Economic Capital Estimation for Consumer Portfolios

RETAIL RISK

by Fang Du his article has six sections: 1) an introduction to the general practice related to economic capital; 2) regulatory capital and Tits differences to economic capital; 3) the methodology of estimating the credit risk for consumer portfolios; 4) research results on estimation of default variance-covariance; 5) a focus on the Monte Carlo method by simulating the loss distribution of a portfolio based on the estimated default rate, default rate volatility and default rate covariance between different obligors; and 6) a summary of findings. Both regulatory capital and ures not only show a difference within the same consumer portfo- economic capital focus on a bank’s but also show a dramatic diver- lio is assumed to be homoge- risk of insolvency in the face of gence. neous, regardless of its credit adverse events. A bank, for exam- Most banks currently use a score, loan-to-value (LTV) ratio, ple, maintains regulatory capital or top-down approach to assign eco- debt-to-income ratio, tenure, and economic capital as a financial nomic capital to their consumer sensitivity to macroeconomic con- source to protect itself against portfolios, including residential ditions. In other words, all of the insolvency. Theoretically, regula- mortgages, home equity loans and valuable information reflecting tory and economic capital should lines (also known as closed-end each customer’s creditworthiness converge because both cover the and open-end home equity loans), is ignored under this approach. In asset loss due to credit risk, mar- automobile installment loans, stu- consumer credit, most banks and ket risk, operational risk, interest dent loans, credit cards, and oth- financial services firms commonly risk, reputational risk, and so ers. Under this approach, the use a FICO credit score (a generic forth. In reality, these two meas- credit risk for each consumer loan credit score to predict a cus- © 2003 by RMA. Fang Du is head of the Financial Engineering and Architecture Team, Counterparty & Market Risk Information, Business Development & Strategy, FleetBoston Financial Corp. Opinions expressed here are those of the author alone and do not necessarily reflect the opinions of FleetBoston Financial Corp. The author thanks Tom Freeman and Larry Mielnicki for their support of this research project, Michael Delman and Zhi Yi Sun for their research assistance, and several other reviewers for their valuable comments and suggestions.

70 The RMA Journal December 2003–January 2004 Economic Capital Estimation for Consumer Portfolios tomer’s default probability) to form capital number or ratio for asset included in the portfolio rel- assess each borrower’s creditwor- each of their consumer sub-port- ative to the return of the portfolio thiness. Generally speaking, a folios defined by product type. and individual securities. That is customer with a FICO score of The categorization for sub-portfo- exactly what Markowitz’s portfolio 800 has a much lower probability lios is much broader. Some banks theory advocates. The analogous of defaulting within the coming treat the home equity loans the relationship should be expected 12 months than a customer with a same as the home equity lines, for consumer loan portfolios as FICO score of 500 for the same and the automobile installment well. Since each consumer portfo- time horizon. Unfortunately, the loans the same as other secured lio includes at least several thou- top-down approach does not dis- installment loans. The worst case sand individual loans, the risk at tinguish differences in creditwor- is that a number of banks assign the portfolio level is expected to thiness between these two cus- only one capital ratio to their be much smaller than the weight- tomers. In the same fashion, entire consumer portfolio regard- ed sum of individual asset risks. another noticeable risk factor— less of whether they are secured For a consumer portfolio, only the the LTV for secured consumer or unsecured sub-portfolios. This systematic risk caused by macro- portfolios—plays no role in the approach implies that the credit economic factors is expected to economic capital allocation card sub-portfolio possesses the exist, because the unsystematic process. The top-down approach same credit risk as the secured risks or unique risks cancel each treats a customer with a LTV of mortgage sub-portfolio. other out. less than 50% the same as another A third problem caused by In the real consumer credit one with a LTV of 100%. the top-down approach is that it world, unfortunately, the informa- Therefore, the effectiveness of all ignores the variance and covari- tion depicting the relationships risk factors, such as the remaining ance between individual con- among consumer loans is neglect- time to maturity, the position sumer loans. The variance-covari- ed, due either to the limited according to credit cycle, and pay- ance matrix depicts the quantita- knowledge in this area or to ment performance, are not taken tive measure of how two loans avoidance of heavy and lengthy into account when using a top- behave over time: whether they calculations. The economic capital down approach. move in the same or opposite requirement is increased dramati- The process of setting eco- directions or have no association cally because of the incorrect nomic capital for consumer portfo- pattern at all. This relationship assumption of a perfect linear lios is progressing at differing also can be measured by the prod- relationship between individual rates among banks. Some banks, uct of correlation coefficient and loans. In other words, the portfo- for example, treat home equity the standard deviations of individ- lio theory plays no role in this cir- loans differently from home equi- ual loans. The concept of correla- cumstance. Any banks using a ty lines because of different lend- tion coefficients plays a significant top-down approach to quantify ing policies and repayment sched- role in portfolio management. In the economic capital should rec- ules between outstanding balance the U.S. equity market, the typi- ognize these drawbacks. and exposures. Several national cal correlation coefficient falls into banks are evolving faster in this the 0.6-0.7 range for two stocks. Regulatory versus Economic area by not only assigning the This correlation coefficient is rela- Capital economic capital at the sub-port- tively high but not perfectly lin- Some banks set capital by fol- folio1 level but also differentiating early related, so a portfolio manag- lowing the regulatory require- capital by decomposing the risk er chooses a position by carefully ments and may not focus on characteristics. Therefore, even picking diversified securities to whether this requirement accu- within the same equity sub-port- compose a portfolio. This type of rately reflects the underlying portfolio, different capital rates are security selection results in a portfolio risk. The distinction, howev- assigned according to risk levels. folio with an associate risk level er, between economic capital and The majority of banks set a uni- that will be less than any single regulatory capital is quite clear.

71 Economic Capital Estimation for Consumer Portfolios

Regulatory capital is a fixed mini- one-size-fits-all. Basel II comes the risk of a mortgage portfolio or mum capital requirement (1988 closer to recommending a risk- using the risk in a consumer sub- Basel Accord) that banks have to based approach. The credit risk portfolio to infer the risk of a hold. Fixed minimum capital embedded in assets is measured whole consumer portfolio over- requirements are defined as the by three approaches: 1) states the capital requirement, ratio of capital to total risk-weight- Standardized Approach, 2) because risky assets in the portfo- ed assets. Until Basel II goes into Foundation Internal Ratings- lio are not perfectly related linear- effect, banks are required to Based Approach, and 3) Advanced ly. Generally speaking, there are maintain a minimum capital of 8% Internal Ratings-Based Approach. several thousand loans—if not tens of weighted exposure. Both regulatory and economic or hundreds of thousands—in a Economic capital is the capital capital deal with the solvency consumer sub-portfolio and there needed to offset the bank’s com- issue. A target insolvency rate is little chance of all loans default- bined credit risk, market risk, and usually is chosen to be consistent ing at the same time. The risk operational risk. Based on estimat- with a bank’s desired credit rat- existing in the portfolio is smaller ed unexpected loss, a bank volun- ings for its liabilities. For instance, than the weighted sum of individ- teers to hold the economic capital the solvency rates are 7 bps, 3 ual risks. to cover losses in the unlikely, but bps, and 1 bp, respectively, for Uneven sophistication of risk fully possible, case of an unex- banks with single A, double-A, management systems is another pected adverse event and still and triple-A risk-rating liabilities. factor causing regulatory capital to meet the insolvency target. These A number of banks choose a differ from economic capital. are voluntary versus involuntary 0.05% solvency rate for their con- Banks with a sophisticated risk issues. sumer portfolios. Robert Giltner management system and a strong As mentioned earlier, the risk recommended three standard risk management team are able to management techniques, prac- deviations of loan-loss estimate to monitor the credit quality fre- tices, and skills are quite diver- set sufficient economic capital. quently—daily, weekly, or at least gent among banks. This diver- Huge discrepancies exist monthly—and to make strategy gence becomes more significant between regulatory capital levels adjustments as necessary. In con- in the consumer credit risk world. and experts’ opinions about eco- trast, some banks are still hanging While some banks may make only nomic capital. Why? What are the on to outdated risk management limited use of credit scores, others major factors causing this gap? systems because of the tremen- already fully utilize the automated Many national banks inherently dous costs to replace them. Their score decision, credit limit assign- have a significant amount of port- risk monitoring systems cannot ments, and account payment folio diversification. This is espe- elicit warning signals in a timely monitor system. While some cially true in consumer loan portfo- fashion. A new risk management banks use only a generic or stan- lios. All the portfolios within a tool or instruments cannot upload dard score system, other banks bank are not perfectly correlated into the systems because of capac- extend the risk management due to the nature of the lines of ity and programming constraints. scope by implementing new com- business. One reason that regulato- As a consequence, the aggregate puter programs, such as a neural ry capital is higher than economic risk could be much higher, even network or artificial intelligence, capital is the exclusion of the though the individual risk levels to explore a new marketing diversification effect. According to are similar. Basel II will partially regime or mimic the fraud pat- Markowitz’s portfolio theory, the correct this issue by allowing some terns in their fraud protection pro- risk for any portfolio is smaller banks to evaluate their credit risk grams. The 1988 Basel Accord than the sum of risks of the indi- using internal bank information if cannot provide any incentive for vidual assets included in the port- they have the ability to estimate those banks with sophisticated folio with an imperfect linear rela- their credit risk fairly and in an risk management tools and knowl- tionship. Using the risk of one unbiased manner. Therefore, if a edge because its very nature is individual mortgage loan to infer bank has sophisticated internal

72 The RMA Journal December 2003–January 2004 Economic Capital Estimation for Consumer Portfolios credit rating models that reflect ity is directly related to hierarchy • What are the risk characteris- the true credit risks, the regulatory levels. It’s common to find a tics for commercial and con- agency would be more likely to longer history at an aggregate level sumer loans? support a bank’s internal credit but less information when drilling • How do the macroeconomic capital assessment. If a bank lacks down to a more detailed level for a factors impact on commercial risk management systems and consumer-specific portfolio. and consumer loans? models, the regulatory agency will Moody’s, Standard and Poor’s, • How will the commercial loan recommend the standard regulato- and Fitch Investors Service pos- information be used to make ry capital as the optimal solution. sess much longer historical credit a fair reference to consumer information on investment-grade loans? Credit Risk in the Consumer bonds, high-yield bonds, and non- To date, these issues have not Portfolio rated bonds. Fleet uses Moody’s been discussed in the literature. About 10 years ago, most eight bond ratings—spanning 30 Another remedy for lack of national banks started to pay close years, from 1970 to 1999—to test data at a particular bank is to use attention to collecting and storing the three standard deviations of the aggregated and pooled con- consumer-credit-related informa- unexpected loan-loss estimate. sumer information from other tion, such as credit scores at loan Results show that the three- sources. Although aggregated data origination, updated credit scores, standard-deviation criterion is only cannot fully represent the charac- payment history time series, and good enough to cover the worst- teristics of consumer portfolios in a other consumer credit application year loss for bonds rated B or Ba. particular bank, at least they pro- information. At the beginning of For bonds rated Baa or better, vide a directional benchmark by the data collection process, the three standard deviations are not covering a longer consumer credit scope for using the data was nar- sufficient to cover the worst credit history. Fleet collaborated with the rower, focusing only on asset qual- stress. Due to the non-normal FDIC’s credit card research group ity reporting or monitoring. nature of default risk, five stan- to explore consumer credit data Although some banks enlarged the dard deviations should be used for from 1984 to 1999. The average collection of detailed information rating Baa bonds and six standard net charge-off rate was 180 bps, in customers’ payment perform- deviations for rating A or above. and the volatility measured in stan- ances, it was done mostly on an ad Of course, these results are dard deviation equaled 57 bps for hoc basis and not updated regular- derived based on historical data consumer products in aggregate. In ly or stored properly. For example, sets and are time sensitive, but at this period, the minimum and tapes containing updated credit least they provide a guideline or maximum net charge-off rates scores from the credit bureau direction to set the economic capi- were 61 bps and 286 bps, respec- stayed in a risk manager’s drawer tal. Therefore, combining the tively. Three standard deviations for months and were discarded knowledge and information of as a proxy of economic capital afterwards. Therefore, the data commercial credit risks will correct requirement are good enough to quality may be questionable in the for the defect of short history of sustain the worst-year loss based first one or two years of collection. consumer credit data. Before using on this 15-year period. Noticeably, The norm of reliable data history this publicly available information, using three standard deviations as on consumer portfolios is seven to practitioners have to ask them- a criterion to set the economic cap- eight years, although some banks selves the following questions: ital is suitable only for a consumer may have longer histories. In addi- • Should the commercial loans portfolio as a whole and is not good tion, data quality is not always uni- and consumer loans be treat- for a specific consumer sub-portfo- form for different consumer sub- ed in the same way or in a lio, such as mortgages, home equi- portfolios. There may be more his- different manner? ty loans, automobile installment torical information on residential • What are the similarities and loans, and credit cards. It’s impor- mortgages than on credit cards. differences between commer- tant to remember that this three- Another issue is that the data qual- cial and consumer loans? standard-deviation criterion as an

73 Economic Capital Estimation for Consumer Portfolios economic capital proxy is data Table 1 dependent or data sensitive. Using Default Probability—Unsecured Consumer Sub-portfolio A a different historical data set may yield a different conclusion. Expected Default Rate Fleet conducted another Factor 2 study using Fitch’s securitized Factor 1 Segment 1 Segment 2 Segment 3 credit card data. There were 119 Segment 1 28 62 95 monthly annualized charge-off Segment 2 76 173 253 observations from January 1991 to Segment 3 156 363 494 November 2000 in this data set. Three, six, and eight standard Segment 4 373 640 859 deviations were equal to 284 bps, Segment 5 573 1,148 1,318 596 bps, and 758 bps, respectively. fective in an unsecured consumer 10%. A consumer with a credit The worst loss within this period sub-portfolio. In addition, the sen- score above 750 behaves quite was 693 bps. Obviously, eight sitivities for the same factor differ differently from another with a standard deviations would be among consumer sub-portfolios. score of 550. For evenly distrib- required to properly assign the For example, the impact of credit uted credit score bands, the credit economic capital in this case. The scoring on a mortgage is definitely risk increases exponentially. most notable phenomenon is that not the same as for a credit card. If Therefore, the credit risk charac- the FDIC data does not support the resource and computational teristics should be explored not the assumptions that the expected systems are sufficient, it’s prefer- only for different sub-consumer default is smaller during the eco- able to conduct detailed studies portfolios but also within the nomic expansion than during the sub-portfolio by sub-portfolio. same sub-portfolio. Fleet used economic recession. The default When several sub-portfolios are 1992-2000 data to study several rate for an aggregated consumer lumped together, valuable infor- secured and unsecured consumer portfolio for the most recent eight mation is lost and this can cause sub-portfolios. The research years of economic boom (1992- inaccurate credit risk estimation. results support this argument. 2000) actually is higher than the Even within the same sub- Table 1 shows the estimate of past 16 years’ default rate, which portfolio, different loans carry dif- annualized default probabilities covers at least two economic ferent credit characteristics. on an unsecured consumer sub- recessions—a minor recession in Generally, every consumer sub- portfolio measured in basis points. 1987 and a severe recession in portfolio includes thousands of 1991. Therefore, when dealing loans. It may not be worth it to Variance-Covariance Matrixes with consumer portfolios, practi- use detailed analysis of each loan, The first step in determining tioners must understand their because gains diminish due to economic capital for a commercial characteristics and differences intensive computation and time portfolio is to explore how these from the commercial portfolio and consumption. Clustering loans commercial loans react to adverse the impact on the macroeconomy. with similar credit risk characteris- occurrences. Analogously, the reac- Most banks currently use tics into several segments to be tion—as measured by correlation logistic regression with dichotomy treated as synthetic securities is coefficients—toward external of dependent variable—say, feasible and offers a large benefit effects for loans in a consumer default or no default—to estimate while losing little information. portfolio should be estimated at the default probability for their The intersegment risk scale does the very beginning. Theoretically, consumer portfolios. Factors not increase in a linear fashion. In it is possible to estimate correlation change corresponding to consumer other words, you cannot say that coefficients for every pair of loans sub-portfolios. The LTV ratio the risk will increase by 10% within the same consumer portfo- plays a significant role in a secured when the credit score worsens by lio. Let’s assume a hypothetical consumer sub-portfolio but is inef-

74 The RMA Journal December 2003–January 2004 Economic Capital Estimation for Consumer Portfolios consumer portfolio of 10,000 loans. the relationship derived from the default rate and loss amounts start- To fully explore the association historical data may be time ed 30 years ago in the consumer within any pair of loans, we need dependent and unstable. In other credit world, there is almost no to estimate 49,995,000 correlation words, the magnitude of variance- research geared to the estimation of coefficients.2 These coefficients covariance may change when unexpected losses. While most risk can be estimated, but the calcula- using a different time period. For managers in charge of consumer tion task could be arduous and instance, a variance-covariance portfolios understand the concept costly. The most feasible and effi- matrix based on a recessionary of expected credit loss very well, cient approach is to synthesize the period may yield a very different they have little quantitative knowl- loans based on their credit charac- picture from one based on a edge about loss volatility. The teristics by using a bottom-up strong economic period. Which majority of commercial banks have approach. Loans that fall into each relationship should the bank chosen a constant parameter to segment are assumed homoge- adopt? Risk managers should be assign the economic capital rates to neous, measured by several credit- aware of these issues when their consumer portfolios, but can- related factors such as credit score, attempting to calculate correlation not rationalize the link between LTV ratio, loan tenor, and delin- coefficients. Fleet adds the sce- this parameter and the underlying quency status. Let’s define aggre- nario analyses, particularly the loss distribution. gated loans in the same segment as macroeconomic changes, into vari- A Monte Carlo simulation a synthetic security, then estimate ance-covariance matrix estimation. methodology can be used to simu- the correlation coefficients for each late the potential loss distribution pair of synthetic securities using Monte Carlo Simulation for each consumer sub-portfolio. historical and projected future Techniques for estimating Before starting this process, there information. credit risk, market risk, and opera- must first be an estimation of the If banks have over 30 years of tional risk have evolved rapidly in expected loss rate and the stan- historical default data at the con- recent years, although some tech- dard deviation of the loss rates for sumer sub-portfolio level, the esti- niques appear to be state-of-the-art each segment, as well as the mation of the correlation coeffi- and some appear theoretically covariance between all pairs of cients between consumer sub-port- sound but inapplicable in practice. segments using historical informa- folios and between individual loans If the credit, market, operational, tion and scenario analysis results. within the same sub-portfolio and interest risks can be measured We assume a normally distributed would be feasible. However, it’s accurately, the task to set economic loss rate in every segment, doubtful that any bank stores this sustainable provision and economic although the descriptive statistics much data on any of its consumer capital becomes much easier. such as mean and variance vary dra- portfolios. For the estimation pur- During the past five years, a hand- matically from one segment to pose, the minimum of three years, ful of studies are related to credit another. In general, the sample at least, of trailing 12-month risk and economic capital for big size is large enough for most seg- default history can be used to esti- commercial banks, but nearly all ments. But the small sample size mate the variance-covariance studies focus on commercial loan and nonconsumer credit history matrix. portfolios. The economic capital could be an issue in estimating the The first problem is that this model for the consumer portfolio is variance-covariance matrix, and estimated variance-covariance rarely seen. In the consumer credit risk managers and/or modelers matrix depicts the historical rela- world, models are concentrated on should adjust estimates. Weights tionship. As most financial practi- default, bankruptcy, fraud, and line assigned to each segment are tioners know, the future financial assignment. Default models are determined by their outstanding relationship among these con- commonplace, but mark-to-market exposures. The portfolio is ran- sumer loans may not be a repeti- methods are almost nonexistent. domly simulated using 100,000 tri- tion of their history. Although the research on estimat- als for each consumer sub-portfo- The second problem is that ing and forecasting the expected lio. Every trial must meet the con-

75 Economic Capital Estimation for Consumer Portfolios

Figure 1 Monte Carlo Simulation of Loss Distribution—A Secured Consumer Sub-portfolio

0% 10 14 19 23 28 32 37 41 46 50 55 59 64 68 73 77 82 88 91 95 100 104 109 Fitted Distribution Chi-Square Goodness-of-Fit Gamma 5018.14

dition of distribution at each seg- The vertical axis represents fre- derivatives, or combinations of ment as well as the correlation quencies and the horizontal axis portfolios. Currently, most banks coefficient between these seg- represents the loss rate measured assume that all loans in the con- ments. in basis points. sumer portfolio default at the The last step in the simulation same time. The diversification process is to test the loss distribu- Conclusion effect is totally ignored. Finally, tion based on these 100,000 gener- The methodology introduced using the Monte Carlo simulation ated observations. Two sequential in this article estimates and allo- after synthesizing the homoge- null hypotheses are proposed. The cates economic capital for con- neous loans makes it feasible to first assumption is that the simulat- sumer portfolios better than does estimate economic capital. VaR is ed distribution is normally distrib- a constant capitalization rate now easily calculated by using simulat- uted. If this hypothesis is rejected, used by most banks. First, the ed loss distribution. ❐ the simulated results do not sup- default probability, default proba- Fang Du can be reached by e-mail at port the normally distributed loss bility volatility, and the covariance [email protected]. distribution. Then the second relationship between loans can be hypothesis comes into the picture estimated to reflect a bank’s con- Notes 1 A particular consumer product, for example, a by assuming that the simulated sumer portfolio credit profile. residential mortgage, is defined as one consumer distribution is a gamma distribu- Second, using a longer history sub-portfolio. tion. All six simulated loss distribu- than is available in a bank’s own 2 The number of permutations of n things k at a time n ϭ n tions but one fail to reject the consumer portfolio offers greater [k] (nϪk)!k! gamma distribution hypothesis. reliability. As a result, the eco- Two parameters, alpha and beta, are nomic capital calculations not only References estimated. The maximum losses cover the portfolios under the "Credit Ratings and Complementary Sources of are provided corresponding to the economic boom conditions but Credit Quality Information,” Basel Committee on Banking Supervision Working Papers, No. 3— bank’s risk tolerance. Most banks also include considerations of eco- August 2000. chose the likelihood of solvency at nomic recession in both minor Carey, Mark (2000), "Dimensions of Credit Risk a 99.95%, 99.97%, or 99.99% confi- and severe scenarios. Economic and Their Relationship to Economic Capital dence interval. The economic cap- capital rates derived in this man- Requirements," NBER Working Paper 7269. ital (Value at Risk, or VaR), is ner better represent the credit Giltner, R. C. (1998), "Using Profitability Data to measured by the difference risk embedded in consumer port- Price for Risk," Commercial Lending Review, Vol. 13, Number 2, Spring 1998. between this maximum loss and folios. Third, the modern portfolio expected loss. Figure 1 shows a theory helps consumer portfolio Ronan O'Connor, James F. Golden, and Robert Reck, "A Value-at-Risk Calculation of Required simulated distribution for a diversification analyses as it did Reserves for Credit Risk in Corporate Lending Portfolios," North American Actuarial Journal, secured consumer sub-portfolio. commercial loan, equity, bond, Volume 3, Number 2: 72-83.

76 The RMA Journal December 2003–January 2004