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Economic Capital Estimation for Consumer Portfolios

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Economic Capital Estimation for Consumer Portfolios RETAIL RISK Economic Capital Estimation for Consumer Portfolios 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 port- folio, different capital rates are security selection results in a port- folio 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.
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