Transcript Slide 1

Chapter
20
McGraw-Hill/Irwin
Mortgage-Backed
Securities
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
Mortgage-Backed Securities
• Our goal in this chapter is to examine the investment
characteristics of mortgage pools.
• Mortgage pools are simply sets of home mortgages,
which are "bonds" issued by home owners.
20-2
A Brief History of
Mortgage-Backed Securities
• Traditionally, local banks wrote most home mortgages
and then held the mortgages in their portfolios of interestearning assets.
• Then, when market interest rates climbed to near 20% in
the early 1980s, bank customers flocked to withdraw
funds from their savings deposits to invest in money
market funds.
• Today, a mortgage originator usually sells the mortgage
to a mortgage repackager, who accumulates them into
mortgage pools.
20-3
A Brief History of
Mortgage-Backed Securities, Cont.
• Financed by mortgage-backed bonds (also called
mortgage pass-throughs), each mortgage pool is set up
as a trust fund.
• A servicing agent collects the mortgage payments from
the home-owners and then passes the cash flows
through to the bondholders.
• The transformation from mortgages to mortgage-backed
securities (MBSs) is called mortgage securitization.
20-4
Fixed-Rate Mortgages
• A Fixed-Rate Mortgage is a loan that specifies constant
monthly payments at a fixed interest rate over the life of
the mortgage.
• The size of the monthly payment is determined by the
requirement that the present value of all monthly
payments, based on the financing rate specified in the
mortgage contract, be equal to the original loan
amount.
20-5
Fixed-Rate Mortgage, Monthly Payments
• The equation to calculate the payment required to “retire”
a fixed rate mortgage is:
M onthlypaym e nt
loan am ount r
1

1 r
1
12

T 12
12
• In the equation, r is the annual mortgage financing rate,
and T is the number of years in the mortgage term.
20-6
Mortgage Payments Using a Spreadsheet
Monthly Payments for a 30-Year Mortgage
A 30-year mortage specifies an annual interest rate of 8 percent
and a loan amount of $100,000. What are the monthly payments?
Hint: Use the Excel function PMT.
-$733.76 =PMT(0.08/12,360,100000,0,0)
Monthly interest is 8% / 12 = 0.667%
Number of monthly payments is 12 x 30 = 360.
Initial principal is $100,000.
First zero indicates complete repayment after last monthly payment.
Second zero indicates end-of-month payments.
For a 15-year mortgage, we get a bigger monthly payment.
-$955.65 =PMT(0.08/12,360,100000,0,0)
20-7
Mortgage Payments, by Rate and Time
20-8
Fixed-Rate Mortgage Amortization
• Each monthly mortgage payment has two separate
components:
– Payment of interest on outstanding mortgage principal
– Pay-down, or amortization, of mortgage principal
• The relative amounts of each component change
throughout the life of the mortgage.
20-9
Example: Fixed-Rate Mortgage Amortization
• Suppose a 30-year $100,000 mortgage loan is financed at a fixed
interest rate of 8%.
MonthlyPaym ent
$100,000  .08 12
1  1 1  .08 12
30 12
 $733.76
• In the first month:
Interest payment = $100,000  .08/12 = $666.67
Principal payment = $733.76 – $666.67 = $67.09
New principal = $100,000 – $67.09 = $99,932.91
• In the second month:
Interest payment = $99,932.91  .08/12 = $666.22
Principal payment = $733.76 – $666.22 = $67.54
New principal = $99,932.91 – $67.54 = $99,865.37
20-10
Fixed-Rate Mortgage Amortization
• Mortgage amortization can be described by an
amortization schedule.
• An amortization schedule states the scheduled principal
payment, interest payment, and remaining principal owed
in any month.
20-11
Fixed-Rate Mortgage Amortization,
Using a Spreadsheet
Amortization Schedule for a 30-Year Mortgage
A 30-year mortage specifies an annual interest rate of 8 percent
and a loan amount of $100,000. What are the monthly interest and principal payments?
Hint: Use the Excel functions IPMT and PPMT.
After 10 years, i.e., for the 120th payment interest and principal payments are:
-$585.82 =IPMT(0.08/12,120,360,100000,0)
-$147.95 =PPMT(0.08/12,120,360,100000,0)
After 20 years, i.e., for the 240th payment interest and principal payments are:
-$405.38 =IPMT(0.08/12,240,360,100000,0)
-$328.39 =PPMT(0.08/12,240,360,100000,0)
Remaining Balance for a 30-Year Mortgage
A 30-year mortage specifies an annual interest rate of 8 percent
and a loan amount of $100,000. What is the remaining balance?
Hint: Use the Excel function CUMPRINC.
After 8 years and 4 months, the remaining balance is the present value of payment
number 101 through payment number 360.
#NAME?
=CUMPRINC(0.08/12,360,100000,101,360,0)
20-12
Mortgage Payments, by Rate and Time
20-13
Mortgage Interest and Principal,
by Age of Mortgage
20-14
Fixed-Rate Mortgage Prepayment
and Refinancing
• A mortgage borrower has the right to pay off all or part
of the mortgage ahead of its amortization schedule.
This is similar to the call feature of corporate bonds and
is known as mortgage prepayment.
• During periods of falling interest rates, mortgage
refinancings are an important reason for mortgage
prepayments.
• This means that mortgage investors face the risk of a
reduced rate of return.
20-15
Government National Mortgage Association
• The Government National Mortgage Association
(GNMA), or “Ginnie Mae,” is a government agency
charged with the mission of promoting liquidity in the
secondary market for home mortgages.
• GNMA mortgage pools are based on mortgages issued
under programs administered by
– The Federal Housing Administration (FHA)
– The Veteran’s Administration (VA), and
– The Farmer’s Home Administration (FmHA).
20-16
Government National Mortgage Association
• Mortgages in GNMA pools are said to be fully modified
because GNMA guarantees bondholders full and timely
payment of both principal and interest.
• Although investors in GNMA pass-throughs do not face
default risk, they still face prepayment risk.
– Prepayments are passed through to bondholders.
– If a default occurs, GNMA fully “prepays” the bondholders.
20-17
GNMA Clones
• Besides GNMA, there are two other significant mortgage
repackaging sponsors.
– Federal Home Loan Mortgage Corporation (FHLMC), or “Freddie
Mac,” and
– Federal National Mortgage Association (FNMA), or “Fannie
Mae.”
• Both are government-sponsored enterprises (GSEs) and
trade on the New York Stock Exchange.
20-18
GNMA Clones, Cont.
• Like GNMA, both FHLMC and FNMA operate with
qualified underwriters who accumulate mortgages into
pools financed by an issue of bonds.
• However, because FHLMC and FNMA are only GSEs,
their fully modified pass-throughs do not carry the same
default protection as GNMA fully modified passthroughs.
• That is, Congress may or may not be willing to rescue a
financially strapped GSE.
20-19
PSA Mortgage Prepayment Model, I.
• Mortgage prepayments are typically described by stating
a prepayment rate, which is the probability that a
mortgage will be prepaid in a given year.
• Conventional industry practice states prepayment rates
using a model specified by the Public Securities
Association (PSA).
– Prepayment rates are stated as a percentage of a PSA
benchmark.
20-20
PSA Mortgage Prepayment Model, II.
• In the PSA model, the rates are conditional on the age of
the mortgages in the pool. They are conditional
prepayment rates (CPRs).
• For seasoned ( > 30 months old) mortgages, the CPR is
constant at 6% annually for 100% of the PSA benchmark
(100 PSA).
• For unseasoned (< 30 months old) mortgages, the CPR
rises steadily in each month until it reaches an annual
rate of 6% in month 30 (for 100 PSA).
20-21
PSA Mortgage Prepayment Model, III.
20-22
PSA Mortgage Prepayment Model, SMM
• By convention, the probability of prepayment in a given
month is stated as a single monthly mortality (SMM).
• The SMM is based on the conditional prepayment rate,
CPR.
• The equation for an SMM is:
SMM = 1 – (1 – CPR)1/12
20-23
PSA Mortgage Prepayment Model,
Average Life
• The average life of a mortgage in a pool is the average time for a
single mortgage in the pool to be paid off, either by prepayment
or by making scheduled payments until maturity.
• For a pool of 30-year mortgages:
Prepayment Schedule
50 PSA
100 PSA
200 PSA
400 PSA
Average Mortgage Life (years)
20.40
14.68
8.87
4.88
20-24
Cash Flow Analysis
GNMA Fully Modified Mortgage Pools
• Each month, GNMA mortgage-backed bond investors
receive pro rata shares of cash flows derived from fully
modified mortgage pools.
• Each monthly cash flow has three components (less the
servicing and guarantee fees):
– Payment of interest on outstanding mortgage principal.
– Scheduled amortization of mortgage principal.
– Mortgage principal prepayments.
20-25
Principal and Cash Flows for a GNMA Bond
20-26
Macaulay Durations
for GNMA Mortgage-Backed Bonds
• The interest rate risk for a bond is often measured by
Macaulay duration, which assumes a fixed schedule of
cash flow payments.
• However, the schedule of cash flow payments for
mortgage-backed bonds is not fixed.
– With falling interest rates, prepayments speed up, and vice versa.
20-27
Macaulay Durations
for GNMA Mortgage-Backed Bonds
• Historical experience indicates that interest rates
significantly affect prepayment rates, and that Macaulay
duration is a very conservative measure of interest rate
risk.
• In practice, effective duration is used to calculate
predicted prices for mortgage-backed securities based on
hypothetical interest rate and prepayment scenarios.
20-28
Collateralized Mortgage Obligations
• Collateralized mortgage obligations (CMOs) are
securities created by splitting mortgage pool cash flows
according to specific allocation rules.
• The three best-known types of CMOs are:



interest-only (IOs) and principal-only (POs) strips,
sequential CMOs, and
protected amortization class securities (PACs).
20-29
Interest-Only and Principal-Only Strips
• Interest-only strips (IOs) pay only the interest cash flows
to investors, while principal-only strips (POs) pay only the
principal cash flows to investors.
• IO strips and PO strips behave quite differently in
response to changes in prepayment rates and interest
rates.
– Faster prepayments imply lower IO strip values and higher PO
strip values, and vice versa.
20-30
Cash Flows for GNMA IO and PO Strips
20-31
Sequential CMOs, I.
• Sequential CMOs carve a mortgage pool into a number
of tranches (slices).
– For example, A, B, C, and Z-tranches.
• Each tranche is entitled to a share of mortgage pool
principal and interest on that share of principal.
• However, because cash flows are distributed
sequentially, this creates securities with a range of
maturities.
20-32
Sequential CMOs, II.
• Cash flows are passed through as follows:
– All principal payments goes to the topmost tranche (in
alphabetical order), until all the principal in that tranche has been
paid off.
– Except for the Z-tranche, all tranches receive proportionate
interest payments, which are passed through immediately.
– Until all the principal in the topmost tranche has been fully paid
off, interest on Z-tranche principal is paid as cash to the topmost
tranche in exchange for an equal amount of principal.
20-33
Sequential CMO Principal and Cash Flows
20-34
Protected Amortization Class Bonds
• Protected amortization class (PAC) bonds take priority
for scheduled payments of principal.
• The residual cash flows are paid to PAC support (or
companion) bonds.
• PAC cash flows are predictable as long as prepayments
remain within a specified band.
20-35
Protected Amortization Class Bonds, Cont.
• Creating a PAC bond entails three steps.

Specify two PSA prepayment schedules that form the upper and
lower prepayment bounds of the PAC bond. These bounds define
a PAC collar.

Calculate principal-only (PO) cash flows for the two prepayment
schedules specified in .

On a priority basis, at any point in time, PAC bondholders receive
payments of principal according to the PSA prepayment schedule
with the lower PO cash flow as calculated in .
20-36
PAC Cash Flows and Total Cash Flows
20-37
Yields for MBSs and CMOs
• The yield to maturity for a mortgage-backed security,
conditional on an assumed prepayment pattern, is called
the cash flow yield.
• Essentially, cash flow yield is the interest rate that
equates the present value of all future cash flows on the
mortgage pool to the current price of the pool, assuming
a particular prepayment rate.
20-38
MBS Yields
20-39
Useful Websites
• www.investinginbonds.com (for information on bonds, bonds, bonds)
• www.ginniemae.gov (GNMA)
• www.hud.gov (HUD)
• www.fanniemae.com (FNMA)
• www.freddiemac.com (FHLMC)
• www.bondmarkets.com (Visit the Public Securities Association)
20-40
Chapter Review, I.
• A Brief History of Mortgage-Backed Securities
• Fixed-Rate Mortgages
– Fixed-Rate Mortgage Amortization
– Fixed-Rate Mortgage Prepayment and Refinancing
• Government National Mortgage Association
– GNMA Clones
• Public Securities Association Mortgage Prepayment
Model
20-41
Chapter Review, II.
• Cash Flow Analysis of GNMA Fully Modified Mortgage
Pools
– Macaulay Durations for GNMA Mortgage-Backed Bonds
• Collateralized Mortgage Obligations
– Interest-Only and Principal-Only Mortgage Strips
– Sequential Collateralized Mortgage Obligations
– Protected Amortization Class Bonds
• Yields for Mortgage-Backed Securities and Collateralized
Mortgage Obligations
20-42