Systematic and Liqudity Risk in Sub-prime Mortgage-backed Assets

Systematic and Liqudity Risk in Sub-prime

Mortgage-backed Assets. ∗

Mardi Dungey+ Gerald P. Dwyer# and Thomas Flavin&+CFAP, University of Cambridge and University of Tasmania

#Federal Reserve Bank of Atlanta and University of Carlos III, Madrid& National University of Ireland Maynooth

12 July 2010

Abstract

The subprime mortgage backed securities market declined dramati-cally before and during the Financial Crisis of 2008. To understand thefactors driving its demise we utilise a latent factor model representingcommon effects, asset rating effects, vintage of issuance effects and idio-syncratic effects - extending the recent representation of CDO pricing inLongstaff and Rajan (2008). The common factor is shown to have anincreasing influence on the performance of the ABX-HE indices, with therole of vintage factors changing dramatically from January 2006 to April2009. Consistent with other evidence, risk from systematic factors hastransferred risk to more highly rated tranches of these structured financeproducts. The common shock is found to be related to conditions inthe real estate sector, liquidity and counterparty risk as well as generalfinancial market volatility.

JEL Classification: G12, G01, C32

Keywords: credit crunch, asset backed securities, factor models, Kalmanfilter

1 Introduction

A consensus is emerging that the Financial Crisis of 2007-2008 began with adeterioration in the quality of securities based on subprime mortgages. Falling

∗We are grateful to Belén Nieto and participants at the INFINITI2010 conference andthe Federal Reserve "Day Ahead" conference on Financial Markets 2009 for helpful com-ments. Dwyer thanks the Spanish Ministry of Education and Culture for support of projectSEJ2007-67448/ECON. Any errors are our responsibility. The views expressed here are oursand not necessarily those of the Federal Reserve Bank of Atlanta or the Federal ReserveSystemAuthor contact details: Dungey: [email protected], Dwyer: Dwyer: [email protected], Flavin: [email protected].

real estate prices sparked a period of turmoil in financial markets as participantsbegan to realize the shortcomings of their pricing models. Financial market par-ticipants subsequently had difficulties estimating the values of securities relatingto subprime mortgages and trading associated financial assets. The spread ofthis crisis from a relatively small sector of the financial system across marketsand international borders resulted in widespread financial distress.1 Amongother effects, the banking sector across much of the world suffered huge lossesand a period of serious retrenchment and restructuring. The turbulence andensuing lack of confidence spread to other asset markets and the real economy.Brunnermeier (2009) and Dwyer and Tkac (2009) among others document theevolution and spread of the crisis.

The crisis emerged after a period of unprecedented growth in structured fi-nancial products and the extensive creation of subprime-mortgage asset-backedsecurities. Figure 1 highlights the growth in this sector from 1995 to 2007.2

These products were tranched and rated before being sold to investors in much ofthe world. Among others, DeMarzo (2005) provides a rationale for the issuanceof pooled and tranched securities by informed sellers who enjoy an informationaladvantage regarding the quality of the asset. Although pooling alone may re-duce value, the combination of pooling and tranching, may be value enhancingdue to the transformation of risk through tranching. Furthermore, this effectincreases with the size of the underlying pool of assets. DeMarzo suggests thatasymmetric information is the friction most consistent with the emergence andsuccess of the CDO market. Whatever the underlying reason, as the creation ofCDOs generated profits, there was an increased demand for underlying assetswhich could be included in a pool, a feature most clearly observed in growth inthe market for subprime mortgages. Whether due to CDOs or increased demandfor the related assets by the government-sponsored enterprises Fannie Mae andFreddie Mac, Mian and Sufi (2009) provide strong evidence that less stringentmortgage criteria and increased levels of securitization became increasingly im-portant for subprime mortgages in less affluent geographical areas in the U.S.They also provide evidence consistent with the demand for securitized productscontributing to the growth of such mortgages. Likewise, Benmelech and Dlugosz(2009) show that investor demand was important for the growth of CDOs andsimilar tranched products.

The mis-perception and mis-evaluation of risk in many of these structuredfinancial products has been central to the financial crisis. Some market partici-pants equated the risk of AAA-rated tranches to the risk of AAA-rated corporatebonds and failed to take account of the very different risks of the two assets.Possibly this affected valuations. In addition to possible mispricing, the valu-ation of CDO tranches is particularly problematic in the event of widespreaddefaults (Smithson 2009), a feature not apparent before defaults increased in2007. Valuation models have four key inputs: asset default rates, prepayment

1Dwyer and Tkac (2009) estimate that the subprime mortgages are no more than onepercent of global bond values, stock values and bank deposits.

2Ashcraft and Schuermann (2008) document a range of potential explanantions for therapid expansion of subprime mortgage originations.

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risk, recovery rates and asset default correlations. Problems estimating the lasttwo of these were important aspects of the financial crisis. Default correlationsinevitably are based on historical data, leading to underestimation as the shorttime span available to assess them reflected a period of increasing house pricesand economic expansion. As default correlations increase the probability of ob-serving large-scale defaults affecting senior tranches of CDOs increases and thereare substantial consequences for their prices. Recovery rate estimates were sim-ilarly affected. Consequently, the risk priced in the different CDO tranches wasunder-estimated (Coval, Jurek and Stafford, 2009), and its realization amplifiedthe downward pressure on tranche prices. Brennan, Hein and Poon (2009) andCoval, Jubek and Stafford (2009) analyze the risk inherent in the securitizationprocess and in particular how risk is transferred between tranches in the eventof increasing importance of a large common factor such as falling housing prices.

A consequence of these findings is that a better understanding of the riskfactors underlying these subprime-mortgage backed assets is important for un-derstanding their role in the crisis. The aim of this paper is to characterize thedriving forces behind the spectacular collapse of mortgage asset-backed assetsand analyze the factors associated with the dramatic decreases in the valuesof collateralized debt obligations (CDOs). Our approach extends the empiri-cal model of Longstaff and Rajan (2008). They show how a pricing model forCDOs can be represented as a three factor model, with the factors represent-ing the credit rating of the asset, a global factor and an idiosyncratic factor.Their work is applied to pricing tranches of the CDX index, which is compiledfrom the credit derivatives of 125 single name corporate entities. Using data forthe period October 2003 to October 2005 they estimate that idiosyncratic de-fault risk and common events account for roughly 65% and 8% of the CDX riskpremium respectively. In an application to the more recent period, Bhansali,Gringrich and Longstaff (2008) show the substantial increase in common-eventrisk occurring in the 2007-2008 period.

The application in this paper is to credit derivatives based on subprimemortgages. The subprime mortgage asset backed indices are distinct in theirvintage of issuance as well as other dimensions. Thus, the empirical model isextended to include an additional factor representing vintage effects. The directsplicing of different issuances as in Longstaff and Rajan (2008) is problematicduring this period, particularly during periods of turmoil. Loan-level analysisof subprime mortgages by Demyanyk and Van Hemert (2009) offers support forthe inclusion of a vintage factor. After controlling for a variety of borrower,lender and macroeconomic conditions, they find strong empirical support for agradual and persistent deterioration of loan quality from 2001 to 2007.

The model is applied to returns data for three different asset tranches (AAA,AA and BBB-) of mortgage backed securities using the MarkiT ABX.HE indicesfor three vintages of issuance over the period January 2006 to April 2009. Fenderand Scheicher (2009) estimates the relationship between returns on these indicesand Mizrach (2009) documents their jump behaviour. Our results show thedistinct characteristics of the tranches in terms of the four factors. First, in2006, all factors have a discernible role in the returns of the assets. Second, the

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common factor plays an increasing role over the sample period, where its effecton AAA tranches of various vintages escalates over time. The common factoroverwhelms the role of vintage and ratings factors for all but the equity trancheduring the high-volatility period of July 2007 onward. Third, the higher riskBBB- tranche is affected less by the common factor but shows a great deal ofexposure to the idiosyncratic factor and, in later vintages, both credit ratingand vintage factors. Finally, intermediate tranches display the greatest mixtureof risk exposures, with all of the factors contributing to the variation of returns.

The paper is structured as follows. Section 2 describes the ABX dataand highlights its unique features which are accommodated in our econometricmodel. Section 3 presents the econometric set up and describes our Kalmanfilter approach to estimating the factor model. Section 4 presents and discussesour results, while section 5 contains our concluding remarks.

2 Data

The price declines in asset backed securities during the financial difficulties from2007 to 2009 are dramatic. These declines are partly associated with declinesin the value of the underlying assets, but also seem to represent a significantreassessment of the risks of such assets. We analyze the risk factors inherent inthese tranched pools by examining the relatively new indices of values of CDOsbased on trades of Credit Default Swaps (CDSs) written on mortgage-backedsecurities. These indices, entitled ABX.HE, are produced by MarkiT and werefirst introduced in January 2006. Financial market participants use ABX.HEindexes to track the subprime-mortgage market. Each index is represented byfive different tranches, varying from AAA (best rating) to BBB- (lowest rating).Ratings are based on those produced by both Moody’s and S&P, with the lowerof the two ratings taken when different. Initially, each index is set equal to100 with a subsequent decrease or increase signalling that credit spreads havewidened or tightened. Fender and Scheicher (2008) represent the ‘price’ of theindex as

100 + PV(coupons) - PV(writedowns, shortfalls).

In this representation, deviations from 100 indicate that the coupon paymentsare greater or less than the required compensation for the risk of anticipatedlosses.

Each vintage of the index is based on twenty mortgage-backed CDO dealswith tranches covering all of the credit ratings over the prior six month period,For example, the ABX.HE 06-1 index is constructed from deals underwrittenin the second half of 2005. The issuers are the largest originators.3 There arestrict requirements that must be met by the deals to qualify for inclusion inthe construction of the index. For example, the value of each deal must be at

3Licensed Dealers in the ABX.HE indices include the following: ABN AMRO; Bank ofAmerica; Barclays Capital; Bear Stearns; BNP Paribas; Calyon; Citigroup; Credit Suisse;Deutsche Bank; Goldman Sachs; JPMorgan; Lehman Brothers; Merrill Lynch; Morgan Stan-ley; RBS Greenwich; UBS; and Wachovia.

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Table 1:Correlation coefficients between assets of different credit ratings within

Vintages.

06_1 Vintage 06_2 Vintage 07_1 Vintage 07_2 VintageCorr(AAA,AA) 0.842 0.695 0.644 0.683Corr(AAA,A) 0.547 0.460 0.348 0.454Corr(AAA,BBB) 0.426 0.294 0.312 0.326Corr(AAA,BBB-) 0.443 0.258 0.323 0.273Corr(AA,A) 0.684 0.658 0.580 0.664Corr(AA,BBB) 0.482 0.463 0.436 0.492Corr(AA,BBB-) 0.501 0.407 0.402 0.438Corr(A,BBB) 0.678 0.635 0.538 0.480Corr(A,BBB-) 0.638 0.532 0.492 0.454Corr(BBB,BBB-) 0.852 0.787 0.861 0.824

least $500 million and each tranche must have an average life of between fourand six years, except for the AAA tranche, which must have a weighted averagelife greater than five years. Furthermore, no loan originator can have more thatfour deals included, thus ensuring each index is diversified across issuers.

These indices were ‘rolled’ every six months with indices commencing inJanuary 2006, July 2006, January 2007 and July 2007. There have been nofurther rolls due to an insufficient number of new deals meeting the eligibilityrequirements.4 In common with corporate bond markets, these new rolls ensurethat the indices can reflect the most traded securities recently created. Theseindices are not suitable for splicing between issuances to create a continuousdata series of the most traded securities. Rather each new roll is best viewed asa unique vintage profile with the risk of the reference portfolio of CDS likely tochange between rolls. The set of underlying loans for each vintage reflects mort-gages created in market conditions in the preceding six months and representquite different risks in our time period. The changing coupon rates attachedto each tranche across vintages is evidence of this changing perception of risksupported by subsequent price changes. Table 1 shows the weakening degree ofcomovement of the assets across vintages. These correlations show quite differ-ent relationships between the tranches over time, and they suggest that eachvintage is better viewed as a unique asset rather than the most recent vintagebeing the best indicator of the current value of the same security. Interestingly,the most senior (AAA & AA) and most junior claims (BBB & BBB-) exhibitthe largest levels of comovement.

This paper explicitly analyzes tranches from three of the vintages acrossthree credit ratings. We omit the vintage issued in June 2006 because it behaves

4As of this writing in 2010, there has been very little securitization since 2008.

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Table 2:Summary statistics for assets by Vintage.

Mean Std Dev Min Max Skewness Kurtosis No. obs

Vintage 06-1

AAA -0.00046 0.0088 -0.082 0.076 -1.137 24.426 822

AA -0.00217 0.0175 -0.140 0.115 -1.237 16.157 822

BBB- -0.00391 0.0212 -0.187 0.112 -1.818 13.247 822

Vintage 07-1

AAA -0.00066 0.0106 -0.082 0.076 -0.893 16.071 571

AA -0.00313 0.0209 -0.140 0.115 -0.904 10.343 571

BBB- -0.00563 0.0252 -0.187 0.112 -1.350 8.283 571

Vintage 07-2

AAA -0.00082 0.0120 -0.082 0.076 -0.751 11.928 445

AA -0.00396 0.0236 -0.140 0.116 -0.702 7.446 445

BBB- -0.00650 0.0276 -0.187 0.112 -1.208 6.826 445

similarly to the first vintage and leaving it out reduces dimensionality problemsin our econometric model. The three credit ratings — AAA, AA and BBB- — arechosen to span the spectrum without unnecessarily increasing the dimensionalityof our estimation. We work with daily returns of each series, where returns arecomputed as the difference in log index values. Our analysis covers the periodfrom January 19, 2006 to April 30, 2009. Figure ?? plots the data. Note thatthe data set is unbalanced. Although all vintages exist at the end of the period,the vintages arrive progressively. This feature is captured by the use of thedummy variables in the modelling framework. Table 2 presents some summarystatistics for the index values. Within each vintage, the standard deviation ofreturn is inversely related to the credit rating of the asset. Across vintages,the standard deviation increases with the most recent vintage displaying thehighest volatility. Consistent with most asset return data, the distributions arenegatively skewed with the absolute value of the minimum return greater thanits corresponding maximum. It is noteworthy that within vintages, AAA-ratedtranches exhibit the highest levels of excess kurtosis but kurtosis declines acrossvintages. This may suggest that AAA securities experienced the most seriousrevision in the crisis.

3 Modelling framework for ABX data

Longstaff and Rajan (2008) and Bhansali, Gringrich and Longstaff (2008) treatthe asset backed securities data as a continuous stream from an homogenousasset. In particular, asset backed securities of this type are issued at regulartime intervals, with the intent that there would be a continued market for rolling

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over positions from one contract to others, as well as a continued secondarymarket for older vintages of issue - in this way resembling the on-the-run andoff-the-run bond markets, as opposed to the expiration of a futures contract.They deal with the need for a continuous stream of data to represent prices orreturns in this market by simply splicing the data together at a point in time -in their papers they point this out, and indeed it seems to make little differencein the non-crisis period they cover. However, one of the defining features of theasset backed securities markets during the sample period is a perception thatthe underlying assets were declining in quality. From Figure 2, it is clear thatthe behavior of the price declines in these assets, as the financial difficulties fromJuly 2007 to 2009 unfold, differs for each tranche. Much interesting informationwould be lost by splicing to form a single series for each tranche.

In this paper, we extend the analysis on asset backed securities to exploitinformation on the credit rating of the asset, the common and idiosyncratic char-acteristics as in Longstaff and Rajan (2008) and also incorporate the informationpertaining to the vintage of the issuance. The global, rating and vintage factorsare all expected to be important in dealing with mortgage-backed securities,as these are more susceptible to economic conditions compared to single-namecredit derivatives. The unbalanced nature of our dataset and the explicit dif-ferences in ratings allows us to identify these factors from the characteristics ofthe data rather than applying labels to the factors ex-post.

Extending the framework developed in Dungey, Martin and Pagan (2000)and Dungey and Martin (2007) we propose a latent factor model where, yi,j,trepresents the return, at time t, of an asset-backed security of vintage i (wherethe vintage represents the date of issue of that security) and credit rating j. Thereturns are modelled as a linear combination of responses to shocks common toall assets in the dataset, wt, a vintage factor representing the vintage to which areturn belongs, vi,t, a ratings factor representing the rating of the tranche, kj,t,and idiosyncratic shocks, fi,j,t. This linear model is similar in construct to thatresulting from the theoretical set up in Longstaff and Rajan (2008)5 and can beexpressed as:

yi,j,t = α0 + βi,jwt + θi,jvi,t + ϕi,jkj,t + φi,jfi,j,t. (1)

To capture serial correlation in the data, factors are modelled as autore-gressive processes. We estimate AR(1) processes for the common, ratings andvintage factors. In line with evidence from previous research on factor models(Dungey et al. 2005), we do not try to estimate persistence in the idiosyncratic

5Note that although Longstaff and Rajan (2008) test their three factor model againstreduction to a two or one factor model, they do not consider expansion to further factors.

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shocks. The full specification of the model can be written

wt = ρwwt−1 + ηw,t (2)

vi,t = ρv,ivi,t−1 + ηv,i,t (3)

kj,t = ρk,jkj,t−1 + ηk,j,t (4)

fi,j,t = ηi,j,t (5)

ηm,n,t ∼ N(0, 1) for all m,n (6)

It is clear from the data that the conditional variances of our asset returns varyover time and we account for this feature of the data. Since our model is alreadyheavily parameterized, we cannot accommodate an ARCH specification directlyinto the set up (as in Dungey and Martin, 2007). Instead, we pre-filter thereturns by estimating an IGARCH(1,1) model and use the standardized returnsin the factor model.6

This framework can be conveniently rewritten in state-space form as

Yt = Zαt + Sεt (7)

αt+1 = Υαt +Rut (8)

where Yt is the vector of the returns in each asset, E[εt] = 0, E[εtε′t] = H,E[ut] =0, and E[utu

′t] = Q. The evolving latent factors are contained in the vector αt

and the idiosyncratic factors, fi,j,t are contained in the vector εt. The identity ofthe Kalman filter and the factor model can be seen by the following definitionsof the matrices for the 3 vintages and 3 asset ratings case:

Z =

β1,AAA θ1,AAA 0 0 ϕ1,AAA 0 0β1,AA θ1,AA 0 0 0 ϕ1,AA 0β1,BBB θ1,BBB 0 0 0 0 ϕ1,BBBβ2,AAA 0 θ2,AAA 0 ϕ2,AAA 0 0β2,AA 0 θ2,AA 0 0 ϕ2,AA 0β2,BBB 0 θ2,BBB 0 0 0 ϕ2,BBBβ3,AAA 0 0 θ3,AAA ϕ3,AAA 0 0β3,AA 0 0 θ3,AA 0 ϕ3,AA 0β3,BBB 0 0 θ3,BBB 0 0 ϕ3,BBB

(9)

αt =

wtv1,tv2,tv3,t

kAAA,tkAA,tkBBB,t

. (10)

Defining Υ as a 7×7 diagonal matrix of the autoregressive parameters, ρ = [ρwρv,i ρk,j ] for all i, j, St as a 9× 9 matrix with the parameters φi,j on the main

6Prefiltering the data may result in some inefficiencies in the second stage of estimation.However, the consistency of our estimates is unaffected. We adopt a univariate filteringapproach in common with much of the existing literature, eg Diebold and Nerlove (XXXX).

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diagonal, and R is the appropriately sized identity matrix where the variances ofthe factors are standardized to one the parameters can then be estimated usingthe standard Kalman filter procedure.7 The standard Kalman filter predictionequations are given by

at+1 = Υat|t (11)

Pt|t+1 = ΥPt|tΥ′ + SQS′ (12)

where Pt|t+1 is the prediction vector. The updating equations are given by

at|t = at + PtZ′F−1t vt (13)

Pt|t = Pt − PtZ′F−1t ZP ′t (14)

where

vt = Yt − Zαt (15)

Ft = ZPtZ′ + Z. (16)

Furthermore, we accommodate the unbalanced nature of our data by construct-ing a dummy matrix, Dt, as follows;

Dt =

1 1 0 0 1 0 01 1 0 0 0 1 01 1 0 0 0 0 1d1t 0 d1t 0 d1t 0 0d1t 0 d1t 0 0 d1t 0d1t 0 d1t 0 0 0 d1td2t 0 0 d2t d2t 0 0d2t 0 0 d2t 0 d2t 0d2t 0 0 d2t 0 0 d2t

(17)

where d1t takes the value of 1 from the initiation of the 07-1 vintage onwardsand 0 otherwise and d2t is similarly defined with respect to the vintage 07-2. The Kalman filter equations are then modified by replacing Z with Z ◦ Dt

wherever it appears in the filter with the operator ◦ indicating element-by-element multiplication.

4 Results

Figures 3-5 succinctly summarize the results of estimating the model of theprevious section.8 For each vintage, we present the squared standardized returnsin the first panel and subsequent panels show how much of the movement inthis return is due to a common factor, a vintage factor, a ratings factor and an

7Starting values are obtained from unconditional estimates of the factor model in equation(1) using GMM.

8Parameter values are available from the authors upon request.

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idiosyncratic factor respectively. Thus, in the first column of Figure 3, the toppanel presents the standardized returns. The panels underneath show that inthe early part of the sample the ratings factors was an important contributor tothe returns for this asset, but that from mid-2007 onwards the common factorplays a much larger role. Vintage and Idiosyncratic factors are less importantfor the AAA:06_1 tranche, however, they play a more important role in lowerranked tranches. There is sufficient time variation and volatility in each factorto justify its inclusion in our estimated model. We discuss each of the factorsin turn before delving more deeply into the sources of the common shock.

4.1 The common factor

Looking across the asset vintages in Figures 3 to 5, it is apparent that the roleof the common factor is increasingly important over time. In all cases, the influ-ence of the common factor is negligible during the relatively tranquil conditionsthat characterized the financial system before July 2007. The limited role forthis risk source dictated that asset default correlations remained relatively lowduring this period, consistent with the low credit default spreads demanded forprotection against default of the pooled assets. For example, the spread forthe AAA tranche of the 06-1 vintage was a mere 18 basis points, falling evenfurther to 9 bps for the 07-1 vintage and finally increasing to 76 bps in the lastvintage 07-2. It is plausible that this low realization of the common shock, morethan anything else, contributed to the under-estimation of risk by credit ratingagencies and some market participants. Brennan, Hein and Poon (2009) showthat if investors relied exclusively on credit rating agencies to accurately assesscreditworthiness, this can lead to mispricing of CDO’s (and similar products’)tranches. Classens et al. (2010) argue that many investors actually did relytotally on credit ratings.

As the crisis emerges in mid-2007, the role of the common shock in con-tributing to asset volatility increases noticeably. The pervasive nature of thesystematic downturn affects all assets in the underlying pool and thus heightensthe pairwise correlation of those assets. The results show that the AAA-ratedassets are most vulnerable to common shocks, consistent with the argument ofCoval, Jubek and Stafford (2009) that an amplified common shock effectivelytransfers risk from lower to more senior tranches. From mid-2007 onwards, allother factors are swamped by the common factor in determining the volatility ofthe most senior tranche returns. The other factors are unimportant, suggestingthat all AAA-rated assets increasingly behaved the same without any distin-guishing vintage effects. The increasing levels of comovement in the underlyingpool of assets quickly eroded the buffer protecting the AAA tranche and inrelative terms implies investors in these assets were worst hit by the commonshock.

A number of other studies document a similar pattern for systematic shocksin different asset markets. Eichengreen et al. (2009) use a principal compo-nents analysis on the CDS spreads of 45 international financial institutions anddocument an increasing role for a common factor as the financial crisis evolves,

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with its largest influence in the aftermath of the Lehman collapse. Similarly,Longstaff and Myers (2009) show that a common factor can explain a substantialproportion of bank and CDO equity return variation.

4.2 Ratings and vintage factors

Both the rating and vintage factors exert a time-varying influence on assetreturn variability in the results. At various times in the life of these subprime-mortgage asset backed assets, the specific rating and vintage helped to differ-entiate between assets. For the earliest vintage 06-1, ratings matter and thisfactor accounts for a non-trivial amount of asset return variability. For latervintages, ratings matter little, probably due to the increasing importance of thecommon shock. The vintage factor behaves in a less systematic manner. Itsmost striking role appears in the BBB- rated tranche of the July 2007 vintage,for which it exerts a large influence. Clearly, it is bad news to be a BBB- ratedtranche of a CDO based on tranches of securities based on subprime mortgagesthat is originated in the first half of 2007.

Overall, rating and vintage play a more limited role in determining assetreturns than the common and idiosyncratic factors. There is sufficient evidence,though, to show that they have the potential to affect the asset returns and thatthe time-varying nature of their effects is captured by our modelling approach.These two factors are more important during a non-crisis period such as theearly part of the period covered by our data, but their role from July 2007 onis superseded by the systematic shock.

4.3 The idiosyncratic factor

Just as the common factor exerted the greatest influence upon the most seniorclaim, idiosyncratic shocks have their greatest effect on the other end of therating spectrum. In the earliest vintage, idiosyncratic risk exclusively affects theBBB- rated tranche. Idiosyncratic shocks held little danger for holders of moresenior claims of this vintage as the BBB- and equity tranches absorbed them. Inlater vintages, there is a greater role for idiosyncratic shocks as other mezzaninetranches also exhibit some vulnerability to it. In this case the equity buffer isobviously not sufficient to prevent losses from moving into higher rated tranches.Finally, in the vintage initiated at almost the same time as the escalation of asubprime mess into the beginnings of a full-scale financial crisis, the effects ofidiosyncratic risk are quite disparate and much less than on earlier CDO deals.Again this probably reflects the all consuming nature of the common shockwhich left little scope for the idiosyncratic risk influence. It may also reflectthat prices for the BBB- tranche flattened out due to little trading volume bythis time, and such ‘stale prices’ are known to dampen asset volatility (see, Ahnet al., 2002).

The behavior of the idiosyncratic shock is consistent with the argumentsoutlined earlier. In normal market conditions, when assets in the underlyingpool exhibited relatively low correlation, idiosyncratic risk resulted in a few

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random subprime mortgage defaults whose effects were absorbed by the equitytranche or other lower rated tranches. The onset of the crisis in mid-2007 ledto this risk source being swamped by the common shock, limiting its impact onasset return volatility.

4.4 What drives the factors?

Although latent factors extract both observed and unobserved sources of com-monality across the assets, it can be informative to examine how the factorscorrelate with a number of observed variables which are widely accepted asbeing associated with and affected by the financial turmoil. The relationshipswith observed variables may shed light on the driving forces behind the factors,while simultaneously indicating the extent to which unobserved forces, such aschanges in investor perception and re-assessment of the actual nature and riskof the CDO tranches, influenced the observed outcomes. We extract the optimalset of generated factors following the methods of Dungey and Martin (2007).These are then filtered to reduce noise and pick up the long-run trend in theprocess.9 The extracted factors are presented in Figure 6.

Initially, we focus on the common component. Section 3 showed that thecommon factor played a a major part in the increasing risk profile of the mostsenior tranches of subprime mortgage backed assets. Since AAA tranches are themajority of many CDOs, we examine the main drivers of this risk source.10 Thecommon factor exhibits a substantial increase in volatility across the sample.This reflects the onset and deepening of the crisis and deterioration of the creditquality of mortgages as housing prices fell. For example, the mortgage poolunderlying the 07-2 indices was likely to fall into negative equity sooner thanearlier originated mortgages, which had benefited from the run up in real estateprices throughout 2006.

Feasible observable economic variables which may have contributed to thedeteroiration of these derivative markets are proxies for real estate prices, liq-uidity risk, counterparty risk and general financial market volatility. We use adaily price index for the U.S. real estate sector to reflect news about housingprices. Liquidity and counterparty default risk are measured by two 3-monthinterest rate spreads: the spread between the London Interbank Borrowing Rate(LIBOR) and the overnight indexed swap rate (OIS); and the spread betweenthe OIS rate and the U.S. Treasury Bill rate. The LIBOR-OIS spread can beviewed as representing counterparty risk from the standpoint of a lender toanother institution. This spread also can be viewed as representing liquidityfrom the perspective of borrowers who believe they are not risky counterpar-ties. The TED spread - the spread between LIBOR and the Treasury Bill rate

9The filtering technique reported here is to compute weekly averages of the daily observa-tions. However, our results and conclusions are robust to various other filtering techniques,such as the HP filter, 10- and 20-day moving averages etc.

10For example, Hu (2007) reports that for CDOs issued in 2006, AAA-rated assets accountedfor 85% of dollar value and 36% of the number of tranches, while the figures for Baa and lowerrated assets were 3.7% and 24% respectively. Many deals had more than one AAA tranche.The ABX index is based on the most subordinate AAA tranche.

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Table 3:Correlation coefficients and R-squared statistics for extracted and filtered

factors with observed variables.

factor Libor-OIS OIS-Tbill VIX REIT ∆REITPanel A: Correlationscommon wt -0.1916 -0.1004 -0.2149 0.1530 0.3625vint 06-1 v06−1,t 0.0544 -0.0106 0.0163 -0.0279 -0.0114vint 07-1 v07−1,t 0.1610 0.1483 0.2078 -0.1566 -0.1443vint 07-2 v07−2,t -0.1690 -0.2399 -0.2265 0.2550 0.0606AAA rated kAAA,t -0.0984 -0.0900 -0.0932 0.0649 0.0598AA rated kAA,t -0.0419 0.0118 -0.0061 0.0302 0.0437BBB rated kBBB,t -0.0379 0.0295 0.0007 -0.1266 -0.0342Panel B: R-squared statisticscommon wt 0.037 0.010 0.046 0.023 0.159vint 06-1 v06−1,t 0.003 0.000 0.000 0.001 0.000vint 07-1 v07−1,t 0.026 0.022 0.043 0.025 0.011vint 07-2 v07−2,t 0.029 0.057 0.051 0.065 0.006AAA rated kAAA,t 0.010 0.008 0.009 0.004 0.005AA rated kAA,t 0.002 0.000 0.000 0.001 0.006BBB rated kBBB,t 0.002 0.000 0.000 0.016 0.001

- is the other common measure of liquidity and counterparty risk and would bepartly redundant with the inclusion of the LIBOR-OIS spread. Instead of theTED spread, we include the spread between OIS and the Treasury Bill rate,thus excluding the section already represented by LIBOR-OIS. The spread be-tween OIS and the Treasury Bill rate is the spread that is the clearest possibleindicator of liquidity issues because the OIS rate is the rate for almost fullycollateralized private transactions and the Treasury Bill rate is a nominal riskfree rate. General financial market volatility is measured by the VIX index. TheVIX index is a forward-looking variable which reflects the expectations of stockmarket volatility over the next 30 days. Figure 7 presents the observed factorsemployed in our analysis.

The correlation coefficients for each of the factors with the observed variablesand the R-squared statistics from univariate regressions are reported in Table3.11

Among all the extracted factors, the strongest bivariate correlations observedare between the common factor and the observed variables. Strong correlationsare observed with both the level of the REIT, which represents the underlyingasset for the ABX data (approximately 15%) and with the rate of change the

11The strong correlations between all these indices effectively prohibits a meaningful mul-tivariate regression analysis of these relationships.

13

REIT (i.e. REIT returns) at 36%. Thus, the strongest influence on the com-mon factor stems from the underlying asset for the subprime mortgage backedsecurities. In fact, the R-squared statistics in panel B of Table 3 show thatonly REIT returns have any economic significance in their relationship with thecommon factor.

Figure 8 shows the fitted values of the univariate regressions between thecommon factor and the potential explanators, and reinforces that the REITand particularly REIT returns have the major role. The common factor is alsocorrelated with the VIX, at 21%, suggesting a reflection of the general increasein financial turmoil through out the period. Both counterparty and liquidityrisk are reflected in the common factor with around 20% correlations with eachof the interest rate spreads. While each of these observed variables is somewhatcorrelated with the common factor, there is substantially more to be explained.The latent factor is picking up other (possible unobservable) common influencessuch as changes in investor perception of asset quality, reassessment of the riskof these assets, as well as potentially changing weights on different variablesover time. This latter points particularly to the lack of success of fixed weightregression analysis in this arena.

A similar analysis is applied to the vintage factors, which as they are or-thogonal to the common factor, pick up factors common to particular vintagesadditional to the overall common effects. The vintage factors show a wide rangeof correlation behaviour with the observable variables. For example, the 06-1vintage exhibits very little correlation with the observed variables and conse-quently they have little explanatory power for the factor behavior. Interestingly,the degree of correlation with, and the explanatory power of, the observed vari-ables increases with the vintage. This suggests that the tranches of later vintageshave more common features than the earliest vintage. All of the observed vari-ables exert an ‘excess’ influence on the return behavior of these later-initiatedassets. In particular, the REIT index is important, consistent with the argu-ment that the underlying pool of mortgages was of changing quality over time.Likewise, tightening in liquidity, increasing counterparty risk and the expec-tation of persistent financial market volatility impact upon these assets. Themain conclusion drawn from this analysis is that both observed and unobserveddrivers imply that the vintages issued in 2007 were of poorer quality and morerisky than the issue of 2006.

Finally, we focus on the ratings factors. The results show little or no ‘ex-cess’ influence on the different tranches across vintages over and above thatcaptured by the common factor. All ratings factors exhibit low correlationwith the observable assets. This is consistent with the idea that the commonshock blurred the boundaries between different asset tranches, with commonrisk sources across all ratings.

In summary, the common shock incorporates both observed factors, such asconditions in the underlying real estate market; general financial market volatil-ity; and liquidity and counterparty risk in credit derivative markets. However,there is also a major component of the common factor attributable to other,potentially unobservable, factors including changes in the attitude of investors

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to subprime mortgage backed assets. The re-evaluation of these CDO instru-ments is an important feature of the return generating process, and its progressis evident in the factors. In general, the common factor subsumes all othersand we find little differentiation by rating. All assets of a similar rating ex-hibit little excess reaction to the observable variables. Vintage factors mattermore. These differentiate the issuances of assets and indicate that later vin-tages exhibit increased sensitivity to the level of real estate prices, volatilityand liquidity. None of the factors have high correlation with the observed vari-ables, which demonstrates the difficulty of attributing the common changes inasset behaviour to individual observed indicators. The situation displays farmore complexity than simple observed variables can replicate - and latent fac-tors which can take into account observed and unobserved influences as wellas potentially changing weights on those components provide a uesful means ofapproaching this decomposition.

5 Conclusion

Our analysis focuses on the characterization of indices of subprime mortgagebacked assets during the unfolding of the Financial Crisis of 2007-2008. In par-ticular, we seek to gain a better understanding of the sources of the declineof this market, for example via liquidity and counterparty risk. To do so, weapply a latent factor model to an unbalanced panel of tranched asset returns. Inthis case, the unbalanced nature of the data allows identification of four factorsfrom the returns; a common factor, vintage factor relating to the issuance of theasset, a credit ratings factor and an idiosyncratic factor. All factors exert a time-varying influence on the volatility of asset returns. The factor common to alltranches and vintages of indices exhibits the most important change in variationover time. Before July 2007, the common factor’s influence is negligible. This isconsistent with market participants underpricing, and credit agencies underes-timating, the coming financial difficulties. (This of course is easier to see now.)Given the structure of CDOs, the most senior tranches are quite vulnerable tothe miscalculation of asset risk. The increasing magnitude of common undi-versifiable shocks changes the return behavior of AAA tranches dramaticallyas the crisis unfolds. In addition, the demarcation between tranches becomesblurred as assets within the underlying pool becoming increasingly correlated.Consequently, it is the common shock that is most closely associated with themain damage to the values of CDOs. As suggested by Coval, Jubek and Stafford(2009), the securitization process led to more vulnerability to common risk thathad been unimportant during the low volatility environment before 2007, butcame to the fore with a vengeance during the subsequent downturn. At theother end of the spectrum, the role of idiosyncratic shocks in determining as-set returns is predominantly associated with the lowest rated tranche, but eventhere is largely overwhelmed by the common factor after July 2007. Similarly,in the earlier tranquil market conditions, both the ratings and vintage factorsare important for some tranches but again their influence is dwarfed by the

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common factor during the financial crisis.Given its prevalence and its effects on the largest segment of the market,

the AAA-rated tranches, we delve deeper into the origins of the common shock.Specifically, we relate the extracted common shock to a range of observable vari-ables that are commonly cited as being crucial in the initiation and transmissionof the crisis. Variables that capture the real estate downturn, general financialmarket volatility, market liquidity shortages and increasing counterparty risk areall related to the common factor responsible for the downturn in asset backedsecurity performance. However, our latent factor approach captures two impor-tant features of the crisis. Firstly, the relationship with ‘fundamental’ factorsis likely to be time-varying and secondly, unobserved sources of commonality,such as changes in investor perception of risk and appetite for these assets, werealso important determinants of the demise of this market.

Further analysis of our latent factors reveals an important characteristic ofCDOs. The structured product is only as good as the quality of the underlyingasset. While the ratings factors are largely unaffected by our observed variables(in excess of that captured by the common shock), the vintage factors serve asan important source of asset differentiation. As the quality of the underlyingasset deteriorated (through conditions in the real estate sector and less strin-gent underwriting standards), the vintage factor becomes more correlated withobservables implying an excess influence over and above the common factor.

References

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[2] Ashcraft, A., Schuermann, T., 2008. Understanding the securitization ofsubprime mortgage credit, Federal Reserve Bank of New York staff reportno. 318.

[3] Benmelech, E., Dlugosz, J., 2009. The alchemy of CDO credit ratings,Journal of Monetary Economics, 56 (5), 617-634.

[4] Bhansali, V., Gingrich, R., Longstaff, F., 2008. Systemic credit risk: what isthe market telling us?, manuscript, University of California at Los Angeles.

[5] Brennan, M.J., Hein, J., Poon, S., 2009. Tranching and Rating, EuropeanFinancial Management, 15 (5), 891-922.

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[8] Classens, S., Dell’Ariccia, G., Igan, D., Laeven, L., 2010. Lessons and policyimplications from the global financial crisis, International Monetary Fundworking paper, WP/10/44.

[9] Coval, J., Jubek, J., Stafford, E., 2009. The Economics of Structured Fi-nance. Journal of Economic Perspectives, 23 (1), 3-25.

[10] DeMarzo, P., 2005. The pooling and tranching of securities: a model ofinformed intermediation, Review of Financial Studies, 18, 1-35.

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[13] Dungey, M., Pagan, A., Martin V., 2000. A Multivariate Latent FactorDecomposition of International Bond Yield Spreads. Journal of AppliedEconometrics, 15, 697-715.

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[15] Eichengreen, B., Mody, A., Nedeljkovic, M., Sarno, L., 2009. How the sub-prime crisis went global: evidence from bank credit default swap spreads.National Bureau of Economic Research working paper no. 14904.

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[17] Fender, I., Scheicher, M., 2009. The pricing of subprime mortgage risk ingood times and bad: evidence from the ABX.HE indices. Applied FinancialEconomics, 19, 1925-1945.

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6 Appendix: Details on Data Series

The data series used in this paper are described below:ABX Data:

• ABX.HE-A 06-1: 0.54% Coupon Closing Price, RED ID: 0A08AFAA7

• ABX.HE-A 07-1: 0.64% Coupon Closing Price, RED ID: 0A08AFAC0

• ABX.HE-A 07-2: 3.69% Coupon Closing Price, RED ID: 0A08AFAD8

• ABX.HE-AAA 06-1: 0.18% Coupon Closing Price, RED ID:0A08AHAA1

• ABX.HE-AAA 07-1: 0.09% Coupon Closing Price, RED ID:0A08AHAC6

• ABX.HE-AAA 07-2: 0.76% Coupon Closing Price, RED ID:0A08AHAD4

• ABX.HE-BBB 06-1: 1.54% Coupon Closing Price, RED ID:0A08AIAB6

• ABX.HE-BBB 07-1: 2.24% Coupon Closing Price, RED ID: 0A08AIAC4

• ABX.HE-BBB 07-2: 5.00% Coupon Closing Price, RED ID: 0A08AIAD2

Other series:

• US Real estate sector price index - Datastream code: DJAREIT

• VIX: CBOE Market volatility index

• Interest rates: 3-month LIBOR; OIS rate and 3-month Treasury bill rate

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Figure 3. Results for ABX indices originated in Jan 06AAA:06_1 AA:06_1 BBB:06_1

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Figure 4. Results for ABX indices originated in Jan 07AAA:07_1 AA:07_1 BBB:07_1

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Figure 5. Results for ABX indices originated in July 07AAA:07_2 AA:07_2 BBB:07_2

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Filtered FactorsCommo n F actor

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D J F M A

2006 2007 2008

-4

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06-1 Vin tag e Factor


2006 2007 2008

-4

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2006 2007 2008

-4

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AAA-rated Facto r

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D J

2006 2007 2008

-1.5

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AA-rated F acto r


2006 2007 2008

-3

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BBB-rated Facto r


2006 2007 2008

-4

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Figure 1:

Observable variables3-month Libor-OIS spread


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3-month O IS-Tbill Spread


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Figure 2:

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Fitted Values v Common Factor for all observablesLibor-OIS Spread


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OIS-Tbill Spread


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Log VIX


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Log REIT


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Figure 3:

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Systematic and Liqudity Risk in Sub-prime Mortgage-backed Assets

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