BEY for MBS
- Thread starter rickm123
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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
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
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.
This seems far too simplistic to be on the exam. So, thank you.
Thanks Chad, my question (IMO) reflects the assigned Fabozzi text. Just as an FYI, I happen to agree with Schweser's definition, please see http://forum.bionicturtle.com/threa...ed-security-mbs-fabozzi-mbs-2nd-edition.5482/
... but I'm unwilling to contradict Fabozzi's 2nd edition, I assume either I'm wrong or it hasn't been sufficiently addressed. Alas, this is not helpful, sorry ...
... but I'm unwilling to contradict Fabozzi's 2nd edition, I assume either I'm wrong or it hasn't been sufficiently addressed. Alas, this is not helpful, sorry ...
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.
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.
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!
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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