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Answers to Chapter 7
Questions:
1. Mortgage markets are examined separately from bond and stock markets for several reasons. First, mortgages are
backed by a specific piece of real property. If the borrower defaults on a mortgage, the financial institution can take
ownership of the property. Only mortgage bonds are backed by a specific piece of property that allows the lender to
take claim in the event of a default. All other corporate bonds and stocks give the holder a general claim to a
borrower’s assets. Second, there is no set denomination for primary mortgages. Rather, the size of each mortgage
2. Four basic categories of mortgages are issued by financial institutions: homes, multifamily dwellings,
commercial, and farms. Home mortgages ($9.86 trillion outstanding in 2013) are used to purchase one- to
four-family dwellings. Multifamily dwelling mortgages ($0.86 trillion outstanding) are used to finance the purchase
of apartment complexes, townhouses, and condominiums. Commercial mortgages ($2.21 trillion outstanding) are
3. A lien is a public record attached to the title of the property that gives the financial institution the right to sell the
property if the mortgage borrower defaults or falls into arrears on his or her payments. The mortgage is secured by
4. Federally insured mortgages are originated by financial institutions, but repayment is guaranteed by either the
Federal Housing Administration (FHA) or the Veterans Administration (VA). In order to qualify, FHA and VA
mortgage loan applicants must meet specific requirements set by these government agencies. Further, the maximum
5. A fixed rate mortgage locks in the borrower=s interest rate and thus required monthly payments over the life of
the mortgage, regardless of how market rates change. In contrast, the interest rate on an adjustable rate mortgage
Mortgage borrowers generally prefer fixed rate loans to ARMs, particularly when interest rates in the
economy are low. In fact if interest rates rise, ARMs may cause borrowers to be unable to meet the promised
payments on the mortgage. In contrast, most mortgage lenders prefer ARMs when interest rates are low. When
6. By refinancing the mortgage at a lower interest rate, the borrower pays less each month—even if the new
mortgage is for the same amount as the current mortgage. Mortgage refinancing involves many of the same details
and steps involved in applying for a new mortgage and can involve many of the same fees and expenses. Mortgages
are most often refinanced when a current mortgage has an interest rate that is higher than the current interest rate. As
7. A borrower pays points on a mortgage up front in exchange for a reduced interest rate and, consequently, reduced
monthly payments. The choice of points (and lower monthly payments) versus no points (and higher monthly
8. Jumbo mortgages are those mortgages that exceed the conventional mortgage conforming limits. Limits are set
by the two government-sponsored enterprises, Fannie Mae and Freddie Mac (discussed below) and are based on the
maximum value of any individual mortgage they will purchase from a mortgage lender. In 2013, the general limit
was $417,000 for most of the U.S. (the limit is set higher in high cost areas of the country). Because the large size
9. Subprime mortgages are mortgages to borrowers that do not qualify for prime mortgages because of weakened
credit histories including payment delinquencies, and possibly more severe problems such as charge-offs,
judgments, and bankruptcies. Subprime borrowers may also display reduced repayment capacity as measured by
It was subprime mortgages and the huge growth in them that was a major instigator of the financial crisis.
The low interest rate environment in the early and mid-2000s led to a dramatic increase in the demand for residential
mortgages, especially among those who had previously been excluded from participating in the market because of
their poor credit ratings, i.e., subprime borrowers. To boost their earnings, FIs began lowering their credit quality
10. Option ARMs, also called pick-a-payment or pay-option ARMs, are 15- or 30-year adjustable rate mortgages
that offer the borrower several monthly payment options. The four major types of payment options include:
Minimum payment option. The minimum payment is the lowest of the four payment options and carries the most
risk. With these option ARMs, the monthly payment is set for 12 months at an initial interest rate. After that, the
payment changes annually, and a payment cap limits how much it can increase or decrease each year (generally 7.5
The minimum payment on most option arm programs is 1percent fully amortized. Every time the borrower
makes the minimum payment, the difference between the minimum payment and the interest-only payment is tacked
Interest-only payment: An interest-only option ARM requires the borrower to pay only the interest on the loan
during the initial period of the loan. During this period, no principal must be repaid. After the interest-only period,
the mortgage must amortize so that the mortgage will be paid off by the end of its original term. This means that
Interest-only payment option ARMs carry a great deal of payment-shock risk. Not only do the payments have the
30-year fully amortizing payment: With fully amortizing option ARMs, the borrower pays both principal and interest
15-year fully amortizing payment: This option ARM is similar to the 30-year fully amortizing payment option ARM,
with a full principal and interest payment, but with a larger amount of principal paid each month. This amount
11. The secondary mortgage markets were created by the federal government to help boost U.S. economic activity
during the Great Depression. As borrowers defaulted on mortgages, banks and thrifts found themselves strapped for
cash. To create liquidity in the mortgage markets and to raise levels of home ownership and the availability of
affordable housing, in 1938 the government established the Federal National Mortgage Association (FNMA or
Further, by the late 1960s, fewer veterans were obtaining guaranteed VA loans. As a result, the secondary market for
Mortgage Association (GNMA or Ginnie Mae) and the Federal Home Loan Mortgage Corporation (FHLMC or
12. A mortgage sale occurs when a financial institution originates a mortgage and sells it with or without recourse to
an outside buyer. Mortgage sales usually involve no creation of new types of securities. Securitization of mortgages
13. Mortgage-backed securities allow mortgage issuers to separate the credit risk exposure from the lending process
itself. That is, FIs can assess the creditworthiness of loan applicants, originate loans, fund loans, and even monitor
and service loans without retaining exposure to loss from credit events, such as default or missed payments. This
decoupling of the risk from the lending activity allows the market to efficiently transfer risk across counterparties.
14. Pass-through mortgage securities promise payments of principal and interest on pools of mortgages created by
financial institutions to secondary market participants (mortgage-backed bondholders) holding an interest in these
pools. After a financial institution issues mortgages, they pool them and sell interests in these pools to pass-through
15. The Government National Mortgage Association (GNMA), or Ginnie Mae, began in 1968 when it split off from
the Federal National Mortgage Association (FNMA). GNMA is a government-owned agency with two major
functions: sponsoring mortgage-backed securities programs by financial institutions such as banks, thrifts, and
mortgage bankers and acting as a guarantor to investors in mortgage-backed securities regarding the timely
16. Originally created in 1938, the Federal National Mortgage Association (FNMA or Fannie Mae), is the oldest of
the three mortgage-backed security-sponsoring agencies. It is now a private corporation owned by shareholders with
its common stock traded on the New York Stock Exchange, but in the minds of many investors, it still has implicit
directly to finance those purchases.
Specifically, FNMA creates mortgage-backed securities (MBSs) by purchasing packages of mortgage loans
from banks and thrifts; it finances such purchases by selling MBSs to outside investors such as life insurers or
pension funds. In addition, FNMA engages in swap transactions by which it swaps MBSs with a bank or thrift for
17. Together FNMA and FHLMC represent a huge presence in the financial system as they have over
60 percent of the single-family mortgage pools in the United States. Some regulators and politicians have argued
Also, in the early 2000s, these two agencies came under fire for several reasons. First, in September 2002, Fannie
Mae was criticized for allowing a sharp increase in interest rate risk to exist on its balance sheet. The Office of
Federal Housing Enterprise Oversight (OFHEO), a main regulator of Fannie Mae, required Fannie Mae to submit
weekly reports to the OFHEO on the company’s exposure to interest rate risk. The OFHEO also instructed Fannie
Mae to keep regulators apprised of any challenges associated with returning its interest rate risk measure to more
acceptable levels and warned that additional action would be taken if there were adverse developments with Fannie
Underlying the concerns about the actions of these two GSEs was the widespread perception among investors that
neither would be allowed to fail if they got into trouble. This perception created a subsidy for the agencies and
allowed them to borrow more cheaply than other firms with similar balance sheets. The fear was that the two
agencies used their implicit federal backing to assume more risk and finance expansion through increased debt. Such
actions created a source of systemic risk for the U.S. financial system. These fears and concerns became reality
GSE status, however, enabled them to continue to fund their operations by selling debt securities, because the
market believed that Fannie and Freddie debt was implicitly guaranteed by the government. In July 2008, however,
viability. As a result, the federal government concluded that “the companies cannot continue to operate safely and
soundly and fulfill their critical public mission, without significant action” to address their financial weaknesses.
The Housing and Economic Recovery Act of 2008, enacted July 30, 2008, gave the authority for the government’s
takeover of the GSEs. The act created a new GSE regulator, the Federal Housing Finance Agency (FHFA), with the
authority to take control of either GSE to restore it to a sound financial condition. The act also gave the Treasury
The takeover of Fannie and Freddie, and specifically the commitment to meet all of the firms’ obligations to debt
holders, exposes the U.S. government to a potentially large financial risk. At the time the FHFA took over, debt
issued or guaranteed by the GSEs totaled more than $5 trillion. The risks of not acting, however, clearly appeared
In February 2011, the Obama administration recommended phasing out the GSEs and gradually reducing the
government’s involvement in the mortgage market. In the proposal, any dismantling of Fannie and Freddie would
Complicating these efforts, as the U.S. economy and housing market slowly recovered, so did the GSEs. In 2012,
FNMA and Freddie Mac reported net income of $17.2 billion and $11.0 billion, respectively, the best year ever for
both companies. By mid-2013 the companies’ stocks were trading at $4.08 and $3.75, respectively, up from
18. A CMO can be viewed as a multiclass pass-through with a number of different bondholder classes or tranches.
Unlike a pass-through which has no guaranteed annual “coupon,” each bondholder class has a different guaranteed
coupon just as a regular T-bond has, but more importantly, the allocation of any excess cash flows over and above
CMOs can be created either by packaging and securitizing whole mortgage loans or, more usually, re-securitizing
19. MBBs differ from pass-throughs and CMOs in two key dimensions. First, while pass-throughs and CMOs help
cash flows on the bond instrument issued. By contrast, the relationship for MBBs is one of collateralization; the cash
20. Figure 7–8 shows the distribution of mortgages outstanding in 1992, 2007, and 2010 by type of mortgage holder
—the ultimate investor. Notice in Figure 7–8 the growth in the importance of mortgage securitization pools over the
period (40.42 percent of all mortgages outstanding in 1992 versus 55.35 percent in 2007 and 60.01 percent in 2013).
Actual holdings of mortgages by specialized mortgage companies (such as Sierra Pacific Mortgage Company and
Blue Water Mortgage Corp. of New Hampshire) are small (1.49 percent in 1992, 3.65 percent in 2007, and 1.33
percent in 2013). Mortgage companies, or mortgage bankers, are financial institutions 9 that originate mortgages and
collect payments on them. Unlike banks or thrifts, mortgage companies typically do not hold on to the mortgages
they originate. Instead, they sell the mortgages they originate but continue to service the mortgages by collecting
Problems:
1. You will make a down payment of 20 percent of the purchase price, or you will make a down payment of $20,000
(0.20 x $100,000) at closing and borrow $80,000 through the mortgage.
a. For your mortgage:
Thus, your monthly payment is $601.01.
c. The 225th payment of $601.01 is split as follows: $364.32 to interest and $236.69 to principal.
2. You will make a down payment of 20 percent of the purchase price, or you will make a down payment of $35,000
(0.20 x $175,000) at closing and borrow $140,000 through the mortgage.
Thus, your monthly payment is $1,317.79.
b. The 60th payment of $1,317.79 is split as follows: $713.07 to interest and $604.72 to principal.
c. The 180th payment of $1,317.79 is split as follows: $8.46 to interest and $1,309.33 to principal.
d. The total payments over the life of the mortgage amount to payments of $237,201.48 ($1,317.786 x 15 x 12):
$140,000 to the repayment of principal and $97,201.48 to the payment of interest.
3. You will make a down payment of 20 percent of the purchase price, or you will make a down payment of $16,000
(0.20 x $80,000) at closing and borrow $64,000 through the mortgage.
a. For your mortgage:
$64,000 = PMT{[1 - (1/(1 + 0.08/12)15(12))]/(0.08/12)}
or PMT = $64,000/{[1 - (1/(1 + 0.08/12)15(12))]/(0.08/12)}
therefore PMT = $64,000/104.6406 = $611.617
Thus, your monthly payment is $611.62.
b. The 127th payment of $611.62 is split as follows: $184.39 to interest and $427.23 to principal.
c. The 159th payment of $611.62 is split as follows: $83.17 to interest and $528.45 to principal.
d. The total payments over the life of the mortgage amount to payments of $110,091.60 ($611.62 x 15 x 12):
$62,000 to the repayment of principal and $46,091.60 to the payment of interest.
4. You will make a down payment of 20 percent of the purchase price, or you will make a down payment of $30,000
(0.20 x $150,000) at closing and borrow $120,000 through the mortgage.
a. For your mortgage: $120,000 = PMT{[1 - (1/(1 + 0.0525/12)15(12))]/(0.0525/12)}
or PMT = $120,000/{[1 - (1/(1 + 0.0525/12)15(12))]/(0.0525/12)}
therefore PMT = $120,000/124.3970 = $964.65
Thus, your monthly payment is $964.65.
b. Amortization Schedule for first 6 payments (months)
Beginning Ending
Loan Loan
Month Balance Payment Interest Principal Balance
1 $120,000.00 $964.65 $525.00 $439.65 $119,560.35
2 119,560.35 964.65 523.08 441.57 119,118.78
3 119,118.78 964.65 521.14 443.51 118,675.27
4 118,675.27 964.65 519.20 445.45 118,229.82
5 118,229.82 964.65 517.26 447.39 117,782.43
6 117,782.43 964.65 515.30 449.35 117,333.08
5. You will make a down payment of 20 percent of the purchase price, or you will make a down payment of $40,000
(0.20 x $200,000) at closing and borrow $160,000 through the mortgage.
a. For your mortgage: $160,000 = PMT{[1 - (1/(1 + 0.0650/12)30(12))]/(0.0650/12)}
or PMT = $160,000/{[1 - (1/(1 + 0.0650/12)30(12))]/(0.0650/12)}
therefore PMT = $160,000/158.2108 = $1,011.31
Thus, your monthly payment is $1,011.31.
b. Amortization Schedule for first 6 payments (months)
Beginning Ending
Loan Loan
Month Balance Payment Interest Principal Balance
1 $160,000.00 $1,011.31 $866.67 $144.64 $159,855.36
2 159,855.36 1,011.31 865.88 145.43 159,709.93
3 159,709.93 1,011.31 865.10 146.21 159,563.72
4 159,563.72 1,011.31 864.30 147.01 159,416.71
5 159,416.71 1,011.31 863.51 147.80 159,268.91
6 159,268.91 1,011.31 862.71 148.60 159,120.31
6. EXCEL Problem: Payment = $1,245.62
Payment = $1,286.13
Payment = $1,390.52
Payment = $1,521.40
7. EXCEL Problem: Payment = $875.36
Payment = $923.58
Payment = $1,048.82
Payment = $1,206.93
8. For the either mortgage, you will make a down payment of 20 percent of the purchase price: or a down payment
of $40,000 (0.20 x $200,000) at closing and borrow $160,000 through the mortgage.
a. Total payments on the 15-year mortgage are $250,878.60, of which $90,878.60 is interest. This compares to
interest of $232,932.80 on the 30-year mortgage (a difference of $142,054.20, disregarding time value of money).
The mortgage borrower’s interest payments are reduced significantly with the 15-year mortgage relative to the
30-year mortgage.
b. For the 30-year mortgage: $160,000 = PMT{[1 - (1/(1 + 0.0725/12)30(12))]/(0.0725/12)}
or PMT = $160,000/{[1 - (1/(1 + 0.0725/12)30(12))]/(0.0725/12)}
therefore PMT = $160,000/146.5897 = $1,091.48
For the 15-year mortgage: $160,000 = PMT{[1 - (1/(1 + 0.0650/12)15(12))]/(0.0650/12)}
or PMT = $160,000/{[1 - (1/(1 + 0.0650/12)15(12))]/(0.0650/12)}
therefore PMT = $160,000/114.7964 = $1,393.77
The borrower must pay $1,393.77 per month with the 15-year mortgage compared to $1,091.48 with the 30-year
mortgage, a difference of $302.29 per month. This may be difficult if the borrower’s income level is not very high.
9. For the either mortgage, you will make a down payment of 20 percent of the purchase price: or a down payment
of $48,000 (0.20 x $240,000) at closing and borrow $192,000 through the mortgage.
a. Total payments on the 15-year mortgage are $273,297.60, of which $81,279.60 is interest. This compares to
interest of $211,365.60 on the 30-year mortgage (a difference of $130,068.00, disregarding time value of money).
The mortgage borrower’s interest payments are reduced significantly with the 15-year mortgage relative to the
30-year mortgage.
b. For the 30-year mortgage: $192,000 = PMT{[1 - (1/(1 + 0.0575/12)30(12))]/(0.0575/12)}
or PMT = $192,000/{[1 - (1/(1 + 0.0575/12)30(12))]/(0.0575/12)}
therefore PMT = $192,000/171.3582 = $1,120.46
For the 15-year mortgage: $192,000 = PMT{[1 - (1/(1 + 0.0500/12)15(12))]/(0.0500/12)}
or PMT = $192,000/{[1 - (1/(1 + 0.0500/12)15(12))]/(0.0500/12)}
therefore PMT = $192,000/114.7964 = $1,518.32
The borrower must pay $1,518.32 per month with the 15-year mortgage compared to $1,120.46 with the 30-year
mortgage, a difference of $397.86 per month. This may be difficult if the borrower’s income level is not very high.
10. You will make a down payment of 20 percent of the purchase price, or you will make a down payment of
$23,000 (0.20 x $115,000) at closing and borrow $92,000 through the mortgage.
a. If Option 2 is chosen you pay $92,000 x 0.02 = $1,840 in points and receive $90,160 at closing ($92,000 -
$1,840), although the mortgage principal is $92,000. To determine the best option, we first calculate the monthly
payments for both options as follows
Option 1: $92,000 = PMT {[1 - (1/(1 + 0.0900/12)30(12))]/(0.0900/12)} => PMT = $740.25
Option 2: $92,000 = PMT {[1 - (1/(1 + 0.0885/12)30(12))]/(0.0885/12)} => PMT = $730.35
In exchange for $1,840 up front, Option 2 reduces your monthly mortgage payments by $9.90. The present value of
these savings (evaluated at 8.85 percent) over the 30 years is
PV = $9.90 {[1 - (1/(1 + 0.0885/12)30(12))]/(0.0885/12)} = $1,248.06
Option 1 is the better choice. The present value of the monthly savings, $1,248.06, is less than the points paid up
front, $1,840.
b. If Option 1 is chosen you pay $92,000 x 0.01 = $920 in points and receive $91,080 at closing ($92,000 - $920),
although the mortgage principal is $92,000. If Option 2 is chosen you pay $92,000 x 0.025 = $2,300 in points and
receive $89,700 at closing ($92,000 - $2,300). The difference in savings on the points is $1,380.
To determine the best option, we calculate the monthly payments for both options as follows
Option 1: $92,000 = PMT {[1 - (1/(1 + 0.1025/12)30(12))]/(0.1025/12)} => PMT = $824.413
Option 2: $92,000 = PMT {[1 - (1/(1 + 0.1000/12)30(12))]/(0.1000/12)} => PMT = $807.366
In exchange for $1,380 up front, Option 2 reduces your monthly mortgage payments by $17.047. The present value
of these savings (evaluated at 10.00 percent) over the 30 years is
PV = $17.047 {[1 - (1/(1 + 0.1000/12)30(12))]/(0.1000/12)} = $1,942.52
Option 2 is the better choice. The present value of the monthly savings, $1,942.52, is less than the points paid up
front, $1,380.
