CAPITAL MANAGEMENT Credit Measurement: Avoiding Unintended Results

Part 2: Weighting on Defaults—Knowing Your Institution’s Metrics

by Peter O. Davis and Darrin Williams robability of default is one of the most fundamental metrics in credit analysis. It is used to calculate expected credit loss— Pa concept central to dual ratings systems, loan loss reserves, frameworks, and, potentially, regulatory capital under Basel II. The calculation of probability of default is generally unambiguous and straightforward. As shown in this article, the appli- cation of default rates may be less so. efault risk can be meas- likely to go to default over a given necessarily produce different ured in two ways. First, time horizon. This exposure- results. If the average balance on Dwe can measure the prob- weighted metric provides a meas- defaulted loans is equal to the ability that an obligor will default ure of the dollars expected to go to average balance on outstanding over a given time horizon. A 2% default over a given time period. loans, incidence-based and dollar- default rate would indicate that In recent years, large defaults, based default rates will be the two out of 100 obligors are expect- such as Enron and WorldCom, same. However, in cases where ed to default over a given period. have demonstrated how different this is not true, using the two This incidence-based default rate these two metrics can be. While metrics interchangeably may measures the number of borrowers these two firms only counted as result in a significant mismeasure- that are likely to default. two “incidents,” they represented ment of . Given that Alternatively, we can measure the over $30 billion in defaulted cor- default probabilities are a founda- probability that a certain amount porate obligations, driving tion input to calculations of credit of obligations will be defaulted on up the dollar-based risk, misstating default risk will over a given time horizon. In this default rate in 2001 and 2002. cause all other dependent metrics case, a 2% default rate would indi- While these two metrics are (such as expected loss and credit cate that $2 out of every $100 are clearly different, they may not capital) to be off significantly. © 2004 by RMA. Peter Davis and Darrin Williams are members of Ernst & Young LLP's Global Financial Services Advisory practice, where Davis is the director of Credit Risk Services.

82 The RMA Journal May 2004 Credit Risk Measurement: Avoiding Unintended Results Part 2

Measuring Default Risk ed loss figures are often applied to rates to calculate expected loss in Default models are designed loan loss reserves, economic capi- dollars have to assume that there to measure the likelihood that an tal frameworks, and various port- is not a significant difference obligor will default over a given folio risk analyses and reporting. between the size of defaulted time horizon. This is true both for The challenge with using credits and other credits in the judgment-based grading frame- incidence-based default probabili- portfolio. The question is, how works and model-driven default ty for expected loss calculations is well does this assumption hold? frameworks. Default grades/mod- that it says nothing about the dol- Addressing differences in the els assess the likelihood that an lar-weighted default rate. A port- two metrics seems obvious: When obligor will fail to meet its finan- folio with exposure to 100 borrow- calculating expected loss, use dol- cial obligations. While there is a ers—99 for $10,000 and one for $1 lar-weighted rather than inci- link between a lender’s exposure million—could lose over half its dence-based default probabilities. to a given borrower and the dollar value (assuming zero recov- Unfortunately, incidence-based assessment of that borrower’s ery) and still have only a 1% inci- probabilities are the primary basis default risk (reflected in the bor- dence-based default rate. for the quantification of defaults: rower’s leverage), default assess- Moreover, the incidence-based in third-party credit models, inter- ments are generally an incidence- rate cannot be compared directly nal ratings systems, vendor based measure. For example, a with the historical loss since it default databases, and ratings large corporate customer may be implies a loss of $19,900 (1% of agencies’ bond default studies. rated a four on a lender’s internal $1.99 million), not the $1 million Further, the use of a dollar- rating scale, regardless of whether that was actually lost. weighted default rate creates the amount lent to that borrower Expected loss frameworks complications when working with was $3 million or $30 million. based on incidence rates of usage given default (UGD) Default models are typically default may implicitly assume assumptions for unused commit- validated at the time of develop- that the underlying portfolios are ments. If a dollar-weighted ment and back-tested over time perfectly granular—in other default rate is applied, the impact to ensure that the realized default words, the portfolio is reasonably future draws have on expected probabilities on an incidence basis “fine-grained” with exposures loss is already captured, making it fall within a predefined range being evenly spread out across a difficult to appropriately measure established by risk-rating band. large number of obligors. If com- UGD for unused commitments. This default validation process mercial portfolios were perfectly says nothing about whether inci- granular, incidence-based and dol- A Tale of Three Portfolios dence-based default rates equal lar-weighted default rates would As an illustration of the dollar-based default rates for a always be the same. impact of dollar-weighted vs. inci- given lender. Since commercial portfolios dence-based default rates, imagine are not perfectly granular, three banks with loan portfolios of Using Default Rates using incidence-based default $100 million divided among the It is not uncommon for insti- tutions to assume that dollar- Exhibit 1 based and incidence-based Formula for Expected Loss default rates are equal. The stan- Expected Loss (EL) = Outstanding balance dard expected loss formula is x probability of default shown in Exhibit 1 (for disbursed x closed-end loans). Using an inci- dence-based default probability in Probability of Default: = number of obligors that default during period this formula implicitly assumes Incidence Basis total number of obligors at start of period that the two default metrics are Probability of Default: = dollar value of loans to obligor that defaulted during period equal. These dollar-based expect- Dollar-Weighted Basis dollar value of all loans at start of period

83 Credit Risk Measurement: Avoiding Unintended Results Part 2

Exhibit 2 rate is based on the number of Implications of Incidence-Based and Dollar-Weighted PDs defaults and the average values of the loans (three defaults times Comments Obligor ID A Bank B Bank C $10 million). But because the size 1 10 25 3 discrepancy of the loans is so —All banks have loans outstanding to the 2 10 3 25 large, the average value hides same 1- obligors, but in different amounts. more than it reveals. A key piece 3 10 3 3 of information—the size of the —Obligors 1, 5 and 8 (in gray) default dur- 4 10 3 25 ing the period; the others do not. positions in the defaulting oblig- 5 10 25 3 ors—has been lost. —The incidence-based PD is identical for 6 10 4 4 the three banks: 30%. Bank C: Small positions in 7 10 4 25 —The dollar-weighted PD ranges from 10% loans to defaulting obligors. At to 75%, depending on the size of the loans 8 10 25 4 Bank C, the credit decision was to obligors that default. 9 10 4 4 handled differently. This bank has 10 10 4 4 positions in the same 10 obligors but holds balances of $3 million in Portfolio Statistics two of the defaulting obligors and 1. Outstanding Balances $100 $100 $100 $4 million in the other. The aver- 2. Number of Defaults 3 3 3 age size of the other balances is 3. Number of Obligors 10 10 10 larger. In this case, the dollar loss 4. Incidence-Based PD (2 ÷ 3) 30% 30% 30% is far lower than the incidence- 5. Dollar Loss Implied by Incidence-Based PD (1 x 4) $30 $30 $30 based default rates imply. 6. Principal Value of Defaults $30 $75 $10 7. Dollar-Weighted PD (6 ÷ 1) 30% 75% 10% The Loss Severity Adjustment 8. Average Charge-off Balance (6 ÷ 2) $10 $25 $3.33 In the cases of Bank B and 9. Average Current Balance (1 ÷ 3) $10 $10 $10 Bank C, the use of an incidence- 10. Loss Severity Adjustment (8 ÷ 9) 1 2.5 .33 based PD alone may not provide for complete transparency and the same 10 borrowers, three of which doesn’t matter (since every loan is resulting expected loss estimate default. The obligors in the port- the same size). The dollar loss may not reflect certain trends in folio all have the same risk rating implied by the incidence-based the portfolio. To account for these and incidence-based default rates. default rate is the same as the his- trends, an adjustment, which we Assume the loss-given-default rate torical loss. referred to as the loss severity for the defaulted loans is 100% (in adjustment, may be incorporated. Bank B: Large positions in other words, no recoveries). The loss severity adjustment is loans to defaulting obligors. Finally, assume the portfolios are the ratio of the average charge-off Bank B illustrates what happens comprised 100% of closed-end balance (Line 8) to the average when the largest loans are to loans, alleviating the complications balance (Line 9). obligors that default. Like all of usage-given-default assump- The loss severity adjustment three banks, Bank B starts with tions for unused commitments. restores the information buried in $100 million from 10 obligors for The three banks are shown in the averages, reconciling the inci- an average balance of $10 million Exhibit 2. dence-based default rates with (Line 9). The three $25 million Perhaps the most simple and the bank’s loss in dollars. In the loans (in gray) are far larger than straightforward is the experience case of Bank B, where the largest the average. At the end of the of Bank A, which holds a portfolio credits have a higher propensity period, these three borrowers of $10 million loans spread evenly for default, the losses implied by default. The dollar loss implied across 10 obligors. At Bank A, size incidence-based default rates by the incidence-based default need to be adjusted upward by a 84 The RMA Journal May 2004 Credit Risk Measurement: Avoiding Unintended Results Part 2 factor of 2.5, the loss severity default rate? Should I easy enough to describe. But a adjustment. After the adjustment, redesign my ratings assign- consensus on the concepts doesn’t the dollar losses reflect historical ment process? necessarily translate into agree- figures and the trend in the port- • If large loans are more sensi- ment on a number representing folio towards higher dollar-weight- tive to cyclical factors, is the the credit risk of a loan portfolio. ed default probabilities. The difference between dollar- Seemingly minor differences in appropriate level for making this based and incidence-based assumptions can result in large adjustment may be at the product default rates driven by the disparities in estimates of credit and rating grade level. recent economic cycle? risk—with potentially far-reaching • Is the composition of my effects on a bank’s ability to meas- What About Your Bank? portfolio across large corpo- ure and manage credit risk. As the case of Bank A illus- rate and smaller, middle- Beyond the issue of credit trates, the issue of incidence- market borrowers driving the measurement is a more basic based versus dollar-weighted differences between the two theme: the importance of under- defaults disappears when the default measures? standing the metrics that drive loans that default are the same • What impact do these ongo- your business. There is no right or size as those that don’t. The two ing trends in dollar-based vs. wrong way to measure the proba- metrics diverge only when loans incidence-based default rates bility of default. Each method is to defaulting borrowers are larger have on economic capital, appropriate for different uses. It is or smaller than the average credit loan loss reserves, and other important to know which method in the portfolio. risk metrics? your bank uses for what purposes. To diagnose where your bank Otherwise, it’s easy to be misled stands on this issue, it’s useful to Know Your Metrics by the very metrics that are ask: As the first article in this intended to create transparency • Is there a consistent bias in series pointed out, the basic con- and improve business decisions. ❒ my ratings system toward a cepts of credit risk measure- higher or lower dollar-based ment—default probability, recov- Contact Davis by e-mail at [email protected]; contact Williams default vs. incidence-based ery rate, —are at [email protected].

Next Month in The RMA Journal

RMA–The Association Observes Our 90th Year of Service to the Banking Community

85