978-1259919688 Chapter 19

Solutions to Questions – Chapter 19

The Secondary Mortgage Market: Pass-Through Securities

Question 19-1

What is the secondary mortgage market? List three reasons why it is important.

Question 19-2

What were the three principal activities of FNMA under its 1954 charter? What is its principal function now?

Question 19-3

Name two ways that FNMA currently finances its secondary mortgage operations.

Question 19-4

When did GNMA come into existence? What was its original function? What is its main function now?

Question 19-5

Why was the formation of FHLMC so important?

Question 19-6

What is a mortgage-related security? What are the similarities and differences between mortgage securities and

corporate bonds?

Question 19-7

Name the principal types of mortgage-related securities. What are the difference between them?

Question 19-8

There are several ways that mortgages can be sold in the secondary market. Choose two and compare and

contrast their length of distribution channel, relative ease of transaction, and efficiency as it relates to maximizing

funds flow from sale.

Question 19-9

What is the function of the optional delivery commitment?

Question 19-10

What is a mortgage swap certificate?

Question 19-11

Name five important characteristics of mortgage pools. Tell why each is important.

Question 19-12

In general, would a falling rate of market interest cause the price of an MPT security to increase or decrease?

Would the increase or decrease be greater if the security was issued at a discount? Would an increase in

prepayment be likely or unlikely? Describe with an example.

Solutions to Problems – Chapter 19

The Secondary Mortgage Market: Pass-Through Securities

Problem 19-1

(REFER TO TEMPLATE 19_1.XLS)

ASSUMPTIONS:

Principal

$10,000

Coupon rates:

(Bond 1) Annual

10.50%

(Bond 2) Zero

0.00%

Term in years

Initial

25

years

Years into future

5

Investors interest rate

12.00%

Market interest rate

9.50%

Number of compounding periods

50

(a) Initial price of each bond (compounded annually):

Annual compounding on both MBBs

Bond 1

Bond 2

Principal

$10,000.00

Coupon rate

10.50%

0.00%

Term

25

Investors interest rate

12.00%

The present value of the coupon payments

$8,235.30

$0.00

The present value of the principal

$588.23

Initial price of each bond

$8,823.53

$588.23

The price of the annual coupon bond is the present value of 25 payments at 10.5% times the initial principal discounted at the

(b) Initial price of each bond (compounded semi-annually):

Semi-annual compounding on both MBBs

Principal

$10,000.00

Coupon rate

10.50%

0.00%

Term

25

Investors interest rate

12.00%

Number of compounding periods

50

The present value of the coupon payments

$8,274.98

$0.00

The present value of the principal

$542.88

Initial price of each bond

$8,817.86

$542.88

Number of mortgages in initial pool

Average mortgage balance

Initial mortgage pool balance

Prepayment rate

Coupon rate

(e)

1.0000

$2,077,381

829,928

$7,500,000

$8,264,095

(c) Value each bond at the end of the fifth year. Market interest rates fall to 9.50% and the bonds are compounded annually:

Future Value

Principal

$10,000.00

Coupon rate

10.50%

0.00%

Term

20

Market interest rate

9.50%

The present value of the coupon payments

$9,253.00

$0.00

The present value of the principal

$1,628.24

Value of bond in dollars

$10,881.24

$1,628.24

Value of the bond in % of par

108.81%

16.28%

Problem 19-2

(REFER TO TEMPLATE 19_2AB.XLS)

ASSUMPTIONS:

(b) The pool factor at any given time is the outstanding principal balance divided by the initial principal of the pool.

If the market interest rate is 12.00%, the price that Green could obtain is the PV of the remaining cash flows discounted at the

current market interest rate. (Take the PV of column d for years 6-10.)

11.00%

Price to Green

Value of MPT

$7,872,299

$78,723

(d) Issuance of 100 Mortgage Pass Through Securities: (Change 10.00% prepayment rate to 20.00% and 9.50% market

interest rate to 8.00%. All other variables are constant.)

ASSUMPTIONS:

Data Input Box:

Number of mortgages in initial

pool

75

Average mortgage balance

$100,000

Initial mortgage pool balance

$7,500,000

Prepayment rate

20.00%

Coupon rate

11.50%

Servicing and Guarantee Fee

0.5%

Total rate for P&I on Pass

Through

12.0%

Market interest rate

8.00%

Issuance of 100 Mortgage Pass Through Securities (MPT)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

Total Principal

Guarantee

Total

Pmt to

Principal

Principal and

and Interest

and

Payments

Individual

Pool

due to

Interest Pmts

Pmts to Issuer

Service Fees

to Investors

Investor

Year

Balance

Prepayment

to Issuer

(b)+(c)

(a)x(0.5%)

(d)-(e)

(f)/100

0

$7,500,000

($75,000)

1

5,535,119

1,500,000

1,327,381

2,827,381

37,500

2,789,881

27,899

2

4,025,809

1,107,024

1,038,825

2,145,849

27,676

2,118,173

21,182

3

2,873,208

805,162

810,407

1,615,568

20,129

1,595,439

15,954

4

1,999,415

574,642

629,571

1,204,213

14,366

1,189,846

11,898

5

1,343,155

399,883

486,309

886,192

9,997

876,195

8,762

6

856,383

268,631

372,604

641,235

6,716

634,520

6,345

7

501,640

171,277

281,951

453,227

4,282

448,945

4,489

8

250,143

100,328

208,857

309,185

2,508

306,677

3,067

9

80,872

50,029

148,009

198,038

1,251

196,787

1,968

10

0

90,576

404

90,172

902

11.00%

Price to Green

Value of MPT

$8,104,331

$81,043

Problem 19-3

(a) See result for 7.5% in the table below.

Discount rate

Price to Green

Value of MPT

7.50%

$1,069,843

$26,746

9.50%

$1,000,000

$25,000

8.50%

$1,033,908

$25,848

10.50%

$967,969

$24,199

11.50%

$937,679

$23,442

(b) See result for 11.5% in the table above.