spot rates (or using the binomial tree with forward rates), then we will probably come upon a price that is different than the current market price (ie, if treasury spot rates are the appropriate benchmark rates, these are most likely lower than the rerquired rates given that the risk of the bond > risk of treasury bond). Ie, we will come up with a higher price. We know that these rates can’t be appropriate, however, because the risk of a bond (before assuming options here) from Ford is much different than a Treasury bond. So, we need to add some amount to each of those rates to make sure that the market price is equal to the price that our binomial tree spits out. How much do we add to each rate? The z spread.

Imagine FORD issues a noncallable bond. And we discount each cash flow at the benchmark rates, to come up with a price of 120. But, the market price is more like 102, so we should probably adjust those benchmark rates up to a level that will produce the market price. The z spread is a constant spread added to all of the benchmark rates so that our model spits out 102 instead of 120. Higher rate = lower price.


OAS - with OAS, we are accounting for the fact that the CASH FLOW will change due to the embedded option. Ie, if in our tree rates fall to a certain point with a callable bond, the issuer will probably call the bond. In which case the bond price is limited by the par value (issuer will pay par to redeem). So, if our falling interest rate in our binomial tree is such that the price at a node becomes 115 when the rate falls below the call rate, we dont discount the value of 115 anymore because we expect the bond to be called at 100.

So, the CASH flow will be lower at that time period (remember, the embedded option has no bearing on the benchmark rates) - so now if we discount the cash flows using the benchmark rates, we will get a lower valuation, right?

Assume a similar example as above, except now FORD has a callable bond that is identical to the one they issued above. (Assume the volatility in this example is set high enough that the bond will be called in the down scenario). We can expect the cash flows to be lower if the bond is called, because we are expecting the price to be 115 in a down scenario, but in reality we will only get 100. So, the value will be lower than the first example, so now we don’t need to add as much spread to the benchmark rates for valuation because the decrease in cash flows is already reducing the value closer to the market price

the option cost is relevant when you are comparing two bonds with embedded options. If two bonds have the same OAS but one has a lower option cost (meaning value of noncallable bond = value of callable + option cost), take the one with the lower option cost.

OAS vs z spread is relevant when comparing a bond without an embedded option to a bond with an embedded option (I’m 95% sure)

That’s very helpful…but one confusing part is sometimes we say the z-spread = 8%, for example, while at other times we say the z-spread is only the number of basis points we add to the benchmark spot rates…however, the z-spread is a constant number of points while the spot rates are many, so do I say the Z-spread is, for example 75 bps, or add it to the spot rate? But there are many spot rates! Add it to which one?

Let us look at some scenario:

Callable Bond A has a nominal spread (NS) = 150 bps, i.e., NS = 1.5%.

Option-free Bond B has NS = 125 bps

A’s Z-spread - 125 bps.

A’s OAS = 100 bps.

So, Bond A appears to be undervalued because it has a higher NS (150 bps versus 125 bps). But when we look at its OAS of 100 bps, we see that Bond B is better (it has a NS of 125 bps).

To make a long story short, I need to go back and read the darn thing!

A zspread is the spread added to ALL of the spot rates. You cant really quote the rate with it, because if you add it to all of the spot rates it will be a different rate at each point in time. Unfortunately this section of the book is laid out poorly IMO (ie, goes over a concept and explains it a few pages later)

For example, if the treasure curve from 1 year to 3 year in year increments are




If we use these rates to discount the cash flow of a Ford bond, we might get some really high price that doesnt make sense, because we know the risk of Ford isnt similar to that of the US treasury. We could add a different amount to all of the rates in this curve, but that doesnt help us much because its tough to compare bonds this way. Say we use these rates and get a price of 120, where the market price is 102.

Enter the z spreads what is the constant amount we can add to all of these rate to bring the value from the model to 102. For the sake of argument, let’s add 75 bps to each rate.




Now, using these rates, our bond price is 102, which is the market price. How much did we have to add to each rate to prevent arbitrage? 75 bps = zspread.

You don’t compare nominal spread to z spread or oas. Basically both z spread and OAS are just the bps that make your cash flow equal to market value. Like ppl were saying before nominal spread is just ytm - treasury rate. Tells no info about bond return.

For you question about spot rate. It’s basically like this. Say you have 20 cash flows for your bond. Each cash flow has a different spot rate. The z spread is basically the bps added to all the spot rate so your discounted cash flow is equal to the market place. The discount rate on each cash payment is different ( floating rate of that period plus), not just because of Compounding, but also cause of changing rates.

Thats why higher z spread higher return, all else equal. Higher spread mean like money you pay for the bond. The cash flow will be the same in the future regardless of spot rate (compare to other bonds with same coupon maturity and risk), it’s just ur paying less for it

That’s clear…how about some problems on OAS/Z-spread stuff…anyone?

2 am in hong kong, but if you can wait I think there was 3 hard question in schweser exam book 2. I can post it to you on this thread tmr. In 14 hours maybe.


the OAS is what you will earn in average ( above the spot ). you make 10000 scenario, you calculate the yield you earn on each scenario, then you average it. so it’s bassicily saying that you will earn that spread over spot in average.

the z-spread is the spread over the spot of 1 scenario ( the actual spot rate curve ). in fact, that scenario is the base case ( the actual ) scenario of your monte carlo simulation. so if you are saying that OAS is smaller than Z-spread, it’s like saying that the 1 scenario you are evaluating is an above average scenario.

if i tell you,

1)you can buy a bond with a z-spread of 3% with a OAS of 2% or

2)you can buy a bond with a a z-spread of 3% whit a OAS of 1%. similar credit risk / maturity

if i were you, i would prefer to earn in average 2% than earn average of 1% even if the base case scenario ( current yield curve ) is telling me that if everyting stay the same i will earn 3%

Can someone explain in layman’s terms how the OAS considers the option cost when in fact the spread excludes the cost of the option…seems counterintuitive?