Economic capital estimation for consumer portfolios

This article has six sections: 1) an introduction to the general practice related to economic capital; 2) regulatory capital and its 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 economic capital focus on a bank's risk of insolvency in the face of adverse events. A bank, for example, maintains regulatory capital or economic capital as a financial source to protect itself against insolvency. Theoretically, regulatory and economic capital should converge because both cover the asset loss clue to credit risk, market risk, operational risk, interest risk, reputational risk, and so forth. In reality, these two measures not only show a difference but also show a dramatic divergence.

Most banks currently use a top-clown approach to assign economic capital to their consumer portfolios, including residential mortgages, home equity loans and lines (also known as closed-end and open-end home equity loans), automobile installment loans, student loans, credit cards, and others. Under this approach, the credit risk for each consumer loan within the same consumer portfolio is assumed to be homogeneous, regardless of its credit score, loan-to-value (LTV) ratio, debt-to-income ratio, tenure, and sensitivity to macroeconomic conditions. In other words, all of the valuable information reflecting each customer's creditworthiness is ignored under this approach. In consumer credit, most banks and financial services firms commonly use a FICO credit score (a generic credit score to predict a customer's default probability) to assess each borrower's creditworthiness. Generally speaking, a customer with a FICO score of 800 has a much lower probability of defaulting within the coming 12 months than a customer with a FICO score of 500 for the same time horizon. Unfortunately the top-down approach does not distinguish differences in creditworthiness between these two customers. In the same fashion, another noticeable risk factor--the LTV for secured consumer portfolios--plays no role in the economic capital allocation process. The top-down approach treats a customer with a LTV of less than 50% the same as another one with a LTV of 100%. Therefore, the effectiveness of all risk factors, such as the remaining time to maturity, the position according to credit cycle, and payment performance, are not taken into account when using a top-down approach.

The process of setting economic capital for consumer portfolios is progressing at differing rates among banks. Some banks, for example, treat home equity loans differently from home equity lines because of different lending policies and repayment schedules between outstanding balance and exposures. Several national banks are evolving faster in this area by not only assigning the economic capital at the sub-portfolio (1) level but also differentiating capital by decomposing the risk characteristics. Therefore, even within the same equity sub-portfolio, different capital rates are assigned according to risk levels. The majority of banks set a uniform capital number or ratio for each of their consumer sub-portfolios defined by product type. The categorization for sub-portfolios is much broader. Some banks treat the home equity, loans the same as the home equity lines, and the automobile installment loans the same as other secured installment loans. The worst case is that a number of banks assign only one capital ratio to their entire consumer portfolio regardless of whether they are secured or unsecured sub-portfolios. This approach implies that the credit card sub-portfolio possesses the same credit risk as the secured mortgage sub-portfolio.

A third problem caused by the top-down approach is that it ignores the variance and covariance between individual consumer loans. The variance-covariance matrix depicts the quantitative measure of how two loans behave over time: whether they move in the same or opposite directions or have no association pattern at all. This relationship also can be measured by the product of correlation coefficient and the standard deviations of individual loans. The concept of correlation coefficients plays a significant role in portfolio management. In the U.S. equity market, the typical correlation coefficient falls into the 0.6-0.7 range for two stocks. This correlation coefficient is relatively high but not perfectly linearly related, so a portfolio manager chooses a position by carefully picking diversified securities to compose a portfolio. This type of security selection results in a portfolio with an associate risk level that will be less than any single asset included in the portfolio relative to the return of the portfolio and individual securities. That is exactly what Markowitz's portfolio theory advocates. The analogous relationship should be expected for consumer loan portfolios as well. Since each consumer portfolio includes at least several thousand individual loans, the risk at the portfolio level is expected to be much smaller than the weighted sum of individual asset risks. For a consumer portfolio, only the systematic risk caused b v macroeconomic factors is expected to exist, because the unsystematic risks or unique risks cancel each other out.

In the real consumer credit world, unfortunately, the information depicting the relationships among consumer loans is neglected, due either to the limited knowledge in this area or to avoidance of heavy and lengthy calculations. The economic capital requirement is increased dramatically because of the incorrect assumption of a perfect linear relationship between individual loans. In other words, the portfolio theory plays no role in this circumstance. Any banks using a top-down approach to quantify the economic capital should recognize these drawbacks.

Regulatory versus Economic Capital

Some banks set capital by following the regulatory requirements and may not focus on whether this requirement accurately reflects the underlying portfolio risk. The distinction, however, between economic capital and regulatory capital is quite clear. Regulatory capital is a fixed minimum capital requirement (1988 Basel Accord) that banks have to hold. Fixed minimum capital requirements are defined as the ratio of capital to total risk-weighted assets. Until Basel II goes into effect, banks are required to maintain a minimum capital of 8% of weighted exposure.

Economic capital is the capital needed to offset the bank's combined credit risk, market risk, and operational risk. Based on estimated unexpected loss, a bank volunteers to hold the economic capital to cover losses in the unlikely, but fully possible, case of an unexpected adverse event and still meet the insolvency target. These are voluntary versus involuntary issues.

As mentioned earlier, the risk management techniques, practices, and skills are quite divergent among banks. This divergence becomes more significant in the consumer credit risk world. While some banks may make only limited use of credit scores, others already fully utilize the automated score decision, credit limit assignments, and account payment monitor system. While some banks use only a generic or standard score system, other banks extend the risk management scope by implementing new computer programs, such as a neural network or artificial intelligence, to explore a new marketing regime or mimic the fraud patterns in their fraud protection programs. The 1988 Basel Accord cannot provide any incentive for those banks with sophisticated risk management tools and knowledge because its very nature is one-size-fits-all. Basel II comes closer to recommending a risk-based approach. The credit risk embedded in assets is measured by three approaches: 1) Standardized Approach, 2) Foundation Internal Ratings-Based Approach, and 3) Advanced Internal Ratings-Based Approach.

Both regulatory and economic capital deal with the solvency issue. A target insolvency rate usually is chosen to be consistent with a bank's desired credit ratings for its liabilities. For instance, the solvency rates are 7 bps, 3 bps, and 1 bp, respectively, for banks with single A, double-A, and triple-A risk-rating liabilities. A number of banks choose a 0.05% solvency rate for their consumer portfolios. Robert Giltner recommended three standard deviations of loan-loss estimate to set sufficient economic capital.

Huge discrepancies exist between regulatory capital levels and experts' opinions about economic capital. Why? What are the major factors causing this gap? Many national banks inherently have a significant amount of portfolio diversification. This is especially true in consumer loan portfolios. All the portfolios within a bank are not perfectly correlated due to the nature of the lines of business. One reason that regulatory capital is higher than economic capital is the exclusion of the diversification effect. According to Markowitz's portfolio theory, the risk for any portfolio is smaller than the sum of risks of the individual assets included in the portfolio with an imperfect linear relationship. Using the risk of one individual mortgage loan to infer the risk of a mortgage portfolio or using the risk in a consumer sub-portfolio to infer the risk of a whole consumer portfolio overstates the capital requirement, because risky assets in the portfolio are not perfectly related linearly. Generally speaking, there are several thousand loans--if not tens or hundreds of thousands--in a consumer sub-portfolio and there is little chance of all loans defaulting at the same time. The risk existing in the portfolio is smaller than the weighted sum of individual risks.

Uneven sophistication of risk management systems is another factor causing regulatory capital to differ from economic capital. Banks with a sophisticated risk management system and a strong risk management team are able to monitor the credit quality frequently--daily, weekly, or at least monthly--and to make strategy adjustments as necessary. In contrast, some banks are still hanging on to outdated risk management systems because of the tremendous costs to replace them. Their risk monitoring systems cannot elicit warning signals in a timely fashion. A new risk management tool or instruments cannot upload into the systems because of capacity and programming constraints. As a consequence, the aggregate risk could be much higher, even though the individual risk levels are similar. Basel II will partially correct this issue by allowing some banks to evaluate their credit risk using internal bank information if they have the ability to estimate their credit risk fairly and in an unbiased manner. Therefore, if a bank has sophisticated internal credit rating models that reflect the true credit risks, the regulatory agency would be more likely to support a bank's internal credit capital assessment. If a bank lacks risk management systems and models, the regulatory agency will recommend the standard regulatory capital as the optimal solution.

Credit Risk in the Consumer Portfolio

About 10 years ago, most national banks started to pay close attention to collecting and storing consumer-credit-related information, such as credit scores at loan origination, updated credit scores, payment history time series, and other consumer credit application information. At the beginning of the data collection process, the scope for using the data was narrower, focusing only on asset quality reporting or monitoring. Although some banks enlarged the collection of detailed information in customers' payment performances, it was done mostly on an ad hoc basis and not updated regularly or stored properly. For example, tapes containing updated credit scores from the credit bureau stayed in a risk manager's drawer for months and were discarded afterwards. Therefore, the data quality may be questionable in the first one or two years of collection. The norm of reliable data history on consumer portfolios is seven to eight years, although some banks may have longer histories. In addition, data quality is not always uniform for different consumer sub-portfolios. There may be more historical information on residential mortgages than on credit cards. Another issue is that the data quality is directly related to hierarchy levels. It's common to find a longer history at an aggregate level but less information when drilling down to a more detailed level for a consumer-specific portfolio.

Moody's, Standard and Poor's, and Fitch Investors Service possess much longer historical credit information on investment-grade bonds, high-yield bonds, and non-rated bonds. Fleet uses Moody's eight bond ratings--spanning 30 years, from 1970 to 1999--to test the three standard deviations of unexpected loan-loss estimate. Results show that the three-standard-deviation criterion is only good enough to cover the worst-year loss for bonds rated B or Ba. For bonds rated Baa or better, three standard deviations are not sufficient to cover the worst credit stress. Due to the non-normal nature of default risk, five standard deviations should be used for rating Baa bonds and six standard deviations for rating A or above. Of course, these results are derived based on historical data sets and are time sensitive, but at least they provide a guideline or direction to set the economic capital. Therefore, combining the knowledge and information of commercial credit risks will correct for the defect of short history of consumer credit data. Before using this publicly available information, practitioners have to ask themselves the following questions:

* Should the commercial loans and consumer loans be treated in the same way or in a different manner?

* What are the similarities and differences between commercial and consumer loans?

* What are the risk characteristics for commercial and consumer loans?

* How do the macroeconomic factors impact on commercial and consumer loans?

* How will the commercial loan information be used to make a fair reference to consumer loans?

To date, these issues have not been discussed in the literature.

Another remedy for lack of data at a particular bank is to use the aggregated and pooled consumer information from other sources. Although aggregated data cannot fully represent the characteristics of consumer portfolios in a particular bank, at least they provide a directional benchmark by covering a longer consumer credit history. Fleet collaborated with the FDIC's credit card research group to explore consumer credit data from 1984 to 1999. The average net charge-off rate was 180 bps, and the volatility measured in standard deviation equaled 57 bps for consumer products in aggregate. In this period, the minimum and maximum net charge-off rates were 61 bps and 286 bps, respectively. Three standard deviations as a proxy of economic capital requirement are good enough to sustain the worst-year loss based on this 15-year period. Noticeably, using three standard deviations as a criterion to set the economic capital is suitable only for a consumer portfolio as a whole and is not good for a specific consumer sub-portfolio, such as mortgages, home equity loans, automobile installment loans, and credit cards. It's important to remember that this three-standard-deviation criterion as an economic capital proxy is data dependent or data sensitive. Using a different historical data set may yield a different conclusion.

Fleet conducted another study using Fitch's securitized credit card data. There were 119 monthly annualized charge-off observations from January 1991 to November 2000 in this data set. Three, six, and eight standard deviations were equal to 284 bps, 596 bps, and 758 bps, respectively. The worst loss within this period was 693 bps. Obviously, eight standard deviations would be required to properly assign the economic capital in this case. The most notable phenomenon is that the FDIC data does not support the assumptions that the expected default is smaller during the economic expansion than during the economic recession. The default rate for an aggregated consumer portfolio for the most recent eight years of economic boom (1992-2000) actually is higher than the past 16 years' default rate, which covers at least two economic recessions--a minor recession in 1987 and a severe recession in 1991. Therefore, when dealing with consumer portfolios, practitioners must understand their characteristics and differences from the commercial portfolio and the impact on the macroeconomy.

Most banks currently use logistic regression with dichotomy of dependent variable--say default or no default--to estimate the default probability for their consumer portfolios. Factors change corresponding to consumer sub-portfolios. The LTV ratio plays a significant role in a secured consumer sub-portfolio but is ineffective in all unsecured consumer sub-portfolio. In addition, the sensitivities for the same factor differ among consumer sub-portfolios. For example, the impact of credit scoring on a mortgage is definitely not the same as for a credit card. If the resource and computational systems are sufficient, it's preferable to conduct detailed studies sub-portfolio by sub-portfolio. When several sub-portfolios are lumped together, valuable information is lost and this can cause inaccurate credit risk estimation.

Even within the same sub-portfolio, different loans carry different credit characteristics. Generally, every consumer sub-portfolio includes thousands of loans. It may not be worth it to use detailed analysis of each loan, because gains diminish due to intensive computation and time consumption. Clustering loans with similar credit risk characteristics into several segments to be treated as synthetic securities is feasible and offers a large benefit while losing little information. The intersegment risk scale does not increase in a linear fashion. In other words, you cannot say that the risk will increase by 10% when the credit score worsens by 10%. A consumer with a credit score above 750 behaves quite differently from another with a score of 550. For evenly distributed credit score bands, the credit risk increases exponentially. Therefore, the credit risk characteristics should be explored not only for different sub-consumer portfolios but also within the same sub-portfolio. Fleet used 1992-2000 data to study several secured and unsecured consumer sub-portfolios. The research results support this argument. Table 1 shows the estimate of annualized default probabilities on an unsecured consumer sub-portfolio measured in basis points.

Variance-Covariance Matrixes

The first step in determining economic capital for a commercial portfolio is to explore how these commercial loans react to adverse occurrences. Analogously, the reaction--as measured by correlation coefficients--toward external effects for loans in a consumer portfolio should be estimated at the very beginning. Theoretically, it is possible to estimate correlation coefficients for every pair of loans within the same consumer portfolio. Let's assume a hypothetical consumer portfolio of 10,000 loans. To fully explore the association within any pair of loans, we need to estimate 49,995,000 correlation coefficients. (2) These coefficients can be estimated, but the calculation task could be arduous and costly. The most feasible and efficient approach is to synthesize the loans based on their credit characteristics by using a bottom-up approach. Loans that fall into each segment are assumed homogeneous, measured by several credit-related factors such as credit score, LTV ratio, loan tenor, and delinquency status. Let's define aggregated loans in the same segment as a synthetic security, then estimate the correlation coefficients for each pair of synthetic securities using historical and projected future information.

If banks have over 30 years of historical default data at the consumer sub-portfolio level, the estimation of the correlation coefficients between consumer sub-portfolios and between individual loans within the same sub-portfolio would be feasible. However, it's doubtful that any bank stores this much data on any of its consumer portfolios. For the estimation purpose, the minimum of three years, at least, of trailing 12-month default history can be used to estimate the variance-covariance matrix.

The first problem is that this estimated variance-covariance matrix depicts the historical relationship. As most financial practitioners know, the future financial relationship among these consumer loans may not be a repetition of their history.

The second problem is that the relationship derived from the historical data may be time dependent and unstable. In other words, the magnitude of variance-covariance may change when using a different time period. For instance, a variance-covariance matrix based on a recessionary period may yield a very different picture from one based on a strong economic period. Which relationship should the bank adopt? Risk managers should be aware of these issues when attempting to calculate correlation coefficients. Fleet adds the scenario analyses, particularly the macroeconomic changes, into variance-covariance matrix estimation.

Monte Carlo Simulation

Techniques for estimating credit risk, market risk, and operational risk have evolved rapidly in recent years, although some techniques appear to be state-of-the-art and some appear theoretically sound but inapplicable in practice. If the credit, market, operational, and interest risks can be measured accurately, the task to set economic sustainable provision and economic capital becomes much easier. During the past five years, a handful of studies are related to credit risk and economic capital for big commercial banks, but nearly all studies focus on commercial loan portfolios. The economic capital model for the consumer portfolio is rarely seen. In the consumer credit world, models are concentrated on default, bankruptcy, fraud, and line assignment. Default models are commonplace, but mark-to-market methods are almost nonexistent. Although the research on estimating and forecasting the expected default rate and loss amounts started 30 years ago in the consumer credit world, there is almost no research geared to the estimation of unexpected losses. While most risk managers in charge of consumer portfolios understand the concept of expected credit loss very well, they have little quantitative knowledge about loss volatility. The majority of commercial banks have chosen a constant parameter to assign the economic capital rates to their consumer portfolios, but cannot rationalize the link between this parameter and the underlying loss distribution.

A Monte Carlo simulation methodology can be used to simulate the potential loss distribution for each consumer sub-portfolio. Before starting this process, there must first be an estimation of the expected loss rate and the standard deviation of the loss rates for each segment, as well as the covariance between all pairs of segments using historical information and scenario analysis results. We assume a normally distributed loss rate in every segment, although the descriptive statistics such as mean and variance vary dramatically from one segment to another. In general, the sample size is large enough for most segments. But the small sample size and nonconsumer credit history could be an issue in estimating the variance-covariance matrix, and risk managers and/or modelers should adjust estimates. Weights assigned to each segment are determined by their outstanding exposures. The portfolio is randomly simulated using 100,000 trials for each consumer sub-portfolio. Every trial must meet the condition of distribution at each segment as well as the correlation coefficient between these segments.

The last step in the simulation process is to test the loss distribution based on these 100,000 generated observations. Two sequential null hypotheses are proposed. The first assumption is that the simulated distribution is normally distributed. If this hypothesis is rejected, the simulated results do not support the normally distributed loss distribution. Then the second hypothesis comes into the picture by assuming that the simulated distribution is a gamma distribution. All six simulated loss distributions but one fail to reject the gamma distribution hypothesis. Two parameters, alpha and beta, are estimated. The maximum losses are provided corresponding to the bank's risk tolerance. Most banks chose the likelihood of solvency at a 99.95%, 99.97%, or 99.99% confidence interval. The economic capital (Value at Risk, or VaR), is measured by the difference between this maximum loss and expected loss. Figure 1 shows a simulated distribution for a secured consumer sub-portfolio. The vertical axis represents frequencies and the horizontal axis represents the loss rate measured in basis points.

[FIGURE 1 OMITTED]

Conclusion

The methodology introduced in this article estimates and allocates economic capital for consumer portfolios better than does a constant capitalization rate now used by most banks. First, the default probability, default probability volatility, and the covariance relationship between loans can be estimated to reflect a bank's consumer portfolio credit profile. Second, using a longer history than is available in a bank's own consumer portfolio offers greater reliability. As a result, the economic capital calculations not only cover the portfolios under the economic boom conditions but also include considerations of economic recession in both minor and severe scenarios. Economic capital rates derived in this manner better represent the credit risk embedded in consumer portfolios. Third, the modern portfolio theory helps consumer portfolio diversification analyses as it did commercial loan, equity, bond, derivatives, or combinations of portfolios. Currently, most banks assume that all loans in the consumer portfolio default at the same time. The diversification effect is totally ignored. Finally, using the Monte Carlo simulation after synthesizing the homogeneous loans makes it feasible to estimate economic capital. VaR is easily calculated by using simulated loss distribution.

Table 1
Default Probability--Unsecured Consumer Sub-portfolio A

                   Expected Default Rate

                         Factor 2

Factor 1    Segment 1   Segment 2   Segment 3

Segment 1       28           62          95
Segment 2       76          173         253
Segment 3      156          363         494
Segment 4      373          640         859
Segment 5      573        1,148       1,318

Notes

(1) A particular consumer product, for example, a residential mortgage, is defined as one consumer sub-portfolio.

(2) The number of permutations of n things k at a time [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

References

"Credit Ratings and Complementary Sources of Credit Quality Information," Basel Committee on Banking Supervision Working Papers, No. 3--August 2000.

Carey, Mark (2000), "Dimensions of Credit Risk and Their Relationship to Economic Capital Requirements," NBER Working Paper 7269.

Giltner, R. C. (1998), "Using Profitability Data to Price for Risk," Commercial Lending Review, Vol. 13, Number 2, Spring 1998.

Ronan O'Connor, James F. Golden, and Robert Reck, "A Value-at-Risk Calculation of Required Reserves for Credit Risk in Corporate Lending Portfolios," North American Actuarial Journal, Volume 3, Number 2: 72-83.

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.

Fang Du can be reached by e-mail at fang_du@fleet.com.

COPYRIGHT 2003 The Risk Management Association
COPYRIGHT 2005 Gale Group