13-1

Mortgages

Chapter 13

13-2

Standard Fixed Rate

Variable Rate

Refinancing and Prepayments

Marketable Mortgages

Mortgages

13-3

P = Principal

M = Periodic payment

Y = Interest rate

Fixed Rate Mortgage

10 2 … n

P M …M M

.

PVAP

M

PVAMP

)y1(

M

)y1(

My1

MP

y,n

y,n

n2

13-4

P = $100, y = 10%, n = 20

Example

.75.115136.8100

M

Total Payments = (20)(11.75) = 235.

Interest = 235 – 100 = 135 = Total – Principal.

13-5

Repayment

Time P Interest of P

0 100

1 98.25 10 1.75 = 11.75 – 10.00

2 96.33 9.83 1.92 = 11.75 – 9.83

3 9.63

13-6

AMj = Amortization of principal in period j

Amount of Repayment of Principal Called Amortization

1jnj

)y1(

1MAM

If n = 20, P = 100, y = 10%, j = 10

.12.4)10.1(

175.11AM 1102010

13-7

The interest in period j = Ij

Ij = M – AMj

$ Interest = – $ Amortization

I10 = 11.75 – 4.12 = 7.63.

MortgagePayment

13-8

Remaining Principal at time j = Pj

Pj = [M][PVAn-j]

P10 = [11.75][PVA20-10,10%]

= [11.75][6.1446] = 72.20.

13-9

%.20.725136.81446.6

PVA

PVA

Periods j after

Remaining P %

n

jn

%.80.275136.8

1446.65136.8

PVAPVAPVA

PVA

PVAPVA

Periods j after

Repaid P %

20

1020

n

jnn

13-10

Current rate = Index + Premium.

Annual cap on change

Lifetime cap + minimum

Teaser rate

Borrower bears risk of changing interest rates

Variable Rate Mortgage, Floating Rate, Adjustable Rate

13-11

Due on sale clause

Assumable

13-12

Borrower has right to repay early.

Reasons:

A. Moving

B. Lower interest rates

C. Improved financial condition of

borrower

Prepayment Option

13-13

Refinancing Because of Lower Interest Rates

Costs include points, loan initiation fees, legal costs, surveying, etc.

j0 n

Issued Prepay Maturity

.CostsPVAMMBenefit

financingReNew,jnNewOld

13-14

P = $100, n = 20, yOld = 10%, yNew = 7%, j = 10, costs = 6%.

Refinancing Example – 10 Years Remaining

.99.5$

)06.0)(20.72(0236.728.1075.11

CostsPVAMMBenefit

gRefinancinNew,jnNewOld

.28.100236.7

20.72

%7,10

10 PVA

PM New

13-15

Prepayment Pattern

Public Securities Association—PSAConstant Prepayment Rate—CPR

Change in Interest Rates

Moving & Other

Lower Rates

LowerRates

0 HigherRates

% Prepaid

13-16

Phase 1 of Mortgage Market until 1980

13-17

1.Bank or savings & loan holds mortgages and absorbs defaults.

2.Prime borrowersA. Sizable down payment

B. Verified income

C. Good credit rating

3.FDIC insures deposits.

4.Typically fixed-rate loans.

13-18

Phase 2 of Mortgage Market 1980 – 2000

13-19

1.Typically fixed-rate loans Investors bear prepayment risk.

2.Default guarantees make pools of mortgages Essentially default free. Trade like U.S. Treasuries except for

prepayment risk.

13-20

Original pools – PassThroughs

All investors share proportionally.

Later pools divided into tranches or slices.

Tranche1

Tranche2

Tranche3

13-21

1.Many ways of setting up tranches.

2.Typically Tranche 1 gets first prepayments, then #2, etc.

3.Some tranches were divided into interest only and principal only parts.

13-22

Phase 3 of Mortgage Market 2000 – Now

13-23

1.Many floating-rate loans with teaser rates for first two years.

2.Many subprime and Alt-A mortgages Prime has

A. Down payment B. Verified incomeC. Good credit rate

Alt-A is missing one or two. Subprime is missing all three.

3.Typically no default guarantee.

13-24

I. Qualifying1) High credit score

2) Adequate down payment

3) Documented sufficient income

II. Alt-A Missing one or two of the above

III. Subprime Missing all three of the above

Three Types of Mortgage Borrowers

13-25

ExampleBorrower 1 Borrower 2 Borrower 3 Borrower 4

Originator 1 Originator 2

Pool Organizer

Trust

Tranche 1 Tranche 2 Tranche 3

Rating

Percent of Pool

AAA A BB

60% 20% 20%

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1) Borrower lies.

2) Originator falsifies documents.

3) Originator gets fees from borrower and/or pool organizer.

4) Once mortgage is sold into pool, originator has no liability.

5) Pool organizer works with rating agency to set up tranches.

Potential Problems

13-27

6) Rating agency gets paid by pool organizer—may give rating agencies incentives to give higher ratings to attract more business.

7) Pool organizer has no liability once mortgages are put into the trust.

8) Originators and pool organizers have incentives to process as many mortgages as possible to maximize fees.

Potential Problems

13-28

Advantages of Marketable Mortgages

Advantage: Diversification

Disadvantages:

1. Conflicts of Interest.

2. Asymmetric Information.

3. Moral Hazard.

13-29

EXAMPLES OF DIFFERENT TYPES OF TRANCHING

1. Sequential Pay2. Planned Amortization Class3. Principal Only and Interest Only

13-30

Sequential Pay

Prepayments go to Class 1 until paid off.

Then prepayments go to Class 2, then to Class 3.

Suits some buyers better.

Some get higher prepayment risk and some get lower prepayment risk.

Size of each class is small, resulting in reduced liquidity.

13-31

Early classes have precisely defined cash flows.

Residual class cash flows vary widely in timing.

Planned Amortization Class (PAC)

13-32

Principal Only (PO)

Interest Only (IO)

Division of Principal and Interest Classes