CHAPTER 11
MORTGAGE PASS-THROUGH SECURITIES
ANSWERS TO QUESTIONS FOR CHAPTER 11
(Questions are in bold print followed by answers.)
2. Describe the cash flow of a mortgage pass-through security.
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.
The monthly cash flow for a pass-through is less than the monthly cash flow of the underlying
mortgages by an amount equal to servicing and other fees. The other fees are those charged by
the issuer or guarantor of the pass-through for guaranteeing the issue. The coupon rate on a passthrough, called the pass-through coupon rate, is less than the mortgage rate on the underlying
pool of mortgage loans by an amount equal to the servicing and guaranteeing fees.
The timing of the cash flow, like the amount of the cash flow, is also different. The monthly
mortgage payment is due from each mortgagor on the first day of each month, but there is a
delay in passing through the corresponding monthly cash flow to the security holders. The length
of the delay varies by the type of pass-through security.
Because of prepayments, the cash flow of a pass-through is also not known with certainty.
4. What are the different types of agency pass-through securities?
There are three major types of pass-throughs, guaranteed by three organizations: Government
National Mortgage Association (Ginnie Mae), Federal Home Loan Mortgage Corporation
(Freddie Mac), and Federal National Mortgage Association (Fannie Mae). These are called
agency pass-throughs.
An agency can provide one of two types of guarantees. One type of guarantee is the timely
payment of both interest and principal, meaning that interest and principal will be paid when due,
even if some of the mortgagors fail to make their monthly mortgage payments. Pass-throughs
with this type of guarantee are referred to as fully modified pass-throughs. The second type
also 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. Pass-throughs with this type of
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guarantee are called modified pass-throughs.
6. If the borrower whose mortgage is included in an agency pass-through fails to make a
mortgage payment, what is the impact on the cash flow to the investor?
Unless the agency is fully guaranteed, any failure to make a payment can have a negative effect
at least in the long-run because the lender’s return will be decreased. There are three major types
of pass-throughs, guaranteed by three organizations: Government National Mortgage Association
(Ginnie Mae), Federal Home Loan Mortgage Corporation (Freddie Mac), and Federal National
Mortgage Association (Fannie Mae). These are called agency pass-throughs. An agency can
provide one of two types of guarantees. One type of guarantee is the timely payment of both
interest and principal, meaning that interest and principal will be paid when due, even if some of
the mortgagors fail to make their monthly mortgage payments. Pass-throughs with this type of
guarantee are referred to as fully modified pass-throughs.
8. What is the disadvantage of a nonagency pass-through that is credit enhanced with a
corporate guarantee?
The disadvantage of nonagency pass-through securities hinges on the fact a nonconforming
mortgage does not meet the underwriting standards established by Federal Home Loan Mortgage
Corporation and the Federal National Mortgage Association. Thus, these securities do not meet
those standards established by these agencies for being in a pool of mortgages underlying a
security that they guarantee.
10. Why is overcollateralization a form of credit enhancement for a nonagency passthrough security?
Nonagency pass-throughs are not backed by the full faith of the government. Credit enhancement
lowers the credit risk of a nonagency pass-through security. One of the most common forms of
internal credit enhancement is overcollateralization. This form enhances credit for a pass-through
by establishing a pool of assets with a greater principal amount than the principal amount of the
pool of mortgage loans. For example, the principal amount of an issue may be $400 million, but
the principal amount of the pool of mortgages is $410 million.
12. What does a conditional prepayment rate of 8% mean?
One benchmark for projecting prepayments and the cash flow of a pass-through requires that one
assumes some fraction of the remaining principal in the pool is prepaid each month for the
remaining term of the mortgage.
The prepayment rate assumed for a pool, called the conditional prepayment rate (CPR), is
based on the characteristics of the pool (including its historical prepayment experience) and the
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current and expected future economic environment. It is referred to as a conditional rate because
it is conditional on the remaining mortgage balance.
The CPR is an annual prepayment rate. To estimate monthly prepayments, the CPR must be
converted into a monthly prepayment rate, commonly referred to as the single-monthly
mortality rate (SMM).
A formula can be used to determine the SMM for a given CPR:
SMM = 1 – (1 – CPR)1/12.
For our problem we want to know what a conditional prepayment rate of 8% means. Assuming
the CPR used to estimate prepayments is 8%, the corresponding SMM is
SMM = 1 – (1 – 0.08)1/12 = 1 – (0.92)0.08333 = 1 – 0.9930756 = 0.0069244 or 0.69244%.
An SMM of 0.69244% means that approximately 0.69244% of the remaining mortgage balance
at the beginning of the month, less the scheduled principal payment, will prepay that month. That
is, prepayment for month t is equal to
(beginning mortgage balance for month t – scheduled principal payment for month t).
For example, suppose that an investor owns a pass-through in which the remaining mortgage
balance at the beginning of some month is $90 million. Assuming that the SMM is 0.69244%
and the scheduled principal payment is $1 million, the estimated prepayment for the month
(using the above equation) is:
0.0069244($90,000,000 – $1,000,000) = 0.0069244($89,000,000) = $616,270.05.
14. Answer the following questions.
(a) Complete the following table:
CPR Assuming:
Month 100% PSA 70% PSA 320% PSA
1
4
9
27
40
120
340
The PSA benchmark assumes the following CPRs for 30-year mortgages: (i) a CPR of 0.2% for
the first month, increased by 0.2% per year per month for the next 30 months when it reaches 6%
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per year, and (ii) a 6% CPR for the remaining years. This benchmark, referred to as “100% PSA”
or simply “100 PSA,” and can be expressed as follows: if t ≤ 30: CPR = 6% (t / 30); if t > 30:
CPR = 6% where t is the number of months since the mortgage originated.
Slower or faster speeds are then referred to as some percentage of PSA. For example, 75 PSA
means 0.75 times the CPR of the PSA benchmark prepayment rate; and, 320 PSA means 3.2
times the CPR of the PSA benchmark prepayment rate. A prepayment rate of 0 PSA means that
no prepayments are assumed.
Given the above information and the months from the above table, we compute the CPRs as
given below.
With 100 PSA, we get the below CPR values.
For month 1: CPR = 6%(1 / 30) = 0.2%; 100 PSA = 1.00(0.2%) = 0.2% or 0.002.
For month 4: CPR = 6%(4 / 30) = 0.8%; 100 PSA = 1.00(0.8%) = 0.8% or 0.008.
For month 9: CPR = 6%(9 / 30) = 1.8%; 100 PSA = 1.00(1.8%) = 1.8% or 0.018.
For month 27: CPR = 6%(27 / 30) = 5.4%; 100 PSA = 1.00(5.4%) = 5.4% or 0.054.
For months 40, 120, & 340: CPR = 6.0%; 100 PSA = 1.00(6.0%) = 6.0% or 0.060.
With 70 PSA, we get the below CPR values.
For month 1: CPR = 6%(1 / 30) = 0.2%; 70 PSA = 0.70(0.2%) = 0.14% or 0.0014.
For month 4: CPR = 6%(4 / 30) = 0.8%; 70 PSA = 0.70(0.8%) = 0.56% or 0.0056.
For month 9: CPR = 6%(9 / 30) = 1.8%; 70 PSA = 0.70(0.1.8%) = 1.26% or 0.0126.
For month 27: CPR = 6%(27 / 30) = 5.4%; 70 PSA = 0.70(5.4%) = 3.78% or 0.0378.
For months 40, 120, & 340: CPR = 6.0%; 70 PSA = 0.70(6.0%) = 4.20% or 0.0420.
With 320 PSA, we get the below CPR values.
For month 1: CPR = 6%(1 / 30) = 0.2%; 320 PSA = 3.20(0.2%) = 0.64% or 0.0064.
For month 4: CPR = 6%(4 / 30) = 0.8%; 320 PSA = 3.20(0.8%) = 2.56% or 0.0256.
For month 9: CPR = 6%(9 / 30) = 1.8%; 320 PSA = 3.20(1.8%) = 5.76% or 0.0576.
For month 27: CPR = 6%(27 / 30) = 5.4%; 320 PSA = 3.20(5.4%) = 17.28% or 0.1728.
For months 40, 120, & 340: CPR = 6%; 320 PSA = 3.20(6.0%) = 19.20% or 0.1920.
Inserting the CPR values into the above table, we have:
CPR Assuming:
Month 100% PSA 70% PSA 320% PSA
1
0.2%
0.14%
0.64%
4
0.8%
0.56%
2.56%
9
1.8%
1.26%
5.76%
27
5.4%
3.78%
17.28%
40
6.0%
4.20%
19.20%
120
6.0%
4.20%
19.20%
220
340
6.0%
4.20%
19.20%
(b) Complete the following table:
SMM Assuming:
Month 100% PSA 70% PSA 320% PSA
1
4
9
27
40
120
340
With 100% PSA, we get the below SMM values using the formula: SMM = 1 – (1 – CPR)1/12.
For month 1: CPR = 6%(1 / 30) = 0.2% = 0.002; 100 PSA = 1.00(0.002) = 0.002;
SMM = 1 – (1 – 0.002)1/12 = 1 – (0.998)0.083333 = 0.0001668 or 0.01668%.
For month 4: CPR = 6%(4 / 30) = 0.08% = 0.008; 100 PSA = 1.00(0.008) = 0.008;
SMM = 1 – (1 – 0.008)1/12 = 1 – (0.992)0.083333 = 0.0006691 or 0.06691%.
For month 9: CPR = 6%(9 / 30) = 1.8% = 0.018; 100 PSA = 1.00(0.018) = 0.018;
SMM = 1 – (1 – 0.018)1/12 = 1 – (0.982)0.083333 = 0.0015125 or 0.15125%.
For month 27: CPR = 6%(27 / 30) = 5.4% = 0.054; 100 PSA = 1.00(0.054) = 0.054;
SMM = 1 – (1 – 0.054)1/12 = 1 – (0.946)0.083333 = 0.0046154 or 0.46154%.
For months 40, 120, and 340: CPR = 6% = 0.06; 100 PSA = 1.00(0.06) = 0.06;
SMM = 1 – (1 – 0.06)1/12 = 1 – (0.94)0.083333 = 0.0051430 or 0.51430%.
With 70 PSA, we get the below SMM values.
For month 1: CPR = 6%(1 / 30) = 0.2% = 0.002; 70 PSA = 0.70(0.002) = 0.0014.
SMM = 1 – (1 – 0.0014)1/12 = 1 – (0.9986)0.083333 = 0.0001167 or 0.01167%.
For month 4: CPR = 6%(4 / 30) = 0.8% = 0.008; 70 PSA = 0.70(0.008) = 0.0056.
SMM = 1 – (1 – 0.0056)1/12 = 1 – (0.9944)0.083333 = 0.0004679or 0.04679%.
For month 9: CPR = 6%(9 / 30) = 1.8% = 0.018; 70 PSA = 0.70(0.018) = 0.0126.
SMM = 1 – (1 – 0.0126)1/12 = 1 – (0.9874)0.083333 = 0.0010561 or 0.10561%.
For month 27: CPR = 6%(27 / 30) = 5.4% = 0.054; 70 PSA = 0.70(0.054) = 0.0378.
SMM = 1 – (1 – 0.0378)1/12 = 1 – (0.9622)0.083333 = 0.0032059 or 0.32059%.
For months 40, 120, & 340: CPR = 6% = 0.06; 70 PSA = 0.70(0.06) = 0.0420.
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SMM = 1 – (1 – 0.042)1/12 = 1 – (0.958)0.083333 = 0.0035692 or 0.35692%.
With 320 PSA, we get the below SMM values.
For month 1: CPR = 6%(1 / 30) = 0.2% = 0.002; 320 PSA = 3.20(0.002) = 0.0064.
SMM = 1 – (1 – 0.064)1/12 = 1 – (0.9936)0.083333 = 0.0005349 or 0.05349%.
For month 4: CPR = 6%(4 / 30) = 0.8% = 0.008; 320 PSA = 3.20(0.008) = 0.0256.
SMM = 1 – (1 – 0.0256)1/12 = 1 – (0.9744)0.083333 = 0.0021588 or 0.21588%.
For month 9: CPR = 6%(9 / 30) = 1.8% = 0.018; 320 PSA = 3.20(0.018) = 0.0576.
SMM = 1 – (1 – 0.0576)1/12 = 1 – (0.9424)0.083333 = 0.0049316 or 0.49316%.
For month 27: CPR = 6%(27 / 30) = 5.4% = 0.054; 320 PSA = 3.20(0.054) = 0.1728.
SMM = 1 – (1 – 0.01728)1/12 = 1 – (0.8272)0.083333 = 0.0156848 or 1.56848%.
For months 40, 120, & 340: CPR = 6% = 0.06; 320 PSA = 3.20(0.06) = 0.1920.
SMM = 1 – (1 – 0.1920)1/12 = 1 – (0.8080)0.083333 = 0.0176092 or 1.76092%.
Inserting the SMM values into the above table, we have:
SMM Assuming:
Month 100% PSA
1
0.01668%
4
0.06691%
9
0.15125%
27
0.46154%
40
0.51430%
120
0.51430%
340
0.51430%
70% PSA 320% PSA
0.01167% 0.05349%
0.04679% 0.21588%
0.10561% 0.49316%
0.32059% 1.56848%
0.35692% 1.76092%
0.35692% 1.76092%
0.35692% 1.76092%
16. Answer the following questions.
(a) What is meant by prepayments due to housing turnover?
Housing turnover means existing home sales. The two factors that impact existing home sales
include (1) family relocation due to changes in employment and family status (e.g., change in
family size, divorce), and (2) trade-up and trade-down activity attributable to changes in interest
rates, income, and home prices. In general, housing turnover is insensitive to the level of
mortgage rates.
(b) What is meant by prepayments due to cash-out refinancing?
Cash-out refinancing means refinancing by a borrower in order to monetize the price
appreciation of the property. Prepayments due to cash-out refinancing will depend on the
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increase in housing prices in the economy or region where the property is located. Adding to the
incentive for borrowers to monetize price appreciation is the favorable tax law regarding the
taxation of capital gains. The federal income tax rules exempt gains up to $500,000. Thus, cashout refinancing may be economic despite a rising mortgage rate and considering transaction
costs. Basically, cash-out refinancing is more like housing turnover refinancing because of its tie
to housing prices and its insensitivity to mortgage rates.
(c) What is meant by prepayments due to rate/term refinancing?
Rate/term refinancing means that the borrower has obtained a new mortgage on the existing
property to save either on interest cost or shortening the life of the mortgage with no increase in
the monthly payment. The homeowner’s incentive to refinance is based on the projected present
value of the dollar interest savings from the lower mortgage rate after deducting the estimated
transaction costs to refinance.
18. What is the S-curve for prepayments and explain the reason for the shape?
The S-curve for prepayment is a graph where values for the “CPR%” are given along the
vertical line and values for the “WAC/Mortgage Rate” ratio are found along the horizontal axis.
The reason for the observed S-curve for prepayments is that as the rate ratio increases, the CPR
(i.e., prepayment rate) increases. There is some level of the rate ratio, however, at which the
prepayment rate tends to level off. The reason for this leveling of the prepayment rate is because
the only borrowers remaining in the pool are those that cannot obtain refinancing or those who
have other reasons why refinancing does not make sense.
The S-curve is not sufficient for modeling the refinancing rate/term refinancing. This is because
the S-curve fails to adequately account for two dynamics of borrower attributes that impact
refinancing decisions: (i) the burnout effect and (ii) the threshold media effect.
20. Why was the PSA Standard Default curve introduced?
The PSA Standard Default curve was introduced to give the annual default rate for a mortgage
pool as a function of the seasoning of the mortgages. More details are given below.
In agency pass-through securities, the cash flow is not affected by defaults and delinquencies.
For nonagency pass-throughs, the effect of defaults and delinquencies must be considered. With
the increase in the issuance of nonagency pass-through securities (as well as nonagency CMOs),
a standardized benchmark for default rates has been introduced by the Public Securities
Association (PSA).The PSA standard default assumption (SDA) benchmark gives the annual
default rate for a mortgage pool as a function of the seasoning of the mortgages. The PSA SDA
benchmark, or 100 SDA, specifies the following:
(i) The default rate in month 1 is 0.02% and increases by 0.02% up to month 30, so that in month
30, the default rate is 0.60%.
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(ii) From month 30 to month 60, the default rate remains at 0.60%.
(iii) From month 61 to month 120, the default rate declines from 0.60% to 0.03%.
(iv) From month 120 on, the default rate remains constant at 0.03%.
As with the PSA prepayment benchmark, multiples of the benchmark are found by multiplying
the default rate by the assumed multiple.
22. What is the average life of a pass-through, and what does it depend on?
A measure commonly used to estimate the life of a pass-through is its average life. Consider a
mortgage-back security guaranteed by Ginnie Mae, which is a fully modified pass-through. The
average life of a mortgage-backed security is the average time to receipt of principal payments
(scheduled principal payments and projected prepayments), weighted by the amount of principal
expected. Mathematically, the average life is expressed as follows:
T
average life = 
t 1
t (principal received at time t )
12(total principal )
where T is the number of months. The average life of a pass-through depends on the PSA
prepayment assumption. To see this, the average life is shown in Exhibit 11-7 for different
prepayment speeds for the pass-through used to illustrate the cash flow for 100 PSA and 165
PSA in Exhibits 11-4 and 11-5.
24. Answer the following questions.
(a) Distinguish between a TBA and specified pool trade.
Pass-throughs are quoted in the same manner as U.S. Treasury coupon securities. They are
identified by a pool prefix and pool number. Many trades occur while a pool is still unspecified,
and therefore no pool information is known at the time of the trade. This kind of trade is known
as a “TBA” (to be announced) trade. The seller has the right in this case to deliver pass-throughs
backed by pools that satisfy the PSA requirements for good delivery.
(b) What delivery options are granted to the seller in a TBA trade?
When an investor purchases, say, $1 million GNMA 8s on a TBA basis, the investor can receive
up to three pools, with pool numbers being announced shortly before the settlement date. Three
pools can be delivered because the PSA has established guidelines for standards of delivery and
settlement of mortgage-backed securities, under which TBA trade permits three possible pools to
be delivered. The option of what pools to deliver is left to the seller, as long as selection and
delivery satisfy the PSA guidelines. In contrast to TBA trades, a pool number may be specified.
In this case the transaction will involve delivery of the pool specifically designated.
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