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Residential Mortgage-Backed SecuritiesModeling: A Fundamental Approach

Stanislav Perchev

This article surveys the recent developments in the credit markets paying special attention to the issuessurrounding the valuation of residential mortgage-backed securities (RMBS) and related collateralizeddebt obligations (CDOs). It also offers a modeling framework whose purpose is to provide a robust andtransparent approach to the valuation of securities backed by real estate assets. The proposed frameworkutilizes a stochastic Monte Carlo approach based on econometric analysis of underlying data at theindividual loan level paired with accurate reflection of the transactions financial structure, whileaccounting for liquidity risk.

The RISConsulting Group LLC, Boston, MA

he recent developments in the creditmarkets have illuminated one veryimportant but often ignored aspect of the

financial world the more than occasionaldichotomy between value and price. Or, maybeit is between high-powered academic researchand real business applications? Or, perhaps itis between the views of deal execution teamsand quantitative researchers in leading financial

institutions across the world? Or betweenunderwriting standards and mortgageorigination practices? It is all of the above, andwe by no means claim for this to be a completelist of issues and facts explaining the creditmarkets meltdown that has been propagatingover the past year and which many believe isonly gaining momentum.

While we at RISC do not think we can helpfinancial institutions and investors alleviate allof the above problems, we believe we can be of

great value by extending what we have donefor other businesses and industries offer atransparent framework for valuation of creditinstruments by focusing on the fundamentaldrivers of the risk. Not surprisingly, we havestarted with the most severely affected sector atthis stage the residential mortgage-backedsecurities (RMBS) and the resulting suite ofexotic derivative instruments (collateralized

debt obligations, or CDOs, in all their forms),whose complexity has been singled out as aroot cause of the market crash. Of course, weall know that there were many roads leading upto that collapse and the inability to properlyvalue and account for the risk in complexstructured finance products was nothing but acrossroad of manifested shortcomings evidentin practices and methods. What we offer is an

opportunity to leave it just as that a crossroad,rather than a final destination.

For years we have promoted a simple butpowerful framework for risk estimation andvaluation Monte Carlo simulations ofunderlying drivers based on econometricanalysis of the data and processes at hand.When implemented correctly, the datageneration processes allow you to samplethrough the range of potential outcomes andevaluate different financial instruments

relevant cash flows with a great deal of comfortas you are relying upon a scientific frameworkbased on hard, real data. This approacheliminates stress case assumptions and levertoggling based on subjective judgments orreliance upon no-arbitrage financial models thatmake arbitrageurs smile. Instead, it relies uponrelationships tested through time, which in theirapparent and powerful simplicity provide the

T

The RISConsulting Group LLC January 2008


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needed transparency and are accessible to awide base of investors.

General Trends and Market

Developments

The year 2007 marked a dramatic turnaround ofwhat many believed to be a bull market forcredit and credit-related structured finance.The credit markets collapsed in the wake ofrising delinquencies on subprime mortgagesand the liquidation of two high profile hedgefunds, which led to the demise of the structuredinvestment vehicles (SIV) market followed bysignificant write-offs posted by banks. Amidstit all, rating agencies have been called to taskfor their alleged failure to accurately measurerisk. In addition to its short-term intervention,

the government is looking at policies to shoreup industry practices and to help avoid futurecrises, adding indirect cost and the threat ofincreased regulation to the mix.

Credit ratings and traditional methods ofvaluation of risky debt in highly structuredfinancial instruments, such as CDOs, havecome into question and investors are facing theneed for more information transparency, withsome (we believe far too few) searching formore robust risk analysis and valuation tools.

The causes of the residential mortgage crisisthat has led to the more general meltdown ofthe structured finance market go beyondsubprime and have their roots in thefundamentals of the housing market cycle.

The United States experienced a real estateboom in the period of 1996-2005, during whichthe percentage of home-owning householdsincreased from 65.4% to 68.9%, with homeprices constantly on the rise, reaching annualgrowth rates of 11.4% between 2000 and 2005.

This rapid expansion, however, has come to asudden halt. Growth in home prices sloweddramatically in Q1 2006, and in Q1 2007,prices fell for the first time since 1991.

1The

median prices for new and existing homes weredown 13.2% and 6.3%, respectively, year-to-

1 McDonald and Thornton (2008)

year in October, 2007 (largest decline since1968).

2

These price declines, combined with higherinterest rates, led to increased mortgagedelinquencies, especially in what has become

known as the subprime mortgage market.Based on its December 2007 NationalDelinquency Survey, the Mortgage BankersAssociation reports that the level ofdelinquencies is at 5.59% of all loansoutstanding in Q3 2007, not including the loansalready in foreclosure (the highest level since1986).

3They go on to point out that the

percentage of loans in foreclosure stands at1.69%, the highest level ever recorded. In aJanuary 2008 press release, RealtyTracreports that the U.S. foreclosure activityincreases by 75% in 2007 (Figure 1).

4

Figure 1

Source: RealtyTrac

Clearly the market conditions are not painting avery favorable picture there are signs that thecrisis is far from over and the situation isexpected to deteriorate even further, but moreon that later. First, lets cover some mortgagebasics.

Mortgages and Mortgage-Backed

Securities

An excellent source for a general introductionto the field is Lucas (2006). We will coverbriefly some of the basics for the sake ofcompleteness.

2 Mortgage Bankers Association (Dec.14, 2007)3 Mortgage Bankers Association (Dec.6, 2007)4 RealrtTrac (2008)



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A mortgage is a typical loan with real estateserving as collateral. Its basic characteristicsinclude: loan amount, loan term, schedule forrepayment, and contracted interest rate. Thereare many different types of mortgages, mainlydepending on how the interest rate enters into

the contract:

Fixed rate, exhibiting fixed monthlypayment for the duration of the loan (mostcommon, 70% of total mortgage market),

Adjustable rate (ARM), where the base rateadjusts periodically based on a benchmarkrate (LIBOR, Constant Maturity Treasury,etc). Increased in popularity after 2002,

Hybrid ARM, where the rate is fixed for aninitial period and then switches toadjustable (e.g., 5/1 hybrid ARM, 3/27hybrid ARM, etc), and

Interest only (IO), where borrower paysonly interest for a number of years. Can beboth fixed rate and (hybrid) ARM.

Mortgage loans are financed on a primary and asecondary market basis. Traditionally theprimary market has been much larger than thesecondary one. With the creation of theGovernment National Mortgage Association(Ginnie Mae) and the government-sponsoredenterprises such as the Federal NationalMortgage Association (Fannie Mae) and the

Federal Home Loan Mortgage Corporation(Freddie Mac). Aided by growth in theseagencies, the secondary market began toexpand rapidly in the 1990s and now plays amajor role in mortgage finance. This growthwas turbo-charged by the increasedsophistication of the US and global financialmarkets, along with the introduction offinancial instruments and financial engineeringtechniques that resulted from increasedspecialization in mortgage finance. Incombination, these factors led to:

5

More liquidity in trading the underlyingmortgages,

Greater utilization of capital markets withthe development of securitizations, and

A significant increase in mortgage loanavailability to all types of households withlower transaction costs.

5 Bernanke (2007)

The loans typically vary in terms of the criteriathey satisfy between agencies (to the list ofFannie Mae and Freddie Mac we would have toadd the Government National MortgageAssociation or Ginnie Mae) and private issuers,with those by private issuers having less

stringent underwriting standards.

The exposition would not be complete withoutaddressing some of the common securitiesbacked by residential mortgages (RMBS). Thesimplest one is a mortgage passthroughsecurity, where the payments from theunderlying pool are distributed to investors on apro-rata basis. The next level is a strippedMBS, where the payments from the underlyingpool are directed towards an interest-only class(or IO mortgage strip) and a principal-onlyclass (or PO strip). Once individual loans or

pools of passthroughs are tranched intoseniority-of-payment tranches, the resultingsecurity is referred to as a collateralizedmortgage obligation (or CMO). Further, adiversified pool of collateral comprising one ormore of the above structures, results in what isknown as a Structured Finance CollateralizedDebt Obligation (or SF CDO). Tranches ofCDOs themselves, when packaged together, arereferred to as CDO

2(where the order could be

higher than 2). Structured RMBS securities aredesigned to distill the different risks associatedwith mortgage portfolios and spread themacross the base of investors according to theirrisk appetite.

Risks

The risks associated with mortgage lending aredefault risk (that the borrower may default onthe mortgage payments) and prepayment risk(the speed of repaying the mortgage, whichaffects the size and timing of the correspondingcash flows).

Default risk is quite intuitive in the event ofdefault, the borrower no longer meets thecontractual obligations and the cash flows stop.A lender or an investor in a security backed bya pool to which such a mortgage belongs couldexperience a loss, depending on the amount ofcollateral coverage. However, in the wake offalling prices, full collateral coverage is hardlythe expected norm.



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Prepayment risk is essentially reinvestmentrisk. Prepayments affect the timing of the cashflows and thus, inject uncertainty.Prepayments are a well established risk ofmortgages, but occurrence at any rate differentthan the expected is not a welcome feature in a

dynamic environment when interest rateschange.

As interest rates fall, borrowers are likely toprepay, which is what lenders and investors inmortgage instruments would like to avoid,because the opportunity set for reinvestmentavailable in the market for comparableinvestments would have shrunk relative to whatwas available on the prepaid mortgage. Thus,while the value of the mortgage or theinstrument should actually rise with a fall ininterest rates, it does so with a percentage gain

smaller than the percentage loss for a large risein interest rates (i.e., there is convexity risk).

6

As interest rates rise, borrowers are slower atprepaying and this is exactly when the investorswould like to see increasing prepayments, asthey can invest in instruments yielding higherreturns. Thus, the decline in price of themortgage or the instrument backed by themortgage is larger (i.e., there is extension risk).

There is a great deal of research addressing thefundamental drivers of the mortgage exposurerisk. Metrics such as the FICO7 scores, loansize, and loan-to-value ratio (to name a few)have long been recognized as indicators of thelikelihood to default or prepay. Other factorsaffecting the loss severity in the event of adefault are the time it takes to foreclose and thethen prevailing interest rates, as well as thevalue of the real estate asset serving as themortgage collateral (to name a few).

Subprime Mortgage Market

Since there has recently been a great deal ofattention in the media stemming frominvestments in securities backed by subprimemortgages, our discussion would not be

6 Lucas (2006)7 FICO scores are developed by the Fair IsaacCorp., see http://www.fairisaac.com/fic/en.

complete without focusing on this segment ofthe market.

Subprime mortgages refer to mortgage loansmade to borrowers who usually displayprevious delinquencies, foreclosure or

bankruptcy, have low FICO credit scores, and aratio of debt service to income of 50% orgreater.

8The subprime mortgage market

offers a wider range of mortgage products thantypically found in the prime sectors. It was anew and rapidly growing sector of themortgage market, which, by expanding the poolof credit to a larger base of borrowers,increases homeownership and the opportunityto create wealth. To give one a sense of thelevel of growth in this segment: subprime loanscategorized as B and C increased from $65 BNin 1995 to $332BN in 2003.

9The increased

securitization of subprime mortgage loans hasfueled this growth to a large degree. As theauthors of the referenced study note, all thesocial good that the rapid expansion in thismarket has brought does not come without aprice they suggest that the probability ofdefault on non-prime mortgages is at least sixtimes higher than for prime loans and thatelevated foreclosures adversely impact thevalue of properties in the affectedneighborhoods as a whole.

To put things further in perspective, the marketsize for subprime mortgages is estimated at$1.3 trillion outstanding loans (out of $10.4trillion of total home mortgages outstanding).

10

Subprime mortgages with adjustable interestrates account for two-thirds of subprime first-lien mortgages or about 9% of total first-lienmortgages outstanding.

11Now, consider the

above-mentioned statistic and the fact that 43%of all foreclosures started during Q3 of 2007belong to subprime mortgages with adjustablerates.

12

8 For an in-depth discussion of the subprimemortgage market, see Chomsisengphet andPennington-Cross (2006)9 Ibid.10 Poole (2007)11 Bernanke (2007)12 Mortgage Bankers Association (Dec.6, 2007)



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How can this happen, you might ask? After all,all years up to 2006 were marked by strongmortgage credit quality and unprecedentedgrowth in the credit markets.

The answer, with the benefit of hindsight, lies

in the combination of home price decelerationand a general economic slowdown with a largenumber of ARMs issued during a periodmarked by a steep yield curve (2002-2004,suggesting rising short term interest rateexpectations).

Add to this the fact that mortgage originatorsincentives were influenced by high fees andsubstantial spreads on non-prime ARMs, not toforget the increased investor appetite for highersecuritization yields driving demand for moreand more securitizations, and

Figure 2

7/1 /2007 11/1/2007 3 /1 /2008 7/1/2008 11/1/20080

5

10

15

20

25

30

35

40

45

50

USDb

illions

Reset Schedule for Hybrid ARMs by Sector

Source: Federal Reserve Bank of Dallas/Bank of America

Agency Alt-A Jumbo Subprime

top it off with the fact that rating agenciesincentives favor pumping more and morevolume through the system,

13and you have an

answer. Better yet, a disaster. So, was it reallya surprise that the crisis happened? Moreover,a good number of sources suggest that theworst is yet to come. An economiccommentary by David Rosenberg at MerrillLynch suggests that the ARM resets are justbeginning with more than $170 billion of resetsexpected in 2008, with 70% of the volumefalling into the subprime category.

14A similar

picture is painted by Bank of America (Figure2)

15.

13 Mason and Rosner (2007)14 Rosenberg (2007)15 DiMartino (2007)

Add to this the deterioration of home pricesover the last year and the expectation that theyare expected to go down further, and you get asense of where we might be heading (Figure3)

16.

Figure 3

1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008-10

-5

0

5

10

15

20

25Case-Shiller Price Index: Year to Year Percent Change

PercentChange

Source: S&P/Case-Shiller Home Price I ndex

Before wrapping up the mortgage marketsurvey, we address the issues surrounding themore exotic products, such as the CDOs. Theexcessive liquidity in the global financialmarkets, the spike in the development and useof innovative financial structures, fallinginterest rates and tightening credit spreadsincreased the demand for CDOs by investorsseeking yield enhancement against a backdropof relatively low volatility. CDOs outpacedcorporate and municipal bond sales with about

$500 billion sold in 2006, up from $99 billionin 2003.

17It is reported that almost half of all

CDOs sold in the U.S. in 2006 containedsubprime debt, with more than $175 billion insubprime mortgage mezzanine tranches.

18

With the unraveling of the mortgage crisis,investors are realizing that they have no reliableway of quantifying the risk and valuing thesecomplex instruments. The ratings issued byrating agencies have lost credibility as robustindicators of underlying risk. The collapse ofthe Bear Sterns hedge funds ignited a rash ofdowngrades on subprime mortgage transactions

16 Source: S&P Case-Shiller Index(http://www2.standardandpoors.com/portal/site/sp/en/us/page.topic/indices_csmahp/0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0.html), adapted from Rosenberg(2007)17 Evans (2007)18 Ibid.



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which, in turn, began a period of panic sellingof structured debt with subprime components,as investors fled to safety by moving theirholdings to US Treasuries and money marketfunds. In the meantime, the origination andtrading of structured mortgage products has

virtually ground to a halt. Inevitably, therhetorical question arises: what will it take toget another structure with subprime debt ratedor placed in the market?

By introducing transparency and fundamentalrisk drivers into our analysis, we offer amodeling framework to assist in filling thecurrent valuation and risk-assessment vacuum,support ongoing risk transfer activity andrestore some of the confidence in RMBS andderivative securities that has been lost in therecent past.

Modeling Aspects

While the preceding discussion covered a lot ofground, we by no means view it as an in-depthanalysis of the recent crisis. We do, believe,however, that a few key issues around thecurrent state of modeling rise to the surface:

Complexity of an unprecedented nature,the often inappropriate use of availabledata, poor overall transparency (risk,

model, date methodology), failure toaccount for illiquidity,

Investors inability to measure their levelsof exposure to subprime sector CDOs orthe corresponding risk,

Absence of reliable sources of statisticalinformation with respect to the defaultrates for many of the CDOs,

Traditional methodologies and creditratings that are no longer consideredaccurate or adequate,

Rating agencies no longer seen as objectivesince they play an active role in assemblingCDOs,

Presence of perverse incentives as asubstantial portion of the agenciesrevenues comes from rating structuredfinance instruments,

Rating agencies too slow and opaque intheir tackling of the subprime crisis,

An over-reliance by investors on ratings atthe expense of doing their homework,

Modeling of sudden liquidity withdrawal iscritical but missing,

Data may be unreliable and aggregate /high-level modeling approach

inappropriate.

Where this all takes us to is the belief that thereis a clear need for independent pricing andvaluation based on a transparent and accessibleframework, which utilizes analyses derivedfrom reliable and appropriate data (includinghistorical loan and securities performance aswell as transaction structures). A framework,in short, that applies robust modeling focusedon the underlying asset pools at the individualloan level, allowing for stochastic modeling ofthe risks, and accounting for the presence ofliquidity risk.

RISC RMBS Stochastic

Modeling Framework

We believe that the appropriate analysis ofRMBS requires a forward-looking stochasticmodel that combines macroeconomiccomponents (such as US real GDP growth ratesand interest rates), industry-specificmeasurements (such as state-level grossproduct growth rates and unemployment levels,industrial production concentration), combinedwith individual loan level analysis. In order tocapture the specific aspects of a certaintransaction, it is critical to accurately capture itsfinancial structure and corresponding cash-flowdynamics. And, of course, the model has toaccount for both the originator and servicerpractices, as well as market liquidity risk.

The model we are alluding to will produce cashflows generated in a Monte Carlo stochasticsimulation environment, which are then flown

through the transactional waterfall. As such, itwill produce probability distributions of cashflows to each tranche, which, in turn, will givean accurate representation of the risk to each ofthe corresponding tranches, and producevaluation and risk analysis calculations(expected values, percentiles, etc.)



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RISC RMBS Stochastic Modeling Framework

Each of the stochastic components of themodels will be based on econometric analysisof historical data sets at the highest level ofresolution (such as loan-by-loan historicalexperiences) and will provide a robust andtransparent framework for understanding theanalysis assumptions and implications.

Think of this framework as a fully integratedstochastic model, which bases its analyses on

scientific analysis of data and provides its userswith a full set of analytics, derived from thegenerated probability distributions filteredthrough the contractual details of the analyzedtransaction. This approach to quantifying riskhas worked for us and our clients and webelieve it will work for you.

Conclusions

The market needs a new approach when itcomes to valuation of residential mortgage-

backed securities and the more exoticstructured credit products derived from RMBS.We propose a stochastic framework for cashflow generation and risk estimation based oneconometric analysis of historical data. Thefocus is on the loan-level data and the inclusionof key risks (other than default andprepayment) into the framework, such asmarket liquidity risk.

References

Bernanke, Ben S. The Subprime MortgageMarket. Speech at the Federal ReserveBank of Chicagos 43

rdAnnual Conference

on Bank Structure and Competition,Chicago, Illinois, May 17, 2007;http://www.federalreserve.gov/newsevents/speech/bernanke20070517a.htm

Chomsisengphet, Soupala and Pennington-Cross, Anthony. The Evolution of theSubprime Mortgage Market. FederalReserve Bank of St. LouisReview,January/February 2006, 88(1), pp.31-56.

DiMartino, Danielle, and Duca, John V. TheRise and Fall of Subprime Mortgages.Federal Reserve Bank of DallasEconomicLetterVol.2, No.11, November 2007;http://dallasfed.org/research/eclett/2007/el0711.pdf

Evans, David. Subprime Infects $300 Billionof Money Market Funds, BloombergPress, August 20, 2007;http://www.bloomberg.com/apps/news?pid=20601109&sid=aEUtlgwzL_qc



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Lucas, Douglas L., Goodman, Laurie S., andFabozzi, Frank J. CollateralizedDebt Obligations: Structures and Analysis,2nd Ed. Hoboken, NJ: Wiley, 2006.

Mortgage Bankers Association, No Sign of

Housing Market Stabilization, FinancialCommentary, December 14, 2007;http://www.mortgagebankers.org/files/Bulletin/InternalResource/58916_.pdf

Mortgage Bankers Association, Delinquenciesand Foreclosures Increase in Latest MBANational Delinquency Survey, PressRelease, December 6, 2007;http://www.mortgagebankers.org/NewsandMedia/PressCenter/58758.htm

Mason, Joseph R. and Rosner, Joshua. :Where

Did the Risk Go? How Misapplied BondRatings Cause Mortgage Backed Securitiesand Collateralized Debt Obligation MarketDisruptions. Hudson Institute WorkingPaper, May 3, 2007;http://faculty.lebow.drexel.edu/MasonJ/mason_rosner_v8nrl.pdf

McDonald, Daniel J. and Thornton, Daniel L.A Primer on the Mortgage Market andMortgage Finance. Federal Reserve Bankof St. LouisReview, January/February2008, 90(1), pp.31-45.

Poole, William. Reputation and the Non-Prime Mortgage Market. Speech to theSt.Louis Association of Real EstateProfessionals, St.Louis, Missouri, July 20,2007; http://stlouisfed.org/news/speeches/2007/07_20_07.html

RealtyTrac Staff, U.S. Foreclosure ActivityIncreases 75 Percent in 2007, January 29,2008,http://www.realtytrac.com/ContentManagement/pressrelease.aspx?ChannelID=9&ItemID=3988&accnt=64847

Rosenberg, David A. Bidding au revoirto thecredit cycle. Economic Commentary,Merrill Lynch. 30 July 2007


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