THE ROLE OF CORRELATION IN THE CURRENT CREDIT RATINGS SQUEEZE. Eva Porras

Transcription

1 THE ROLE OF CORRELATION IN THE CURRENT CREDIT RATINGS SQUEEZE Eva Porras IE Business School Profesora de Finanzas C/Castellón de la Plana Madrid Esaña Abstract A current matter of reoccuation is the financial crisis in the US, a nd Euroe. This event is the consequence of a l arge number of credit rating downgrades in AAA structures of mortga ges that have affected the US real estate industry since March 007. This a er focuses on one as ect of credit risk analysis: the imor tance of de fault correlation in me asuring credit risk in subrime ortfolios as a k ey variable in the cu rrent financial crisis. We show emirically how different estimates of such correlation coefficient imact the sigmas of the ortfolio of assets significantly. We roose three reasons to exlain the underestimation of these coefficients in the ast. This aer suorts the idea that bet ter understanding of the correlations imlied wit hin subrime loan ortf olios would hel rating comanies, lenders, and regulators imrove their evaluation of default risks. Keywords Credit risk, subrime, correlation, structured finance

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3 1. Introduction During the last few months, a toic of discussion in the financial ress has been the subrime mortgage financial crisis, which has yet to be resolved. The crisis develoed subsequent to an unrecedented increase in the number of foreclosures in the subrime mortgage market. As doubts about the extent of the crises began to mount, market articiants concerns sread rovoking a downfall in the stock rices of comanies within the subrime mortgage industry, and some large lenders. The subsequent flight to safety resulted in additional liquidity concerns. At the eak of the crises, several large subrime mortgage lenders shut down or filed for bankrutcy, and a number of hedge funds become worthless i. Originally, the crisis affected the US market. Nevertheless, by May 007, worries over the exosures to US mortgages affected financial markets worldwide, and by July the crisis had turned global ii. The relevance of the crises triggered by subrime loan lending is better understood when the size of this industry and its interrelations with other sectors of the economy are made clear. As of March, 007, there were $6.5 trillion mortgage backed securities in the U.S., of which 0% were subrime. Between July and Setember of the same year, almost half a million U.S. homes were facing some kind of foreclosure activity, and by October, 16% of the subrime loans with adjustable rate mortgages (ARM) were 90-days into default or in foreclosure roceedings iii. Structural and circumstantial reasons have been roosed to exlain the shar increase in the number of foreclosures, and the turmoil ignited around it. Even though the crisis is not over and information is still being analyzed, there seems to be consensus in that rising interest rates, together with a downturn in roerty values, originated the crises (Jorion, 007). Nevertheless, in addition, a number of ractices, organizations, and institutions have also been blamed for their contribution to the deth and width of the crisis, most notably: redatory lending ractices of subrime lenders and discrimination on the basis of race iv, mortgage brokers encouraging borrowers to take loans they could not afford, the increase in the number of subrime mortgages issued by lenders, araisers with inflated housing values, borrowers over-stating their incomes and entering into loan agreements they could not fulfil, the offer of adjustable interest rates and deals with low rates that increased sharly after the initial eriod or ayment otion loans, Wall Street investors backing u subrime mortgage securities without verifying the strength of the ortfolios, rating agencies for either not valuing the risks correctly or not being alert to introduce modifications in their recommendations early enough, and lack of effective government oversight v. This aer focuses on the relevance of default correlations as a key variable in this crisis. In our analysis, we use the findings of authors such as Cowan and Cowan (004), Carey (000), Gordy (000), and Jorion (007) among others, to roose that additional attention should be aid in measuring default correlations within subrime loan ortfolios, since these behave in ways that differ from those reorted for rime and commercial bonds and loans. This aer strongly suorts the idea that imroved understanding of the correlations imlied within subrime loan ortfolios would hel rating comanies, lenders, and regulators imrove their evaluation of default risks. 1

4 Background Subrime lending Subrime lending refers to the credit status of the loan borrower. Even though there is no official definition that describes a subrime borrower, in 001 the U.S. Deartment of Treasury issued the following guideline: "Subrime borrowers tyically have weakened credit histories that include ayment delinquencies, and ossibly more severe roblems such as charge-offs, judgments, and bankrutcies. They may also dislay reduced reayment caacity as measured by credit scores, debt-to-income ratios, or other criteria that may encomass borrowers with incomlete credit histories. vi Therefore, subrime denotes the troubled credit status of the loan borrower. Since these subrime loans have a higher default rate than those within the rime category, these borrowers are considered higher risk. Consequently, subrime lending alies to a series of credit instruments, such as credit cards, car loans, and mortgages available to a tye of borrower that has no access to the general credit market. Because of this risk, a subrime loan is offered at a rate higher than A-aer loans. Although numerous variables are considered to qualify a loan as subrime, in the United Stated the regulatory benchmark credit score Fair Isaac Cororation (FICO) for subrime is 660, and most eole within this credit class have a score under 60 vii. The FICO credit score is assigned at the time of origination based on an analysis of a erson's credit record. This score reresents the likelihood of default, and it is used to decide if and how a erson qualifies for a loan viii. In addition, along with the credit score, to determine the mortgage rate and credit limit, lenders consider the loan to value ratio ix. Current income and emloyment history do not influence the FICO score, but they are weighed when alying for credit (Chomsiseghet and Pennington-Cross, 006). Subrime mortgage loans are a subset of the subrime loan industry x. As such, these mortgages are granted to borrowers unable to qualify under more severe criteria. Subrime mortgage loans have a much higher rate of default than rime mortgage loans, and are riced based on the risk assumed by the lender. There are different kinds of subrime mortgages, including: interest-only mortgages; ick a ayment loans; fixed rate mortgage; negative amortization mortgage; balloon ayment mortgage; and adjustable rate mortgages (ARM). All adjustable rates transfer art of the interest rate risk from the lender to the borrower: the borrower benefits if the interest rate falls and loses out if interest rates rise. xi Securitization and Risks As it has been mentioned, ARMs generally ermit borrowers to lower their ayments in exchange for acceting the risk of interest rate changes, which is then transferred from the mortgage issuer to the holder. Another way in which mortgage originators control risk, is by selling or securitizing their mortgages. Securitization is a structured finance rocess in which certain assets are acquired, groued into sets, and offered as collateral for third-arty investment. Therefore, securitization involves the selling of financial instruments that are backed by the cash flow or value of the

5 underlying assets. Investors "buy" these assets by making loans. To reduce the risk of bankrutcy and obtain lower interest rates from otential lenders, securitization utilizes a secial urose vehicle (SPV). In the real estate industry, securitization is alied to ools of leased roerty, and in the lending industry, it is alied to lenders' claims on mortgages, home equity loans, student loans, and other debts xii. Tranching xiii allows the cash flow from the underlying asset to be diverted to the various investor grous. Therefore, this is the mechanism used to generate different investment classes for the securities created in the structured finance world. The addition of all the tranches together make u the deal's caital or liability structure. Tranches with a first claim on the assets are "senior tranches", the safer investments. Tranches with either a second lien or unsecured are the "junior notes". Most often, the more senior rated tranches have higher ratings than the lower rated tranches. However, ratings can fluctuate after the debt is issued, and even senior tranches could be rated below investment grade. Tranches are generally aid sequentially from the most senior to most subordinate, although certain tranches with the same security may be aid at the same time. The following (see Grah 1 below) is a simlified examle of how a tyical securitization transaction and tranching works with mortgage backed securities (MBS) as the underlying collateral. Introduce Grah 1 A bank negotiates hundreds of subrime mortgages with different customers. The bank transfers the risk of the loan ortfolio by entering into a default swa with a "ring-fenced" SPV. These mortgages are groued together in, for examle, one $50 million dollar bucket to create an MBS. Several of these MBS are ooled together adding u to, let us say, one billion. The one billion dollar asset back security ot is sliced into different tranches. The SPV sells the tranches of credit linked notes with the waterfall structure as in examle rovided in Table 1: Introduce Table 1 The equity investors absorb the first loss u to ten ercent of the value of the ortfolio: out of one hundred equal value mortgages, the first ten that fail. Mezzanine will accet the next losses from ten to forty ercent, and senior debt looses only if failures are larger than forty ercent. The tranches which absorb the first losses are sold to investors who desire greater returns, while tranche A is destined to investors who are looking for more secured investments. In summary, through securitization the rights to these mortgage ayments have been reackaged into investment securities, such as mortgage-backed securities (MBS) or collateralized debt obligations (CDO). Due to tranching, some of the securities created have a rating higher than the average rating of the underlying collateral asset ool. Therefore, the most senior claims are exected to be insulated from the default risk of the underlying asset ool through the absortion of losses by the more junior claims. That is, a set of bonds with a 3

6 much lower robability of total default are created. In our examle, 40% of the mortgages would need to default before the senior claims would feel any adverse effects. Although tranching is very useful for the urose of sreading risks, some of its more roblematic side effects have surfaced during the current subrime meltdown. These outcomes are the consequence of the intricacies of evaluating the distribution of losses under every likely state of affairs, as well as the challenge of valuing the risks entrenched in the high-yield debt, and MBS backing the roducts. This is articularly the case in times when the market value of the underlying assets is decreasing. In many instances, when the asset value is reduced the CDO is asked to liquidate the collateral, further deressing its value, and creating a downward siral in rice deression. Furthermore, the volatility in the value of the collateral linked to the subrime mortgage loans, affects the ability of comanies to issue aer. As a result, the interest rates charged by investors increase. In short, innovations in securitization sread widely the risks related to the inability or unwillingness of homeowners to make their mortgage ayments. Stating the roblem: trenching and the correlation coefficient The focus of this aer is the imortance of default correlation estimations in measuring credit risk in subrime ortfolios. Default correlation, defined by Nagal and Bahar (001) as the relationshi between default robabilities and joint default robabilities, is a measure of the deendence among risks. Therefore, it is a key variable in the evaluation of the credit loss distribution, and a necessary inut in the assessment of the value of the ortfolio at risk due to credit. The risk of the ortfolio, and the caital needed to manage that risk, will be underestimated if the effect of shocks to the ortfolio through correlation are ignored (Gordy, 000) (Carey, 000). In general, the notion of default correlation considers that common underlying factors, such as macroeconomic or geograhically secific events, cause the default events to cluster (Calem and LaCour-Little, 001). Based on observations of historical rates of default, Nagal and Bahar (001) reort that credit events are correlated. In the case of subrime lending, Davis and Pennington (007) find that increases in home values and local market conditions are significant redictors of default. In reference to commercial ortfolios, numerous studies show that as the credit quality of the ortfolio declines, default correlation becomes more relevant. Among others, Zhou (1997) finds that imlied default correlations which are close to zero in the case of highly rated firms, become much larger for firms with lower ratings. Along the same lines, Lucas et al. (001) results show that for a given correlation, a better quality ortfolio reduces extreme credit loss quantiles. Lastly, Loffler (003) reorts that, for uncertainty in the 1% value-at-risk, correlation uncertainty for lower quality ortfolios is more significant than for better rated ortfolios. With regards to subrime lending, Cowan and Cowan (004) also find that default correlation increases as the internal ratings of the lender decline. In addition, they conclude the subrime sector shows larger default correlations than commercial bonds and loans ortfolios. 4

7 Furthermore, during a recent conference, Jorion (007) defended that deal breaks are deendent, articularly in falling markets, suorting the idea that ortfolio risk deends heavily in correlations. In summary, the common findings of these authors reinforce the idea that underestimating default correlations results in greater model risk. Several methodologies have been used to estimate default correlations within ortfolios. For examle, using Merton s (1974) assumtion that default can take lace at a single moment in time, one can emloy the firms liability structures, asset values, and variance/covariance matrices, to find an analytical solution for correlation. First-assage-time models of default risk eliminate this assumtion. Using this aroach, Loffler (003) estimated default correlations based on the joint distribution of asset values, while Crouhy et al. (000) utilized equity rices. Default risk has also been estimated using Monte Carlo simulation. Lastly, some authors such as Cowan and Cowan (004) use historical default volatilities to determine default correlations. In this case, their estimations deend on two assumtions: that all loans within a risk class have identical default rates, and that internal credit ratings are consistent. Until recently though, correlation between different chunks of debt was thought to be small. The reason was that the underlying risks were assumed to be idiosyncratic, and the likelihood of numerous comanies defaulting at the same time was believed to be insignificant. However, during this ast crisis the observed large rice swings, and the significant downgrades in AAA structures of the mortgages and their effect in the quality of the debt, have been interreted as investors becoming more fearful of systemic risk due to rice correlation within the CDO market, the otential rise in default correlation, and asset correlation (Fender and Hördahl, 007). In the case of our current crisis, the underlying factors might have been the downturn in the value of the real estate roerties used as loan collateral, and the increasing interest rates. How does subrime lending and mortgages lay into the current crises? What factors differentiate this crisis from those of 1987 and 1998? Given that the downturn in the real estate market and the raising interest rates have been roosed to exlain the crises, in reading the descrition of events at the beginning of the aer, one has to consider the interaction between the real estate market and the subrime industry, and how news feedback into the market. Could there be a relationshi between these events and the observation that the correlation coefficient among trades of ools of credit derivatives has been moving in unusual ways xiv? The correlation coefficient shows the strength and direction of a linear relationshi between variables. If the variables are indeendent, the correlation is 0. The oosite is not true, since the correlation coefficient only recognizes linear deendencies between two variables. The correlation is 1 in the case of an increasing linear relationshi, 1 in the case of a decreasing linear relationshi, and some value in between in all other cases. The interretation of this coefficient deends on the context, but the closer it is to either 1 or 1, the stronger the correlation between the variables. 5

8 We define the correlation coefficient ρ xy, between two random variables X and Y with exected (mean) values µ x and µ y, and standard deviations x and y as: ρ xy, cov( XY, ) E(( X µ x)( Y µ y)) = = X Y X Y Where E is the exected value oerator and cov means covariance. The Pearson coefficient defined below is the best estimate of the correlation of X and Y if X and Y are both normally distributed when using data from a samle: r xy = ( x x)( y y) i ( n 1) s s x i y Where we have a series of n measurements of X and Y written as x i and y i with i = 1,,..., n, x and y are the samle means of X and Y, s x and s y are the samle standard deviations of X and Y, and the sum is from i = 1 to n. How likely is senior to exerience a loss? What from a risk management oint of view might inform us of the reasons for the significant downgrades in AAA structures of mortgages? In our discussion about securitization, we mentioned that by ooling many mortgages with similar default robabilities a bond with lower robability of total default could be created. However, one has to consider that the mortgage loan ortfolio s volatility is a function of the correlation coefficient of the assets that make u the ortfolio. We define the standard deviation of a ortfolio ( ) as: = where the variance is = i jww i j i jρ ij and w = the weights of the total wealth invested in each asset ρ = the correlation coefficient between the assets For examle, a three asset ortfolio, the variance is: = w A A + w B B + w C C + w A w B ρ AB A B + w A w C ρ AC A C + w B w C ρ BC B C The number of covariance terms (ρ AC A C ) that need to be comuted as the number of assets nn ( 1) in the ortfolio increases is equal to: 6

9 Let us say we have a ortfolio of two mortgages, A and B. Both have a standard deviation () of 10, and 50% of our funds are invested in each mortgage (w = 0.50). If the correlation coefficient (ρ) is 1, then the standard deviation of the ortfolio ( ) is: = w + w + w w ρ = A A B B A B AB A B *0.5*0.5*1*10*10 = 10 On the other hand, if the correlation coefficient (ρ) is 0, then the standard deviation of the ortfolio ( ) is: = w + w + w w ρ = A A B B A B AB A B *0.5*0.5*0*10*10 = 7.07 Let us say we have a ortfolio with one hundred mortgages. Every individual mortgage has a standard deviation () of 10, and an equal roortion of our funds are invested in each of them. If the correlation coefficient (ρ) among those mortgages is 1, then the standard deviation of the ortfolio ( ) is: ortfolio = = (1/100) 100*100 + * * *1*10*10* 4950 = nn ( 1) Where 4950 is the covariance term calculated as:, and n is the number of assets in the ortfolio. Other things equal, but with a correlation coefficient (ρ) among those mortgages of zero, the standard deviation of the ortfolio ( ) is reduced to: = + = ( ) *100*100 * * *0*10*10* Therefore, if each mortgage within the ortfolio has the same standard deviation (), and there is erfect correlation among the underlying assets, the standard deviation of the ortfolio is equal to the standard deviation of each of the mortgages. No diversification of risk has been achieved: the standard deviation is the same as if there was just one asset in the ortfolio, and default on one mortgage is the same as default on all. On the other hand, if the underlying assets are comletely uncorrelated, then the standard deviation of the ortfolio would equal ( ). That is, if we were to have one hundred n 7

10 mortgages that haened to hold a correlation coefficient of zero, the standard deviation of the ortfolio ortfolio =. In this case, the standard deviation is 10 times smaller than if 10 correlated ( ). Therefore, if the assets are uncorrelated, there is virtually no chance of n default (see Table A in the Aendix for comlete results). In summary, the critical factor is not the number of assets within the ortfolio er se, but the correlation coefficient among the assets. Thus, correlation is the key element in estimating the likelihood of loss in senior trade. At this oint, at least two questions come to mind: why is the correlation a key factor, articularly in subrime MBSs? What could exlain the underestimation of the standard deviations of these ortfolios? Let us recall that the structured financial transactions related to the subrime mortgage industry we have been revising, can be viewed as a number of small loans of a similar tye ackaged together into a series of "buckets", which are then sliced into "tranches". During our descrition of the crisis, one recurrent event that fed back into the roblem was the market volatility as suggested by large rice swings with sreads. Since the interest rate of each tranche is a function of the credit rating originally assigned by the credit rating comany (CRA), CRAs have been blamed for contributing to the deth of the crises due to errors of judgement and/or slow resonse to changing conditions. Such criticisms intensified in the wake of large losses in the CDO market desite the roducts to ratings. Particularly, in the cases of AAA roducts, which in many instances were subsequently downgraded or defaulted xv. Given these considerations, at least three reasons can be roosed to exlain these facts. First of all, standard deviations and correlation coefficients are estimated with historical data. If the recent rior exerience is of a rising housing market, the use of a historical data from revious eriods to calculate standard deviations may result in a number that is inadequate in a cycle of decreasing housing values. The reason is that in a booming housing market, equity is created by the homeowners and the willingness or need to default under those circumstances is ameliorated. On the other hand, in a decreasing value cycle, equity is being destroyed and a larger number of homeowners could be erceived as being more willing to default. This is consistent with Danis and Pennington-Cross (007) observations, and Jorion s (007) comments. A second motive correlation coefficients among subrime mortgages could be underestimated is that, unlike with traditional rime rated mortgages which use income and assets as collateral, subrime mortgages are only asset rice based. That is, the loans are granted on the base of the value of the underlying collateral, namely the roerty being mortgaged. The fact that asset values are more correlated than income could exlain the findings that the correlation coefficients in the subrime loan sector behave in a different way than those in the rime lending industry. 8

11 Lastly, the third reason roosed in this aer, is that the teaser rates on ARMs structures reset all at same time. This would result in jums on loan ayments that, on an increasing interest rate environment like the one recently exerienced, could go from for examle, $700 to $,500 monthly. The ressure of the significantly larger liquidity needs on the art of the loan holders to cover the ayments could result on higher default correlation since everyone within this loan class is exosed to the increase at the same time. Conclusion This aer focuses on the relevance of default correlations as a key variable in the current financial crisis. We roose that the correct estimation of the correlation coefficient among the values of the underlying collateral of the MBSs is critical in assessing default risks. We show emirically how different estimates of such correlation coefficient imact the sigmas of the ortfolio of assets significantly. We roose three reasons to exlain the underestimation of these coefficients in the ast: the use of recent historical data in bull housing markets, the fact that subrime mortgages are only asset rice based, and lastly the event of teaser rates resetting at the same time. This aer suorts the idea that imroved understanding of the correlations imlied within subrime loan ortfolios would hel rating comanies, lenders, and regulators imrove their evaluation of default risks. 9

12 REFERENCES Calem, P.S., LaCour-Little, M., (001) Risk-based caital requirements for mortgage loans, The Federal Reserve Board, Financial and Economics Discussion Series, November, Working aer Carey, M. (000) Dimensions of credit risk and their relationshi to economic caital requirements, National Bureau of Economic Research, March, Working Paer 769. Chomsisenghet, S., Pennington-Cross, A., (006) The Evolution of the subrime mortgage market, Federal Reserve Bank of St. Louis Review, January/February, 88(1), Cowan, A.M., Cowan, C., D., (004) Default correlation: An emirical investigation of a subrime lender, Journal of Banking & Finance 8, Crouhy, M., Galai, D., Mark, R., (000) A comarative analysis of current credit risk models, Journal of Banking and Finance 4, Fender, I., Hordahl, P., (007) Overview: credit retrenchment triggers liquidity squeeze, BIS Quarterly Review, Setember, Gordy, M. (000) A comarative anatomy of credit risk models, Journal of Banking and Finance 4, Jorion, P. ( 007 December) Risk Management for event driven funds, ICBI Presentation, Geneve. Loffler, G. (003) The effects of estimation error on measures of ortfolio credit risk, Journal of Banking and Finance 7, Lucas, A., Klaassen, P., Sreij, P., Straetmans, S., (001) An analytic aroach to credit risk of large cororate bond and loan ortfolios, Journal of Banking and Finance 5, Merton, R. (1974) On the Pricing of Cororate Debt: The Risk Structure of Interest Rates," Journal of Finance, 9, Morgan, J.P. (1997) Credit MetricsTM Technical Document. J.P. Morgan & Co. Incororated, New York, available from htt:// Nagal, K., Bahar, R., (001) Measuring default correlation, Risk 14, Zhou, C. (1997) Default correlation: An analytical result, Working Paer, Federal Reserve Board, Washington, DC. 10

13 APPENDIX - TABLE A This table shows the standard deviations of different ortfolios with assets from 1 to 100, and correlation coefficients 0, 1, and 0.5. Where, the standard deviation of a ortfolio is: = where the variance is columns: NA- Number of Assets, CT- Covariance Terms, Correlation Coefficient 0, ρ0.5 - Correlation Coefficient 0.5 = i jww i j i jρij With i - standard deviation for Asset i, wi - wealth for asset i. In the w - % Wealth, w - wealth squared, ρ1 - Correlation Coefficient 1, ρ0 - NA CT w w ρ 1 ρ 0 ρ 0.5 ρ1 ρ1 ρ0 ρ0 ρ0.5 ρ 0.5 NA CT w w ρ1 ρ0 ρ0.5 ρ1 ρ1 ρ0 ρ 0 ρ 0.5 ρ ,00 1,0010,00 100, ,5100,0010,00 100,0010,00 100,0010, ,040,00 10,00100, ,5100,00 10,003,85 1,9651,9 7,1 10,50 0,510,00 100, ,5100,0010,00 50,00 7,07 75,00 8, ,040,00 10,00100, ,5100,00 10,003,70 1,951,85 7,0 3 30,33 0,1110,00 100, ,5100,0010,00 33,33 5,77 66,67 8, ,040,00 10,00100, ,5100,00 10,003,57 1,8951,79 7,0 4 60,5 0,0610,00 100, ,5100,0010,00 5,00 5,00 6,50 7, ,030,00 10,00100, ,5100,00 10,003,45 1,8651,7 7, ,0 0,0410,00 100, ,5100,0010,00 0,00 4,47 60,00 7, ,030,00 10,00100, ,5100,00 10,003,33 1,8351,67 7, ,17 0,0310,00 100, ,5100,0010,00 16,67 4,08 58,33 7, ,030,00 10,00100, ,5100,00 10,003,3 1,8051,61 7, ,14 0,010,00 100, ,5100,0010,00 14,9 3,78 57,14 7, ,030,00 10,00100, ,5100,00 10,003,13 1,7751,56 7, ,13 0,010,00 100, ,5100,0010,00 1,50 3,54 56,5 7, ,030,00 10,00100, ,5100,00 10,003,03 1,7451,5 7, ,11 0,0110,00 100, ,5100,0010,00 11,11 3,33 55,56 7, ,030,00 10,00100, ,5100,00 10,00,94 1,7151,47 7, ,10 0,0110,00 100, ,5100,0010,00 10,00 3,16 55,00 7, ,030,00 10,00100, ,5100,00 10,00,86 1,6951,43 7, ,09 0,0110,00 100, ,5100,0010,00 9,09 3,0 54,55 7, ,030,00 10,00100, ,5100,00 10,00,78 1,6751,39 7, ,08 0,0110,00 100, ,5100,0010,00 8,33,89 54,17 7, ,030,00 10,00100, ,5100,00 10,00,70 1,6451,35 7, ,08 0,0110,00 100, ,5100,0010,00 7,69,77 53,85 7, ,030,00 10,00100, ,5100,00 10,00,63 1,651,3 7, ,07 0,0110,00 100, ,5100,0010,00 7,14,67 53,57 7, ,030,00 10,00100, ,5100,00 10,00,56 1,6051,8 7, ,07 0,0010,00 100, ,5100,0010,00 6,67,58 53,33 7, ,030,00 10,00100, ,5100,00 10,00,50 1,5851,5 7, ,06 0,0010,00 100, ,5100,0010,00 6,5,50 53,13 7, ,00,00 10,00100, ,5100,00 10,00,44 1,5651, 7, ,06 0,0010,00 100, ,5100,0010,00 5,88,43 5,94 7, ,00,00 10,00100, ,5100,00 10,00,38 1,5451,19 7, ,06 0,0010,00 100, ,5100,0010,00 5,56,36 5,78 7, ,00,00 10,00100, ,5100,00 10,00,33 1,551,16 7,15 11

14 191710,05 0,0010,00 100, ,5100,0010,00 5,6,9 5,63 7, ,00,00 10,00100, ,5100,00 10,00,7 1,5151,14 7, ,05 0,0010,00 100, ,5100,0010,00 5,00,4 5,50 7, ,00,00 10,00100, ,5100,00 10,00, 1,4951,11 7, ,05 0,0010,00 100, ,5100,0010,00 4,76,18 5,38 7, ,00,00 10,00100, ,5100,00 10,00,17 1,4751,09 7,15 310,05 0,0010,00 100, ,5100,0010,00 4,55,13 5,7 7, ,00,00 10,00100, ,5100,00 10,00,13 1,4651,06 7, ,04 0,0010,00 100, ,5100,0010,00 4,35,09 5,17 7, ,00,00 10,00100, ,5100,00 10,00,08 1,4451,04 7, ,04 0,0010,00 100, ,5100,0010,00 4,17,04 5,08 7, ,00,00 10,00100, ,5100,00 10,00,04 1,4351,0 7, ,04 0,0010,00 100, ,5100,0010,00 4,00,00 5,00 7, ,00,00 10,00100, ,5100,00 10,00,00 1,4151,00 7,14 Table A (cont.) NA CT w w ρ 1 ρ 0 ρ0.5 ρ1 ρ1 ρ0 ρ0 ρ0.5 ρ 0.5 NA CT w w ρ1 ρ0 ρ0.5 ρ1 ρ1 ρ0 ρ 0 ρ 0.5 ρ ,00,00 10,00100, ,5100,00 10,001,96 1,4050,98 7, ,010,00 10,00100, ,5100,00 10,001,3 1,1550,66 7, ,00,00 10,00100, ,5100,00 10,001,9 1,3950,96 7, ,010,00 10,00100, ,5100,00 10,001,30 1,1450,65 7, ,00,00 10,00100, ,5100,00 10,001,89 1,3750,94 7, ,010,00 10,00100, ,5100,00 10,001,8 1,1350,64 7, ,00,00 10,00100, ,5100,00 10,001,85 1,3650,93 7, ,010,00 10,00100, ,5100,00 10,001,7 1,1350,63 7, ,00,00 10,00100, ,5100,00 10,001,8 1,3550,91 7, ,010,00 10,00100, ,5100,00 10,001,5 1,150,63 7, ,00,00 10,00100, ,5100,00 10,001,79 1,3450,89 7, ,010,00 10,00100, ,5100,00 10,001,3 1,1150,6 7, ,00,00 10,00100, ,5100,00 10,001,75 1,350,88 7, ,010,00 10,00100, ,5100,00 10,001, 1,1050,61 7, ,00,00 10,00100, ,5100,00 10,001,7 1,3150,86 7, ,010,00 10,00100, ,5100,00 10,001,0 1,1050,60 7, ,00,00 10,00100, ,5100,00 10,001,69 1,3050,85 7, ,010,00 10,00100, ,5100,00 10,001,19 1,0950,60 7, ,00,00 10,00100, ,5100,00 10,001,67 1,950,83 7, ,010,00 10,00100, ,5100,00 10,001,18 1,0850,59 7, ,00,00 10,00100, ,5100,00 10,001,64 1,850,8 7, ,010,00 10,00100, ,5100,00 10,001,16 1,0850,58 7, ,00,00 10,00100, ,5100,00 10,001,61 1,750,81 7, ,010,00 10,00100, ,5100,00 10,001,15 1,0750,57 7, ,00,00 10,00100, ,5100,00 10,001,59 1,650,79 7, ,010,00 10,00100, ,5100,00 10,001,14 1,0750,57 7, ,00,00 10,00100, ,5100,00 10,001,56 1,550,78 7, ,010,00 10,00100, ,5100,00 10,001,1 1,0650,56 7, ,00,00 10,00100, ,5100,00 10,001,54 1,450,77 7, ,010,00 10,00100, ,5100,00 10,001,11 1,0550,56 7,11 1

15 ,00,00 10,00100, ,5100,00 10,001,5 1,350,76 7, ,010,00 10,00100, ,5100,00 10,001,10 1,0550,55 7, ,010,00 10,00100, ,5100,00 10,001,49 1,50,75 7, ,010,00 10,00100, ,5100,00 10,001,09 1,0450,54 7, ,010,00 10,00100, ,5100,00 10,001,47 1,150,74 7, ,010,00 10,00100, ,5100,00 10,001,08 1,0450,54 7, ,010,00 10,00100, ,5100,00 10,001,45 1,050,7 7, ,010,00 10,00100, ,5100,00 10,001,06 1,0350,53 7, ,010,00 10,00100, ,5100,00 10,001,43 1,050,71 7, ,010,00 10,00100, ,5100,00 10,001,05 1,0350,53 7, ,010,00 10,00100, ,5100,00 10,001,41 1,1950,70 7, ,010,00 10,00100, ,5100,00 10,001,04 1,050,5 7, ,010,00 10,00100, ,5100,00 10,001,39 1,1850,69 7, ,010,00 10,00100, ,5100,00 10,001,03 1,050,5 7, ,010,00 10,00100, ,5100,00 10,001,37 1,1750,68 7, ,010,00 10,00100, ,5100,00 10,001,0 1,0150,51 7, ,010,00 10,00100, ,5100,00 10,001,35 1,1650,68 7, ,010,00 10,00100, ,5100,00 10,001,01 1,0150,51 7, ,010,00 10,00100, ,5100,00 10,001,33 1,1550,67 7, ,010,00 10,00100, ,5100,00 10,001,00 1,0050,50 7,11 13

16 TABLE 1 The first and second columns show the tranches and ratings assigned to each. The last column describes the risks assumed by each tranche of investors. Rating Tranche Descrition BBB- E (equity) absorbs the first 10% of losses on the ortfolio BBB D (mezzanine) absorbs the next 10% of losses A C (mezzanine) absorbs the following 10% of losses AA B (mezzanine) the next 10% AAA A (senior) would absorb the final losses Grah 1

17 Footnotes i The crisis is ongoing and so far more than 100 subrime mortgage lenders failed or file for bankrutcy, most rominently New Century Financial Cororation, reviously the nation's second biggest subrime lender. The failure of these comanies has caused rices in the $6.5 trillion mortgage backed securities market to collase, threatening broader imacts on the U.S. housing market and economy as a whole. For a summary of events see htt://en.wikiedia.org/wiki/007_subrime_mortgage_financial_crisis. ii Exansión, November 7 th 007, age 9. iii htt://biz.yahoo.com/a/071101/foreclosure_rates.html. iv The Federal Reserve Board's Regulation B (imlementing the Equal Credit Oortunity Act), rohibits credit-scoring considering "rohibited bases" such as race, skin color, religion, national origin, sex, and marital status. htt:// v htt://money.cnn.com/galleries/007/real_estate/0704/gallery.aly_the_subrime_blam e_game/index.html?section=money_realestate vi Material Loss Review of Next Bank, NA (OIG-03-04) November 6, 00, age 48, can be retrieved from htt:// vii Sources: Material Loss Review of Next Bank, NA (OIG-03-04) November 6, 00,. 14 which can be retrieved from htt:// htt:// and htt:// viii The FICO score distribution ranges between 300 and 850, it is skewed to the left with 60% of scores between 650 and 799, has a median of 73, and an average of 678. FICO has disclosed some of the variables considered when calculating an individual s score: unctuality of ayment in the ast, the amount of debt exressed as the ratio of current revolving debt to total available revolving credit, length of credit history, tyes of credit used, and recent search for credit and/or amount of credit obtained recently (htt:// ix A debt-to-income ratio (DTI) is the ercentage of a consumer's monthly gross income that goes toward aying debts. There are two main kinds of DTI: the front ratio, which indicates the ercentage of income that goes toward total housing costs, and the back ratio, which shows the ercentage of income that goes toward aying all recurring debt ayments. x By 005, about twenty ercent of all mortgage originations in the U.S. were subrime, totalling $600 billion. (Reort and Recommendations by the Majority Staff of the Joint Economic Committee October 007,.10, which can be retrieved from htt://jec.senate.gov/documents/reorts/ octobersubrimereort.df). The aroximate amount of subrime mortgages outstanding as of March 007 is $1,3 trillion (htt:// ). xi Interest-only mortgages, allow borrowers to ay only interest for a eriod of time; in ick a ayment loans, borrowers choose their monthly ayment (full ayment, interest only, or a minimum ayment which may be lower than the ayment required to reduce the balance of the loan); and with adjustable rate mortgages (ARM), they set an initial fixed rate that converts to variable within a eriod of time. xii In the Global Financial System s January 005 reort, age 1, "The role of ratings in structured finance: issues and imlications", the following definition of structured finance is rovided. "Structured finance instruments can be defined through three key 15

18 characteristics: (1) ooling of assets (either cash-based or synthetically created); () tranching of liabilities that are backed by the asset ool; (3) de-linking of the credit risk of the collateral asset ool from the credit risk of the originator, usually through use of a finite-lived, standalone secial urose vehicle (SPV)."(Can be access from: htt:// 1 ). xiii The Committee on the Global Financial System exlained tranching in the following manner: "A key goal of the tranching rocess is to create at least one class of securities whose rating is higher than the average rating of the underlying collateral ool or to create rated securities from a ool of unrated assets. This is accomlished through the use of credit suort (enhancement), such as rioritization of ayments to the different tranches." (Global Financial System s January 005 reort, age 1, can be access from: htt:// ). xiv See Financial Times, November 6 th 007, age 41 xv For instance, losses on $340.7 million worth of collateralized debt obligations (CDO) issued by Credit Suisse Grou added u to about $15 million, desite being rated AAA or Aaa by Standard & Poor's, Moody's Investors Service and Fitch Grou.(Can be retrieved from htt:// ) 16

19 NOTAS

20 NOTAS Deósito Legal: M-0073 I.S.S.N.: