Transcript Mortgage-Backed Securities

Residential Mortgages and
Mortgage-Backed Securities
1
Mortgage-Backed Securities
2
Mortgage-Backed Securities
 A mortgage originator with a pool of mortgages has the
option of holding the portfolio, selling it, or selling it to be
used to securitize a MBS issue or deal.
 Depending on the types of mortgages, the originator who
sells mortgages to become a securitized asset can sell
them to one of the three agencies (Fannie Mae, Ginnie
Mae, or Freddie Mac) or to a private-sector conduit.
 As noted in Chapter 7, Fannie Mae and Freddie Mac are Governmentsponsored enterprises (GSEs), whereas Ginnie Mae is a federal
agency. In our discussion of MBSs, we will refer to all three as being
agencies.
3
Mortgage-Backed Securities
 Agency MBSs are MBSs created by one of the agencies;
they are collectively referred to as agency MBSs,
 Nonagenecy MBS are MBS created by private conduits;
also called private labels.
4
Mortgage-Backed Securities
 Residential mortgages can be divided into prime and
subprime mortgages.
 Prime mortgages include those that are both
conforming (meet the agency’s underwriting
standards) and nonconforming but still meeting credit
quality standards.
 Subprime mortgages include those with low credit
ratings.
5
Mortgage-Backed Securities
Note:
 Typically, agency residential MBSs are created from
conforming loans.
 In more recent periods, though, agency MBS issues
backed by pools of lower quality mortgages were issued.
 All other mortgages that are securitized are nonagency
MBS.
6
Mortgage-Backed Securities
 After the mortgages are sold to an agency or private
conduit, the originator typically continues to service the
loan for a service fee (that is, collect payments, maintain
records, forward tax information, and the like).
 The service fee is typically a fixed percentage (25 to 100
basis points) of the outstanding balance.
 The originator can also sell the servicing to another party.
 Investors who buy the MBSs receive a pro rata share from
the cash flow of the pool of mortgages.
7
Ginnie Mae Mortgage-Backed Securities
 Ginnie Mae (Government National Mortgage
Association's (GNMA)) is a true federal agency.
 As such, the MBSs that it guarantees are backed by the
full faith and credit of the U.S. government.
8
Ginnie Mae Mortgage-Backed Securities
Creation
 Ginnie Mae MBSs are put together by a lender/originator
(bank, thrift, or mortgage banker), who presents a block of
mortgages that meets Ginnie Mae’s underwriting
standards.
 If Ginnie Mae finds them in order, it will issue a guarantee
and assign a pool number that identifies the MBS that is to
be issued.
 The lender will then transfer the mortgages to a trustee,
and then issue the pass-through securities as a Ginnie Mae
pass-through security.
9
Ginnie Mae Mortgage-Backed Securities
Features
 Ginnie Mae provides the guarantee, but does not issue the
Ginnie Mae MBS.
 Thus, different from the standard MBS that is issued by
the other agencies or a conduit, Ginnie Mae MBSs are
issued by the lenders.
 The minimum denomination on a Ginnie Mae passthrough is $25,000 and the minimum pool is $1 million.
10
Ginnie Mae Mortgage-Backed Securities
Types
 The mortgages underlying Ginnie Mae MBSs can be
grouped into one of two Ginnie Mae MBS programs:
Ginnie Mae I and Ginnie Mae II.
1. The Ginnie Mae I program consists of MBSs backed
by single-family and multifamily mortgage loans that
have a fixed note rate and are sold by only one issuer.
2. The Ginnie Mae II program consists of just singlefamily mortgage loans that can have either fixed or
adjustable rates and have multiple issuers.
11
Fannie Mae and Freddie Mac
Mortgage-Backed Securities
 Fannie Mae and Freddie Mac are Government-sponsored
enterprises (GSE) initially created to provide a secondary
market for mortgages.
 Today, there activities include not only the buying and
selling of mortgages, but also creating and guaranteeing
mortgage-backed pass-through securities, as well as
buying MBSs.
12
Fannie Mae and Freddie Mac
Mortgage-Backed Securities
Note:
 Both GSEs are regulated by the Office of Federal
Housing Enterprise Oversight (OFHEO) and both were
placed in conservatorship in September 2008.
 Prior to being placed in conservatorship, the Fannie
Mae and Freddie Mac MBSs were guarantee by each
of the companies, but not the government.
 As part of the banking bailout in 2008, though,
government backing was provided to their MBSs.
13
Fannie Mae and Freddie Mac
Mortgage-Backed Securities
 Freddie Mac issues MBSs that it refers to as
participation certificates (PCs).
 Freddie Mac and Fannie Mae have regular MBSs (also
called a cash PC), which are backed by a pool of
conforming mortgages that they have purchased from
mortgage originators.
 They also offer a pass-though formed through their
Guarantor/Swap Program. In this program, mortgage
originators can swap mortgages for a Fannie Mae or
Freddie Mac pass-through.
14
Fannie Mae and Freddie Mac
Mortgage-Backed Securities
 Unlike Ginnie Mae, Fannie Mae’s and Freddie Mac's
MBSs are formed with more heterogeneous mortgages.
 The minimum denomination on a Freddie Mac and
Fannie Mae pass-through is $100,000 and their
mortgage pools range up to several hundred million
dollars.
15
Nonagency MBS
 Nonagency pass-throughs or private labels are sold by
commercial banks, investment banks, other thrifts, and
mortgage bankers.
 As noted, nonagency pass-throughs are often formed
with prime or subprime nonconforming mortgages.
 Larger issuers of nonagency MBSs include Citigroup,
Bank of America, and G.E. Capital Mortgage.
16
Nonagency MBS
Features
 Nonagency MBSs are often guaranteed against default
through external credit enhancements, such as the
guarantee of a corporation or a bank letter of credit or by
private insurance from a monocline insurer.
 Many are also guaranteed internally through the
creation of senior and subordinate classes of bonds
with different priority claims on the pool's cash flows in
the case some of the mortgages in the pool default.
 The more subordinate claims sold relative to the
senior claims, the more secure the senior claims.
17
Nonagency MBS
Features
Nonagency MBSs are rated by Moody's
and Standard and Poor's.
They must be registered with the SEC
when they are issued.
18
Nonagency MBS
Features
 Most financial entities that issue private-label MBSs or
derivatives of MBSs are legally set up so that they do not
have to pay taxes on the interest and principal that passes
through them to their MBS investors.
 The requirements that MBS issuers must meet to ensure
tax-exempt status are specified in the Tax Reform Act of
1983 in the section on trusts referred to as Real Estate
Mortgage Investment Conduits, REMIC.
 Private-labeled MBS issuers who comply with these
provisions are sometimes referred to as REMICs.
19
Nonagency MBS
Features
 Nonagency residential MBSs differ fundamentally from
agency MBSs in that their cash flows are subject to
default risk, whereas agency MBSs with their
government and agency guarantees are considered
default free.
20
Cash Flows
 Cash flows from MBSs are generated from the cash
flows from the underlying pool of mortgages, minus
servicing and other fees.
 Typically, fees for constructing, managing, and
servicing the underlying mortgages (also referred to as
the mortgage collateral) and the MBSs are equal to the
difference between the rates associated with the
mortgage pool and the rate that is paid to the MBS
investors (pass-through (PT) rate).
21
Cash Flows: Terms
1. Weighted Average Coupon Rate, WAC:
Mortgage portfolio's (collateral’s) weighted
average rate.
2. Weighted Average Maturity, WAM: Mortgage
portfolio's weighted average maturity.
3. Pass-Through Rate, PT Rate: Interest rate paid
on the MBS; PT rate is lower than WAC—the
difference going to the MBS issuer.
4. Prepayment Rate or Speed: Assumed prepayment
rate.
22
Cash Flow from a MBS
Example
 The next slide shows the monthly cash flows for a
MBS issue constructed from a $100 million mortgage
pool with the following features:
1. Current balance = $100 million
2. WAC = 8%
3. WAM = 355 months
4. PT rate = 7.5%
5. Prepayment speed equal to 150% of the standard
PSA model: PSA = 150
23
Projected Cash Flows from an Agency MBS Issue
Mortgage Portfolio = $100,000,000, WAC = 8%, WAM = 355
Months, PT Rate = 7.5%, Prepayment: 150 PSA
24
Cash Flow from a MBS
Notes:
1. The first month's CPR for the MBS issue reflects a 5month seasoning in which t = 6, and a speed that is
150% greater than the 100 PSA. For the MBS issue, this
yields a first month SMM of .0015125 and a constant
SMM of .0078284 starting in month 25.
2. The WAC of 8% is used to determine the mortgage
payment and scheduled principal, whereas the PT rate of
7.5% is used to determine the interest.
3. The monthly fees implied on the MBS issue are equal to
.04167% = (8% − 7.5%)/12 of the monthly balance.
25
Cash Flow from a MBS
 First Month’s Payment:
$100,000,000
p 
 $736,268
355
11 /(1(.08 / 12)) 


.
08
/
12


WAC
26
Cash Flow from a MBS
 From the $736,268 payment, $625,000 would go towards
interest and $69,601 would go towards the scheduled
principal payment:
PT Rate
WAC
 RA 
 .075
F0  
Interest  
$100,000,000  $625,000
12
12




Scheduled P r incipal P ayment  p  Interest  $736,268 [(.08 / 12)($100,000,000)]
Scheduled P r incipal P ayment $69,601
27
Cash Flow from a MBS
 Using 150% PSA model and seasoning of 5 months
the first month SMM = .0015125:
 6 
CPR  1.50 .06  .018
 30 
SMM  1  [1.018]1/12  .0015125
28
Cash Flow from a MBS
 Given the prepayment rate, the projected prepaid
principal in the first month is $151,147
prepaid principal  SMM [F0  Scheduled principal]
prepaid principal  .0015125
[$100,000,000 $69,601]
prepaid principal  $151,147
Allow for slight rounding differences
29
Cash Flow from a MBS
 Thus, for the first month, the MBS would generate an estimated
cash flow of $845,748 and a balance at the beginning of the
next month of $99,779,252:
CF  Interest Scheduled principal prepaid principal
CF  $625,000  $ 69,601  $151,147  $845,748
Beginning Balance for Month 2  F0  Scheduled principal prepaid principal
Beginning Balance for Month 2  $100,000,000  $69,601  $151,147
Beginning Balance for Month 2  $99,779,252
Allow for slight rounding differences
30
Cash Flow from a MBS
 Second Month: Payment, Interest, Scheduled Principal,
Prepaid Principal, and Cash flow:
p 
$99,779,252
 $735,154
354
11 /(1(.08 / 12)) 


.08 / 12


 RA 
 .075
F0  
Interest  
$99,779,252  $623,620
12
12




Scheduled P r incipal P ayment p  Interest  $735,154 [(.08 / 12)($99,779,252)]
Scheduled P r incipal P ayment $69,959
 7 
CP R  1.50 .06  .021
 30 
SMM  1  [1.021]1/12  .0017671
prepaid principal  SMM [F0  Scheduled principal]
prepaid principal  .0017671[$99,779,252 $69,959]  $176,194
CF  Interest  Scheduled principal prepaid principal
CF  $623,620  $69,959  $176,194  $869,773
Allow for slight rounding differences
31
Market
 As noted, investors can acquire newly issued
mortgage-backed securities from the agencies,
originators, or dealers specializing in specific passthrough.
 There is also a secondary market consisting of
dealers who operate in the OTC market as part of the
Mortgage-Backed Security Dealers Association.
 These dealers form the core of the secondary market
for the trading of existing pass-through.
32
Market
 MBSs are normally sold in denominations
ranging from $25,000 to $250,000, although
some privately-placed issues are sold with
denominations as high as $1 million.
33
Price Quotes
 The prices of MBSs are quoted as a percentage of the
underlying MBS issue’s balance.
 The mortgage balance at time t, Ft, is usually calculated
by the servicing institution and is quoted as a proportion
of the original balance, F0.
 This proportion is referred to as the pool factor, pf:
pft 
Ft
F0
34
Price Quotes
Example:
 A MBS backed by a mortgage pool originally worth $100 million
 Current pf of 0.92
 quoted at 95 - 16 (Note: 16 is 16/32)
 The current balance, Ft, would be $92 million and the market
value would be $87.86 million:
Ft  (pft )F0
Ft  (.92)($100,000,000)  $92,000,000
Market Value  (.9550)($92,000,000)  $87,860,000
35
Price Quotes
Note:
 The market value is the clean price; it does not take into
account accrued interest.
 For MBS, accrued interest is based on the time period
from the settlement date (typically two days after the
trade) and the first day of the next month.
36
Price Quotes
Example:
 If the time period is 20 days, the month is 30 days, and the
WAC = 9%, then the accrued interest is $460,000:
 20  .09 
Accrued Interest   
 $92,000,000  $460,000
 30  12 
 The full market value (clean price plus accrued interest)
would be $88,320,000:
Full Mkt Value  $87,860,000  $460,000
Full Mkt Value  $88,320,000
37
Price Quotes
 The market price per share is the full market value
divided by the number of shares.
Example:
 If the number of shares is 400, then the price of the
MBS based on a 95 - 16 quote would be $220,800:
$88,320,000
400
MBS priceper share  $220,800
MBS priceper share 
38
Extension Risk
 Like other fixed-income securities, the value of
a MBS is determined by the MBS's future cash
flow (CF), maturity, default risk, and other
features germane to fixed-income securities.
M
VMBS
CFt
 
t
(
1

R
)
t 1
VMBS  f (CFt , R )
39
Extension Risk
 In contrast to other bonds, MBSs are also
subject to prepayment risk.
 Prepayment affects the MBS’s CF.
 Prepayment, in turn, is affected by interest rates.
40
Extension Risk
 Thus, interest rates affects the MBS’s CFs:
VMBS  f (CF, R)
CF  f (R )
41
Extension Risk
 With the CF a function of rates, the value of a
MBS is more sensitive to interest rate changes
than those bonds whose CFs are not.
 This sensitivity is known as extension risk.
42
Extension Risk
 If interest rates decrease, then the prices of MBSs, like
the prices of most bonds, would increase as a result of
the lower discount rates.
 However, the decrease in rates will also augment
prepayment speed, causing the earlier cash flow of the
mortgages to be larger which, depending on the level of
rates and the maturity remaining, could also contribute
to increasing the MBS’s price.
43
Extension Risk
Rate Decrease
like most bonds
 R   lower discount rate  VM 
 R   Increases prepayment Earlier CFs   VM  or 
44
Extension Risk
 If interest rates increase, then the prices of
MBSs will decrease as a result of higher
discount rates and possibly the smaller
earlier cash flow resulting from lower
prepayment speeds.
45
Extension Risk
Rate Increase
like most bonds

R   greaterdiscount rate  VM 

R   Decreases prepayment Earlier CFs   VM  or 
46
Average Life
 The average life of a MBS or mortgage portfolio is the
weighted average of the security’s time periods, with the
weights being the periodic principal payments (scheduled
and prepaid principal) divided by the total principal:
1 T
Average Life 
t

12 t 1
 principal received at

total principal

t


47
Average Life
 The average life for the MBS issue with WAC = 8%, WAM
= 355, PT Rate = 7.5%, and PSA = 150 is 9.18 years
1  1($220,748)  2($246,153)      355($49,061
Average Life  

12 
$100,000,000

Average Life  9.18 years
48
Average Life
 The average life of a MBS depends on
prepayment speed:
 If the PSA speed of the $100 million MBS issue were
to increase from 150 to 200, the MBS’s average life
would decrease from 9.18 to 7.55, reflecting greater
principal payments in the earlier years.
 If the PSA speed were to decrease from 150 to 100,
then the average life of the MBS would increase to
11.51.
49
Average Life and Prepayment Risk
 For MBSs and mortgage portfolios, prepayment risk can be
evaluated in terms of how responsive a MBS's or mortgage
portfolio’s average life is to changes in prepayment speeds:
Average Life
prepayment risk 
PSA
50
Average Life and Prepayment Risk
 A MBS with an average life that did not change with PSA
speeds, in turn, would have stable principal payments over
time and would be absent of prepayment risk.
 Av life
 0  Zero prepayment risk
PSA
51
MBS Derivatives
52
MBS Derivatives
 One of the more creative developments in the security
market industry over the last three decades has been
the creation of derivative securities formed from
MBSs and mortgage portfolios that have different
prepayment risk characteristics, including some that
are formed that have average lives that are invariant
to changes in prepayment rates.
 The most popular of these derivatives are
 Collateralized Mortgage Obligations, CMOs
 Stripped MBS
53
Collateralized Mortgage Obligations
 Collateralized mortgage obligations, CMOs, are
formed by dividing the cash flow of an
underlying pool of mortgages or a MBS issue into
several classes, with each class having a different
claim on the mortgage collateral and with each
sold separately to different types of investors.
54
Collateralized Mortgage Obligations
 The different classes making up a CMO are
called tranches or bond classes.
 There are two general types of CMO tranches:
1. Sequential-Pay Tranches
2. Planned Amortization Class Tranches, PAC
55
Sequential-Pay Tranches
 A CMO with sequential-pay tranches, called a
sequential-pay CMO, is divided into classes with
different priority claims on the collateral's principal.
 The tranche with the first priority claim has its principal
paid entirely before the next priority class, which has its
principal paid before the third class, and so on.
 Interest payments on most CMO tranches are made until
the tranche's principal is retired.
56
Sequential-Pay Tranches
Example:
 A sequential-pay CMO is shown in Slide 59.
 This CMO consist of three tranches, A, B, and C, formed
from the collateral making up the $100 million MBS in
the previous example: F = $100 million, WAM = 355,
WAC = 8%, PT Rate = 7.5%, PSA = 150.
 Tranche A = $50 million
 Tranche B = $30 million
 Tranche C = $20 million
57
Sequential-Pay Tranches
 Priority Disbursement Rules:
1.
Tranche A receives all principal payment from the collateral
until its principal of $50 million is retired. No other tranche's
principal payments are disbursed until the principal on A is paid.
2.
After tranche A's principal is retired, all principal payments from
the collateral are then made to tranche B until its principal of
$30 million is retired.
3.
Finally, tranche C receives the remaining principal that is equal
to its par value of $20 million.
4.
Although the principal is paid sequentially, each tranche does
receive interest each period equal to its stated PT rate (7.5%)
times its outstanding balance at the beginning of each month.
58
Cash Flows from Sequential-Pay CMO
Collateral: Balance = $100m, WAM = 355 Months, WAC = 8%, PT Rate = 7.5%,
Prepayment: 150 PSA, Tranches: A: $50 million, B = $30 million, C = $20 million
59
Sequential-Pay Tranches
 Given the assumed PSA of 150, the first month cash
flow for tranche A consist of a principal payment
(scheduled and prepaid) of $220,748 and an interest
payment of $312,500:
Interest = (.075/12)($50,000,000) = $312,500
 In month 2, tranche A receives an interest payment of
$311,120 based on the balance of $49,779, 252 and a
principal payment of $246,153.
60
Sequential-Pay Tranches
 Based on the assumption of a 150% PSA speed, it takes
88 months before A's principal of $50M is retired.
 During the first 88 months, the cash flows for tranches B
and C consist of just the interest on their balances, with no
principal payments made to them.
 Starting in month 88, tranche B begins to receive the
principal payment.
 Tranche B is paid off in month 180, at which time
principal payments begin to be paid to tranche C.
 Finally, in month 355 tranche C's principal is retired.
61
Sequential-Pay Tranches
Features of Sequential-Pay CMOs
 By creating sequential-pay tranches, issuers
of CMOs are able to offer investors
maturities, principal payment periods, and
average lives different from those defined by
the underlying mortgage collateral.
62
Sequential-Pay Tranches
Features of Sequential-Pay CMOs
 Maturity:





Window: The period between the beginning and ending principal
payment is referred to as the principal pay-down window:





Collateral's maturity = 355 months (29.58 years)
Tranche A’s maturity = 88 months (7.33 years)
Tranche B's maturity = 180 months (15 years)
Tranche C’s maturity = 355 months (29.58 years)
Collateral’s window = 355 months
Tranche A’s window = 87 months
Tranche B's window = 92 months
Tranche C's window =176 months
Average Life:




Collateral's average = 9.18 years
Tranche A’s average life = 3.69 years
Tranche B’s average life = 10.71 years
Tranche C’s Average life = 20.59 years
63
Sequential-Pay Tranches
Features of Sequential-Pay CMOs
 A CMO tranche with a lower average life is still susceptible
to prepayment risk.
 The average life of each of the tranches still varies as
prepayment speed changes.
PSA
50
100
150
200
300
Collateral
14.95
11.51
9.18
7.55
5.5
Tranche A
7.53
4.92
3.69
3.01
2.26
Tranche B
19.4
14.18
10.71
8.51
6.03
Tranche C
26.81
23.99
9.18
17.46
12.82
64
Sequential-Pay Tranches
Note:
 Issuers of CMOs are able to offer a number
of CMO tranches with different maturities
and windows by simply creating more
tranches.
65
Different Types of Sequential-Pay Tranches
 Sequential-pay CMOs often include tranches with
special features. These include:
1. Accrual Bond Tranche
2. Floating-Rate Tranche
3. Notional Interest-Only Tranche
66
Accrual Tranche
 Many sequential-pay CMOs have an accrual bond
class.
 Such a tranche, also referred to as the Z bond, does not
receive current interest but instead has it deferred.
 The Z bond's current interest is used to pay down the
principal on the other tranches, increasing their speed
and reducing their average life.
67
Accrual Tranche
Example:
 Suppose in our preceding sequential-pay CMO example
we make tranche C an accrual tranche in which its
interest of 7.5% is to paid to the earlier tranches and its
principal of $20 million and accrued interest is to be paid
after tranche B's principal has been retired
 Slide 69 shows the principal and interest payments from
the collateral and Tranches A, B, and Z.
68
Cash Flows From Sequential-Pay CMO with Z Tranche
Collateral: Balance = $100M, WAM = 355 Months, WAC = 8%, PT Rate =
7.5%, Prepayment: 150 PSA, Tranches: A: $50M, B = $30M, C = $20M
69
Accrual Tranche
Features

Since the accrual tranche's current interest of $125,000 is now used to
pay down the other classes' principals, the other tranches now have lower
maturities and average lives.

For example, the principal payment on tranche A is $345,748 in the first
month ($220,748 of scheduled and projected prepaid principal and
$125,000 of Z's interest); in contrast, the principal is only $220,748 when
there is no Z bond.

As a result of the Z bond, tranche A's window is reduced from 87 months
to 69 months and its average life from 3.69 years to 3.06 years.
Tranche
A
B
Window
Average Life
69 Months 3.06 Years
54 Months 8.23 Years
70
Floating-Rate Tranche
 In order to attract investors who prefer floating-rate
securities, CMO issuers often create floating-rate and
inverse floating-rate tranches.
 The monthly coupon rate on the floating-rate tranche is
usually set equal to a reference rate such as the London
Interbank Offer Rate, LIBOR, while the rate on the
inverse floating-rate tranche is determined by a formula
that is inversely related to the reference rate.
71
Floating-Rate Tranche
 Example: Sequential-pay CMO with a floating and
inverse floating tranches
Tranche
A
FR
IFR
Z
Total

Par Value
$50 million
$22.5 million
$7.5 million
$20 million
$100 million
PT Rate
7.5%
LIBOR + 50bp
28.3 – 3 LIBOR
7.5%
7.5%
Note: The CMO is identical to the preceding CMO, except that
tranche B has been replaced with a floating-rate tranche, FR, and an
inverse floating-rate tranche, IFR.
72
Floating-Rate Tranche
 The rate on the FR tranche, RFR, is set to the LIBOR plus
50 basis points, with the maximum rate permitted being
10%.
 The rate on the IFR tranche, RIFR, is determined by the
following formula:
RIFR = 28.5 − 3 LIBOR
 This formula ensures that the weighted average coupon
rate (WAC) of the two tranches will be equal to the
coupon rate on tranche B of 7.5%, provided the LIBOR is
less than 9.5%.
73
Floating-Rate Tranche
 Example: If the LIBOR is 8%, then the rate on the FR
tranche is 8.5%, the IFR tranche's rate is 4.5%, and the
WAC of the two tranches is 7.5%:
LIBOR  8%
R FR  LIBOR  50bp  8.5%
R IFR  28.5  3 LIBOR  4.5%
WAC  .75R FR  .25R IFR  7.5%
74
Notional Interest-Only Class
 Each of the fixed-rate tranches in the previous CMOs
have the same coupon rate as the collateral rate of 7.5%.
 Many CMOs are structured with tranches that have
different rates.
 When CMOs are formed this way, an additional tranche,
known as a notional interest-only (IO) class, is often
created.
 The notional interest-only tranche receives the excess
interest on the other tranches’ principals, with the excess
rate being equal to the difference in the collateral’s PT
rate minus the tranches’ PT rates.
75
Notional Interest-Only Class
Example:
 A sequential-pay CMO with a Z bond and notional IO
tranche is shown in the next slide.
 This CMO is identical to the previous CMO with a Z
bond, except that each of the tranches has a rate lower
than the collateral rate of 7.5% and there is a notional
IO class.
76
Sequential-Pay CMO with Notional IO Tranche
Collateral: Balance = $100m, WAM = 355 Months, WAC = 8%, PT
Rate = 7.5%, Prepayment: 150 PSA, Tranches: A: $50m, B = $30m,
Z = $20m, Notional IO = $15.333333m
77
Notional Interest-Only Class
 The notional IO class receives the excess interest on each
tranche's remaining balance, with the excess rate based on
the collateral rate of 7.5%.
 In the first month, for example, the IO class would receive
interest of $87,500:
 .075 .06 
 .075 .065
Interest 
$50,000,000  
$30,000,000
12
 12 


Interest $62,500  $25,000  $87,500
78
Notional Interest-Only Class
 The IO class is described as paying 7.5% interest on a
notional principal of $15,333,333.
 This notional principal is determined by summing each
tranche's notional principal.
 A tranche's notional principal is the number of dollars
that makes the return on the tranche's principal equal to
7.5%.
79
Notional Interest-Only Class
 The notional principal for tranche A is $10,000,000, for
B, $4,000,000, and for Z, $1,333,333, yielding a total
notional principal of $15,333,333:
($50,000,000)(.075 .06)
 $10,000,000
.075
$30,000,000)(.075 .065)
B' s Not ionalprincipal
 $4,000,000
.075
($20,000,000)(.075 .07)
Z' s Not ionalprincipal
 $1,333,333
.075
A ' s Not ionalprincipal
T ot alNot ionalprincipal $15,333,333
80
Planned Amortization Class, PAC
 A CMO with a planned amortization class, PAC, is
structured such that there is virtually no prepayment
risk.
 In a PAC-structured CMO, the underlying mortgages or
MBS (i.e., the collateral) is divided into two general
tranches:
1. The PAC (also called the PAC bond)
2. The support class (also called the support bond or
the companion bond)
81
Planned Amortization Class, PAC
 The two tranches are formed by generating two
monthly principal payment schedules from the
collateral:
 One schedule is based on assuming a relatively low
PSA speed – lower collar.
 The other schedule is based on assuming a
relatively high PSA speed – upper collar.
 The PAC bond is then set up so that it will receive a
monthly principal payment schedule based on the
minimum principal from the two principal payments.
82
Planned Amortization Class, PAC
 The PAC bond is designed to have no
prepayment risk provided the actual
prepayment falls within the minimum and
maximum assumed PSA speeds.
 The support bond, on the other hand,
receives the remaining principal balance and
is therefore subject to prepayment risk.
83
Planned Amortization Class, PAC
Example
 PAC and support bond formed from the $100 million
collateral with WAC = 8%, WAM = 355 months, and
PT rate = 7.5%
 Minimum monthly principal payments for the PAC
generated using 100 and 300 collars:
 Lower Collar = 100 PSA: Minimum speed of 100%
PSA
 Upper Collar = 300 PSA: Maximum speed of 300%
PSA
84
Planned Amortization Class, PAC
 The next slide shows the cash flows for the PAC,
collateral, and support bond. The exhibit shows:
 In columns 2 and 3 the principal payments
(scheduled and prepaid) for selected months at both
collars.
 In the fourth column the minimum of the two
payments.
 For example, in the first month the principal payment is
$170,085 for the 100% PSA and $374,456 for the
300% PSA; thus, the principal payment for the PAC
would be $170,085.
85
PAC And Support Bonds
PAC formed 100 and 300 PSA Model
Collateral: Balance = $100m, WAM = 355 Months,
WAC = 8%, PT Rate = 7.5%, Prepayment: 150 PSA
86
Planned Amortization Class, PAC
Note:
 For the first 98 months, the minimum principal
payment comes from the 100% PSA collar,
and from month 99 on the minimum principal
payment comes from the 300% PSA collar.
87
Planned Amortization Class, PAC
 Based on the 100-300 PSA range, a PAC bond
can be formed that would promise to pay the
principal based on the minimum principal
payment schedule shown in the exhibit.
 The support bond would receive any excess
monthly principal payment.
88
Planned Amortization Class, PAC
 The sum of the PAC's principal payments is $63.777
million. Thus, the PAC can be described as having:
 Par value of $63.777 million
 Coupon rate of 7.5%
 Lower collar of 100% PSA
 Upper collar of 300% PSA
 The support bond, in turn, would have a par value of
$36.223 million ($100 million − $63.777 million) and
pay a coupon of 7.5%.
89
Planned Amortization Class, PAC
 The PAC bond has no prepayment risk as long as the
actual prepayment speed is between 100 and 300.
 This can be seen by calculating the PAC's average life
given different prepayment rates.
 The next exhibit shows the average lives for the
collateral, PAC bond, and support bond for various
prepayment speeds ranging from 50% PSA to 350%
PSA.
90
Planned Amortization Class, PAC
 The average lives for the collateral, PAC bond, and support
bond for various prepayment speeds ranging from 50% PSA
to 350% PSA.
PSA
50
100
150
200
250
300
350
Collateral
14.95
11.51
9.18
7.55
6.37
5.50
4.84
Average Life
PAC
7.90
6.98
6.98
6.98
6.98
6.98
6.34
Support
21.50
19.49
13.05
8.55
5.31
2.91
2.71
91
Planned Amortization Class, PAC
Features:
 The PAC bond has an average life of 6.98 years between
100% PSA and 300% PSA; its average life does change,
though, when prepayment speeds are outside the 100300 PSA range.
 In contrast, the support bond's average life changes as
prepayment speed changes.
 Changes in the support bond's average life due to
changes in speed are greater than the underlying
collateral's responsiveness.
92
Other PAC-Structured CMOs
 The PAC and support bonds can be divided into different
classes.
 Often the PAC bond is divided into several sequentialpay tranches, with each PAC having a different priority
in principal payments over the other.
 Each sequential-pay PAC, in turn, will have a constant
average life if the prepayment speed is within the lower
and upper collars.
 In addition, it is possible that some PACs will have
ranges of stability that will increase beyond the actual
collar range, expanding their effective collars.
93
Other PAC-Structured CMOs
 A PAC-structured CMO can also be formed with PAC
classes having different collars.
 Some PACs are formed with just one PSA rate. These
PACs are referred to as targeted amortization class
(TAC) bonds.
 Different types of tranches can also be formed out of
the support bond class. These include sequential-pay,
floating and inverse-floating rate, and accrual bond
classes.
94
Stripped MBS
 Stripped MBSs consist of two classes:
1. Principal-only (PO) class that receives only
the principal from the underlying mortgages.
2. Interest-only (IO) class that receives just the
interest.
95
Principal-Only Stripped MBS

The return on a PO MBS is greater with greater
prepayment speed.

For example, a PO class formed with $100 million of
mortgages (principal) and priced at $75 million would
yield an immediate return of $25 million if the
mortgage borrowers prepaid immediately. Since
investors can reinvest the $25 million, this early return
will have a greater return per period than a $25 million
return that is spread out over a longer period.
96
Principal-Only Stripped MBS

Because of prepayment, the price of a PO MBS tends to
be more responsive to interest rate changes than an
option-free bond.
97
Principal-Only Stripped MBS

If interest rates are decreasing, then like the price of most
bonds, the price of a PO MBS will increase.

In addition, the price of a PO MBS is also likely to
increase further because of the expectation of greater
earlier principal payments as a result of an increase in
prepayment caused by the lower rates.
(1)  prepayment
  ret urn   VPO 
R
(2)  lower discount rat e  VPO 
98
Principal-Only Stripped MBS

If rates are increasing, the price of a PO MBS will
decrease as a result of both lower discount rates and
lower returns from slower principal payments.
(1)  prepayment
  ret urn   VPO 
R
(2)  great erdiscount rat e  VPO 
99
Principal-Only Stripped MBS
 Thus, like most bonds, the prices of PO MBSs
are inversely related to interest rates, and, like
other MBSs with embedded principal
prepayment options, their prices tend to be
more responsive to interest rate changes.
VPO
0
R
100
Interest-Only Stripped MBS
 Cash flows from an I0 MBS come from the
interest paid on the mortgages portfolio’s
principal balance.
 In contrast to a PO MBS, the cash flows and
the returns on an IO MBS will be greater, the
slower the prepayment rate.
101
Interest-Only Stripped MBS

If the mortgages underlying a $100 million, 7.5% MBS with PO and
IO classes were paid off in the first year, then the IO MBS holders
would receive a one-time cash flow of $7.5 million:
$7.5m = (.075)($100m)

If $50 million of the mortgages were prepaid in the first year and the
remaining $50 million in the second year, then the IO MBS investors
would receive an annualized cash flow over two years totaling $11.25
million:
$11.25m = (.075) ($100m) + (.075)($100m − $50m)

If the mortgage principal is paid down $25 million per year, then the
cash flow over four years would total $18.75 million:
$18.75m = (.075)($100m) + (.075)($100m − $25m)
+ (.075)($75m − $25m) + (.075)($50m − $25m)
102
Interest-Only Stripped MBS

Thus, IO MBSs are characterized by an inverse
relationship between prepayment speed and returns:
the slower the prepayment rate, the greater the total
cash flow on an IO MBS.
103
Interest-Only Stripped MBS

Note:
If inverse relationship between prepayment speed and
returns dominates the price and discount rate relation,
then the price of an IO MBS will vary directly with
interest rates.
(1)  prepayment  ret urn   VIO 
R
(2)  great erdiscount rat e  VIO 
VIO
If 1st effect  2nd effect, t hen
0
R
104
IO and PO Stripped MBS
 An example of a PO MBS and an IO MBS are
shown in the next slide.
 The stripped MBSs are formed from collateral
with





Mortgage Balance = $100 million
WAC = 8%
PT Rate = 8%
WAM = 360
PSA = 100
105
Projected Cash Flows for Stripped PO and IO
Collateral: Mortgage Portfolio = $100 million, WAC = 8%,
WAM = 360 Months, Prepayment: 100% PSA
106
IO and PO Stripped MBS

The table shows the values of the collateral, PO MBS,
and IO MBS for different discount rate and PSA
combinations of 8% and 150, 8.5% and 125, and 9% and
100.
Price
Discount
PSA
Rate

Sensitivity
Value of
Value of
Value of
PO
IO
Collateral
8.00%
150
$54,228,764
$47,426,196
$101,654,960
8.50%
125
$49,336,738
$49,513,363
$98,850,101
9.00%
100
$44,044,300
$51,795,188
$95,799,488
Note: The IO MBS is characterized by a direct relation
between its value and rate of return.
107
Evaluating Mortgage-Backed
Securities
108
Evaluating Mortgage-Backed
Securities
 Like all securities, MBSs can be evaluated in
terms of their characteristics.
 With MBSs, such an evaluation is more complex
because of the difficulty in estimating cash flows
due to prepayment.
 One approached used to evaluate MBS and CMO
tranches is yield analysis.
109
Yield Analysis
 Yield analysis involves calculating the yields on
MBSs or CMO tranches given different prices and
prepayment speed assumptions or alternatively
calculating the values on MBSs or tranches given
different rates and speeds.
110
Yield Analysis
Example
 Suppose an institutional investor is interested in buying a
MBS issue that has a par value of $100 million, WAC =
8%, WAM = 355 months, and a PT rate of 7.5%.
 The value, as well as average life, maturity, duration,
and other characteristics of this security would depend
on the rate the investor requires on the MBS and the
prepayment speed she estimates.
111
Yield Analysis

If the investor’s required return on the MBS is 9% and her estimate
of the PSA speed is 150, then she would value the MBS issue at
$93,702,142.

At that rate and speed, the MBS would have an average life of 9.18
years.

Whether a purchase of the MBS issue at $93,702,142 to yield 9%
represents a good investment depends, in part, on rates for other
securities with similar maturities, durations, and risk, and in part, on
how good the prepayment rate assumption is.

For example, if the investor felt that the prepayment rate should be
100% PSA and her required rate with that level of prepayment is
9%, then she would price the MBS issue at $92,732,145 and the
average life would be 11.51 years.
112
Yield Analysis
 In general, for many institutional investors the decision
on whether or not to invest in a particular MBS or
tranche depends on the price the institution can
command.
 For example, based on an expectation of a 100% PSA,
our investor might conclude that a yield of 9% on the
MBS would make it a good investment.
 In this case, the investor would be willing to offer no
more than $92,732,145 for the MBS issue.
113
Yield Analysis
 One common approach used in conducting a yield analysis
is to generate a matrix of different yields by varying the
prices and prepayment speeds.
 The next slide shows the different values for our illustrative
MBS given different required rates and different
prepayment speeds.
 Using this matrix, an investor could determine, for a given
price and assumed speed, the estimated yield, or determine,
for a given speed and yield, the price. Using this approach,
an investor can also evaluate for each price the average
yield and standard deviation over a range of PSA speeds.
114
Yield and Vector Analysis
Mortgage Portfolio = $100M, WAC = 8%,
WAM = 355 Months, PT Rate = 7.5%
Rate/PSA
50
100
150
7%
8%
9%
10%
Value
$106,039,631
$98,251,269
$91,442,890
$85,457,483
Value
$105,043,489
$98,526,830
$92,732,145
$87,554,145
Value
$104,309,207
$98,732,083
$93,702,142
$89,146,871
Average Life
14.95
11.51
9.18
Rate
7%
8%
9%
10%
Vector
Month Range: PSA
1-50: 200
51-150: 250
151-250: 150
251-355: 200
Value
$103,729,227
$98,893,974
$94,465,328
$90,395,704
Vector
Month Range: PSA
1-50: 200
51-150: 300
151-250: 350
251-355: 400
Value
$103,473,139
$98,964,637
$94,794,856
$90,929,474
Vector
Month Range: PSA
1-50: 200
51-150: 150
151-250: 100
251-355: 50
Value
$104,229,758
$98,756,370
93,826,053
89,,364,229
115
Yield Analysis
 One of the limitations of the above yield analysis is the
assumption that the PSA speed used to estimate the
yield is constant during the life of the MBS.
 In fact, such an analysis is sometimes referred to as
static yield analysis.
 In practice, prepayment speeds change over the life of
a MBS as interest rates change in the market.
116
Vector Analysis
 A more dynamic yield analysis, known as vector
analysis, can be used.
 In applying vector analysis, PSA speeds are assumed to
change over time.
 In the above case, a matrix of values for different rates
can be obtained for different PSA vectors formed by
dividing the total period into a number of periods with
different PSA speeds assumed for each period.
 A vector analysis example is also shown at the bottom of
the last exhibit slide.
117
Web Sites
MBS Price Information:
Wall Street Journal
 Go to http://online.wsj.com/public/us, “Market,” “Bonds, Rates, &
Credit Markets,” and “Mortgage-Backed Securities, CMO.”
Investinginbonds.com
 MBS Price Index: The Merrill Lynch Mortgage-Backed Securities
(MBS) Index is a statistical composite tracking the overall
performance of the mortgage-backed securities market over time. The
index includes U.S. dollar-denominated 30-year, 15-year and balloon
pass-through mortgage securities.
 Go to http://investinginbonds.com/; click “MBS/ABS Market At-AGlance.”
118
Web Sites
Agency MBS Prospectus and other information:
Fannie Mae Information and Prospectus:
 Use Advance Search to find a MBS and its pool number:
 Go to Fannie Mae: www.fanniemae.com; Site Map; MortgageBacked Securities; “More Search Options.”
 Or go to http://sls.fanniemae.com/slsSearch/Home.do
 Use pool number to find information on Fannie Mae MBS
 Information includes: Prospectus and Common Pool
Information
119
Web Sites
Agency MBS Prospectus and other information:
Ginnie Mae Information and Prospectus:
 Go to Ginnie Mae: www.ginniemae.gov
 To find pool number, look for “Multiple Issue Pool Number” found
under “Issuer”
 To find prospectus on MBS, look for “REMIC Offering Circulars”
under “Investors”
 Or go to
http://www.ginniemae.gov/investors/prospectus.asp?Section=Investors
120
Web Sites
Agency MBS Prospectus and other information:
Freddie Mae Information on types of MBS
 www.freddiemac.com
 Go to “Mortgage Securities”
121
Web Sites
For Moody’s information on MBS:
 www.moodys.com
 Search for structured finance, historical performance, and structured
finance default studies.
122
Web Sites
 Office of Federal Housing Enterprise Oversight: www.ficc.com
Rating Agencies
 www.moodys.com
 www.standardandpoors.com
 http://reports.fitchratings.com
123