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12. This is a straight bond valuation just like those in Chapter 10. Using the standard bond

pricing formula, verify that the answer is $966.84724 per $1,000 face. The price would be

quoted at 96:22.

13. This is a standard yield to maturity calculation just like those in Chapter 10. The

bellwether issue matures in 30 years. Its ask price is quoted at 101:18, or $1,015.625 per

$1,000 face. The coupon rate is 5.25 percent, paid semiannually. Given this information,

check that the yield is in fact 5.147 percent. Note however that it is important here that the

bellwether bond matures in almost exactly 30 years. The standard bond pricing formula

implicitly assumes that the first coupon payment is six months away. When this is not true,

a modification is necessary to account for the fractional period.

14. These issues are selling well above par, so they will likely be called in 2009 absent a

tremendous shift in interest rates. Their yields to call are reported, and these yields reflect

the fact the bonds probably will mature early.

15. The equivalent after-tax yield is (1 - .28) multiplied by 7 percent, or 5.04 percent.

16. The marginal tax rate is 1 - .06/.08 = 25%.

17. To a certain extent, itвЂ™ an apples and oranges issue. Munis are much less liquid, have

s

greater default risk, are generally callable fairly early in their lives, and may be subject to

state taxes. These factors increase muni yields. As a result, when critical tax rates are

calculated, they are likely to be too low. A better approach is compare munis to corporate

bonds with similar features and risks. An even better approach is to compare taxable and

nontaxable munis.

18. It is true. The reason is that Treasuries are callable at par. Going back to Chapter 10, if

two premium bonds have the same price and the same coupon rate, but different maturities

(i.e., the call date and the final maturity date), the one with the shorter maturity has the

lower yield. This has to be true because of the вЂњpull to par,вЂќ i.e., the fact that for a given

yield a premium bondвЂ™ price will decline as maturity approaches.

s

19. It is not true in general because agency securities are frequently callable at prices above

par; it may well be that the yield to call is greater for issues selling moderately above par.

FUNDAMENTALS OF INVESTMENTS B-43

20. Once we recognize that this is a premium issue, so its yield to call is reported, this is a

straight yield to maturity calculation. We just pretend the issue matures in 2009. The price

is $1,546.5625 per $1,000 face; the coupon rate is 11.75 percent. It matures in 11 years.

Verify that the calculated yield is actually 5.1722, which rounds to 5.17, or six basis points

higher than reported. The reason is that the price is rounded to nearest 32nd after the yield

is calculated, so it is often not possible to precisely check the numbers, plus the first

coupon will actually arrive in about four months, not exactly six.

B-44 CORRADO AND JORDAN

Chapter 13

Mortgage-Backed Securities

Answers to Questions and Problems

Core Questions

1. Mortgage securitization benefits borrowers by reducing interest rates. Interest rates are

reduced because securitization increases liquidity in the mortgage market. More liquid

mortgages have higher prices and, hence, lower rates.

2. It benefits mortgage originators by allowing them to transfer the risk associated with

holding mortgages and instead focus on what they do best, originate mortgages. Also, and

equally important, by selling mortgages, originators obtain new funds to loan out.

3. We compute the payment as follows:

$180,000 Г—.08 / 12

$1,329.78 =

1

1в€’

(1 + .08 / 12)30 Г—12

4. For the same rate and original balance, the 15-year mortgage will have the higher

payments simply because a larger principal payment must be made each month to pay off

the loan over a shorter time.

5. Only GNMA is a federal agency, and GNMA securities are backed by the full faith and

credit of the U.S. government. The other two, in principle, do not have this backing. As a

practical matter, however, the difference is slight.

6. We solve for the mortgage balance as follows:

Mortgage balance Г—.06 / 12

$1,000 =

1

1в€’

30 Г—12

( )

1 + .06 / 12

Solving for the mortgage balance gets us $166,791.61.

7. It means that timely payment of both principal and interest are guaranteed.

FUNDAMENTALS OF INVESTMENTS B-45

8. Verify that the payment is $1,027.27. The interest in the first month is equal to the original

loan amount ($140,000) multiplied by the interest rate, .08/12 = .067 (actually .0666 . . .)

per month. The interest thus amounts to $933.33. The remaining $1,027.27 - 933.33 =

93.94 is principal. The interest allocation for the second payment is $932.71, and the

principal reduction is $94.56.

9. Mortgages are prepaid because the underlying property is sold, interest rates fall, or the

owner otherwise wishes to refinance (perhaps to increase the loan balance as a way of

obtaining funds for other purposes) or payoff the mortgage. When interest rates fall,

prepayments accelerate. Larger drops lead to sharp increases in prepayment rates.

10. First, check that the payment is $1,264.14 (actually $1,264.136). We calculate the loan

balance as follows:

Mortgage balance Г—.066 / 12

$1,264126 =

.

1

1в€’

(1 + .065 / 12)20 Г—12

Solving for the mortgage balance gets us $169,552.25. Notice that we used the 20 years

remaining in arriving at this balance.

Intermediate Questions

11. The call feature on a bond gives the borrower the right to buy the bond (i.e., pay off the

debt) at a fixed price. The right to prepay on a mortgage gives the borrower the same

right.

12. The original payment is (check this) $1,217.12. After eight years, the balance on the loan

(check this; note the remaining life is seven years) is $75,648.82. For comparability, we

calculate the new payments assuming a loan of $75,648.82, a 7-year life, and a rate of 6

percent. The new payment (check this) is $1,105.12. Thus, the saving is $112 per month.

Notice that it would be misleading to compare the payments on the old loan to a new, 15-

year loan.

13. Prepayments that result purely from interest drops are a risk; they mean that the mortgage

investor will have to reinvest at a lower rate. However, some mortgages are prepaid for

other reasons, such as the sale of the underlying property. This can happen even if interest

rates have risen substantially; such a prepayment benefits the mortgage investors. Thus,

not all prepayments are bad, just those result in the need to reinvest at a lower rate.

B-46 CORRADO AND JORDAN

14. The original payment is (check this) $873.42. After five years, the balance on the loan

(check this; note the remaining life is 25 years) is $130,865.34. For comparability, we

calculate the new payments assuming a loan of the current balance plus $1,000. The

reason is that this is the total amount that must be paid to refinance. Thus, we assume a

loan of $131,865.34, a 25-year life, and a rate of 6 percent. The new payment (check this)

is $849.61. Thus, the saving is $23.81 per month, so it pays to refinance, but not a lot.

15. For a seasoned 100 PSA mortgage, the CPR is 6 percent per year. A 50 (200, 400) PSA is

just half (twice, four times), or 3 (12, 24) percent per year. These CPRs have two more or

less equivalent interpretations. They are an estimate of the probability that any given

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