ANSWERS TO QUESTIONS FOR CHAPTER 12
(Questions are in bold print followed by answers.)
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.
4. In a discussion of the CMO market, the popular press sometimes refers to this sector of
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.
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.
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8. This quotation is taken from a 1991 issue of BondWeek:
“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
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implications of this desire are described below.
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.
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
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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.
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
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
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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.
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.
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
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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.
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.
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
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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
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.
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
Par Amount
(in millions)
$150
$100
$200
$150
$100
$200
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Coupon
Rate (%)
6.50%
6.75%
7.25%
7.75%
8.00%
8.25%
G
$300
?
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?
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
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
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
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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.
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.
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.
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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
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
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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.
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