Hayre_Lakhbir

Modeling of Mortgage Prepayments and Defaults

See the Disclosure Appendix for the Analyst Certification and Other Disclosures.

Lakhbir HayreManaging Director

Fixed Income Quantitative AnalysisCitigroup Global Markets

September 25, 2006

2

Topics

• An Overview of the Mortgage Market

• Challenges in Prepayment and Default Modeling

• Implications for Valuation of Mortgage-Backed Securities

Citigroup Global Markets

3

The US Mortgage Market --Colossus of the Bond World

Sources: Federal Reserve System, Bond Market Association.

All Mortgage Debt $12.3 trillion

Single-Family Mortgage Debt $9.5 trillion

Mortgage-Backed Securities $6.2 trillion

Asset-Backed Securities $2.0 trillion

US Treasuries $4.2 trillion

Corporate Bonds $5.2 trillion

Municipals $2.3 trillion


4

What are Mortgage Securities ?

• A number of mortgage loans - from a few dozen to more than 10,000 - are pooled;

• Each loan pays interest and principal until it matures, is prepaid, or goes into default;

• Cashflows from the loans are paid to investors, after subtraction of administrative (or servicing) fees;

• Cashflows are either simply passed on to investors (pass-through securities) or allocated according to specified rules (structured securities, such as Collateralized Mortgage Obligations (CMOs).


5

Basic Security Features

• Cashflows are monthly, unlike Treasures or corporate bonds, which pay semi-annually;

• Amortizing assets => principal paid out over a period of time;

• For pass-throughs, each monthly payment will tend to include some principal;

• For structured MBS/ABS, principal paid out over a principal window

• Prepayment of principal by borrowers Þ

– call risk key property of many MBS/ABS

– durations much shorter than similar maturity bullet security.


6

Basic MBS is the Pass-Through

• Issued by FHLMC, FNMA, GNMA and Private Entities

• Many mortgages with similar characteristics collectedinto a pool

• Investor receives pro-rata share of monthly payments

• Interest and principal payments are guaranteed bythe issuing agency, or through credit enhancements(for private issuers)


7

Structure of a Pass-Through

Borrower pays 6.5% + principal payments

Investor receives coupon payments of 6% + principal

payments

Fannie/Freddie/Ginniereceives a guarantee fee of 0.15%

Loan servicer receives servicing fee of 0.35%

Source: Citigroup. Actual numbers may vary from pool to pool


8

Valuation of Mortgage Securities

• MBSs are bonds with embedded options;

• More complex than standard callable bonds:

– Each $1 is a separate option

– Option-exercise is inefficient

– High degree of path dependence

• Prepayment models key to valuation;

• Prepayment models combined with Term Structure Models to obtain “option-adjusted” spreads (OAS).


9

Basic Steps in Mortgage Valuation

• Generate a “large” number of interest rate paths, both for discounting and for cash flow generation;

• On each path, call a prepayment model/default model to calculate mortgage cash flows;

• Calculate average PV of cash flows, using benchmark rates plus a spread;

• Spread that equates average PV to market price is the option-adjusted spread (OAS).


10

Prepayment Rates Are Critical in Determining MBS Value

A. Cashflows Assuming No Prepayments

0

2,000

4,000

6,000

8,000

10,000

Cash

Flo

w P

er $

100,

000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Interest Principal Servicing

B. Cashflows Assuming a More Realistic Prepayment Rate

0

5,000

10,000

15,000

20,000

Cash

Flo

w P

er $

100,

000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Interest Principal ServicingSource: Citigroup.


11

Some Difficulties in Developing Prepayment Models

• A large number of important variables

• Continual innovations in mortgage financing implies constantly changing regimes

• Diverse and changing range of mortgage loan types

• A high degree of path dependence

• Unpredictable and “inefficient” borrower behavior

• Limited historical prepayment data and incomplete information


12

A Large Number of Factors Impact Prepayment and Default Rates

• Economic: Mortgage Rates, Housing Inflation, Consumer Confidence, Unemployment, etc.

• Loan: Coupon rate, original term, remaining term, type (Fixed, ARM, Hybrid), loan size, geographical location, etc.

• Borrower: Credit, Socio-Economic Status, Personal Situation

• Other: Past exposure to refinancing opportunities, mortgage origination and servicing process, etc.


13

Changing Environment

• Key determinants change over time: closing costs, choice of loan types, mortgage lending industry, loan origination process,etc.

• Borrowers have become more savvy over the years

• Borrower sentiment (or psychology) plays an important role


14

Changes in the Mortgage Marketover Time

0

10

20

30

40

50

60

70

80

90

0 50 100 150 200 250 300

WAC - "No Point" Mtg Rate (bp)

CPR

(%)

Speeds on 1992 Coupons in Nov 1993

Speeds on 2000 Coupons in Dec 2001

Speeds on 1996 Coupons in Dec 1998

Speeds on 2001 Coupons in Jul 2003

Sources: Fannie Mae, Freddie Mac and Citigroup..


15

The Media Effect Measures Psychological Impact of Multi-Year Lows in Rates

5.0

5.5

6.0

6.5

7.0

7.5

8.0

8.5

9.0

4 Apr 97 4 Jul 97 3 Oct 97 2 Jan 98 3 Apr 98 3 Jul 98 2 Oct 98

Rate

(%)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Mortgage Rate (Left Axis) MBA Refinancing Index (Right Axis)

Rates drop 100bp from April to Year-End’97, but nothing happens

Rates back to early 1998 lows but

nothing happens

Rates hit multi-year low

Rates fall significantly below early 1998 lows

Source: Mortgage Bankers Association, Freddie Mac, Citigroup


16

Loan Type Variation: Term• 30-Year: Most common type in the US;

• 15-Year: Higher monthly payments, so few 1st time home buyers => slower turnover and seasoning ramp. Also common refi vehicle for 30-year mortgages;

• 20-Year. Attracts borrowers who want a 15-year loan, but cannot afford the higher monthly payments;

• 10-Year. Mostly people refinancing out of a 15-year loan;

• 40-Year. A newer product, popular with borrowers stretching to buy a house and who want to minimize the monthly payment.

Notes:

1. For a given difference between the coupons on the current and a new mortgage, the shorter the term, the lower the refinancing incentive;

2. Regardless of the shape of the yield curve, the shorter the term, the lower the mortgage rate.


17

Loan Type Variation: Coupon

• Fixed Rate. Basic mortgage in the US;

• Adjustable Rate. Coupon resets periodically at a stated margin over a specified index (typically 1-year Treasury or 6-month LIBOR). Initial coupon often “teasered” and much lower than on a fixed-rate loan, so ARMs attract lot of 1st time buyers or other people with short time horizons;

• Hybrid. Coupon fixed for the first 3, 5, 7 or 10 years, then adjusts like a standard ARM. The shorter the fixed rate period, the shorter the typical borrower horizon, and the faster the speeds.


18

Loan Type Variation: Credit

• Jumbo. Prime quality loans that are too large for agency pools;

• Fannie May/Freddie Mac. Generally prime quality loans that fall below the “conforming limit”;

• Ginnie Mae. Loans insured by the FHA or the VA. Relative to FN/FH, poorer credit and lower loan balances.

• Alternative (Alt) A. Borrowers are generally moderate to good credit (hence the “A”), but lack “full documentation”

• Sub-Prime. Borrowers with poor credit histories.


19

Loan Type Variation: Other Features

• Loan Size. Has a big impact on speeds.

• Geographical Location. Ditto.

• Prepayment Penalties. Uncommon in prime loans, but prevalent fro sub-primes.

• Amortization Schedule. Traditional mortgages in the US have been fully amortizing. However, strong growth in recent years in loans which pay interest only for a number of years (eg 10/20), or can even have negative amortization (ie. loan balance can increase), such as Option ARMs.


20

Prepayment Speeds on Prime and Subprime Loans


0

10

20

30

40

50

60

70

80

December-02 June-03 January-04 July-04 February-05 August-05 March-06 October-06

Prime Subprime

21

Effect of Loan Balance

Loan Loan Balance (LLB) pools are less reactive to refinancing opportunities, but little difference in turnover speeds

0

10

20

30

40

50

60

200301 200304 200307 200310 200401 200404 200407 200410

CPR

(%)

Generic 6s of 2003 LLB 6s of 2003

Source: Citigroup.


22

Significant Differences inSpeeds by State

Factors include loan size, closing costs, taxes, home price appreciation, and local economic conditions

0

10

20

30

40

50

60

Apr '03 Jun '03 Aug '03 Oct '03 Dec '03 Feb '04 Apr '04 Jun '04 Aug '04 Oct '04

CPR

(%)

CA FL

IL NY

TX US

Source: Citigroup.


23

High Degree of Path Dependence

• Borrowers will differ in their propensity and ability to refinance

• As a pool of borrowers experiences refinancings, most able borrowers leave the pool at higher rates

• Remaining borrowers less responsive (burnout)

• Hence prepayment rates depend on complete history of interest rates


24

Burnout

Sources: Freddie Mac and Citigroup.


0

10

20

30

40

50

60

70

80

Aug-91 May-93 Feb-95 Nov-96 Aug-98 May-00 Feb-02 Nov-035

5.5

6

6.5

7

7.5

8

8.5

9

9.5

10

Freddie Mac 9s of 1991 Freddie Mac 8.5s of 1991 30 Year Mortgage Rate

25

Inefficient Exercise of thePrepayment Option

Burnout and Media Effect

0

10

20

30

40

50

60

70

80

90

0 50 100 150 200 250 300WAC — "No Point" Mtg Rate (bp)

CPR

(%)

Speeds on 2001 Coupons in Jan 2004

Speeds on 2001 Coupons in Jul 2003


26

• First Generation Models (Salomon, 1985)

- Standard Multiple Regression Models

- Many Variables good historical fit, but not robust over time

• Diversity of Collateral and Borrowers and Continuing Changes in Prepayment Environment Suggests More Fundamental Approach (Salomon, 1995)

- Sources of Prepayments (Modular Approach)

- Flexible and Dynamic Inputs and Relationships

History of Prepayment Modeling


27

• Housing Turnover - the sale of a home triggers a prepayment

• Refinancings - the loan is refinanced

• Defaults - foreclosure on the house leads to the loan being paid off

• Curtailments (or partial prepayments) - borrowers make more than their scheduled payment

• Full Payoffs - the loan is paid off: for example, due to a natural disaster

This is true for all loans, regardless of type of loan, country/regionetc. However, the magnitude of each component will depend on cultural, demographic, collateral and economic factors.

Why are Mortgages Prepaid?


28

Structure and Key Features of the Model

Modular Approach:

Projected Speed = Sum of speeds due to

1. Housing Turnover

2. Refinancings - Rate, Cash-Outs and Credit Driven

3. Curtailments

4. Defaults


29

Overall Housing Turnover Rate

0.0%

2.5%

5.0%

7.5%

10.0%

Jul-78 Jul-81 Jul-84 Jul-87 Jul-90 Jul-93 Jul-96 Jul-99 Jul-02 Jul-05 Jul-08

Hous

ing

Turn

over

Rat

e (in

%)

Actual

Projected

-200bp

No shift

+200bp

6

Source: National Association of Realtors, US Census Bureau, Citigroup


30

Housing Turnover-Related Speeds

• Dominant in high-interest-rate environment

• Strong seasonal component

• Seasoning: brand-new pools tend to prepay more slowly

• Lock-in: higher coupons typically have higher turnover rates

Prepayment Rates Fannie Mae 6s of 1993

012345678

Oct-93

Feb-9

4Jun

-94Oct-9

4Fe

b-95

Jun-95

Oct-95

Feb-9

6Jun

-96Oct-9

6Fe

b-97

Jun-97

Oct-97

CP

R (

%)

Source: Citigroup


31

Seasoning Depends on Loan Age and Home Price Appreciation

Loan Age (Months)

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30 35 40 45 50 55

CPR

(%)

125% PSA

Age-related Seasoning is a critical dimension of Turnover

However, Seasoning is Modulated by Appreciation in Home Prices


32

Actual and Projected HomePrice Appreciation

0%

4%

8%

12%

16%Fe

b-71

Feb-

74

Feb-

77

Feb-

80

Feb-

83

Feb-

86

Feb-

89

Feb-

92

Feb-

95

Feb-

98

Feb-

01

Feb-

04

Feb-

07

Feb-

10

Annu

al U

S Ho

me

Pric

e Ap

prec

iatio

n (in

%)

Actual

Projected

Source: Fannie Mae, Freddie Mac, Citigroup


33

Basic Dynamics of Refinancing Model

We assume that there are several classes of borrowers, ranging from slowest to fastest, each class having its own refi curve

Refi Incentive

Ref

i Rat

e

Source: Citigroup.


34

Evolution of Population of Mortgagors

The mix of borrowers changes each month, as faster refinancers leave the pool at a faster rate

The model keeps track of the population mix, and the overall refi rate for month is the aggregate over the remaining borrowers:

Refi Rate = Fraction of pool in class 1 * Refi rate for class 1 + ...... + Fraction of pool in class k * Refi rate for class k

0%

10%

20%

30%

40%

50%

60%

Slowest Slow Fast Fastest

% in

Cla

ss

Initial Distribution

Post-Refi Distribution

Source: Citigroup.


35

Other Aspects of the Refinancing Model

• No consensus on how to calculate the refinancing incentive

- A common approach is to compare PVs of new and old mortgages

- Another approach: # of months to recoup costs of refinancing

• Mortgage rates used to calculate refi incentive need to depend on loan type eg sub-prime rates much higher than prime rates

• Loan balance is an important factor in determining incentive

• A seasoning curve can be introduced using transient costs of refinancing;

• Reactivity to refinancing opportunities depends on FICO, LTV and other loan features.


36

A Simple Default Model – Multiple ofthe SDA Curve

The Standard Default Assumption (SDA Curve)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 30 60 90 120 150 180 210 240 270 300 330 360

Mortgage Age (Months)

CPR

(%)

Pe

Tail


37

A Default Model Framework

• Probability of Default = Probability(LTV > Threshold)*Probability (Trigger Event)

• Likelihood of Trigger Events depends on FICO, Debt-to-Income ratio, unemployment rates, payment shock, etc.

0.0%

0.1%

0.2%

0.3%

0.4%

0.5%

0 3 6 9 12 15 18 21 24 27 30

Age (years)

Def

ault

Pro

bab

ility

AR w ith AffordabilityAR(1)


38

Key Determinants of Trigger Events

Source: Freddie Mac.

Unemployment or Curtailment of Income 38.98 %

Illness or Death of Mortgagor 16.25

Excessive Obligation 9.70

Marital Difficulties 9.45

Illness or Death in Family 7.31

Extreme Hardship 4.06

Business Failure 2.68

Property Problem or Casualty Loss 2.00

Inability to Sell or Rent Properties 1.83

Employment Transfer or Military Service 0.97

All other Reasons 6.77


39

Historical Monthly Transition Rates forSub-Prime Loans

Fixed-Rate Loans To Non-delinq Delinqent Foreclosure REO PayoffFrom (%) (%) (%) (%) (%)Non-delinq 97.2 1.0 0.1 0.0 1.7Delinquent 10.8 73.5 14.4 0.0 1.3Foreclosure 2.9 1.7 88.2 5.2 2.0REO 0.1 0.1 0.2 84.9 14.7

2/28 Hybrids

To

Non-delinq Delinquent Foreclosure REO PayoffFrom (%) (%) (%) (%) (%)Non-delinq 96.6 1.2 0.1 0.0 2.1Delinquent 10.0 72.5 16.0 0.0 1.5Foreclosure 3.3 1.8 87.8 4.8 2.3REO 0.1 0.0 0.2 83.7 16.0

Source: Citigroup.


40

Subprime Collateral DefaultRates by LTV

0

5

10

15

20

25

2002

08

2002

11

2003

02

2003

05

2003

08

2003

11

2004

02

2004

05

2004

08

2004

11

2005

02

2005

05

2005

08

2005

11

2006

02

2006

05

L,10x,75 L,75x,85 L,85x,+


41

Summary and Implications for MBS Valuation

• Modeling of prepayments and defaults as much art as science;

• MBS cashflow generation depends on these models;

• Hence little consensus on valuations, especially for complex MBSderivatives;

• Work by non-practitioners of little value in deciding, say, how much more to pay for a $60,000 average balance Texas pool vs. a $80,000 Illinois pool;

• On a positive note, great employment opportunities for good prepayment modeler;

• A book from John Wiley & Sons, SSB Guide to Mortgage- and Asset-Backed Securities, edited by L. Hayre, provides a great introduction to this area.


42

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