Lecture 23 Valuing MBS Valued similar to bonds fixed incomes Factors Prepayment Weighted average coupon WAC The monthly payment derived from the interest rate charged on the loans Weighted average maturity WAM ID: 219675
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Slide1
Derivatives
Lecture 23Slide2
Valuing MBS
Valued similar to bonds (fixed incomes)
Factors
Prepayment
Weighted average coupon (WAC)
The monthly payment derived from the interest rate charged on the loans.
Weighted average maturity (WAM)
Required yield (YTM)
Default (similar to prepayment)Slide3
Mortgage Backed Securities
Cash Flow Pattern for
BondsSlide4
Mortgage Backed Securities
Cash Flow Pattern for
MORTGAGES
Reflecting PREPAYMENTSlide5
Mortgage Backed Securities
MBS Valuation
MBS Value = PV of cash flows
Steps
Determine the monthly payment
Use prepayment assumption to derive maturity
Calculate the PV of the monthly payment at the YTM.Slide6
Mortgage Backed Securities
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 prepaymentSlide7
MBS Valuation
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?Slide8
MBS Valuation
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 PMTPMT = - 92,682Slide9
MBS Valuation
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 PVPV = $ 12,064,114Slide10
MBS Valuation
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. Slide11
MBS Valuation
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 = 92,682Slide12
MBS Valuation
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 i = 0.54 % ( .065 / 12 )
PV = 13,000,000 n = 180 (15 x 12)solving for the FVFV = - 6,241,454Slide13
MBS Valuation
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
i = 0.6167 % ( .074 / 12 ) FV = - 6,241,454 n = 180 (15 x 12)solving for the PVPV = $ 12,123,449Slide14
MBS Valuation
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. Slide15
Mortgage Strips
REMIC - real estate mortgage investment conduits
Variable maturity tranche
Variable/Fixed rate tranche
IO
PO