BEY for MBS

rickm123

Member
Hi david:

I am able to calculate the BEY of the MBS. However, in reference to calculating the nominal spread through an interpolate process, well it is rather confusing.
We will need to calculate this and if so can you please comment on the procedure if possible.

Thanks

Rick
 

David Harper CFA FRM

David Harper CFA FRM
Subscriber
Hi Rick,

Did you happen see the example in my practice question (.2 below)
http://forum.bionicturtle.com/threa...w-yield-of-mortgage-backed-security-mbs.5371/

This performs a linear interpolation between the 7-year rate at 4% and the 10-year rate at 5.2%. Here is wikipedia http://en.wikipedia.org/wiki/Linear_interpolation

For this, i like to just visualize: we want the 9-year rate, so how far is that, as a fraction of the total distance between 7 and 10? (9-7)/(10-7) = 9 is 2/3rds of the distance between 7 and 10
So we want 2/3rd of the difference (on the y axis) between 4% and 5.2%: we want to add 2/3*(5.2%-4%) to the 4% "starting point"

I hope that helps, here is the question that applies:

Question 112.2
112.2. Assume the bond-equivalent (i.e., semi-annual) yield of the seven and 10-year Treasury securities are, respectively, 4.0% and 5.2%. The bond-equivalent for an mortgage-backed security (MBS) is 5.40%. The average life of the MBS is nine (9) years. Which is nearest to the nominal spread?

a. 20 basis points
b. 54 basis points
c. 60 basis points
d. 140 basis points

Answer:
112.2. B. 54 basis points
First, translate the semi-annual (bond-equivalent) yield of the MBS to a mortgage (cash flow) yield:
Mortgage (cash flow) yield = i(m) = 12*[(BEY/2 + 1)^(1/6) - 1] = 12*[(5.40%/2 + 1)^(1/6) - 1] = 5.3402%;
Second, interpolate the Treasury yield: the (linear) yield at 9 years = 4.0% + (5.2% - 4.0%)*(9-7)/(10-7) = 4.80%.
Nominal spread = Mortgage (cash flow) yield - bond-equivalent Treasury yield = 5.3402% - 4.80% = 0.5402% = 54 basis points
 

ChadWOB

New Member
David, thank you for this explanation and practice question. The Schweser material implies that on the exam, the maturity/life span of the MBS will equal that of the comparable treasury and we can simply calculate nominal spread = BEY - Yield of Comparable Treasury.

This seems far too simplistic to be on the exam. So, thank you.
 

ChadWOB

New Member
Well - I guess I'll study both of them! The calculated nominal spread should come within a few basis points of each other with either formula correct? Hopefully they don't try and trip us up with choices that are very close to each other (but I'm sure they will!)

Schweser does not, however, provide any infomation on interpolating the treasury yield if we aren't given a treasury with the exact maturity as the MBS.
 

David Harper CFA FRM

David Harper CFA FRM
Subscriber
Hi Chad,

Agreed, the difference isn't large. It is the difference due to monthly (mortgage or cash flow) versus semi-annual (BEY) compound frequency. But it's still a real difference; e.g., at 6% continuous yiled, I get a difference of 7.6 basis points, between equivalent monthly and semi-annual rates

But, no, they won't try to trip you up ... the don't write those kind of "near to" questions

I do agree with knowing both. I think the important thing is that you are aware of both definitions. A good question should be specific about the definitions, thanks!
 
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