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CLEAN™: A Risk-Neutral Approach to MBS Valuation

2

What Is an Ideal MBS Valuation Model?

MBS price driven by parsimonious set of risk factorsEach factor is readily observed and measured

Risk factor values and sensitivities match reality

Leads to trading opportunitiesUnhedged risk factors signal rich/cheap opportunities

Provides a robust basis for risk managementProbability distributions for risk factors imply probability distribution for the

MBS price

3

Other Desirable Features

Minimal dependence on historical econometric data

No redesign required when market conditions change

Speed: fast calibration and valuation

4

Initial Observations

Modeling prepayments is only a means to an end The real goal is proper valuation and risk measurement

A mortgage is a callable amortizing bondPrepayment models should be consistent with callable bond models

Bonds (mortgages) are called (refinanced) when the call (refinancing)

option is worth more dead than alive

Bond and MBS models should therefore respond similarly to changes in

interest rate levels and volatilities

5

The CLEAN™ Way

Modeling prepaymentsTurnover and defaults modeled using deterministic speedsRefinancings modeled using stochastic interest rate model

Modeling a mortgageAs a callable amortizing bondA financial engineer will refinance when the option is worth more dead than aliveOthers will refinance too early (never really happens) or too late (“laggards”)

Modeling heterogeneous refinancing behaviorDivide mortgage pool into 10 buckets according to laggard parameterUse a standard laggard distribution for a new pool

Modeling seasoned poolsFastest refinancing buckets disappear first

Automatically accounts for ‘burnout’

6

Risk Factors in the CLEAN™ MBS Model

Interest rateUSD swap curve

Swaption volatilities

PrepaymentLaggard distribution

Turnover speed

Default/buyout speed and recovery percentage

Refinancing cost

Homeowner credit spread

OAS (option-adjusted spread to swap curve)

7

Calibration of CLEAN™:Straightforward and Intuitive

Rarely adjustedLaggard distribution

Default recovery percentage

Refinancing cost

Occasionally adjustedTurnover speed

Default/buyout speed

Adjusted monthlyHomeowner credit spread

8

CLEAN Uses Two Separate Credit Spreads

Homeowner credit spread

Specifies the homeowner’s borrowing curve

Determines when homeowner would refinanceRefinance if refinancing option is worth more dead than alive

OAS

Spread demanded by MBS investor

Used for discounting MBS cash flows

ReflectsCredit spread of guarantor

Plus market discount for unhedged uncertainty in price

9

Homeowner Credit Spread: Key Driver of Refinancing Speed

For current coupon poolConceptually the spread between a “par mortgage curve” and swap curve

Current primary mortgage rate minus volatility minus 10y swap rate

Implies refi option premium of approximately 40 bps

Comparable to single-A/BBB 10-year corporate credit

For higher coupon poolWider than current coupon spread due to credit impairment

Start with current coupon homeowner credit spread

Add difference between WAC minus primary mortgage rate

Fine-tune by matching duration and convexity to dealer consensus

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Estimated Homeowner Credit Spread FNMA TBA Coupon Stack – July 23, 2010

TBA WAC (%)Homeowner Credit

Spread (bps)

FNCL 4 4.585 110

FNCL 4.5 4.950 110

FNCL 5 5.428 175

FNCL 5.5 5.949 240

FNCL 6 6.517 320

FNCL 6.5 6.975 400

FNCL 7 7.645 480

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TBA Price Movements vs. Movement Implied by Model Greeks

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CLEAN™ OAS Tracks Agency Debenture Spread Closely

-50

0

50

100

150

1/1/2009 6/1/2009 10/30/2009 3/30/2010

Sp

rea

ds

(bp

s)

FNCL 4.5 OAS vs. Agency Debenture Spreads(1/2/2009 - 4/13/2010)

FNCL 4.5 OAS

10-yr agency spreads

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CLEAN™ OAS Movements Comparable to JPM OAS Movements

CLEAN vs. JPM FNCL 4.5 OAS (1/2/2009 - 7/19/2010)

-40

0

40

80

120

1/2/2009 7/3/2009 1/1/2010 7/2/2010

Sp

read

(bp

s)

CLEAN OAS (bp)

JPM OAS (bp)

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TBA Duration and Convexity: CLEAN™ vs. Other Models

7/23/2010

Turnover/default

rateHomeowner

credit spreadTBA

price

OAS

CLEAN JPMDealer model

BAML (new)

BAML (old)

FNCL 4 7% 110 101.84 23 8 25 1 -5

FNCL 4.5 9% 110 103.97 33 -2 34 -1 -11

FNCL 5 13% 175 106.19 53 -25 50 0 -33

FNCL 5.5 18% 240 107.72 67 -61 25 11 6

FNCL 6 24% 320 108.83 71 -71 29 16 24

FNCL 6.5 24% 400 109.81 97 -14 101 45 53

Duration Convexity

CLEAN JPMDealer model

BAML (new)

BAML (old) CLEAN JPM

Dealer model

BAML (new)

BAML (old)

FNCL 4 4.9 5.0 5.2 4.5 4.5 -1.8 -2.0 -2.8 -3.0 -3.3

FNCL 4.5 3.5 2.9 4.2 2.6 2.8 -2.9 -3.4 -3.1 -3.9 -1.9

FNCL 5 2.7 1.3 3.7 1.4 1.8 -2.7 -2.9 -2.5 -2.8 0.2

FNCL 5.5 2.1 0.5 1.8 1.1 2.5 -2.2 -0.8 -1.4 -2.0 0.2

FNCL 6 1.9 0.5 1.3 0.6 2.5 -1.8 0.3 -0.9 -1.3 0.4

FNCL 6.5 2.3 1.4 2.9 0.5 2.5 -0.8 0.1 -0.4 -1.4 0.5

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OAS Implied by TBA Prices

FNMA 30-yr TBA OAS of CLEAN (July 23, 2010)

0

40

80

120

4.0 4.5 5.0 5.5 6.0 6.5

MBS coupon (%)

OA

S (

bp

)

10-yr agency spread

CLEAN

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Why CLEAN™ Is Ideal for Trading, Hedging, and Risk Management

Realistic transparent behaviorBased on well established financial and economic principles

Instead of ad hoc mathematical formulas and parameters

Consistent with valuation models for callable bonds and

cancelable swaps

Calibration is straightforward and intuitive

Concretely defined model parametersEasier to simulate

Model behavior always realisticBased on fundamental financial and economic principles

Not on statistical fitting of historical behavior

And ridiculously fastCritical for simulation

17

Challenges Faced by Other Prepayment Models But Not by CLEAN

BurnoutAs pool ages, refinancing speed decreases

Model parameters are mathematical and not economicNeed to be estimated using fit to historical dataRather than direct observation

Ongoing need to update not just parameters but the model itselfEstimating a future primary mortgage rate

Many models assume a fixed formula using spread to an interpolated Treasury yieldBut mortgage rate contains premium for refinancing option, which depends on volatility

Computation speedUse of Monte Carlo forces tradeoff between speed and precision

18

Heard It Through The Grapevine

"The actual sensitivity of MSRs to implied volatility is complex and somewhat controversial”

Ben Golub in “Mark-to-Market Methodology, Mortgage Servicing Rights, and Hedging Effectiveness”

“The model we use doesn’t even get the sign right for volatility hedging of MSRs”

A/L management advisor

“The price response to skew adjustment seems exaggerated”Hedge fund manager

Why do intuition and model disagree

when it comes to volatility?

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Other Prepayment ModelsAre Overly Sensitive to Volatility

-2

-1

0

1

2

20 30 40

Chan

ge in

pric

e (%

of p

ar)

Volatility (%)

30-yr 4.5% MBSPrice: 101 2/32

Base Volatility 30%

CLEAN

Bloomberg

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Why Other Prepayment Models Struggle with Interest Rate Volatility

Others model future mortgage rate as a formulaSay a function of 2-yr and 10-yr Treasuries plus a fixed spread

Where fixed spread is refinancing option premiumDoes not widen when volatility increases

So prepayments overreact to change in volatility

For example, if volatility increaseOption premium spread underestimatedFuture mortgage rates underestimatedRefinancing speed overestimatedHigher-coupon MBS prices decline too much

21

References

Andrew Kalotay & Qi Fu (June 2009), A Financial Analysis of Consumer Mortgage Decisions, Mortgage Bankers Association.

Andrew Kalotay & Qi Fu (May 2008), Mortgage servicing rights and interest rate volatility, Mortgage Risk.

Andrew Kalotay, Deane Yang, & Frank Fabozzi (Vol. 1, 2008), Optimum refinancing: bringing professional discipline to household finance, Applied Financial Economics Letters.

Andrew Kalotay, Deane Yang, & Frank Fabozzi (Vol. 3, 2007), Refunding efficiency: a generalized approach, Applied Financial Economics Letters.

Andrew Kalotay, Deane Yang, & Frank Fabozzi (December 2004), An option-theoretic prepayment model for mortgages and mortgage-backed securities, International Journal of Theoretical and Applied Finance.

Available from http://www.kalotay.com/research