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Mortgage-Backed Securities:An Actuarial Approach to

Cash Flow Valuation

Neal Dihora, ASA, MAAA, CFA Kyle Mrotek, FCAS, MAAA

15th East Asian Actuarial Conference

Seoul, Korea

13 October 2009

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Agenda

MBS Background

Benefits of MBS Valuation

Approach to MBS Valuation

Closing

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U.S. MBS Issuance

A mortgage-backed security is a debt obligation that transfers cash flows from borrowers who have purchased homes to investors looking for a higher yield than government bonds

Agency securities are sold and guaranteed by the U.S. government– Fannie Mae

– Freddie Mac

– Ginnie Mae

Non-agency securities are not backed by any financial institution– Higher risk, higher yield potential

Agency securities have regained their popularity

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Gross Issuance

$0.0

$0.5

$1.0

$1.5

$2.0

$2.5

$3.0

US Gross MBS Issuance ($ trillions)

Agency

Total Non-Agency

Total MBS

Source: Inside MBS & ABS , SIFMA and UBS

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Non-Agency by Type

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

500,000

US Non-Agency Gross MBS Issuance($ millions)

Alt-A

Jumbo

Subprime

Other

Source: Inside MBS & ABS , SIFMA and UBS

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Benefits of MBS Valuation

Improve decision making

Improve transparency

Keep up with compliance

Calculate impact on surplus and capital ratios

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MBS Valuation Flowchart

Collateral(Mortgage Loans )

Performance to date

Underwriting Characteristics

EconomicForecasts

Credit /PrepayModel

SecurityCapital

Structure

Losses

Principal &Interest

Data Models Future Cash Flows

Future

Collateral

Performance Assumptions

Subordinate

Equity

Mezzanine

Senior

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Mortgage Models Structural models

– Focus on underlying dynamics of the mortgage and of trigger events (prepayments and defaults). Do not consider collateral performance to date

– Borrowers are assumed to exercise the option which is in their best interest

Reduced-form models pattern exogenous trigger events with hazard rates or jump processes

Actuarial models– Focus on forecasting mortgage borrowers’ failure to make timely payments

(collateral analysis)

– Future collateral credit loss can be considered as a function of current loss

– Cumulative collateral credit loss can be obtained from many sources, for example, consider the MBS, HEAT 2007-2 2A1:

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Actuarial Methods

Collateral ‘loss’ projection– Amount and timing

– ‘Loss’ is failure to pay timely P&I

Methods– ‘Paid’ Loss Development Factor (LDF)

– ‘Incurred’ LDF

– ‘Paid’ B-F method

– ‘Incurred’ B-F

– Non-exhaustive

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LDF Method Paid LDF

– Normalize loss to exposure -> loss rate

– Ultimate loss = paid loss x cumulative paid LDF

Incurred LDF– Inventory of delinquent loans is used to estimate proxy for case reserves –

delinquency status found to be predictive for future performance

– Incurred loss equals cumulative paid loss plus proxy for case reserves

– Consistent with reserving for mortgage guaranty insurance

– Roll rate model = Frequency/Severity method

– Frequency = Pr (default | status of delinquency)

– Severity (% of loan that is not recoverable)

– ‘Incurred’ loss development factors derived from paid loss development factors and distribution of report to pay lag

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Challenges/Pitfalls

Source: Moody’s Subprime RMBS Loss Projection Update, March 5, 2009

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Case-Shiller Home Price Index Since January 2000

'Case Shiller 20 City Compsite'Source: Standard and Poor's

Jul06: 206.5

Apr 09: 139.2

Decline: -32.6%

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Bornhuetter-Ferguson Method

More appropriate where loss development is volatile and/or immature

Requires loss to date, a priori loss, and a loss development curve

Future loss indications tend to be heavily weighted toward the a priori loss estimate for recent vintages

A priori loss estimate is key

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B-F Method – A Priori

A priori ULR development– Frequency of default

– Severity given default

A priori ultimate loss rate = frequency x severity

Critical considerations– Underwriting characteristics (LTV, documentation, etc.)

– Economic factors

– Persistency

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A Priori Development – Frequency

Amortization

FICO-LTV

Interest Only

Loan Purpose

Property Type

Occupancy

Documentation

Loan Size

Illustrative Loan Characteristics

Prime

Alt-A

Subprime

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Loan to value (LTV) is the ratio of original loan balance to purchase price

Higher LTVs indicate less investment in the home by the borrower, and thus, higher propensity to default

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Loans are available in which the borrower has the option to pay less than the principal and interest needed to completely amortize the loan over its amortization period

Borrowers who consistently pay less than principal and interest may find their outstanding balance actually increase, raising the likelihood of default

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Documentation refers to the information provided by the borrower to obtain the loan

Borrowers with full documentation tend to have lower default likelihood than those with low documentation

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Economic Factors

Source: “Negative equity and foreclosure: Theory and evidence”, Christopher L. Foote, Kristopher Gerardi, Paul S. Willen, Journal of Urban Economics 64 (2008), pp. 234-345

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Severity Given Default

Severity of Default– Home price changes– Costs of foreclosure (realtor, legal, upkeep)– Accrued interest– Stressed sale– Government intervention may impact severity

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B-F Method

Paid B-F Method– Paid loss to date

– Paid LDFs

– A priori loss

– Estimates future paid loss

Incurred B-F– Paid loss to date plus proxy for case reserves = Incurred loss

– ‘Incurred’ LDFs

– A priori loss

– Estimates future paid loss on non-delinquent loans

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MBS Valuation Flowchart

Collateral(Mortgage Loans )

Performance to date

Underwriting Characteristics

EconomicForecasts

Credit /PrepayModel

SecurityCapital

Structure

Losses

Principal &Interest

Data Models Future Cash Flows

Future

Collateral

Performance Assumptions

Subordinate

Equity

Mezzanine

Senior

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Risk Quantification

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100

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0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Intr

insi

c V

alue

Ultimate Loss Rate

Sensitivity of HEAT 2007-2 2A4with Increasing Ultimate Loss Rates

Breakpoint

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Closing

Credit risk previously overlooked Credit risk exists Activities positioned to analyze credit risk Large MBS holders include banks, insurance companies, asset

managers Benefits to accurate MBS valuations

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Mortgage-Backed Securities: An Actuarial Approach to

Cash Flow Valuation

Questions?

kyle.mrotek@milliman.comneal.dihora@milliman.com