PDF Ch.SF, Standard Formulas for the Analysis of Mortgage-Backed ...

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Uniform Practices/Standard Formulas

Chapter SF

Standard Formulas for the Analysis

of Mortgage-Backed Securities and

Other Related Securities

Table of Contents

A.

Computational Accuracy

SF-3

B.

Prepayments

SF-4

1. Cash Flows

SF-4

2. Mortgage Prepayment Models

SF-5

C.

D.

E.

3. Average Prepayment Rates for Mortgage Pools

SF-11

4. ABS Prepayment Rates for Asset Pools

SF-13

Defaults

SF-16

1. Mortgage Cash Flows with Defaults: Description of Basic Concepts

SF-16

2. Specifying Mortgage Default Assumptions: Standards and Definitions

SF-17

3. Standard Formulas for Computing Mortgage Cash Flows with Defaults

SF-18

4. The Standard Default Assumption (SDA)

SF-20

5. Use of the SDA for Products Other Than 30-Year Conventional Mortgages

SF-22

6. Numerical Examples of SDA

SF-22

Assumptions for Generic Pools

SF-39

1. Mortgage Maturity

SF-39

2. Mortgage Age

SF-40

3. Mortgage Coupon

SF-43

Day Counts

SF-44

1. Calendar Basis

SF-44

2. Delay Days

SF-44

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All rights reserved. Reproduction in any form is strictly forbidden. ? 1999 The Bond Market Association.

SF-1

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F.

G.

H.

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Settlement-Based Calculations

SF-45

1. General Rules

SF-45

2. CMO Bonds with Unknown Settlement Factors

SF-46

3. Freddie Mac Multiclass PCs (REMICs)

SF-47

Yield and Yield-Related Measures

SF-48

1. General Rules

SF-48

2. Calculations for Floating-Rate MBS

SF-52

3. Putable Project Loans

SF-55

Accrual Instruments

SF-56

1. Average Life of Accrual Instruments

SF-56

2. Accrual Calculations for CMO Z-Bonds

SF-57

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SF-2

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Uniform Practices/Standard Formulas

A. Computational Accuracy

Many common calculations for mortgage-related securities (yields, durations, prepayment rates,

etc.) require the calculation of a large number of intermediate quantities (cash flows, principal

balances, etc.). All intermediate calculations should be carried out to their full precision, preserving at least ten significant digits of accuracy. This will generally require double-precision computer arithmetic. The only quantities that should be assigned an integer variable type are those

that represent whole numbers of days, months or years.

Only when all computations are complete should the final values be rounded for display. Results

may be shown to any desired number of decimal places, provided that the last digit presented has

been obtained by rounding and not by truncating the complete figure.

The numerical examples that appear throughout the document are intended to provide simple

checks against improper implementation of the Standard Formulas, not an exhaustive set of

benchmarks that would guarantee conformance.

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Uniform Practices/Standard Formulas

B. Prepayments

1. Cash Flows

For a level-payment fixed-rate mortgage pool with gross weighted-average coupon C%, current weighted-average remaining term M months, and M0-M months elapsed since origination, the amortized loan balance (as a fraction of par) is

BAL =

1 ¨C (1 + C 1200)

1 ¨C (1 + C 1200)

?M

?M 0

and the scheduled gross monthly payment (also as a fraction of par) is

GROSS MORTGAGE PAYMENT = PRINCIPAL + INTEREST

= ( BAL1 ? BAL 2 ) + ( BAL1 * C 1200)

=

C 1200

1 ¨C (1 + C 1200) ?M 0 .

The net payment passed through to investors consists of the scheduled gross payment above,

plus unscheduled prepayments, minus a servicing fee of BAL1 * S/1200, where the servicing

percentage (S) is the difference between the gross coupon (C) and the net pass-through

coupon of the security.

The pool factor (F) expresses the principal remaining in the pool each month as a fraction of

the original face amount. The survival factor (F/BAL) represents the fraction of $1.00 unit

loans remaining in the pool from those originally present at issuance:

POOL FACTOR = SURVIVAL FACTOR * AMORTIZED LOAN BALANCE.

By convention, mortgage-related security analysis assumes that all prepayments are whole

prepayments on $1.00 unit loans within the pool.

The cash flows of more complex mortgage securities (CMO bonds, Graduated-Payment

Mortgages, Adjustable-Rate Mortgages, etc.) are governed by specific contractual features

not addressed here.

Example: A mortgage pass-through is issued with a net coupon of 9.0%, a gross coupon of

9.5% and a term of 360 months. If prepayments for the first month are 0.00025022 (as a

fraction of par), then the first cash flow paid to investors will consist of the following

components:

(1) Scheduled Amortization

=

0.00049188,

(2) Unscheduled Prepayments =

0.00025022,

(3) Gross Mortgage Interest

=

0.00791667,

(4) Servicing Fee

=

0.00041667,

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All rights reserved. Reproduction in any form is strictly forbidden. ? 1999 The Bond Market Association.

SF-4

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Pass-Through Principal

Uniform Practices/Standard Formulas

=

=

Pass-Through Interest

=

=

Pass-Through Cash Flow

Next

=

=

(1) + (2)

0.00074210,

(3) ¨C (4)

0.00750000,

(1) + (2) + (3) ¨C (4)

0.00824210.

2. Mortgage Prepayment Models

The prepayment rate of a mortgage pool may be expressed in a number of different ways.

These measures are equally valid, although a particular method may be more useful in a

given instance.

a.

The SMM (Single Monthly Mortality) rate of a mortgage pool is the percentage of the

mortgage loans outstanding at the beginning of a month assumed to terminate during

the month. That is, if in some month the initial and final pool factors are F1 and F2,

respectively (as fractions of the original face amount), and the amortized loan balances

are BAL1 and BAL2 (as fractions of par), then

? BAL 2 ? ? SMM ?

F2 = F1 * ?

?

? * ?1 ?

100 ? .

? BAL1 ? ?

An equivalent means of specifying a one-month prepayment rate is to separate the factor drop for the month (F1¨CF2) into scheduled and unscheduled principal payments. If

there were no unscheduled prepayments during the month, then the factor for the end

of the month would have been

Fsched = F1

BAL 2

BAL1 .

The quantity F1¨CFsched represents amortization for the month, and Fsched¨CF2 represents

early prepayment of principal. The one-month prepayment rate can then be defined as

SMM = 100

Fsched ? F2

Fsched .

02/01/99

All rights reserved. Reproduction in any form is strictly forbidden. ? 1999 The Bond Market Association.

SF-5

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