Lecture 23
Valued similar to bonds (fixed incomes)
Factors
 Prepayment
 Weighted average coupon (WAC)
◦ The monthly payment derived from the interest
rate charged on the loans.
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Weighted average maturity (WAM)
Required yield (YTM)
Default (similar to prepayment)
Cash Flow Pattern for Bonds
Bonds
Loan Payment
12
10
8
Interest
Principal
6
4
2
0
1
2
3
4
5
6
Years
7
8
9
10
Cash Flow Pattern for MORTGAGES Reflecting PREPAYMENT
Mortgages
Loan Payment
12
10
8
Interest
Principal
6
4
2
0
1
2
3
4
5
6
Years
7
8
9
10
MBS Valuation
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MBA Value = PV of cash flows
Steps
1. Determine the monthly payment
2. Use prepayment assumption to derive
maturity
3. Calculate the PV of the monthly payment at
the YTM.
MBS Valuation

Using present value terminology
PV = Price of MBS
Pmt = monthly coupon payment from MBS
i = Yield to Maturity
n = t = Prepayment year assumption
FV = Balance of mortgage at prepayment
Example
A mortgage pool contains $13,000,000 in
loans made to homeowners. The weighted
average maturity of these mortgages is 22
years. The weighted average interest rate
charged on the loans is 6.5%. If the
mortgage pool requires a risk adjusted
yield to maturity of 7.4%, what is the value
of the mortgage pool?
Example
A mortgage pool contains $13,000,000 in loans made to
homeowners. The weighted average maturity of these mortgages
is 22 years. The weighted average interest rate charged on the
loans is 6.5%. If the mortgage pool requires a risk adjusted yield
to maturity of 7.4%, what is the value of the mortgage pool?
Assume NO prepayment.
Step 1 – Find the monthly payment
PV = $ 13,000,000
FV = 0
n = 264 (22 x 12)
i = 0.54 % ( .065 / 12 )
solving for the PMT
PMT = - 92,682
Example
A mortgage pool contains $13,000,000 in loans made to
homeowners. The weighted average maturity of these mortgages
is 22 years. The weighted average interest rate charged on the
loans is 6.5%. If the mortgage pool requires a risk adjusted yield
to maturity of 7.4%, what is the value of the mortgage pool?
Assume NO prepayment.
Step 2 – Find Present Value of the monthly payments at the YTM
PMT = - 92,682
FV = 0
n = 264 (22 x 12)
i = 0.6167 % ( .074 / 12 )
solving for the PV
PV = $ 12,061,114
Example
A mortgage pool contains $13,000,000 in loans made to
homeowners. The weighted average maturity of these mortgages
is 22 years. The weighted average interest rate charged on the
loans is 6.5%. If the mortgage pool requires a risk adjusted yield
to maturity of 7.4%, what is the value of the mortgage pool?
Instead, assume the loans are completely prepaid at the end of
year 15.
Example
A mortgage pool contains $13,000,000 in loans made to
homeowners. The weighted average maturity of these mortgages
is 22 years. The weighted average interest rate charged on the
loans is 6.5%. If the mortgage pool requires a risk adjusted yield
to maturity of 7.4%, what is the value of the mortgage pool?
Instead, assume the loans are completely prepaid at the end of
year 15.
Step 1 – Same as before. Calculate the monthly payment
PMT = 92,682
Example
A mortgage pool contains $13,000,000 in loans made to
homeowners. The weighted average maturity of these mortgages
is 22 years. The weighted average interest rate charged on the
loans is 6.5%. If the mortgage pool requires a risk adjusted yield
to maturity of 7.4%, what is the value of the mortgage pool?
Instead, assume the loans are completely prepaid at the end of
year 15.
Step 2 – NEW – Calculate the balance at the end of year 15.
PMT = - 92,682
PV = 13,000,000
i = 0.54 % ( .065 / 12 )
n = 180 (15 x 12)
solving for the FV
FV = - 6,241,454
Example
A mortgage pool contains $13,000,000 in loans made to
homeowners. The weighted average maturity of these mortgages
is 22 years. The weighted average interest rate charged on the
loans is 6.5%. If the mortgage pool requires a risk adjusted yield
to maturity of 7.4%, what is the value of the mortgage pool?
Instead, assume the loans are completely prepaid at the end of
year 15.
Step 3 – NEW – Calculate the PV of the new cash flows.
PMT = - 92,682
FV = - 6,241,454
i = 0.6167 % ( .074 / 12 )
n = 180 (15 x 12)
solving for the PV
PV = $ 12,123,449
Example - Analysis
Notice the MBS value drops from $ 12,061,114 to $ 12,123,449 when the
prepayment assumption is added.
Why?
The MBS selling at a discount because the YTM was higher than the
coupon. By getting the money sooner, the discount is reduced.
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REMIC - real estate mortgage investment
conduits
Variable maturity tranche
Variable/Fixed rate tranche
IO
PO