Type
Solution Manual
Book Title
Fundamentals of Investments: Valuation and Management 8th Edition
ISBN 13
978-1259720697

978-1259720697 Chapter 20 Lecture Note

January 2, 2020
Chapter 20
Mortgage-Backed Securities
Slides
20-1. Chapter 20
20-2. Mortgage-Backed Securities
20-3. Learning Objectives
20-4. Mortgage-Backed Securities
20-5. A Brief History of Mortgage-Backed Securities, I.
20-6. A Brief History of Mortgage-Backed Securities, II.
20-7. Fixed-Rate Mortgages
20-8. Fixed-Rate Mortgage, Monthly Payments
20-9. Mortgage Payments Using a Spreadsheet
20-10. Mortgage Payments, by Rate and Time
20-11. Fixed-Rate Mortgage Amortization
20-12. Example: Fixed-Rate Mortgage Amortization
20-13. Fixed-Rate Mortgage Amortization
20-14. Amortization Schedules for 15-Year and 30-Year $100,000 Mortgages
20-15. Mortgage Interest and Principal, by Age of $100,000, 30-Year Mortgage with
8% Interest
20-16. Fixed-Rate Mortgage Amortization, Using a Spreadsheet
20-17. Reverse Mortgages, I.
20-18. Reverse Mortgages, II.
20-19. Fixed-Rate Mortgage Prepayment and Refinancing
20-20. Government National Mortgage Association
20-21. Government National Mortgage Association
20-22. GNMA Clones
20-23. PSA Mortgage Prepayment Model, I.
20-24. PSA Mortgage Prepayment Model, II.
20-25. PSA Mortgage Prepayment Model, III.
20-26. PSA Mortgage Prepayment Model, SMM
20-27. PSA Mortgage Prepayment Model, Average Life
20-28. Cash Flow Analysis GNMA Fully Modified Mortgage Pools
20-29. Principal and Cash Flows for a GNMA Bond
20-30. Macaulay Durations for GNMA Mortgage-Backed Bonds
20-31. Macaulay Durations for GNMA Mortgage-Backed Bonds
20-32. Collateralized Mortgage Obligations
20-33. Interest-Only and Principal-Only Strips
20-34. Cash Flows for GNMA IO and PO Strips
20-35. Sequential CMOs, I.
20-36. Sequential CMOs, II.
20-37. Sequential CMO Principal and Cash Flows
20-38. Protected Amortization Class Bonds, I.
20-39. Protected Amortization Class Bonds, II.
20-40. PAC Cash Flows and Total Cash Flows
20-41. Yields for MBSs and CMOs
20-42. MBS Yields
20-43. Useful Websites
20-44. Chapter Review, I.
20-45. Chapter Review, II.
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Mortgage-Backed Securities 20-2
Chapter Organization
20.1 A Brief History of Mortgage-Backed Securities
20.2 Fixed-Rate Mortgages
A. Fixed-Rate Mortgage Amortization
B. Fixed-Rate Mortgage Prepayment and Refinancing
20.3 Government National Mortgage Association
A. GNMA Clones
20.4 Public Securities Association Mortgage Prepayment Model
20.5 Cash Flow Analysis of GNMA Fully Modified Mortgage Pools
A. Macaulay Durations for GNMA Mortgage-Backed Bonds
20.6 Collateralized Mortgage Obligations
A. Interest-Only and Principal-Only Mortgage Strips
B. Sequential Collateralized Mortgage Obligations
C. Protected Amortization Class Bonds
20.7 Yields for Mortgage-Backed Securities and Collateralized Mortgage
Obligations
20.8 Summary and Conclusions
Selected Web Sites
www.investinginbonds.com (for information on bonds, bonds, bonds)
www.aarp.org/money/credit-loans-debt/reverse_mortgages/ (info on reverse
mortgages)
www.homeequityadvisor.org (alternatives to reverse mortgages)
www.ginniemae.gov (GNMA)
www.hud.gov (HUD)
www.fanniemae.com (FNMA)
www.freddiemac.com (FHLMC)
www.sifma.org (Securities Industry and Financial Markets Association)
www.mortgagemag.com (home mortgage business)
www.dtcc.com (Depository Trust and Clearing Corporation)
Annotated Chapter Outline
20.1 A Brief History of Mortgage-Backed Securities
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Mortgage-Backed Securities 20-3
Mortgage Passthroughs: Bonds representing a claim on the cash flows
of an underlying mortgage pool passed through to bondholders.
Mortgage-Backed Securities (MBSs): Securities whose investment
returns are based on a pool of mortgages.
Mortgage Securitization: The creation of mortgage-backed securities
from a pool of mortgages.
Home buyers turn to local banks or mortgage brokers for mortgage financing.
The originator then usually sells the mortgage to a repackager who accumulates
them into mortgage pools. The repackager issues mortgage-backed bonds,
where each bond claims a pro rata share of all cash flows from the pool. Each
mortgage pool is set up as a trust fund, and a servicing agent collects all
mortgage payments and passes the cash flows on to the bondholders. The
collateral for the mortgage-backed securities is the underlying pool of mortgages.
The market has grown from $1 billion of home mortgages securitized into pools
in the 1980s to almost $9 trillion today.
20.2 Fixed-Rate Mortgages
Fixed-Rate Mortgage: Loan that specifies constant monthly payments at
a fixed interest rate over the life of the mortgage.
Most home mortgages are 15- or 30-year fixed-rate mortgages with payments on
a monthly basis. Use the standard time-value-of-money calculation for an annuity
to calculate the constant monthly payment:
where:
r = annual mortgage financing rate
T = mortgage term in years
A. Fixed-Rate Mortgage Amortization
Mortgage Principal: The amount of a mortgage loan outstanding, which
is the amount required to pay off the mortgage.
Mortgage Amortization: The process of paying down mortgage principal
over the life of the mortgage.
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Monthly payment=
loan amt ×r
12
11
(
1+r
12
)
T×12
Mortgage-Backed Securities 20-4
Each monthly payment has two components: principal and interest. To compute
the interest on each payment, take the monthly interest rate times the mortgage's
remaining balance. To find the principal payment, subtract the interest payment
from the monthly mortgage payment. The process of paying down the principal
over the life of the mortgage is called mortgage amortization. An amortization
schedule, or table, describes the mortgage amortization. Figure 20.1 graphically
shows how quickly (slowly) the monthly payments amortize the principal, and
how high the interest payment is in the early years of the loan.
Lecture Tip: Having students calculate the components of a mortgage makes a
somewhat complicated concept much easier. Have them compute the loan
payment on a mortgage, explaining that it is the same calculation as figuring the
payment on an annuity. Then, walk them through two months of an amortization
schedule: compute the interest, the principal payment, and the remaining
balance. One way of reinforcing this concept is to have them set up an
amortization schedule in a spreadsheet. This process will allow them to easily
calculate 360 months of payments. The spreadsheet should show principal,
interest, and the remaining balance for each of the months, as well as a final
balance of zero after the final month. From the spreadsheet they can generate a
graph similar to Figure 20.1. If they vary the inputs, they can see how changing
the interest rate, loan amount, and term allows the other components to vary.
Reverse mortgages
In a reverse mortgage deal, borrowers (with home equity) receive monthly
payments from a lender. The house then reverts to the lender, typically when the
borrower dies. These are generally reserved for older (above 62) individuals.
B. Fixed-Rate Mortgage Prepayment and Refinancing
Mortgage Prepayment: This is the act of paying off all or part of
outstanding mortgage principal ahead of its amortization schedule.
A mortgage borrower has the right to pay off an outstanding mortgage at any
time—this is called a mortgage prepayment. This may occur for a variety of
personal reasons, such as the sale of the residence or refinancing due to falling
interest rates. The borrower may also make extra principal payments on a
monthly basis to allow the loan to be paid off more quickly. The right of the
borrower to prepay and refinance is an advantage for borrowers, but a
disadvantage to mortgage investors. The possibility that falling interest rates will
cause a large number of mortgage refinancings is a risk that mortgage investors
face.
20.3 Government National Mortgage Association
Government National Mortgage Association (GNMA): Government
agency charged with promoting liquidity in the home mortgage market.
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Mortgage-Backed Securities 20-5
Fully Modified Mortgage Pool: Mortgage pool that guarantees timely
payment of interest and principal.
Prepayment Risk: Uncertainty faced by mortgage investors regarding
early payment of mortgage principal and interest.
In 1968, Congress established the GNMA, a government agency charged with
promoting liquidity in the secondary market for home mortgages. GNMA
mortgage pools are based on programs administered by the FHA, VA and FmHA.
GNMA mortgages are fully modified because GNMA guarantees bondholders full
and timely payment of both principal and interest, even in the event of default of
the underlying mortgage. Even though investors do not face default risk, they still
face prepayment risk. GNMA cooperates with private underwriters certified by
GNMA to create mortgage pools, and after verifying that the mortgages comply
with GNMA requirements, the underwriter is authorized to issue mortgage-
backed securities with a GNMA guarantee. Over time, mortgage-backed bond
principal declines because of scheduled mortgage amortization and mortgage
prepayments.
A. GNMA Clones
Federal Home Loan Mortgage Corporation (FHLMC) and Federal
National Mortgage Association (FNMA): Government sponsored
enterprises charged with promoting liquidity in the home mortgage market.
Two government-sponsored enterprises (GSEs) that are also significant
mortgage repackaging sponsors are FHLMC (Freddie Mac) and FNMA (Fannie
Mae). Since FHLMC and FNMA are only GSEs, their fully-modified pass-
throughs don't carry the same default protection as GNMA fully-modified pass-
throughs. But, the government did step in to back them during the recent
financial crisis.
20.4 Public Securities Association Mortgage Prepayment Model
Prepayment Rate: The probability that a mortgage will be prepaid during
a given year.
Seasoned Mortgages: Mortgages over 30 months old.
Unseasoned Mortgages: Mortgages less than 30 months old.
Conditional Prepayment Rate (CPR): The prepayment rate for a
mortgage pool conditional on the age of the mortgages in the pool.
Average Life: Average time for a mortgage in a pool to be paid off.
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Mortgage-Backed Securities 20-6
Mortgage prepayments are described by stating a prepayment rate, which is the
probability that a mortgage will be prepaid in a given year. The higher the
prepayment rate, the faster the principal is paid off and the more rapid the
decline of bond principal supported by the underlying mortgage bond pool.
The prepayment rate varies substantially from year to year depending on
mortgage types and economic factors. Conventional industry practices state
prepayment rates based upon a prepayment model specified by the Public
Securities Association (PSA). Prepayment rates are specified as a percent
deviation from the 100 PSA benchmark, such as 200 PSA for 200% of the 100
PSA benchmark. Prepayment rates are stated as conditional prepayment rates
(CPRs), conditional on the age of the mortgages in a pool. For example, the CPR
for a seasoned 100 PSA mortgage is 6%. By convention, the probability of
prepayment in a given month is stated as a single monthly mortality (SMM),
calculated as
SMM = 1 - (1- CPR)1/12
Since some mortgages in a pool are prepaid earlier or later than average, the
average life of a mortgage is calculated assuming a particular prepayment
schedule. This average life is usually much less than a mortgage's stated
maturity.
20.5 Cash Flow Analysis of GNMA Fully Modified Mortgage Pools
GNMA investors receive pro rata shares of cash flows from three components:
Payment of interest on outstanding mortgage principal.
Scheduled amortization of mortgage principal.
Mortgage principal prepayments.
Reviewing Figure 20.3, notice that 50 PSA prepayments yield a nearly straight-
line amortization of bond principal, whereas with 400 PSA prepayments 90% is
amortized within 10 years of origination. Also note that 50 PSA cash flows are
fairly smooth while 400 PSAs are sharply spiked.
A. Macaulay Durations for GNMA Mortgage-Backed Bonds
Macaulay Duration: A measure of interest rate risk for fixed-income
securities.
Prepayment risk is important because it complicates the effects of interest rate
risk. With falling interest rates, prepayments speed up and the average life of
mortgages in a pool shortens. With rising interest rates, prepayments slow down
and average mortgage life lengthens. Remember from previous chapters that
Macaulay duration was used as a measure of interest rate risk. Macaulay
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Mortgage-Backed Securities 20-7
duration is not a good measure of interest rate risk for mortgage-backed bonds.
This is because Macaulay durations over-predict price increases and under-
predict price decreases for changes in mortgage-backed bond prices caused by
changing interest rates. These errors are caused by the fact that Macaulay
duration does not account for prepayment rates changing in response to interest
rate changes.
As an alternative, practitioners develop projections for mortgage prepayments by
analyzing economic variables. They then calculate predicted prices for mortgage-
backed securities based on various interest rate and prepayment scenarios.
Effective Duration for MBS: Duration measure that accounts for how mortgage
prepayments are affected by changes in interest rates.
20.6 Collateralized Mortgage Obligations
Collateralized Mortgage Obligations (CMOs): Securities created by
splitting mortgage pool cash flows according to specific allocation rules.
Interest-Only Strips (IOs): Securities that pay only the interest cash flows
to investors.
Principal-Only Strips (POs): Securities that pay only the principal cash
flows to investors.
Mortgage-backed securities with specific rules for allocating mortgage cash flows
are called CMOs, and the three best-known are:
Interest-only strips (IOs) and principal-only strips (POs)
Sequential CMOs (a type of CDO – collateralized debt obligation)
Protected amortization class securities (PACS)
A. Interest-Only and Principal-Only Mortgage Strips
Mortgage-backed securities paying only the interest component of mortgage pool
cash flows are called interest-only strips, and those paying only the principal
component are called principal-only strips. The unique structures of IOs and POs
cause bond values to react differently to the effects of changing interest rates
compounded by changing prepayment rates. Holding interest rates constant,
faster prepayments cause lower IO strip values and higher PO values, and
slower prepayments cause higher IO strip values and lower PO values. Changing
interest rates tend to cause a resulting change in the PSA prepayment schedule.
Figure 20.4 graphically shows the differences in cash flows for IOs and POs with
respect to the age of the mortgage pool.
B. Sequential Collateralized Mortgage Obligations
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Mortgage-Backed Securities 20-8
Sequential CMOs: Securities created by splitting a mortgage pool into a
number of slices.
Sequential CMOs divide a mortgage pool into a number of slices, or tranches.
The cash flows from the whole bond are passed through to each tranche
according to the following rules:
Rule 1: Mortgage principal payments. All payments of mortgage
principal, including scheduled amortization and prepayments, are paid first
to the A-tranche and then subsequently to the B, C, …., Z tranches, as
each previous tranche is fully paid.
Rule 2: Interest payments. All tranches receive interest payments in
proportion to the amount of outstanding principal in each tranche. The Z
tranche supports the interest payments required for the earlier tranches.
C. Protected Amortization Class Bonds
Protected Amortization Class Bond (PAC): Mortgage-backed security
that takes priority for scheduled payments of principal.
PAC Support Bond: Mortgage-backed security that has subordinate
priority for scheduled payments of principal. These may also be called
PAC companion bonds.
PAC Collar: Range defined by upper and lower prepayment schedules of
a PAC bond.
A PAC bond carves out a slice of a mortgage pool's cash flows according to a
rule that gives PAC bondholders first priority to promised PAC cash flows. PAC
cash flows are predictable, as long as mortgage pool prepayments remain within
a predetermined band and provide a high degree of cash flow certainty. PAC
support or PAC companion bonds receive the residual cash flow after PAC
bondholders receive their promised cash flows. PAC bonds normally specify the
following two contingency rules:
PAC contingency rule 1: When actual prepayments fall below a PAC
collar's lower bound and there are insufficient cash flows to satisfy a PAC
bond's promised cash flows, the PAC bond receives all available cash
flow. Shortfalls are carried forward and paid on a first-priority basis from
future cash flows. Non-PAC bonds receive no cash flows until all
cumulative shortfalls are paid to PAC bonds.
PAC contingency rule 2: When actual prepayments rise above a PAC
collar's upper bound, principal is paid to the non-PAC support bonds until
the outstanding principal is paid off, possibly before the PAC bond. When
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Mortgage-Backed Securities 20-9
all non-PAC principal is paid off, the PAC cash flow schedule is
abandoned and all mortgage pool cash flows are paid to PAC
bondholders.
20.7 Yields for Mortgage-Backed Securities and Collateralized Mortgage
Obligations
Cash Flow Yield: Yield to maturity for a mortgage-backed security
conditional on an assumed prepayment pattern.
The cash flow yield is the interest rate that equates the present value of all future
cash flow on the mortgage pool to the current price of the pool, assuming a
particular prepayment rate.
20.8 Summary and Conclusions
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