CHAPTER 12
COLLATERALIZED MORTGAGE OBLIGATIONS AND
STRIPPED MORTGAGE-BACKED SECURITIES
CHAPTER SUMMARY
In this chapter we discuss two derivative mortgage-backed securities products: collateralized
mortgage obligations and stripped mortgage-backed securities. These securities derive their cash
flow from underlying mortgage collateral, such as pass-throughs or a pool of whole loans.
COLLATERALIZED MORTGAGE OBLIGATIONS
Collateralized mortgage obligations (CMOs) are bond classes created by redirecting the cash
flows of mortgage-related products so as to mitigate prepayment risk. The mere creation of a CMO
cannot eliminate prepayment risk; it can only transfer the various forms of this risk among
different classes of bondholders.
CMO Structure
A CMO is security backed by a pool of pass-throughs, whole loans, or stripped mortgage-backed
securities. CMOs are structured so that there are several classes of bondholders with varying stated
maturities. When there is more than one class of bondholders with the same level of credit priority,
the structure is called a pay-through structure, as opposed to a pass-through structure in which
there is only one class of bondholders at a given level of credit priority. The bond classes created
are commonly referred to as tranches.
Sequential-Pay Tranches
The first CMO was created in 1983 and was structured so that each class of bond would be retired
sequentially. Such structures are referred to as sequential-pay CMOs.
A CMO is created by redistributing the cash flow—interest and principal—to the different
tranches based on a set of payment rules. There are separate rules for the payment of the coupon
interest and the payment of principal, the principal being the total of the regularly scheduled
principal payment and any prepayments.
Each tranche receives periodic coupon interest payments based on the amount of the outstanding
balance at the beginning of the month. The disbursement of the principal, however, is made in a
special way. A tranche is not entitled to receive principal until the entire principal of the preceding
tranche has been paid off.
The principal pay-down window for a tranche is the time period between the beginning and the
end of the principal payments to that tranche. Tranches can have average lives that are both shorter
and longer than the collateral, thereby attracting investors who have a preference for an average
240
life different from that of the collateral.
There is considerable variability in the average life for the tranches. However, there is some
protection provided for each tranche against prepayment risk. This is because prioritizing the
distribution of principal (i.e., establishing the payment rules for principal) effectively protects the
shorter term tranche against extension risk. This protection must come from somewhere, so it
comes from the other tranches. At the same time these other tranches are provided protection
against contraction risk.
Accrual Bonds
In many sequential-pay CMO structures, at least one tranche does not receive current interest.
Instead, the interest for that tranche would accrue and be added to the principal balance. Such a
bond class is commonly referred to as an accrual tranche, or a Z bond (because the bond is
similar to a zero-coupon bond). The interest that would have been paid to the accrual bond class is
then used to speed up the pay down of the principal balance of earlier bond classes. Thus, the
average lives for the nonaccrual tranches would be shortened as a result of the inclusion of accrual
tranche.
The accrual bond has appeal to investors who are concerned with reinvestment risk. Because there
are no coupon payments to reinvest, reinvestment risk is eliminated until all the other tranches are
paid off.
Floating-Rate Tranches
Floating-rate tranches can be created from fixed-rate tranches by creating a floater and an inverse
floater. We can select any of the tranches from which to create a floating-rate and an inverse
floating-rate tranche. We can even create these two securities for more than one of the four
tranches or for only a portion of one tranche.
Any reference rate can be used to create a floater and the corresponding inverse floater. There is an
infinite number of ways to cut up the monetary value between the floater and inverse floater, and
the final partitioning will be driven by the demands of investors.
Unlike a floating-rate note in the corporate bond market, whose principal is unchanged over the
life of the instrument, the floater’s principal balance declines over time as principal payments are
made. The principal payments to the floater are determined by the principal payments from the
tranche from which the floater is created.
Assume that the reference rate is the one-month LIBOR of 3.75%, then the coupon rate on the
inverse floater takes the following form: K – L (one-month LIBOR) where K is the cap or
maximum coupon rate for the inverse floater, and L is the multiple that determine the coupon rate
for the inverse floater. (L is referred to as the coupon leverage.) If K is set at 28.50% and L at 3,
then the coupon rate for the month is: 28.50% – 3(3.75%) = 17.25%. The higher the coupon
leverage, the more the inverse floater’s coupon rate changes for a given change in one-month
LIBOR.
241
Inverse floaters with a wide variety of coupon leverages are available in the market. Participants
refer to low-leverage inverse floaters as those with a coupon leverage between 0.5 and 2.1,
medium-leverage as those with a coupon leverage higher than 2.1 but not exceeding 4.5, and
high-leverage as those with a coupon leverage higher than 4.5.
As in the case of the floater, the principal pay-down of an inverse floater will be a proportionate
amount of the principal pay-down of the bond class from which it is created.
Because the reference rate (e.g., one-month LIBOR) is always positive, the coupon rate paid to the
floating rate bond class cannot be negative. If there are no restrictions placed on the coupon rate for
the inverse floater, however, it is possible for the coupon rate for that bond class to be negative. To
prevent this, a floor, or minimum, can be placed on the coupon rate. In many structures, the floor is
set at zero. Once a floor is set for the inverse floater, a cap or ceiling is imposed on the floater.
The cap for the floater and the inverse floater, the floor for the inverse floater, the coupon leverage,
and the margin spread are not determined independently. Given four of these variables, the fifth
will be determined.
Planned Amortization Class Tranches
The CMO innovations attracted institutional investors who had previously either avoided
investing in mortgage-backed securities or allocated only a nominal portion of their portfolio to
this sector of the fixed-income market.
Potential demand for a CMO product with less uncertainty about the cash flow increased in the
mid-1980s. In March 1987, the M.D.C. Mortgage Funding Corporation CMO Series 0 included a
class of bonds referred to as stabilized mortgage reduction term (SMRT) bonds; another class
in its CMO Series P was referred to as planned amortization class (PAC) bonds. The Oxford
Acceptance Corporation III Series C CMOs included a class of bonds referred to as a planned
redemption obligation (PRO) bonds. The greater predictability of the cash flow for these classes
of bonds, now referred to exclusively as PAC bonds, occurs because there is a principal repayment
schedule that must be satisfied.
The greater certainty of the cash flow for the PAC bonds comes at the expense of the non-PAC
classes, called support or companion bonds. It is these bonds that absorb the prepayment risk.
Because PAC bonds have protection against both extension risk and contraction risk, they are said
to provide two-sided prepayment protection.
Although there is no assurance that the collateral will prepay between selected PSA speeds, a PAC
bond can be structured to assume that it will. The two speeds used to create a PAC bond are called
the initial PAC collars (or initial PAC bands).
Most CMO PAC structures have more than one class of PAC bonds. From a PAC bond, we can
create other bonds with average lives that are stable and also where all average lives are either
much shorter or longer. Even if prepayments are faster than the initial upper collar, there may be
242
sufficient support bonds to assure the average life is unchanged. The degree of protection against
extension risk increases for shorter PAC bonds. The effective collar can be wider than the initial
collar for shorter PAC tranches.
A PAC window can be wide or narrow. The narrower a PAC window, the more it resembles a
corporate bond with a bullet payment. PAC buyers appear to prefer tight windows, although
institutional investors facing a liability schedule are generally better off with a window that more
closely matches the liabilities. Investor demand dictates the PAC windows that issuers will create.
Investor demand in turn is governed by the nature of investor liabilities.
As we have emphasized several times, the creation of a mortgage-backed security cannot make
prepayment risk disappear. This is true for both a pass-through and a CMO. Thus the reduction in
prepayment risk (both extension risk and contraction risk) that a PAC offers must come from
somewhere.
Where does the prepayment protection come from? It comes from the support bonds. It is the
support bonds that forego principal payments if the collateral prepayments are slow; support bonds
do not receive any principal until the PAC bonds receive the scheduled principal repayment. This
reduces the risk that the PAC bonds will extend. Similarly, it is the support bonds that absorb any
principal payments in excess of the scheduled principal payment that are made. This reduces the
contraction risk of the PAC bonds.
Thus the key to the prepayment protection offered by a PAC bond is the amount of support bonds
outstanding. If the support bonds are paid off quickly because of faster than expected prepayments,
there is no longer any protection for the PAC bonds.
The support bonds can be thought of as bodyguards for the PAC bondholders. When the bullets fly
(i.e., prepayments occur) it is the bodyguards that get killed off first. The bodyguards are there to
absorb the bullets. When all the bodyguards are killed off (i.e., the support bonds paid off with
faster than expected prepayments), the PAC bonds must fend for themselves: they are now
exposed to all the bullets.
Busted means that the prepayment protection is reduced. It is the term used in the CMO market
when a PAC schedule is broken. The initial collars are not particularly useful in assessing the
prepayment protection for a seasoned PAC bond. This is most important to understand, as it is
common for CMO buyers to compare prepayment protection of PACs in different CMO
structures, and conclude that the greater protection is offered by the one with the wider collar. This
approach is inadequate because it is actual prepayment experience that determines the degree of
prepayment protection as well as the expected future prepayment behavior of the collateral.
The way to determine this protection is to calculate the effective collar for a seasoned PAC bond.
An effective collar for a seasoned PAC is the lower PSA and the upper PSA that can occur in the
future and still allow maintenance of the schedule of principal repayments.
The effective collar changes every month. An extended period over which actual prepayments are
below the upper range of the initial PAC collar will result in an increase in the upper range of the
243
effective collar. This is because there will be more bodyguards around than anticipated. An
extended period of prepayments slower than the lower range of the initial PAC collar will raise the
lower range of the effective collar. This is because it will take faster prepayments to make up the
shortfall of the scheduled principal payments not made plus the scheduled future principal
payments.
The PAC schedule may not be satisfied even if the actual prepayments never fall outside the initial
collar. This may seem surprising because our previous analysis indicated that the average life
would not change if prepayments are at either extreme of the initial collar. However, our previous
analysis has been based on a single PSA speed for the life of the structure.
There are two ways to provide greater protection for PAC bonds: lockouts and reverse PAC
structures. One obvious way to provide greater protection for PAC bonds is to issue fewer PAC
bonds relative to support bonds. Such a CMO structure with no principal payments to a PAC bond
class in the earlier years is referred to as a lockout structure. A CMO structure requiring any
excess principal payments to be made to the longer PAC bonds after all support bonds are paid off
is called a reverse PAC structure.
Targeted Amortization Class Bonds
A targeted amortization class (TAC) bond resembles a PAC bond in that both have a schedule
of principal repayment. The difference between a PAC bond and a TAC bond is that a PAC bond
has a wide PSA range over which the schedule of principal repayment is protected against
contraction risk and extension risk. A TAC bond, in contrast, has a single PSA rate from which the
schedule of principal repayment is protected. As a result, the prepayment protection afforded the
TAC bond is less than that for a PAC bond.
The creation of a bond with a schedule of principal repayments based on a single prepayment rate
results in protection against contraction risk but not extension risk. Thus, whereas PAC bonds are
said to have two-sided prepayment protection, TAC bonds have one-sided prepayment protection.
Very Accurately Determined Maturity Bonds
Accrual or Z bonds have been used in CMO structures as support for bonds called very accurately
determined maturity (VADM) or guaranteed final maturity bonds. In this case the interest
accruing (i.e., not being paid out) on a Z bond is used to pay the interest and principal on a VADM
bond.
Interest-Only and Principal-Only Tranches
Stripped mortgage-backed securities are created by paying the entire principal to one bond class
and all the interest to another bond class. These two classes are referred to as the principal-only
(PO) bond class and the interest only (IO) bond class.
Notional IOs
244
In the earlier CMO deals, all of the excess interest between the coupon rate on the tranches and the
coupon interest on the collateral was paid to an equity class referred to as the CMO residual. This
is no longer the practice today. Instead, a tranche is created that receives the excess coupon
interest. This tranche is called a notional interest only (IO) class and is also referred to as a
structured IO.
The notional amount is the amount on which the interest payments will be determined, not the
amount that will be paid to the holder of this bond. Mathematically, this notional amount is found
as follows:
notional amount for 7.5% IO =
(tranche's par value)(excess interest)
0.075
where excess interest = collateral coupon rate – tranche coupon rate.
Support Bonds
The support bonds—or bodyguards—are the bonds that provide prepayment protection for the
PAC tranches. Consequently, they are exposed to the greatest level of prepayment risk. The
support bond can even be partitioned so as to create support bond classes with a schedule of
principal repayments.
Credit Risk
Credit risk exposure depends on who issues the CMO. An issuer is (i) Freddie Mac, Fannie Mae, or
Ginnie Mae, or (ii) a private entity. Those CMOs issued by the former are referred to as agency
CMOs. Those issued by a private entity are called nonagency CMOs and can be divided into two
types. A private entity that issues a CMO but whose underlying collateral is a pool of
pass-throughs guaranteed by an agency is called a private-label CMO. If the collateral for a CMO
is a pool of unsecuritized mortgages loans, the structure is referred to as a whole loan CMO.
Today, the most common type of nonagency CMO is a whole loan CMO. Consequently, market
participants use the terms nonagency CMO and whole loan CMO interchangeably.
Tax Considerations
The issuer of a CMO wants to be sure that the trust created to pass through the interest and
principal payments is not treated as a taxable entity.
STRIPPED MORTGAGE-BACKED SECURITIES
Stripped mortgage-backed securities (MBSs), introduced by Fannie Mae in 1986, are another
example of derivative mortgage products. A pass-through divides the cash flow from the
underlying pool of mortgages on a pro rata basis across the security holders. A stripped MBS is
created by altering the distribution of principal and interest from a pro rata distribution to an
unequal distribution. Some of the securities thus created will have a price/yield relationship that is
different from the price/yield relationship of the underlying mortgage pool. There are three types
245
of stripped MBSs: (i) synthetic-coupon pass-throughs, (ii) interest-only/principal-only securities,
and (iii) CMO strips.
Synthetic-Coupon Pass-Throughs
The first generation of stripped mortgage-backed securities is called synthetic-coupon
pass-throughs. This is because the unequal distribution of coupon and principal results in a
synthetic coupon rate that is different from that of the underlying collateral.
Interest-Only/Principal-Only Strips
In early 1987, stripped MBSs began to be issued where all the interest is allocated to one class (the
IO class) and the entire principal to the other class (the PO class). The IO class receives no
principal payments. IOs and POs are referred to as mortgage strips.
The PO security is purchased at a substantial discount from par value. The yield an investor will
realize depends on the speed at which prepayments are made. The faster the prepayments, the
higher the yield the investor will realize.
When an IO is purchased there is no par value. In contrast to the PO investor, the IO investor wants
prepayments to be slow. The reason is that the IO investor receives only interest on the amount of
the principal outstanding. As prepayments are made, the outstanding principal declines, and less
dollar interest is received. In fact, if prepayments are too fast, the IO investor may not recover the
amount paid for the IO.
CMOs that are backed by POs are referred to as PO-collateralized CMOs.
One of the classes in a CMO structure can be a principal-only or an interest-only class. These are
called CMO strips.
246
ANSWERS TO QUESTIONS FOR CHAPTER 12
(Questions are in bold print followed by answers.)
1. How does a CMO alter the cash flow from mortgages so as to shift the prepayment risk
across various classes of bondholders?
CMOs redirect cash flows from a pass-through to various bond classes making it possible to
redistribute prepayment risk for investors who want to reduce their exposure to prepayment risk.
Because the total prepayment risk of a pass-through will not be changed by altering the cash flows,
other investors must be located who are willing to accept the unwelcomed prepayment risk.
2. Why is a CMO called a pay-through structure?
A CMO is called a pay-through structure because it can satisfy the definition that when there is
more than one class of bondholders with the same level of credit priority, the structure is called a
pay-through structure. More details are given below.
A CMO is a security backed by a pool of pass-throughs, whole loans, or stripped mortgage-backed
securities (explained later in the chapter). CMOs are structured so that there are several classes of
bondholders with varying stated maturities. When there is more than one class of bondholders with
the same level of credit priority, the structure is called a pay-through structure, as opposed to a
pass-through structure in which there is only one class of bondholders at a given level of credit
priority. The bond classes created are commonly referred to as tranches. The principal payments
from the underlying collateral are used to retire the tranches on a priority basis according to terms
specified in the prospectus.
3. Answer the following questions.
(a) “By creating a CMO, an issuer eliminates the prepayment risk associated with the
underlying mortgages.” Do you agree with this statement?
A CMO redirects cash flows making it possible to redistribute prepayment risk so that some
investors reduce their prepayment risk exposure while others increase their prepayment risk
exposure. Thus, one would agree with the statement that a CMO eliminates prepayment risk for
certain investors, but would disagree with the statement that a CMO eliminates prepayment risk
for all investors.
(b) Wall Street often refers to CMOs as “customized securities.” Explain why.
CMOs are “customized securities” in the sense that they can be tailor made to satisfy the
preferences of investors. For example, classes of bonds or tranches can be created which are
customized or structured for individual and institutional investors to meet a particular prepayment
risk that each desire.
4. In a discussion of the CMO market, the popular press sometimes refers to this sector of
247
the mortgage-backed securities market as the riskiest sector and the pass-through sector as
the safest sector. Comment.
Collateralized mortgage obligations derive their cash flow from underlying mortgage collateral
such as pass-throughs or a pool of whole loans. Thus, CMOs can be referred to as a derivative
mortgage-backed securities product. The popular press does not always distinguish between the
speculative and hedging nature of derivates but perceives derivatives as riskier due to greater
variability in outcomes that often result. On the other hand, many pass-throughs are sponsored by
government agencies and thus perceived as being safe. Therefore, the popular press can
erroneously mistake differences in overall or total risk when speaking of the CMO sector and the
pass-through sector. The fact is CMOs are backed by pass-throughs and thus the total risk of each
sector should be the same.
5. Explain the effect on the average lives of sequential-pay structures of including an accrual
tranche in a CMO structure.
The effect of an accrual tranche is to decrease the average lives of the other tranches at the expense
of the accrual tranche. Background information on sequential-pay CMOs and more details on the
effect of an accrual tranche are given below.
The first CMO was created in 1983 and was structured so that each class (or tranche) of bond
would be retired sequentially. Such structures are referred to as sequential-pay CMOs. A CMO is
created by redistributing the cash flow—interest and principal—to the different tranches based on
a set of payment rules. Each tranche receives periodic coupon interest payments based on the
amount of the outstanding balance at the beginning of the month. The disbursement of the
principal, however, is made in a special way. A tranche is not entitled to receive principal until the
entire principal of the preceding tranche has been paid off. Although the priority rules for the
disbursement of the principal payments are known, the precise amount of the principal in each
period is not. This will depend on the cash flow, and therefore principal payments, of the collateral,
which depends on the actual prepayment rate of the collateral. An assumed PSA speed allows the
cash flow to be projected.
The principal pay-down window for a tranche is the time period between the beginning and the
ending of the principal payments to that tranche. Tranches can have average lives that are both
shorter and longer than the collateral, thereby attracting investors who have a preference for an
average life different from that of the collateral. However, there is considerable variability of the
average life for the tranches even though there is some protection provided for each tranche against
prepayment risk. This is because prioritizing the distribution of principal (i.e., establishing the
payment rules for principal) can effectively protect the shorter-term tranches against extension
risk. This protection must come from somewhere, so it comes from the other longer term tranches
that benefit from being protected against contraction risk.
The payment rules for interest provide for all tranches to be paid interest each month. In many
sequential-pay CMO structures, at least one tranche does not receive current interest. Instead, the
interest for that tranche would accrue and be added to the principal balance. Such a bond class is
commonly referred to as an accrual tranche or a Z bond (because the bond is similar to a
248
zero-coupon bond). The interest that would have been paid to the accrual bond class is then used to
speed up or pay down of the principal balance of earlier bond classes. Thus, the average lives for
the other tranches become shorter because of the inclusion of the accrual bond.
6. What types of investors would be attracted to an accrual bond?
The accrual bond has appeal to investors who are concerned with reinvestment risk. Because there
are no coupon payments to reinvest, reinvestment risk is eliminated until all the other tranches are
paid off.
7. Suppose that a tranche from which an inverse floater is created has an average life of five
years. What will be the average life of the inverse floater?
The coupon rate on the tranche from which two classes (floater and inverse floater) are created can
support the aggregate interest payments that must be made to them. As in the case of the floater,
the principal pay-down of an inverse floater will be a proportionate amount of the principal
pay-down of the bond class that created it. Thus, the floater and inverse floater will have a
weighted average life equal to the average life of the tranche from which it is created. In equation
form, we have:
Average life = 5 years = (inverse floater’s weight)(X years) + (floater’s weight)(Y years) where X
equals inverse floater’s average life in years and Y equals floater’s average life in years. Solving
for X, we get:
X years =
5 years  ( floater' s weight )(Y years )
.
inverse floater' s weight
Let’s illustrate. Suppose that the floater and inverse floater are equally-weighted (each weight =
½). If so, then, we have:
X years =
5 years  (1/ 2)(Y years)
5years  (floater 's weight)(Y years)
=

1/ 2
inverse floater 's weight
(1/2)X years = 5 years – (1/2)(Y years)  (1/2)X years + (1/2)Y years = 5 years. Thus, the average
life of the inverse floater would be 5 years.
Now assume that the average life for the floater and inverse floater are equal (X = Y). Further
solving gives: (1/2)X + (1/2)X = 5 years  X = 5 years and Y = 5 years.
If we assume that 2X = Y, then we have: (1/2)X + (1/2)(2X) = 5  (3/2)X = 5  X = 3.33 years
and Y = 6.67 years. Thus, the average life of the inverse floater would be 3.33 years.
Similarly, we could show that if X = 2Y, then the average life of the inverse floater would be 6.67
years.
8. This quotation is taken from a 1991 issue of BondWeek:
249
“First Interstate Bank of Texas will look into buying several different types of
collateralized mortgage obligation tranches when it starts up its buy program sometime
after the second quarter of 1991, according to Jules Pollard. V.P. Pollard said he will
consider replacing maturing adjustable-rate mortgage pass-throughs with short
companion tranches and planned amortization classes because the ARMs have become
rich. . . . Pollard did not provide a dollar figure on the planned investments, which will be
made to match fund the bank’s liabilities. When he does invest he said he prefers
government guaranteed securities or those with implied guarantees.”
Answer the following questions.
(a) Explain the types of securities that Pollard is buying and selling.
Pollard wants to replace (or sell) adjustable-rate mortgage pass-throughs.
Pollard wants to buy various types of CMO tranches. In particular, he wants “short companion”
and “planned amortization” tranches. He prefers these tranches to be government guaranteed
securities or those with implied guarantees.
(b) Given the preference stated in the last sentence of the quotation, what issuers is he likely
to prefer? What issuers would he reject?
Given the last sentence, one would conclude that Pollard wants tranches backed by agency CMOs.
In particular, he would want Ginny Mae, Freddie Mae, and Fannie Mae. He would reject any
tranches backed by nonagency CMOs which are not (implicitly or explicitly) guaranteed by the
government. More details as to what Pollard would prefer are given as follows.
Pollard wants to replace (or sell) adjustable-rate mortgage pass-throughs. The type of security he
no longer wants and the implications of this desire are described below.
A mortgage pass-through security, or simply a pass-through, is a security that results when one or
more mortgage holders form a collection (pool) of mortgages and sell shares or participation
certificates in the pool. The cash flow of a mortgage pass-through security depends on the cash
flow of the underlying mortgages. The cash flow consists of monthly mortgage payments
representing interest, the scheduled repayment of principal, and any prepayments. Payments are
made to security holders each month. Neither the amount nor the timing, however, of the cash flow
from the pool of mortgages is identical to that of the cash flow passed through to investors. Since
Pollard owns adjustable-rate pass-throughs, he is currently free from inflation rate risk. This
implies he thinks that interest rates may be falling and adjustable rate securities will pay lower cash
flows in the future.
Pollard wants to buy various types of CMO tranches. In particular, he wants “short companion”
and “planned amortization” tranches. He prefers these tranches to be government guaranteed
securities or those with implied guarantees. These types of security he now wants and the
implications of this desire are described below.
250
Pollard wants collateralized mortgage obligations (CMOs), which are bond classes created by
redirecting the cash flows of mortgage-related products so as to mitigate prepayment risk for at
least some classes. An accrual tranche can help overcome reinvestment rate risk if that is Pollard’s
main concern. While Pollard appears to be concerned with interest rates falling, he may be more
concerned with mitigating prepayment risk, in particular contraction risk. For example, when
interest rates fall there can be a greater prepayment risk if borrowers want to retire their debt
quicker. Thus, he wants to avoid contraction risk.
The mere creation of a CMO cannot eliminate prepayment risk; it can only transfer the various
forms of this risk among different classes of bondholders. Pollard wants a “short companion”
which indicates he wants a tranche where the principal is paid off early. This is not consistent with
the notion that he believes interest rates are falling because the early pay-off means he would have
to reinvest funds at a lower rate. Thus, we can eliminate this choice.
Pollard’s other choice is “planned amortization” tranches (referred to as PAC tranches). PAC
tranches can reduce prepayment risk in a manner desired by an investor’s preference. However,
despite the redistribution of prepayment risk with sequential-pay and accrual CMOs, there is still
considerable prepayment risk. That is, there is still considerable average life variability for a given
tranche. This problem is mitigated by the PAC tranche. The greater predictability of the cash flow
for PAC bonds occurs because there is a principal repayment schedule that must be satisfied. PAC
bondholders have priority over all other classes in the CMO issue in receiving principal payments
from the underlying collateral. The greater certainty of the cash flow for the PAC bonds comes at
the expense of the non-PAC classes, called support or companion bonds. It is these bonds that
absorb the prepayment risk. Because PAC bonds have protection against both extension risk and
contraction risk, they are said to provide two-sided prepayment protection.
Given all of the above details and Pollard’s assumed desire to reduce prepayment risk, it appears
that Pollard would choose a “planned amortization” tranche. In particular, he would want a PAC
class that avoids contraction risk. If alleviating reinvestment rate risk is also a major concern, then
Pollard could also choose some accrual tranches. Whatever his choice, Pollard would want a
tranche backed by an agency CMO.
9. Describe how the schedule for a PAC tranche is created.
The schedule for a planned amortization class (PAC) tranche is set so that there will be greater
predictability of the cash flow through establishing a principal repayment schedule that must be
satisfied. The schedule will be set so that PAC bondholders have priority over all other classes in
the CMO issue in receiving principal payments from the underlying collateral. The greater
certainty of the cash flow for the PAC bonds comes at the expense of the non-PAC classes, called
support or companion bonds. It is these bonds that absorb the prepayment risk. Because PAC
bonds have protection against both extension risk and contraction risk, they are said to provide
two-sided prepayment protection.
In setting the schedule, one specifies the amount of the collateral from the pass-through, a coupon
rate, a WAC, and a WAM. Given two prepayment speeds (expressed in terms of PSA and called
251
the initial PAC collars), the principal payment or PAC schedule is set. The principal payment
consists of the regularly scheduled principal repayment plus prepayments for chosen collateral
PSA speeds. The minimum principal payment for the PAC schedule is given by the lower PSA
speed (called the lower collar). The characteristic of the collateral allows for the creation of a PAC
bond, assuming that the collateral prepays over its life between the two speeds. A schedule of
principal repayments that the PAC bondholders are entitled to receive (before any other bond class
in the CMO) is specified. Although there is no assurance that the collateral will prepay between the
two speeds, a PAC bond can be structured to assume that it will.
The payment rules state (i) how to disburse periodic coupon interest to each tranche on the basis of
the amount of principal outstanding at the beginning of the period, and (ii) how to disburse
principal payments to tranches based on its schedule of principal repayments. The latter also states
which tranches have priority with respect to current and future principal payments to satisfy the
schedule. When one tranche is paid off completely, all principal payments are to be made to next
tranche specified in the payment rules.
Between the two PSA speeds, the average life for the PAC bond is stable. However, at slower or
faster PSA speeds, the schedule is broken, and the average life changes; it lengtens when the
prepayment speed is less than the lower collar and shortens when it is greater than the upper collar.
Even so, there is much greater variability for the average life of the support bond.
Most CMO PAC structures have more than one class of PAC bonds. Given the prepayment speeds
chosen, it is possible to make the average life for the multiple PAC bonds less than or greater than
that if there was only one class of PAC bonds.
10. Explain the role of a support bond in a CMO structure.
The support bond class in a CMO structure provides for the prepayment protection for the other
bond classes. It is the support bonds that forego principal payments if the collateral prepayments
are slow. Support bonds do not receive any principal until the PAC bonds receive the scheduled
principal repayment. This reduces the risk that the PAC bonds will extend. Similarly, it is the
support bonds that absorb any principal payments in excess of the scheduled principal payment
that is made. This reduces the contraction risk of the PAC bonds. Thus the key to the prepayment
protection offered by a PAC bond is the amount of support bonds outstanding. If the support bonds
are paid off quickly because of faster-than-expected prepayments, there is no longer any protection
for the PAC bonds. In fact, if the support bond is paid off, the structure is effectively reduced to a
sequential-pay CMO.
The support bonds can be thought of as bodyguards for the PAC bondholders. When the bullets fly
(i.e., prepayments occur) it is the bodyguards that get killed off first. The bodyguards are there to
absorb the bullets. When all the bodyguards are killed off (i.e., the support bonds paid off with
faster-than-expected prepayments), the PAC bonds must fend for themselves: they are exposed to
all the bullets.
11. What was the motivation for the creation of PAC bonds?
252
The motivation for the creation of PAC bonds was to diminish the uncertainty in cash flows
including prepayment risk. More details are supplied below.
The CMO innovations attracted many institutional investors who had previously either avoided
investing in mortgage-backed securities or allocated only a nominal portion of their portfolio to
this sector of the fixed-income market. Although some traditional corporate bond buyers shifted
their allocation to CMOs, a majority of institutional investors remained on the sidelines; they were
concerned about investing in an instrument that they continued to perceive as posing significant
prepayment risk because of the substantial average life variability, despite the innovations
designed to reduce prepayment risk.
Potential demand for a CMO product with less uncertainty about the cash flow increased in the
mid-1980s because of two trends in the corporate bond market. First was the increased event risk
faced by investors, highlighted by the RJR Nabisco leveraged buyout in 1988. The second trend
was a decline in the number of AAA rated corporate issues. Traditional corporate bond buyers
sought a structure with both the characteristics of a corporate bond (either a bullet maturity or a
sinking fund type of schedule of principal repayment) and high credit quality. Although CMOs
satisfied the second condition, they did not satisfy the first.
In March 1987, the M.D.C. Mortgage Funding Corporation CMO Series 0 included a class of
bonds referred to as stabilized mortgage reduction term (SMRT) bonds; another class in its
CMO Series P was referred to as planned amortization class (PAC) bonds. The Oxford
Acceptance Corporation III Series C CMOs included a class of bonds referred to as a planned
redemption obligation (PRO) bonds. The characteristic common to these three bonds is that if
the prepayments are within a specified range, the cash flow pattern is known.
The greater predictability of the cash flow for these classes of bonds, now referred to exclusively
as PAC bonds, occurs because there is a principal repayment schedule that must be satisfied. PAC
bondholders have priority over all other classes in the CMO issue in receiving principal payments
from the underlying collateral. The greater certainty of the cash flow for the PAC bonds comes at
the expense of the non-PAC classes, called support or companion bonds. It is these bonds that
absorb the prepayment risk. Because PAC bonds have protection against both extension risk and
contraction risk, they are said to provide two-sided prepayment protection.
12. Suppose that a savings and loan association has decided to invest in mortgage-backed
securities and is considering the following two securities: (i) a Freddie Mac pass-through
security with a WAM of 340 months or (ii) a PAC tranche of a Freddie Mac CMO issue with
an average life of two years. Which mortgage-backed security would probably be better
from an asset/liability perspective?
The following describes the two choices beginning with the Freddie Mac pass-through.
The first choice is a pass-through security. The cash flow of a mortgage pass-through security
depends on the cash flow of the underlying mortgages. A weighted average maturity (WAM) is
found by weighting the remaining number of months to maturity for each mortgage loan in the
pool by the amount of the mortgage outstanding. Freddie Mac issues a pass-through called a
253
participation certificate (PC). In 1990, Freddie Mac introduced its Gold PC, which has stronger
guarantees than its other PCs and will be the only type of PC issued in the future. Specifically,
non-Gold PCs that have been issued are modified pass-throughs. This type of pass-through
guarantees both interest and principal payments, but it guarantees only the timely payment of
interest. The scheduled principal is passed through as it is collected, with a guarantee that the
scheduled payment will be made no later than a specified date. The Freddie Mac pass-through still
entails prepayment risk and uncertainty in cash flows that can be alleviated by creating CMOs.
A CMO is the second choice. A CMO is a security backed by a pool of pass-throughs, whole loans,
or stripped mortgage-backed securities. CMOs are structured so there are several classes of
bondholders with varying stated maturities. When there is more than one class of bondholders with
the same level of credit priority, the structure is called a pay-through structure, as opposed to a
pass-through structure in which there is only one class of bondholders at a given level of credit
priority. The bond classes created are commonly referred to as tranches. The principal payments
from the underlying collateral are used to retire the tranches on a priority basis according to terms
specified in the prospectus. Despite the redistribution of prepayment risk with sequential-pay and
accrual CMOs, there is still considerable prepayment risk. That is, there is still considerable
average life variability for a given tranche. This problem has been mitigated by the creation of a
planned amortization class (PAC) tranche. This type of CMO tranche reduces average life
variability. The bonds included in a CMO structure that provide the better protection for PAC
tranches are the support or companion tranches. There are various ways in which greater
prepayment protection can be provided for some or all of the PAC bonds within a CMO structure.
These include a lockout and a reverse PAC structure.
From the above description, we see that both types are backed by same underlying mortgages and
should share in the same credit risk except to the extent the PAC is chosen to meet the needs of an
investor. Regardless, similar safety exists in terms of the creditability of the underlying assets.
Thus, the savings and loan association can focus on matching assets and liabilities. There is a
significant difference in terms of maturity between the two types. Thus, the savings and loan will
choose the Freddie Mac pass-through security with a WAM of 340 months if their liabilities are
closer to 340 than two years. The savings and loan will choose the PAC tranche of a Freddie Mac
CMO issue with an average life of two years if their liabilities (that they want to match) are closer
to 24 months than 340 months.
13. Suppose that a PAC bond is created assuming prepayments speeds of 80 PSA and 350
PSA. If the collateral pays at 100 PSA over its life, what will this PAC tranche’s average life
be?
As illustrated in Exhibit 12-9, the average life for the PAC bond is stable at 7.26 years as long as
the PSA speed is between the two designated prepayments speeds (i.e., between the lower and
upper collars). However, at slower or faster PSA speeds than the two collar speeds, the schedule is
broken with the average life changing. The average life lengthens when the prepayment speed is
less than the lower collar and shortens when it is greater than the upper collar.
14. Suppose that $1 billion of pass-throughs is used to create a CMO structure with a PAC
bond with a par value of $700 million and a support bond with a par value of $300 million.
254
Answer the following questions.
(a) Which of the following will have the greatest average life variability: (i) the collateral, (ii)
the PAC bond, or (iii) the support bond? Why?
The support bond will have the greatest average life variability because its purpose is to reduce
variability in the cash flows of the PAC bonds, and thus the variability in the average life.
The average life variability for the collateral should lie between that for the PAC bond and the
support bond because the PAC bond class and the support bond class are derived from the
collateral. The support bond class is used to create a more stable average life for the PAC bond
class. Support bondholders have less priority over all other classes in the CMO issue in receiving
principal payments from the underlying collateral.
It is the support bonds that forego principal payments if the collateral prepayments are slow;
support bonds do not receive any principal until the PAC bonds receive the scheduled principal
repayment. This reduces the risk that the PAC bonds will extend. On the other hand, it is the
support bonds that absorb any principal payments in excess of the scheduled principal payment
that are made. This reduces the contraction risk of the PAC bonds. The key to the prepayment
protection offered by a PAC bond is the amount of support bonds outstanding. If the support bonds
are paid off quickly because of faster-than-expected prepayments, there is no longer any protection
for the PAC bonds.
Because the stability for the PAC bond comes at the expense of the support bond, the support bond
will have more variability in its average life than the PAC bond. Thus, in terms of greatest to least
average life variability, we have: the support bond, the collateral, and the PAC bond.
(b) Which of the following will have the least average life variability: (i) the collateral, (ii) the
PAC bond, or (iii) the support bond? Why?
The PAC bond will have the least average life variability because its payment schedule is
structured to achieve stability in the cash flows and thus reduce variability in the average life.
The average life variability for the collateral should lie between that for the PAC bond class and
the support bond class because the PAC bonds and support bonds are derived from the collateral.
The support bond class is used to create a more stable average life for the PAC bond class. PAC
bondholders have priority over all other classes in the CMO issue in receiving principal payments
from the underlying collateral. This gives a lower variability in its average life. Thus, in terms of
least to greatest average life variability, we have: the PAC bond, the collateral, and the support
bond.
15. Suppose that the $1 billion of collateral in Question 14 was divided into a PAC bond with
a par value of $800 million and a support bond with a par value of $200 million. Will the
PAC bond in this CMO structure have more or less protection than the PAC bond in
Question 14?
255
The PAC bond in the structure of $800 million versus $200 million will have less protection than
$700 million versus $300 million. This is because $300 million support is greater than $200
million support. Also, the $300 million has a less amount of PAC bonds to support ($700 million
fewer versus $800 million). In general, more supports bonds will offer greater protection. This is
because the key to the prepayment protection offered by a PAC bond is the number of support
bonds outstanding. If the support bonds are paid off quickly because of faster-than-expected
prepayments, there is no longer any protection for the PAC bonds. In fact, if the support bond is
paid off, the structure is effectively reduced to a sequential-pay CMO.
The support bonds can be thought of as bodyguards for the PAC bondholders. When the bullets fly
(i.e., prepayments occur) it is the bodyguards that get killed off first. The bodyguards are there to
absorb the bullets. When all the bodyguards are killed off (i.e., the support bonds paid off with
faster-than-expected prepayments), the PAC bonds must fend for themselves: they are exposed to
all the bullets.
16. Suppose that $1 billion of pass-throughs is used to create a CMO structure with a PAC
bond with a par value of $700 million (PAC I), a support bond with a schedule (PAC II) with
a par value of $100 million, and a support bond without a schedule with a par value of $200
million. Answer the following questions.
(a) Will the PAC I or PAC II have the smaller average life variability? Why?
The PAC II will have greater average life variability. This is because the primary function of PAC
II is to support PAC I bonds by allowing them to have more stable cash flows and thus less average
life variability.
A support bond can be partitioned so as to create support bond classes with a schedule of principal
repayments. That is, support bond classes that are PAC bonds can be created. In a structure with a
PAC bond and a support bond with a PAC schedule of principal repayments, the former is called a
PAC I bond or level I PAC bond and the latter a PAC II bond or level II PAC bond. Although PAC
II bonds have greater prepayment protection than the support bond classes without a schedule of
principal repayments, the prepayment protection is less than that provided PAC I bonds.
(b) Will the support bond without a schedule or the PAC II have the greater average life
variability? Why?
The support bond without a schedule will have greater average life variability. This is because they
support more stable and certain cash flows, and thus smaller average life variability, for PAC II
bonds.
17. In a CMO structure with several PAC bonds, explain why, when the support bonds are
paid off, the structure will be just like a sequential-pay CMO.
The PAC bonds and support bonds are formed from the sequential-pay CMO. If the support bonds
are paid off earlier than expected, then the structure reverts to a sequential-pay CMO. More details
on the sequential-pay structure are supplied below.
256
The first CMO was created in 1983 and was structured so that each class of bond would be retired
sequentially. Such structures are referred to as sequential-pay CMOs. The payment rules dictate
that each tranche receives periodic coupon interest payments based on the amount of the
outstanding balance at the beginning of the month. However, the disbursement of the principal is
made in a special way. A tranche is not entitled to receive principal until the entire principal of the
preceding tranche has been paid off. More specifically, the first tranche receives all the principal
payments until the entire principal amount owed to that bond class is paid off; then the next tranche
begins to receive principal and continues to do so until it is paid off in entirety. This process
continues until the last tranche is paid off. Tranches that are paid off later have greater maturities
and thus greater average lives.
Although the priority rules for the disbursement of the principal payments are known, the precise
amount of the principal in each period is not. This will depend on the cash flow, and therefore
principal payments of the collateral, which depends on the actual prepayment rate of the collateral.
An assumed PSA speed allows the cash flow to be projected. The principal pay-down window for
a tranche is the time period between the beginning and the ending of the principal payments to that
tranche. Tranches can have average lives that are both shorter and longer than the collateral,
thereby attracting investors who have a preference for an average life different from that of the
collateral.
There is still a major problem: there is considerable variability of the average life for the tranches.
However, there is some protection provided for each tranche against prepayment risk. This is
because prioritizing the distribution of principal (i.e., establishing the payment rules for principal)
effectively protects the shorter-term tranche (which is paid off first) in this structure against
extension risk. This protection must come from somewhere, so it comes from the tranches where
the principal is paid off later. These tranches benefit because they are provided protection against
contraction risk.
18. Suppose that for the first four years of a CMO, prepayments are well within the initial
PAC collar. What will happen to the effective upper collar?
If the prepayments are well within the initial PAC collar, this means that there are more
bodyguards (i.e., support bonds) around than was expected when the PAC was structured at the
initial collar. This will result in an increase in the upper range of the effective collar.
The initial collars are not particularly useful in assessing the prepayment protection for a seasoned
PAC bond. This is most important to understand as it is common for CMO buyers to compare
prepayment protection of PACs in different CMO structures and conclude that the greater
protection is offered by the one with the wider collar. This approach is inadequate because it is
actual prepayment experience that determines the degree of prepayment protection as well as the
expected future prepayment behavior of the collateral.
The way to determine this protection is to calculate the effective collar for a seasoned PAC bond.
An effective collar for a seasoned PAC is the lower PSA and the upper PSA that can occur in the
future and still allow maintenance of the schedule of principal repayments.
257
The effective collar changes every month. An extended period over which actual prepayments are
below the upper range of the initial PAC collar will result in an increase in the upper range of the
effective collar. This is because there will be more bodyguards around than anticipated. An
extended period of prepayments slower than the lower range of the initial PAC collar will raise the
lower range of the effective collar. This is because it will take faster prepayments to make up the
shortfall of the scheduled principal payments not made plus the scheduled future principal
payments.
The PAC schedule may not be satisfied even if the actual prepayments never fall outside the initial
collar. This is because single PSA speed does not necessarily hold for the life of the structure.
Finally, any prepayment speeds faster than the collar jeopardize satisfaction of the principal
repayment schedule and increase extension risk. This does not mean that the schedule will be
busted—the term used in the CMO market when a PAC schedule is broken. It does mean that the
prepayment protection is reduced.
19. Consider the following CMO structure backed by 8% collateral:
Tranche
A
B
C
D
Par Amount
(in millions)
$300
$250
$200
$250
Coupon
Rate (%)
6.50%
6.75%
7.25%
7.75%
Suppose that a client wants a notional IO with a coupon rate of 8%. Calculate the notional
amount for this notional IO.
Notice that for this structure the par amount for the IO class is shown in the table below as
$121,875,000 for a coupon rate of 8.0%. This is an IO class, so there is no par amount. The amount
shown is the amount on which the interest payments will be determined, not the amount that will
be paid to the holder of this bond. Therefore, it is called a notional amount.
Let’s look at how the notional amount is determined. Consider first tranche A. The par value is
$300 million and the coupon rate is 6.5%. Because the collateral’s coupon rate is 8%, the excess
interest is 150 basis points. Therefore, an IO with a 1.5% coupon rate and a notional amount of
$300 million can be created from tranche A. As seen below, this is equivalent to an IO with a
notional amount of $56.25 million and a coupon rate of 8%. Mathematically, this notional amount
is found as follows:
notional amount for 8% IO =
(tranche's par value)(excess interest)
0.08
where excess interest = collateral coupon rate – tranche coupon rate.
258
For example, for tranche A, excess interest = 0.080 – 0.065 = 0.015 and the tranche’s par value =
$300,000,000. Inserting in these values in our equation gives:
notional amount for 8% IO =
($300,000,000)(0.015)
= $56,250,000.
0.08
Similarly, from tranche B with a par value of $250 million, the excess interest is 125 basis points.
Therefore, an IO with a coupon rate of 1.25% and a notional amount of $250 million can be
created. As seen below, this is equivalent to creating an IO with a notional amount of $39,620,500
million and a coupon rate of 8%. For example, for tranche B, excess interest = 0.080 – 0.0675 =
0.0125 and tranche’s par value = $250,000,000. Inserting in these values in our equation gives:
notional amount for 8% IO =
(tranche's par value)(excess interest)
($250,000,000)(0.0125)
=
=
0.08
0.08
$39,062,500.
Similarly, from tranche C with a par value of $200 million, the excess interest is 75 basis points,
and therefore an IO with a coupon rate of 0.75% and a notional amount of $200 million can be
created. As seen below, this is equivalent to creating an IO with a notional amount of $18,750,000
million and a coupon rate of 8%. For example, for tranche C, excess interest = 0.080 – 0.0725 =
0.0075 and tranche’s par value = $200,000,000. Inserting in these values gives:
notional amount for 8% IO =
(tranche's par value)(excess interest)
($200,000,000)(0.0075)
=
=
0.08
0.08
$18,750,000.
Similarly, from tranche D with a par value of $250 million, the excess interest is 25 basis points,
and therefore an IO with a coupon rate of 0.25% and a notional amount of $250 million can be
created. As seen below, this is equivalent to creating an IO with a notional amount of $7,812,500
million and a coupon rate of 8%. For example, for tranche D, excess interest = 0.080 – 0.0775 =
0.0025 and tranche’s par value = $250,000,000. Inserting in these values in our equation gives:
notional amount for 8% IO =
(tranche's par value)(excess interest)
($250,000,000)(0.0025)
=
=
0.08
0.08
$7,812,500.
The previous procedure is shown in the following table for all four tranches.
Tranche
A
B
C
D
Notional Amount for an
Par Amount
Excess Interest (%)
8% Coupon Rate IO
$300,000,000
1.50%
$ 56,250,000
$250,000,000
1.25%
$ 39,062,500
$200,000,000
0.75%
$ 18,750,000
$250,000,000
0.25%
$ 7,812,500
Notional Amount for an 8.0% IO: $ 121,875,000
259
20. An issuer is considering the following two CMO structures:
STRUCTURE I:
Tranche
A
B
C
D
E
F
Par Amount
(in millions)
$150
$100
$200
$150
$100
$500
Coupon
Rate (%)
6.50%
6.75%
7.25%
7.75%
8.00%
8.50%
Tranches A to E are a sequence of PAC I’s, and F is the support bond.
STRUCTURE II:
Tranche
A
B
C
D
E
F
G
Par Amount
(in millions)
$150
$100
$200
$150
$100
$200
$300
Coupon
Rate (%)
6.50%
6.75%
7.25%
7.75%
8.00%
8.25%
?
Tranches A to E are a sequence of PAC I’s, F is a PAC II, and G is a support bond without a PAC
schedule. Answer the following questions.
(a) In structure II, tranche G is created from tranche F in structure I. What is the coupon
rate for tranche G assuming that the combined coupon rate for tranches F and G in
structure II should be 8.5%?
We can solve for tranche G by rearranging the weighted average formula. This is shown below.
We have: 8.5% = ($200/$500)(8.25%) + ($300/$500)(coupon rate). Using algebra to simplify and
rearrange, the coupon rate can be solved for: coupon rate = [8.5% – (0.4)8.25%] / 0.6 = [8.5% –
3.3%] / 0.6 = 8.6667%. Thus, tranche G has a coupon rate of about 8.67%.
(b) What is the effect on the value and average life of tranches A to E by including the PAC
II in structure II?
It has no effect since it is formed from tranche F. Together, tranches F and G in structure II have a
value and an average life equal to that of tranche F in structure I.
(c) What is the difference in the average life variability of tranche G in structure II and
tranche F in structure II?
260
Tranche F in structure II is formed to give more stable cash flows and thus a lower variability in
average life than found in tranche F in structure I. This lower variability in average life comes at
the expense of the support tranche or tranche G, which has a higher average life than tranche F
21. Answer the following questions.
(a) What is the role of a lockout in a CMO structure?
The role of a lockout in a CMO structure is to provide greater prepayment protection to all PAC
bonds.
One obvious way to provide greater protection for PAC bonds is to issue fewer PAC bonds relative
to support bonds. A CMO structure with no principal payments to a PAC bond class in the earlier
years is called a lockout structure. A lockout structure provides greater prepayment protection to
all PAC bonds in the CMO structure. One way to provide greater prepayment protection to only
some PAC bonds is to alter the principal payment rules for distributing principal when all the
support bonds have been paid off. For example, when the support bond is paid off, the structure
can be made to effectively become a sequential-pay structure.
To provide greater protection to a PAC bond, the payment rules after all support bonds have been
paid off can be specified so that any principal payments in excess of the scheduled amount will be
paid to the last PAC bond. Thus this PAC bond is exposed to greater contraction risk, which
provides the other five PAC bonds with more protection against contraction risk. The principal
payment rules would also specify that when the support bond and last PAC bond are paid off, all
principal payments in excess of the scheduled amounts to earlier tranches are to be paid to the
next-to-last PAC bond.
(b) Explain why in a reverse PAC bond structure the longest average life bond can
effectively turn out to be a support bond if all the support bonds in the structure are paid off.
By definition, the support bonds—or bodyguards—are the bonds that provide prepayment
protection for the PAC tranches. In a reverse PAC bond structure, the longest average life bond
performs the same function as a support bond. For example, a CMO structure requiring any excess
principal payments to be made to the longer PAC bonds after all support bonds are paid off is
called a reverse PAC structure. By requiring the longer PAC bonds to receive any excess
principal, these bonds are effectively performing the same function as the support bonds.
22. Answer the following questions.
(a) What type of prepayment protection is afforded a TAC bond?
A targeted amortization class (TAC) bond resembles a PAC bond in that both have a schedule
of principal repayment. The difference between a PAC bond and a TAC bond is that the former has
a wide PSA range over which the schedule of principal repayment is protected against contraction
risk and extension risk. A TAC bond, in contrast, has a single PSA rate from which the schedule of
261
principal repayment is protected. As a result, the prepayment protection afforded the TAC bond is
less than that for a PAC bond.
(b) What type of prepayment protection is afforded a reverse TAC bond?
If mortgage rates rise, the price of any bond will decline. But pass-throughs will decline more
because the higher rates will tend to slow down the rate of prepayment. This is just the time when
investors want prepayments to speed up so that they can reinvest the prepayments at the higher
market interest rate. This adverse consequence of rising mortgage rates is called extension risk.
Some institutional investors are interested in protection against extension risk but are willing to
accept contraction risk. This is the opposite protection from that sought by the buyers of TAC
bonds. The structures created to provide such protection are referred to as reverse TAC bonds.
(c) What type of prepayment protection is afforded a VADM?
Accrual or Z bonds have been used in CMO structures as support for bonds called very accurately
determined maturity (VADM) or guaranteed final maturity bonds. In this case the interest
accruing (i.e., not being paid out) on a Z bond is used to pay the interest and principal on a VADM
bond. This effectively provides protection against extension risk even if prepayments slow down
because the interest accruing on the Z bond will be sufficient to pay off the scheduled principal and
interest on the VADM bond. Thus, the maximum final maturity can be determined with a high
degree of certainty. However, if prepayments are high, resulting in the supporting Z bond being
paid off faster, a VADM bond can shorten.
A VADM is similar o a reverse TAC. For structures with similar collateral, a VADM bond offers
greater protection against extension risk. Moreover, most VADMs will not shorten significantly if
prepayments speed up. Thus, they offer greater protection against contraction risk compared with a
reverse TAC with the same underlying collateral. Compared with PACs, VADM bonds have
greater absolute protection against extension risk, and though VADM bonds do not have as much
protection against contraction risk, the structures that have included these bonds are such that
contraction risk is generally not significant.
23. What types of CMO issues require a credit rating?
CMOs issued by private entities are rated by commercial rating agencies. More details on the risk
of CMOs and what safety elements they contain are given in the following paragraphs.
A CMO can be viewed as a business entity. The assets of this business are the collateral: that is, the
pass-through securities or pool of mortgage loans backing the deal. The collateral for a CMO is
held in trust for the exclusive benefit of all the bondholders. The liabilities are the payments due to
the CMO bond classes. The liability obligation consists of the par value and periodic interest
payment that is owed to each class of bond. The CMO, or equivalently the business, is structured
so that even under the worst possible consequences concerning prepayments, all the liabilities will
be satisfied.
Credit risk exposure depends on who has issued the CMO. An issuer is either an agency CMO
262
(Freddie Mac, Fannie Mae, or Ginnie Mae) or a nonagency CMO (a private entity). Nonagency
pass-through securities are issued by commercial banks, thrifts, and private conduits. The
guarantee of a government-sponsored enterprise depends on the financial capacity of the agency.
CMOs issued by private entities are rated by commercial rating agencies. The primary factors
considered by the nationally recognized rating companies in assigning a rating are the type of
property (single-family residences, condominiums), the type of loan (fixed-rate level payment,
adjustable rate, balloon), the term of the loans, the geographical dispersion of the loans, the loan
size (conforming loans, jumbo loans, the amount of seasoning of the loans, and the purpose of the
loans (purchase or refinancing).
24. What is a whole loan CMO?
Nonagency CMOs can be divided into two types. The first type is a private entity that issues a
CMO but whose underlying collateral is a pool of pass-throughs guaranteed by an agency is called
a private-label CMO. If the collateral for a CMO is a pool of unsecuritized mortgages loans, the
structure is referred to as a whole loan CMO. Today, the most common type of nonagency CMO is
a whole loan CMO. Consequently, market participants use the terms nonagency CMO and whole
loan CMO interchangeably.
25. What is a REMIC?
REMIC stands for Real Estate Mortgage Investment Conduit. A REMIC is an investment-grade
mortgage bond that separates mortgage pools into different maturity and risk classes.
26. Indicate why you agree or disagree with the following statement: “All CMOs are
REMICs.”
One would disagree with the statement: “All CMOs are REMICs.”
The issuer of a CMO wants to be sure that the trust created to pass through the interest and
principal payments is not treated as a taxable entity. A provision of the Tax Reform Act of 1986,
called the Real Estate Mortgage Investment Conduit (REMIC), specifies the requirements that an
issuer must fulfill so that the legal entity created to issue a CMO is not taxable. Most CMOs today
are created as REMICs. Although it is common to hear market participants refer to a CMO as a
REMIC, not all CMOs are REMICs.
27. Answer the following questions.
(a) What is a principal-only security? What is an interest-only security?
In early 1987, stripped MBSs began to be issued where all the interest is allocated to one class (the
IO class) and the entire principal to the other class (the PO class). The IO class receives no
principal payments. IOs and POs are referred to as mortgage strips. Additional details for POs and
IOs are discussed in the following paragraphs.
The PO security is purchased at a substantial discount from par value. The yield an investor will
263
realize depends on the speed at which prepayments are made. The faster the prepayments, the
higher the yield the investor will realize. For example, suppose that there is a pass-through backed
by 30-year mortgages with $400 million in par value and that investors can purchase POs backed
by this pass-through for $175 million. The dollar return on this investment will be $225 million.
How quickly that dollar return is recovered by PO investors determines the yield that will be
realized. In the extreme case, if all the homeowners in the underlying mortgage pool decide to
prepay their mortgage loans immediately, PO investors will realize the $225 million immediately.
At the other extreme, if all homeowners decide to keep their houses for 30 years and make no
prepayments, the $225 million will be spread out over 30 years, which will result in a lower yield
for PO investors.
The price of the PO can be expected to change as mortgage rates in the market change. When
mortgage rates decline below the coupon rate, prepayments are expected to speed up, accelerating
payments to the PO holder. Thus the cash flow of a PO improves (in the sense that principal
repayments are received earlier). The cash flow will be discounted at a lower interest rate because
the mortgage rate in the market has declined. The result is that the price of a PO will increase when
mortgage rates decline. When mortgage rates rise above the coupon rate, prepayments are
expected to slow down. The cash flow deteriorates (in the sense of its taking longer to recover
principal repayments). Coupled with a higher discount rate, the price of a PO will fall when
mortgage rates rise.
When an IO is purchased there is no par value. In contrast to the PO investor, the IO investor wants
prepayments to be slow. The reason is that the IO investor receives only interest on the amount of
the principal outstanding. As prepayments are made, the outstanding principal declines, and less
dollar interest is received. In fact, if prepayments are too fast, the IO investor may not recover the
amount paid for the IO.
(b) How is the price of an interest-only security expected to change when interest rates
change?
The price of an interest-only security (IO) can move in various directions depending on the
direction of the change in interest rates and also the change relative to the coupon rate. Details on
the precise expectations of IO price changes are supplied in the following paragraps.
If mortgage rates decline below the coupon rate, prepayments on the interest-only security (IO) are
expected to accelerate. This results in a deterioration of the expected cash flow for an IO. Although
the cash flow will be discounted at a lower rate (causing an increase in the IO price), the net effect
is typically a decline in the price of an IO. If mortgage rates rise above the coupon rate, the
expected cash flow improves, but the cash flow is discounted at a higher interest rate (causing a
decrease in the IO price). The net effect may be either a rise or a fall for the IO. Thus we see an
interesting characteristic of an IO: tts price tends to move in the same direction as the change in
mortgage rates. This effect occurs (i) when mortgage rates fall below the coupon rate, and (ii) for
some range of mortgage rates above the coupon rate.
An example of this effect can be seen in Exhibit 12-16, which shows for various mortgage rates the
price of (i) a 9% pass-through, (ii) a PO created from this pass-through, and (iii) an IO created from
264
this pass-through. Notice that as mortgage rates decline below 9%, the price of the pass-through
does not respond much. This is the negative convexity (or price compression) property of
pass-throughs. For the PO security, the price falls monotonically as mortgage rates rise. For the IO
security, at mortgage rates above approximately 11%, the price declines as mortgage rates rise; as
mortgage rates fall below about 11%, the price of an IO falls as mortgage rates decline. Both POs
and IOs exhibit substantial price volatility when mortgage rates change. The greater price
volatility of the IO and PO compared with the pass-through from which they were created can be
seen by the steepness of a tangent line to the curves at any given mortgage rate.
28. Suppose that 8% coupon pass-throughs are stripped into two classes. Class X-1 receives
75% of the principal and 10% of the interest. Class X-2 receives 25% of the principal and
90% of the interest. Answer the following questions.
(a) What type of stripped MBS would this be?
The type of stripped MBS described in the question is a synthetic-coupon pass-through because
each class receives an unequal distribution of principal and interest.
Stripped mortgage-backed securities (MBSs), introduced by Fannie Mae in 1986, are another
example of derivative mortgage products. A pass-through divides the cash flow from the
underlying pool of mortgages on a pro rata basis across the security holders. A stripped MBS is
created by altering the distribution of principal and interest from a pro rata distribution to an
unequal distribution.
Some of the securities thus created will have a price/yield relationship that is different from the
price/yield relationship of the underlying mortgage pool. There are three types of stripped MBS:
(i) synthetic-coupon pass-throughs, (ii) interest-only/principal-only securities, and (iii) CMO
strips.
The first generation of stripped mortgage-backed securities is called synthetic-coupon
pass-throughs. This is because the unequal distribution of coupon and principal results in a
synthetic coupon rate that is different from that of the underlying collateral. In the example above,
each class receives an unequal distribution of coupon and principal. Thus, they are
synthetic-coupon pass-throughs.
(b) What is the effective coupon rate on Class X-1?
Class X-1 receives 10% or 0.1 of the interest. Because the coupon rate is 8%, it effectively will
receive 0.1(8%) = 0.8%. More details are supplied below concerning the relationship between
yield and price that Class X-1 investors can expect.
A stripped MBS is created by altering the distribution of principal and interest from a pro rata
distribution to an unequal distribution. Some of the securities thus created will have a price/yield
relationship that is different from the price/yield relationship of the underlying mortgage pool.
Class X-1 receives 75% of the principal and 10% of the interest. Thus, it is more like a PO which is
purchased at a substantial discount from par value. The yield an investor will realize on a PO
265
depends on the speed at which prepayments are made. The faster the prepayments, the higher the
yield the investor will realize.
For example, suppose that there is a pass-through backed by 30-year mortgages with $400 million
in par value and that investors can purchase POs backed by this pass-through for $175 million. The
dollar return on this investment will be $225 million. How quickly that dollar return is recovered
by PO investors determines the yield that will be realized. In the extreme case, if all the
homeowners in the underlying mortgage pool decide to prepay their mortgage loans immediately,
PO investors will realize the $225 million immediately. At the other extreme, if all homeowners
decide to keep their houses for 30 years and make no prepayments, the $225 million will be spread
out over 30 years, which will result in a lower yield for PO investors.
(c) What is the effective coupon rate on Class X-2?
Class X-2 receives 25% of the principal and 90% or 0.9 of the interest. Because the coupon rate is
8%, it effectively will receive 0.9(8%) = 7.2%. More details are supplied below concerning the
relationship between yield and price that Class X-2 investors can expect.
A stripped MBS is created by altering the distribution of principal and interest from a pro rata
distribution to an unequal distribution. Some of the securities thus created will have a price/yield
relationship that is different from the price/yield relationship of the underlying mortgage pool.
Class X-2 receives 25% of the principal and 90% of the interest. Thus, it is more like an IO, which
when purchased has no par value. In contrast to the PO investor, the IO investor wants
prepayments to be slow. The reason is that the IO investor receives only interest on the amount of
the principal outstanding. As prepayments are made, the outstanding principal declines, and less
dollar interest is received. In fact, if prepayments are too fast, the IO investor may not recover the
amount paid for the IO thus realizing a low effective yield.
Exhibit 12-16 shows for various mortgage rates the price of (i) a 9% pass-through, (ii) a PO created
from this pass-through, and (iii) an IO created from this pass-through. Notice that as mortgage
rates decline below 9%, the price of the pass-through does not respond much. This is the negative
convexity (or price compression) property of pass-throughs. For the PO security, the price falls
monotonically as mortgage rates rise. For the IO security, at mortgage rates above approximately
11%, the price declines as mortgage rates rise; as mortgage rates fall below about 11%, the price of
an IO falls as mortgage rates decline. Both POs and IOs exhibit substantial price volatility when
mortgage rates change. The greater price volatility of the IO and PO compared with the
pass-through from which they were created can be seen by the steepness of a tangent line to the
curves at any given mortgage rate.
266