Mortgages and Mortgage Pass-through
1. Mortgages
2. Mortgage Pass-through Securities
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Mortgage
A loan secured by the collateral of specified real estate property, which
obligates the borrower to make a predetermined series of payments. (page
214-215)
Terms: (1) Mortgage originator
(2) Payment-to-income (PTI) ratio
(3) Loan-to-value (LTV) ratio
(4) Contract rate
(5) Conduit
(6) PMI (page 221)
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Lien Status
The lien status of a loan indicates the loan’s
seniority in event of the forced liquidation
of the property due to default of the obligor.
(page 216)
• First lien
• Second lien (junior lien)
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Credit Classification
Prime loan: A loan that is originated where
the borrower is viewed to have high credit
quality.
Subprime loan: A loan that is originated
where the borrower is viewed to have low
credit quality.
Alternative-A loan: in between
(page 216)
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Interest Rate Types
Fixed rate mortgage (FRM)
Adjustable rate mortgage (FRM)
• Periodical rate cap
• Lifetime rate cap and floor
• Hybrid ARM
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Level-payment fixed-rate
mortgage
Each monthly mortgage payment for a level-payment
mortgage is due on the first of each month and consist of
(1) Interest of 1/12 of fixed annual interest rate times the
amount of the outstanding mortgage balance at the
beginning at the beginning of the previous month
(2) A repayment of a portion of the outstanding mortgage
balance (principal)
Monthly payment: page 219
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Example (Amortization Schedule)
Replicate the numbers for month 4 (page 219)
Month payment
Monthly interest
Scheduled principal payment
Ending mortgage balance
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Other Issues
Recasting a loan: resetting the mortgage
payment for an ARM.
Lockup period: during which only interest is
paid (IO product)
Prepayment and prepayment penalty – page
222
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Confirming Loan
Definition: Conventional loans that meets the underwriting
standard of Fannie Mae and Freddie Mac.
Conventional loans: as opposed to government loans, with
explicit guarantee from the federal government, e.g.,
Veterans Administration (VA) loans
Freddi Mac and Fannie Mae: government sponsored enterprises
whose mission to provide liquidity and support to mortgage
market. They receive a chapter from the federal government.
Agency MBS use confirming loans as collateral.
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Risks Associated with Investing in
Mortgages
• Credit risk: homeowner/borrower will
default
• Liquidity risk
• Interest risk
• Prepayment risk
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Mortgage Example
Say you are interested in buying a 2-bedroom condo in
Boston. The price is $300,000. You have a 30-year 3.5%
APR mortgage with 20% down payment.
(1)What would be the monthly mortgage payment?
(2)What if you have 15-year mortgage with the same APR?
(3)Suppose you could rent the place out and the rent you
collect will cover your mortgage payment. What would
be the annual return of your investment if the condo
value stays constant.
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Mortgage example solution
(1)$1077.71
(2) $1715.72
(3) with the 15-year mortgage, investment
return is 11.33%
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Mortgage Pass-through Securities
One or more mortgage holders form a collection of
mortgage and sell shares or participation
certificates in the pool. There are two derivatives
from pass-through:
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Alternative Features
Pass-through rate: less than the underlying
pool of mortgage loan by an amount equal
to the servicing and guaranteeing fees
WAC
WAM
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Agency Pass-through
Ginnie Mae -- MBS
Freddi Mac – participation certificate (PC)
Frannie Mae -- MBS
Fully modified pass-throughs
Modified pass-throughs
Feature: default risk free.
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What Determined Projected Cash
Flow
Projected cash flow
Pass-through rate
Prepayment speed
Cash yield
-- the most important factor is the expected
prepayment rate
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Alternative Prepayment Rates
(1) FHA prepayment experience approach:
assuming no prepayment in the first 12
years, then all the mortgage in the pool
prepay
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Alternative Prepayment Rates
(2) Conditional Prepayment Rate
Based on the characteristics of the pool (including its
historical prepayment experience) and current and
expected future economic environment. Conditioned on
remaining mortgage balance.
Single-month mortality rate (SMM)
SMM=1-(1-CPR)1/12
Monthly Prepayment: SMM x (beginning balance for t–
scheduled principal payment for t)
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PSA Prepayment Benchmark
(3) PSA Prepayment Benchmark published by
Public Securities Association
A monthly series of annual prepayment rates.
Assumes that prepayment rates are low for newly
originated mortgage and then will speed up as the
mortgages become seasoned.
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Standard Benchmark
(100 PSA)
CPRs for a 30-year mortgage:
(1) 0.2% per year for the first month, increased by
0.2% per month per month for the next 30
months
(2) 6% CPR for the remaining years
If t<=30: CPR=6%*(t/30)
If t>30: CPR=6%
Slower or faster speeds: 50 PSA or 300 PSA
P 240
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Examples (page 241)
The SMMs for month 5, month 20, month 31
through 360 assuming 100 PSA
The SMMs for month 5, month 20, month 31
through 360 assuming 165 PSA
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Monthly Cash Flow Construction
• Objective: obtain cash flow
• Key steps:
– Interest
– scheduled principal
– prepayment
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Example 1
Monthly cash flow for a $400 million 7.5%
pass-through rate with a WAC of 8.125%
and WAM of 357 months assuming 100
PSA.
(exhibit 11-6, page 242)
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Example 1 (do month 1)
(1) Find SMM
SMM for month 1 =
(SMM for month 27)=
(2) Find mortgage payment
N I/Y
PV
PMT FV (using WAC here)
(3) Interest: pass-through rate/12*beg balance
(4) Scheduled principal payment=monthly mortgage payment
– gross coupon interest, where gross coupon interest =
WAC*outstanding mortgage balance/12.
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Example 1 (solution)
(5) Prepayment = SMM x (beginning mortgage
balance – scheduled principal payment)
= 0.00067*(400,000,000-267,535)
(6) Total principal
= 267,535+267,470
(7) Cash flow
=2,500,000+535,005
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Example 1 (Solution)
(1) Find SMM
SMM for month 1 = 0.00067
(SMM for month 27)= 0.00514
(2) Find mortgage payment
N
I/Y
PV
PMT
FV
357
0.6771 -400000000
?
0
(3) Interest: pass-through rate/12*beg balance
=7.5%/12*400,000,000
(4) Scheduled principal payment=monthly mortgage
payment – gross coupon interest, where gross coupon
interest = WAC*outstanding mortgage balance/12.
= 2975,868-8.125%/12*400,000,000
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Example 1
(5) Prepayment = SMM x (beginning mortgage
balance – scheduled principal payment)
(6) Total principal
(7) Cash flow
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Question
How much does the pass-through issuer earn?
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Example 2
Monthly cash flow for $400 million 7.5%
pass-through rate with a WAC of 8.125%
and WAM of 357 months assuming 165
PSA
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Factors Affecting Prepayment Behavior
Prevailing mortgage rate
Characteristics of the underlying mortgage loans
Seasonal factors
Home buying peak in summer, decline in fall and winter.
Repayment peak in fall, low in winter
General economic activities
Prepayment models
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Cash Flow for Nonagency Passthroughs
The PSA standard default assumption (SDA)
benchmark gives the annual default rate for
a mortgage pool as a function of the
seasoning of the mortgages.
See page 309 – assumptions on default rate
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Cash Flow Yield
Bond-equivalent yield=2[(1+yM)6-1]
• Limitation: rely on assumptions
• Based on PSA prepayment assumption
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Average Life
Average time to receipt of principal
payment (scheduled principal payment +
projected prepayments)
T
t * Pr incipal _ received _ at _ time _ t
Average _ life  
12 * total _ principal
t 1
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Yield Spread to Treasuries
Page 251
• Spread of agency pass through to treasuries
• Spread of private-label pass through
securities and treasuries
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Prepayment Risk to Investors
When mortgage rate decreases (contraction Risk)
• prepayment risk
• Lower reinvestment return
When mortgage rate increases (Extension Risk)
• Price risk
• High mortgage rate slows down repayment
(the basic idea is mortgage risk will be transferred to
pass through investors)
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Asset/Liability Management
Implications
What kind of liabilities do banks borrow? What
kind of assets do banks hold?
So, thrifts and commercial banks are more
concerned of extension risks.
Insurance companies have the similar problem
when their liabilities are short term
Pension fund managers may concern of the risk
from pass through’s fast prepayments
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Secondary Market Trading
Quoted in the same manner as Treasury coupon
bonds
Pass-through securities are identified by a pool
prefix and pool number provided by the agency
TBA: many trades occur while a pool is still
unspecified
Quotes: see “Mortgage-backed securities” under
“Bond Market Data Bank”
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Nonagency Pass-through
Issued by commercial banks, thrifts, and
private conduits
No guarantees of default risk free
Registered with SEC
Function: credit enhancement
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Credit Enhancement
Structural Credit Enhancement
Shifting Interest Mechanism in a SeniorSubordinated Structure
Originator/Sell-Provided Credit Enhancement
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Summary of Important Points
Mortgage rate
Pass-through rates
Cash flow yield
Conditional prepayment rate (CPR)
Single-Monthly Mortality Rate (SMM)
Scheduled principal payment
Unscheduled (prepaid) principal payment
Cash flow
Nonagency passthrough
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