RCo Behavior Modeling

July 2011Robert J. Wyle, CFA

2

Agenda

» Introduction– What is behavior

– Why is behavior Important

» Mortgage Prepayments– How are mortgage prepayments measured?

– How are prepayment modeled?

– Demo

3

INTRODUCTION

4

What is Behavior

“Where Contractual Terms May Be Varied By Custom or Implication”

» Prepayment Due To Unscheduled, Part Or Full, Principle Repayments

» The Variability and Lack of Sensitivity of Non Maturity Liabilities in Terms of:

– Maturity

– Coupon or Interest Rate Repricing, or Rate Repricing Lag To Market Rates, Or The Rate Off-set Due To High Account Servicing Cost

» Call Options, Put Options

» Caps, Floors

» Changing Credit Card Balances

5

U.S. Mortgage Debt Outstanding as of 2008Residential Real-Estate

$19,429 Billion

$8,790 Billion $11,254 Billion

On-balance Sheet Non-Agency MBS$3,880 Billion $5,068 Billion $282 Billion $2,025 Billion

REITs, Finance Banks & Thrifts Companies, Insurance

$3,375 Billion Companies, etc.$505 Billion

1st Liens 2nd Liens$2,247 Billion $1,128 Billion

Prime / Jumbo Alt-A Subprime Total$530 $530 Billion $880 $880 Billion $770$770 Billion $2,180 Billion

$2,344 Billion AAA AAA AAA AAA

96% $509 95% $836 78% $601 89% $1,9451st Lien

$1,600 Billion $744 Billion

1.5% AA 3% AA 10% AA 5% AA$8.0 $26 $77 $111

1% A 1% A 5% A 2% A$5.3 $8.8 $39 $53

0.5% BBB 0.7% BBB 4% BBB 2% BBB$2.7 $6.2 $31 $40

1.0% Equity 0.3% Equity 3% Equity 1% Equity$5.3 $2.6 $23 $31

Tranche proportions are estimates, based on a sampling of securitizations Some numbers do not sum exactly, given different data sources.

(1) Financial system debt includes financing for $626 billion of debt financing nonfinancial corporate business and nonfarm noncorporate business mortgages. Total household mortgages total $10.6 trillion.

(2) Other includes private and government funded mortgages.

Other (2)

2nd Lien

Publicly Traded, US Banks & Thrifts

Homeowner's Equity

Mortgage Debt Outstanding (1)

Agency

17.4 of global debt are in U.S. residential real estate!

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Why is Modeling Behavior Important?

Understanding correlated behavior is important because it allows risk managers to reflect the impact of market volatility on embedded options.

-2.0% -1.5% -1.0% -0.5% 0.0% 0.5% 1.0% 1.5%-10%

0%

10%

20%

30%

40%

50%

60%

70%

Actual refinancing vs. S-like curve: 5/1 ARMs

Observations

Model

Refi Spread

Refi CPR

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Term Structure Modeling

-2.00%

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

0 4 8 12 16 20 24 72 120

168

216

264

312

360

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Effective Duration

Effective Duration Recognizes that Changes in Yield will Change the Cash Flows of Instruments with Embedded Options

Price

Duration Actual Price

Positive Convexity

Negative Convexity

Yield

Δi Δi

V0 = initial price

V- = price if yield changes by -y

V+ = price if yield changes by +yΔi = change in yield

De =V- - V+

2(V0)(Δi )

EVEExposures

-60.00%

-50.00%

-40.00%

-30.00%

-20.00%

-10.00%

0.00%

10.00%

-300 -200 -100 +100 +200 +300

Parallel Change in Rates

% C

hang

e in

EV

E

Dec-00

Jun-01

Dec-01

Limits

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MORTGAGE PREPAYMENTS

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How are Mortgage Prepayments Measured?

» Single Monthly Mortality (SMM)

» Constant Prepayment Rate (CPR)

» PSA Standard Prepayment Benchmark

PrepaymentSMM

BegBalance ScheduledPrinciple

12

112

1 1

1 1

CPR SMM

SMM CPR

6%* ; 3030

6%; 30

6%*min 1,30n

nCPR n

CPR n

nCPR

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How are Mortgage Prepayments Modeled?

» The purpose of a prepayment model is to define a relationship between projected mortgage rates and the resulting rates of prepayment activity, given all available information regarding the mortgage, the mortgage holder, the current state of the economy, etc. If this relationship were well modeled, it would in turn allow one to answer all of the questions that one may ask as a holder of a mortgage-backed security. » Questions like: the value of the option to refinance, the average advantage of owning a mortgage

vs. owning other instruments, how one can compare a mortgage to a collection of bonds and short positions in interest rate derivatives, etc.

» A well constructed model should capture the differences between short-term projections and long-term projections.

» A well-constructed model should incorporate all known factors that effect a mortgage holder's inclination to move or to refinance, as well as the overall state of the US housing market.

» Typical prepayment factors include: Refinance spread, seasoning, seasonality, burn out, loan size, FICO score, etc.

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Proposed Model

» The prepayment model we are about to build in the slides that follow is the product of a CPR based seasoning ramp and seasonality and refinance multipliers:

actorrefinanceFyIndexSeasonalitPRSeasoningCCPR **

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Seasoning (Age)

Quantification of seasoning (age) factor:

» Remove any sold loans from the bank data

» For each month, calculate the age of the loans at prepayment

» For each month, calculate the Single Monthly Mortality (SMM) and CPR. The CPR is the annualized percentage of the existing mortgage balances expected to be prepaid in a year.

» Finally, calculate the monthly average CPR for each age.

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Seasoning Analysis0

1020

3040

Mon

thly

Ave

rage

CP

R,

%

0 20 40 60 80Age (in month)

CPR and Age

16

Proposed Seasoning Curve0

10

20

30

40

0 20 40 60 80Age (in month)

Monthly Average CPR, % Existing Seasoning CurveProposed Seasoning Curve

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Seasonality Index

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1 2 3 4 5 6 7 8 9 10 11 12

Seas

onal

ity

Inde

x

Month

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Refinance Incentive

» Refinance incentive/spread (RS) is defined as gross weighted average coupon rate minus the current offer rate, which is the sum of 3 year swap rate and 150 basis points pricing spread. If the three year swap rate becomes lower, more people are going to refinance.

» Quantifying refinance incentive:» In each month, group deal level loans by age and refinance spread cohorts.

» The market rate for the loans is assumed to be the three year US swap rate and the 150 basis points are assumed to be the average pricing spread.

» Calculate the monthly average CPR.

» Adjust for other behavior factors i.e. de-season and de-seasonalize the CPR/refi-incentive

%5.13 YearUSttt SwapGWACRS

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De-Seasoned / De-Seasonalized CPR and Refinance Spread

010

20

30

40

Avera

ge C

PR

, by A

ge &

Re

fina

nce S

pre

ad, %

-4 -2 0 2 4 6Refinance Spread

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Refinance Factor

spread refinance factor-6 0.7626-5 0.7963-4 0.8328-3 0.8720

-2.75 0.8821-2 0.9133

-1.75 0.9239-1.5 0.9346

-1.25 0.9454-1 0.9562

-0.75 0.9671-0.5 0.9781

-0.25 0.98900 1

0.125 1.00550.25 1.01100.5 1.0219

1 1.04381.5 1.06542.5 1.10763.5 1.14794.5 1.1858

5 1.20375.5 1.2209

6 1.2374

6.20/}*1.0arctan*05.96.20{

preadrefinancesactorrefinancef

%5.13 YearUSttt SwapGWACRS

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Conclusion

» “Every aspect of a “good” prepayment model must be designed to reflect people’s behavior. History should be used, but only as an indication of what the parameters should be. And, if there is not enough history to set the value of certain parameters that we know exist in the real world, it is better to set them to some reasonable value than not set them at all, and have them implied by other parameters, since the implied value may not be a reasonable one.

» The quality of a model depends ONLY on the accuracy and completeness of the representation of the underlying phenomenon that we know exists in the real world.”

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Appendix A

• “Bond Markets, Analysis, and Strategies”; Frank Fabozzi; 1989

• “The Handbook of Fixed Income Securities”; Frank Fabozzi; 2001

• “Mortgage Backed Securities”; Frank Fabozzi; 2001; 1992