Do Banks Internal Basel Risk Estimates Reflect Risk? *

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1 Do Banks Internal Basel Risk Estimates Reflect Risk? * Irina Barakova Ajay Palvia February 2014 Abstract Using supervisory data for US banks, we evaluate the alignment of Basel II/III AIRB (Advanced Internal Ratings Based) risk estimates with portfolio risk. We use loan performance as a direct measure of portfolio risk as well as less direct market-based measures. Our results document that loan performance is highly correlated with AIRB risk weights and that, in contrast, Basel I risk weights are not reflective of loan performance. We find that capital requirements under the AIRB approach are higher than those under Basel I especially for portfolios recently under stress such as mortgages and some sovereign exposures. The alignment of Basel risk estimates with market-based risk indicators is less robust although, the association is nevertheless stronger for AIRB risk weights relative to Basel I. Our results support the view that internally generated risk weights are determined mostly by portfolio risk and are, as a result, substantially more risk sensitive then the fixed asset type based risk weights of Basel I. Key Words: Basel II, Basel III, Risk Weights, Regulatory Capital * We thank Mark Levonian, Tanya Smith, and Mitch Stengel, participants at the 2012 Risk Quantification Forum, and participants at the WEAI/IBEFA conference for helpful comments and suggestions. All views expressed in this paper are those of the authors alone and do not necessarily reflect those of the Office of the Comptroller of the Currency or the U.S. Department of the Treasury. Credit Risk Analysis Division, Office of the Comptroller of the Currency. Irina.Barakova@occ.treas.gov Policy Analysis Division, Office of the Comptroller of the Currency. Ajay.Palvia@occ.treas.gov 1

2 1. Introduction Under Basel II capital rules and the recently introduced Basel III capital rules, banks subject to the advanced internal-rating-based (AIRB) approach are required to quantify their risk parameters, i.e., probability of default. (PD), loss given default (LGD), and exposure at default (EAD). These estimated parameters are then used to calculate risk weighted assets (RWAs). 1 This is in sharp contrast to the constant risk weights per asset class under Basel I and indeed a key motivation of the Basel AIRB approach is to improve risk alignment for large and systemically important banks by allowing them more discretion in assessing risk. Therefore, substantial differences in AIRB parameters and risk weights across banks are expected and if banks estimate risk accurately, such differences are expected to be primarily driven by the riskiness of bank loan portfolios. While the improved alignment of internally generated risk weights with portfolio risk relative to fixed asset class risk weights is the premise of the Basel II/III AIRB approach, the potential for substantial differences in risk weights due to reasons other than portfolio risk has received a lot of attention by industry observers. The concern is that the inherent flexibility of the AIRB framework may allow for differences in risk weights for reasons other than differences in portfolio risk such as variations in bank modeling and credit risk management practices, conservatism, reference data quality, and regulatory discretion. For example, it has been suggested that financial markets do not trust the new Basel risk weights (see articles by BNP Paribas, 2011, Barclays Capital 2011, Citigroup, 2011). This has also been a subject of further investigation for the Basel committee which issued a report making international comparisons of RWAs. 2 Several recent academic papers have also considered the consistency with which banks measure RWAs. 1 While the proposed Basel III rules include some important changes such as increased capital buffers and supplementary leverage ratio, the basic AIRB risk quantification remains the same with very minor exceptions. 2 The public report from the Basel Supervision and Implementation Group working sub group on banking and trading book RWAs were published in 2013: The analysis faces data limitations with cross jurisdictional comparisons but the general finding is that there are regional differences and around a quarter of RWA differences are practice based and cannot be explained with differences in risk. 2

3 Motivated by the substantial industry and academic questioning of how well Basel internal risk weight estimates reflect risk, we explore three related questions using newly available regulatory data for US AIRB banks. First, we consider whether various AIRB based risk estimates are linked with measures of loan performance. Second, we ask whether the risk ranking of Basel II/III AIRB risk weights has improved relative to Basel I fixed risk weights 3 We hypothesize that if differences in Basel AIRB parameter estimates between banks are driven primarily by differences in risk, rather than non-risk factors, then the link between Basel risk estimates and indicators of loan-performance should be stronger under the AIRB approach relative to Basel I. Third, we consider the relation between market-based risk indicators and portfolio risk. While, there is no direct link between a noisy market-based view of banks default risk and its internal assessment of portfolio risk parameters, to the extent banks are primarily engaged in traditional banking activities (i.e. lending to individuals and businesses), the overall default risk of a bank should be related to its portfolio risk for a given level of leverage. Therefore, we expect that there should be some, albeit perhaps less robust, relation between the market s assessment of the bank default risk and Basel based risk estimates. The current evidence tends to be skeptical that differences in Basel risk weights can mostly be explained by differences in risk. Vallascas and Hagendorff (2011) evaluate the relation between RWA to assets and asset volatility in an international sample of banks and find a statistically positive relation but argue that the economic relation is small and the effect on capital limited. They also suggest there is only a marginal increase in risk sensitivity for banks that have adopted Basel II. Similarly, Das and Sy (2012) document a negative relationship between RWA and stock returns over the periods of financial crisis for European and US banks; however, this association is found to be weaker where there is discretion in the calculation of RWA (such as countries that have implemented Basel II). Mariathasan and Merrouche (2013) directly critique Basel II RWAs as not reflecting actual risk. Firestone and Rezende (2012) evaluate bank internal risk assessments by comparing risk weights on a common set of obligors across US banks; they find significant differences but caution that the evidence may not be representative of the banks' full portfolio. 3 We use the terms Basel II/II risk weights and AIRB risk weights interchangeably as all references in this paper to Basel II/III risk weights. 3

4 A related strand of literature considers differences in capital requirements under Basel II and Basel I. 4 Altman and Sabato (2005), use survey evidence from US, Italy, and Australia, suggesting banks should benefit from lower capital requirements under Basel II. Saurina and Trucharte (2004) also suggest a similar impact in Spanish firms. In a more recent analysis, Antao and Lacerda (2011) suggest that capital requirements are generally lower under Basel II although they suggest that this may depend significantly on the asset class. They do not however directly consider the risk-sensitivity of risk weights and rely on aggregate estimates of Basel II risk parameters. Leslé and Avramova (2012) compare AIRB and Basel I RWAs across banks with the same Moody s ratings and find wide dispersion. Therefore, the current evidence regarding RWA consistency is either based on Pillar 3 information for Basel II/III banks or compares banks internationally under Basel I with those under different levels of AIRB implementation. It also does not focus on U.S. AIRB bank implementation as only supervisors currently have access to granular Basel AIRB data for US banks. Given the importance of U.S. banks to the global financial system, an evaluation of the U.S. AIRB risk weights is important. 5 Also, focusing within a jurisdiction, allows the various risk measures to be more comparable since there are in general no differences in the legal framework, accounting practices, or regulatory enforcement. 6 Moreover, there is no evidence on the differences in sensitivity of AIRB and Basel I risk weights. Our analysis makes use of these supervisory data to evaluate whether there is internal US risk alignment of Basel II/III risk weights and whether the degree of alignment is an improvement relative to Basel I. In our study, we evaluate the relation between several Basel risk measures and several indirect and direct proxies for bank loan portfolio risk. We document that business mix, which we consider to be an indirect proxy for portfolio risk as certain exposure types are inherently riskier, explains a substantial portion of the variation in both Basel I and Basel II/III risk 4 Previous research has also considered whether Basel I risk weights are consistent with actual risk levels. For example Acharya, Schnabl, and Suarez (2013) suggest banks used asset-backed commercial paper conduits to lower capital requirements rather than to transfer risk to investors and therefore to skirt Basel risk rules. 5 For example, the Financial Stability Board a task form initiated by the G20, suggests that about one-fourth of the systemically important global banks are US banks. See for details. 6 While there are several banking regulators within the U.S, the regulatory policies are generally set jointly and in particular, Basel AIRB parameters are reported under a consistent framework. In addition, all major banks are organized as bank holding companies (BHCs) for which the ultimate regulator is the Federal Reserve Board. 4

5 measures. In multi-variate tests, we find that business mix alone explains more than 50% of the variation in our Basel risk measures. In addition, all of our accounting-based loan performance measures are highly correlated with AIRB risk weights after accounting for business mix. Only business mix has a statistically significant association with Basel I risk weights; we interpret this as evidence that as the Basel I approach, which assigns constant portfolio level risk-weights by asset class, is not substantially related to portfolio risk. 7 We directly compare AIRB and Basel I RWAs and find, on average, AIRB RWAs are higher during our sample period; this is especially true for banks with high exposure to residential real-estate and sovereigns while not true for banks with high exposure to corporate loans. In a multivariate setup we also confirm that the difference in AIRB risk weights and Basel I risk weights is largely due to differences in loan performance. This suggests that the Basel II/III AIRB risk weights are more adaptive and forward looking in reflecting the increased risk in these two asset classes. Lastly, we document that the relation between market-based risk measures and AIRB risk-weights are less robust and usually not statistically significant, but still positive in most cases; the relation between Basel I risk weights and market risk indicators such as bond spreads is even weaker and often even negative. Throughout our analysis, we consider various ways to measure AIRB risk-weights and our results suggest some differences based on which measure is considered. In particular, RWA divided by Assets has been used in many prior studies as the primary or only measure of Basel risk. But this measure is based on the regulatory capital formula and does not represent expected losses. The accuracy of bank internal parameter estimates could better be tested using total expected credit losses and portfolio level expected default rate which should have stronger empirical associations with observed portfolio risk; we find this to be particularly true for market based indicators which may not evaluate risk and correlations in the way implied by the Basel capital formula. Some studies have suggested that banks engage in optimization in bank risk weights, whereby banks intentionally vary model assumptions, inputs, etc. to reduce capital requirements 7 While we don t directly assess the risk weights under the standardized approach, it is worth noting that the standardized approach also assigns asset-class based risk weights so our analysis also suggests that the AIRB approach is superior in risk sensitivity compared to that approach. 5

6 without compensating reductions in risk and our analysis indirectly assesses this issue. 8 Though we cannot rule out some degree of non-risk based variation in AIRB bank risk-weights due to optimization, the strong association between loan performance and AIRB risk measures and the relatively high adjusted R-squares in our multivariate tests (in the range of about 60% to 90% depending on specification) suggest that the risk weights are not largely driven by such non-risk based factors. Our results are also related to the market discipline literature. Bliss and Flannery (2002) point out that market discipline is comprised of both market influence and monitoring. Market influence is more difficult to test but market monitoring should be reflected in market indicators such as equity volatility, credit spreads, uninsured deposit rates, etc. and has been explored in several empirical papers. Flannery (1998) offers a review of the early US based evidence which suggests that markets have the potential to improve banks supervision by providing more timely information and by giving regulators the evidence needed to take corrective actions. Several cross-country studies such as Cubillas et al. (2012), Demirguc-Kunt and Huizinga (2004), and Nier and Baumann (2006) also find some support for market discipline. While the literature often controls for very large banks following O hara and Shaw (1990), who show that markets reward banks deemed too-big-to-fail (TBTF), few studies explicitly consider the risk sensitivity of very large systemic institutions. One relatively close exception is a recent work by Acharya, Anginer, and Warburton (2013) who suggest that bondholders are not sensitive to risk for very large institutions; however, this study does not focus exclusively on AIRB banks and considers a period prior to Basel II reporting. Therefore, there are no studies to our knowledge focused on U.S. AIRB banks. Our paper compliments the work of Acharya, Anginer, and Warburton (2013) in showing a weak but usually positive relation between market risk indicators and Basel AIRB risk estimates. While it is beyond the scope of our paper to consider whether the weak market measure sensitivity we find is due to government guarantees, difficulty in isolating out asset risk from the overall institution default risk that market measures generally proxy for, or because of general market volatility during the 8 Aside from differences in asset risk, Basel risk weights can be lower or higher because of differences in modeling methodology, assumptions, choice of reference data, etc. These factors are not observable and, in addition, differences in these factors would not necessarily be informative about optimization because banks can have variation in these variables for legitimate reasons. 6

7 sample period, our results nevertheless suggest limitations in the effectiveness of Pillar 3 disclosures and resulting market discipline. The issues with the market measures also point to accounting portfolio performance measures as more reliable for AIRB monitoring and benchmarking. The rest of the paper is organized as follows. Section 2 describes our research design including an overview of the data and summarizing the methodology and hypotheses. Results are discussed in section 3 and section 4 concludes. 2. Research Design 2.1 Data In the US, banks subject to the advanced approaches are currently required to report to regulators their AIRB parameters and risk weights on a quarterly basis under a uniform template, i.e. the FFIEC 101 report. This data, which is not released publicly, allows for comparison of Basel II/III AIRB risk weights across US banks. 9 Since only very large financial organizations are subject to AIRB, our dataset is relatively small but contains the universe of US banks reporting AIRB parameters over the sample period. This comprises most of the largest and prominent U.S. banking organizations which makes our analysis broadly representative for purposes of evaluating consistency of AIRB banks. 10 The consistent reporting format and large number of reported variables allows for a more accurate and complete cross sectional analysis of AIRB risk weights. 11 The reporting is aggregated at the bank level but also given by asset class (e.g. corporate, commercial real estate, residential mortgage). For the banking book, the report captures the current balance and unused credit lines, an exposure weighted average PD, LGD and EAD by asset class and also by pre-determined PD band. Our data spans from 2010 Q2 to 2012 Q4 and contains 115 bank-quarter observations Following, official Basel II/III implementation, some of this information is expected to be made public. 10 For confidentially reasons, we cannot directly name the banks included in the sample although the total assets of included banks in the sample as of 4 th quarter 2012 is over $11 Trillion. 11 Recent industry studies focus on publicly available data gathered from various sources and do not include Basel II risk weights from US banks. 12 Due to data confidentiality we cannot disclose the number of banks reporting each quarter or present in our sample. 7

8 We consider several Basel based risk measures. First, we construct a total institutionwide ratio of AIRB RWA divided by total bank assets, as reported by FFIEC 101 and the public FR Y-9C report, respectively. For comparison to Basel I, we take the aggregate Basel I RWAs to total assets from the FR Y-9C report. We also construct three banking book AIRB risk measures, in addition to the AIRB RWA measure. While RWA scaled by assets, often termed RWA density in previous studies, is a simple straightforward indicator which allows for easy comparability across banks it captures more than just the loan portfolio risk and suffers from some limitations. 13 Therefore, we consider several banking book Basel risk measures in most of our tests as well. These measures include AIRB Banking Book (BB) RWA/Exposures (exposures being defined as total balances plus unused commitments), AIRB expected credit losses (ECL which is the product of PD, LGD and EAD) / Exposures, and AIRB Average PD. 14 The distribution of Basel risk measures each quarter is shown in figure 1. In Panel A, we illustrate the distribution of Basel I RWA to Assets and AIRB RWA to Assets. We see that there is similar level of variation in both measures over time but still substantial differences in the timing of the ups/downs. In Panel B, we show the distributions of the AIRB BB measures; these measures, in particular the AIRB ECL/Exposures and AIRB PD/Exposures, look very different over time compared to the AIRB RWA to Assets which is consistent with the possibility of different levels of alignment based on which of these measures is used. Bank financial information, including loss and delinquency data, is obtained from FR Y- 9C reports. We obtain proxies for loan performance from the FR Y-9C report at different points in time. We take different accounting measures such as delinquency, non-accrual loans, and charge offs. These indicators measure loan performance which reflects portfolio risk; delinquency and non-accrual loans serve as an ex-ante indicator of riskiness of the current loan portfolio and past-charge-offs denote an ex-post measure of risk for the past portfolio; to the extent banks do not substantially alter their business model or lending in the short term, we expect all three of these measures to be current proxies for portfolio risk. 13 Our specific hypotheses vis-à-vis the different AIRB risk measures are explained in section As a further robustness exercise, we also estimate our main tests using EAD (Exposure at Default) as an alternative to total balances plus unused commitments to measure exposures. These unreported results are similar to our reported results. 8

9 We use various types of data to construct the market risk measures. Our risk measures include Moody s Bank Ratings, bank expected default frequency (edf) estimates from Kamakura s default models, bond spread, and stock return volatility; these measures are meant to be representative of several well established market indicators of bank risk since there is no single universally recognized best measure. 15 In the case of Moody s, the data is not continuous and we use a dummy indicator, Moody s Rating Weak, to denote the rating being Aa3 or worse. 16 The Kamakura PDs are based on a reduced form PD model estimated using logistic regression controlling for several standard accounting ratios such as cash flow and leverage and, in addition, stock market measures such as stock return volatility and capitalization ranking as well as some overall economic condition measures. 17 Other potential sources of external credit risk evaluation are from the equity and bond markets. 18 As one measure, we use the quarterly volatility of daily bank stock returns from the equity markets. 19 Finally, from the bond markets, we take the option adjusted credit spread relative to LIBOR for all the outstanding bonds. 20 Note that unlike the accounting measures, the various market and model measures consider overall institution risk, including banking and trading book risk, as well as the level of capitalization, management quality and possibly other soft information used by rating agencies or market participants. Figure 2 and figure 3 respectively, show the distribution of the loan performance and market risk measures through time. The accounting based measures show some time-based variation but are substantially more stable across time than the market based measures which 15 A limitation of our results is that they do not necessarily apply to all conceivable risk measures but only to the ones we consider. While we acknowledge other such measures exist, most of them are likely to be highly correlated with measures we include so we therefore, consider our measures to be representative of the markets perception of bank risk. 16 The results are similar but somewhat weaker using a continuous measure creating by coding the observed ratings (which range from Aa2 to Baa2). 17 The Kamakura model that we use, Jarrow-Chava is comparable to the Moody s KMV edf measure but is based on a reduced form model incorporating a KMV like edf. More information about Kamakura models can be found at Kamakura and KMV show similar performance of their default metrics on public firms. 18 We obtain spreads data from FactSet. We use all bonds as the categorization was not comprehensive but have tested results using the subset of unsecured bonds as a better proxy for bank credit risk. 19 Other stock market measures, such as returns, market beta, or the idiosyncratic component of volatility could also be used (see Das and Sy 2012). 20 From the derivative markets, in unreported tests, we obtain the 5 year CDS spread for each of the banks. The results, which are based on fewer observations, are not substantively different compared to those of our other measures. 9

10 vary dramatically; to the extent loan risk does not deviate as much from quarter to quarter, this suggests a large noise element embedded in the market measures. Beyond the fact that market measures reflect overall firm risk rather than portfolio risk, they also reflect other factors beyond credit risk. A liquidity premium, interest rates and overall market conditions can all be reflected in stock return volatility or bond spreads. 21 We use the FFIEC 101 data to also construct portfolio mix measures by calculating the shares of corporate loans, residential real estate balances, and sovereign exposure as those are the largest portfolios in our sample of banks and represent very different types of assets and credit risk level; we estimate these shares as the percentage of EAD derived from each of these portfolios. Finally, we create a variable denoting the size of banking book business by dividing total balances by total assets. The wide distribution of this variable, from around 80% to 20% suggests substantial differences in banks banking book relative size; we denote traditional banks as banks with at least 50 percent of their business derived from the banking book. Detailed definitions and summary statistics for all variables are provided in table Methodology and Hypothesis Development Our goal is to compare Basel AIRB risk weights to various loan-performance based and market-based risk indicators in order to assess the degree to which these various measures are aligned; in addition, we seek to assess whether risk alignment is improved under the Basel AIRB approach relative to Basel I. We expect that if Basel risk measures are quantified as intended and are aligned with risk than there should be a positive relationship between Basel risk weights and actual portfolio risk. We do not have a particular expectation on the shape of the relationship between Basel risk weights and asset risk measures except that it should be monotonic. 22 Our empirical analysis begins by considering the association between Basel risk measures and loan performance. We conduct univariate rank correlations for an initial assessment and then turn to a series of multivariate tests with the model defined as shown in equation (1). 21 See Longstaff et al (2005) for a discussion of liquidity premium and bond spreads. 22 Following the Basel II capital formula one may expect convexity of the relationship, but this relationship does not need to translate at the aggregate bank level of risk. 10

11 (1) Basel Risk(t) =f 1 (loan performance, business mix, bank size, quarter) Basel Risk refers to bank asset risk as measured by several indictors of Basel I and Basel II/III AIRB risk. In equation (1), loan performance refers to accounting-based loan performance measures. Business mix denotes controls for corporate, sovereign and residential real-estate exposure in addition to the size of the banking book relative to the bank s overall assets; since different types of assets vary in risk, these controls serve as a first-order measure of risk. Finally, we control for bank size and time effects. We estimate all of our models using OLS with clusterrobust standard errors based on the wild-bootstrapping procedure outlined in Cameron, Gelbach, and Miller (2008). 23 We expect bank losses to be related to the product of the three parameters that AIRB banks are required to estimate internally (PD, LGD, EAD). PD is expected to be correlated positively with delinquencies. Basel I risk weights, on the other hand, are based only on the banks business mix and not based on actual loan performance; thus we expect no relation between Basel I RWA/TA and loan performance after controlling for the business mix. In addition, we expect the greater risk sensitivity of AIRB risk weights is largely attributable to its more precise portfolio risk weights which in turn should lead the difference between AIRB RWA/TA and Basel I RWA/TA being driven by weak loan performance. H1: BII/III AIRB Risk measures are strongly associated with loan performance H2: BI RWA/TA is not associated with loan performance H3: AIRB RWA/TA BI RWA/TA is related to loan performance beyond difference in asset type While a direct link between Basel AIRB risk measures and loan performance is straightforward if Basel AIRB measures indeed reflect risk consistently across banks, many studies have also linked market based risk measures to Basel indicators of risk (see for example Vallascas and Hagendorff (2011) and Das and Sy (2012)). In addition, much of the recent criticism of the Basel AIRB implementation stems from analysts and bankers suggesting that the 23 Due to the small number of groups, the usual cluster-robust standard errors are not appropriate; Woolridge (2003) provides more background on the problem. For robustness, we estimate all of our regressions both without clustering and with the usual cluster-robust standard errors. The results, not reported, are similar. Our implementation of the wild-bootstrapping procedure is based on Stata routines that can be found at 11

12 markets do not trust the Basel risk weights (see articles by BNP Paribas, 2011, Barclays Capital 2011, Citigroup, 2011). However, unlike Basel AIRB risk measures which capture the risk of bank assets, market measures generally reflect overall bank default risk. 24 Therefore, while it is useful to assess in the U.S. AIRB context whether the market view of default risk is similar to the asset risk suggested by Basel risk weights, there is no way of directly assessing this. Our approach borrows from the framework of structural default models in that such models typically represent firm risk as a function of asset volatility and leverage. Based on this approach, we suggest that a bank s asset risk (or more loosely portfolio risk) can be measured by market indicators after partialling out the effect of leverage, which we proxy by the non-risk-weighted capital ratio. Therefore, our model assumes that controlling for capital will allow us to isolate the portfolio component of risk embedded in the market risk measures. Our regression model relating Basel risk weights to market risk indicators is shown in equation (2). 25 (2) Basel Risk(t) = f 2 (risk, business mix, capital ratio, bank size, quarter) In equation (2), risk denotes the market s assessment of risk based on a variety of indicators. Assuming that our inclusion of capital ratio is sufficient to separate out the asset risk component of the market risk measure, we expect that there should be a positive relation between the market risk measure and the Basel measure of risk if banks are consistently quantifying risk accurately. However, given that markets are noisy and can reflect speculation whereas bank portfolio risk may not vary as much, we expect the relation between AIRB risk measures and risk in equation to be on average weaker and less robust than what we find between AIRB risk measures and loan performance; the relation might be even weaker due to government guarantees of too-big-to-fail institutions (TBTF) as argued by Acharya, Anginer, and Warburton (2013). As before, we expect no relation between Basel I risk weights and risk after controlling for asset class mix. H4: BII/III AIRB Risk measures is weakly associated with market assessment of risk H5: BI RWA/TA is not associated with market assessment of risk after controlling for asset class 24 Ideally, one could compare Basel risk weights to market-based portfolio risk indicators but there are no such direct indicators to our knowledge. 25 Theoretically, if under Basel II each bank estimates RWA accurately, and holds capital as to achieve the same level of failure risk (i.e., 0.1%), then markets risk measures would be identical across banks. 12

13 Although our primary measures of Basel risk are AIRB RWA/TA and BI RWA/TA, we also consider three banking book (BB) specific measures. This is for several reasons. First, the numerator of AIRB RWA to assets includes all risk-weighted-assets from both the banking book and trading book of the bank; our loan performance based risk measures are focused on portfolio risk which is related only to the banking book. Using AIRB risk measures that do not focus on the banking book may underestimate the degree of risk alignment. Thus, we also test with the alternative measure AIRB banking book (BB) RWA divided by exposures. A second deficiency of the total RWA measure (and the AIRB BB RWA measure) is that it measures risk through the prism of the regulatory Basel capital formula which is based on a non-linear transformation of the Basel risk parameters (PD, LGD, and EAD); in particular it uses a stressed PD based on a correlation with a systemic factor. The internal bank PD estimates are likely to be more directly related to delinquency and charge of rates. Therefore, we also use the total estimated credit losses (ECL) which is the product of PD, LGD, and EAD divided by total banking book exposures as a Basel risk measure more directly related to observed credit losses. To the extent the non-linear transformation embedded in the AIRB formula distorts the risk alignment, this measure, AIRB ECL/Exposures, should allow for a stronger association. 26 Lastly, a deficiency of RWA to total assets (and the first two banking book based measures) is that these measures do not account for the fact that some Basel parameters may be less precise than others. In particular, there is a lot of uncertainty in estimating both exposure at default and loss given default while default risk is better understood and better measured which should lead to default risk estimates being more reliable and robust. Therefore as our third and last AIRB banking book indicator is the EAD weighted average probability of default, or AIRB BB Avg PD. H6: Risk sensitivity of the AIRB risk measures should be somewhat higher for the banking book AIRB risk measures, in particular, for the PD based measure which is potentially the easiest for banks to accurately measure and is directly comparable to banks non-performing loans ratio 26 Note that the ECL is not necessarily the current conditional forecast of losses for a given quarter, since the required parameters are not the conditional PD, LGD and EAD. Rather, PD needs to be a long-run average annual default frequency while LGD and EAD need to represent expected exposure and loss rates during downturn conditions. In a way ECL is an alternative RWA measure which is based on long-run average PD rather than the stressed PD provided by the Basel II capital formula. 13

14 2.3 Timing and Endogeneity We compare the ranking of institutions by the various RWA measures, as of a particular point-in-time, and then we consider the variation in risk ranking of institutions by a range of risk measures. In all of the univariate and multivariate analysis the timing of the risk measures is an important consideration. For all of the accounting-based and market-based risk measures, we consider the contemporaneous scaled Basel II/III and Basel I risk weights. For the accounting ratios, by definition the risk weights are related to the severely delinquent exposures as those are treated as 100% PD. We use charge offs over the previous 4-quarters as our first accountingbased portfolio risk measure but test other measures such as a historic average over a longer period similar to the Basel II reference data requirements as well as contemporaneous charge offs. We also use the average non-accrual loans rate over the previous 4 quarters and the ratio of loans 30 to 89 days past due as of the current quarter. 27 Note that these accounting measures have a level of persistence such that correlation results may not be sensitive to timing. We also stress that our univariate analysis and regression analysis is intended to aid in identifying whether Basel AIRB risk weights rank risk in alignment with actual loan performance or asset performance inferred from market indicators. We are not suggesting a causal relationship for two reasons. First, RWAs are not determined by market measures of bank risk as there are strict regulatory requirements for estimating AIRB risk parameters and market measures are not determined by RWAs, at least in the US, where Basel II RWAs are still private so markets cannot consider them. Second, although past portfolio performance shapes the reference data that is then used for Basel II parameter estimation, and therefore could affect future RWAs, the accounting measures may not necessarily represent the risk of the current portfolio. Testing the correlation between current risk weights and portfolio performance in the subsequent twelve months is not subject to such criticism and we treat it as a robustness check The Basel definition of default differs for wholesale and retail losses and is based on a different delinquency or non-accrual status (90 days past due for wholesale and 180 days past due for mortgages and credit cards). To be consistent across exposures we use only the non-accrual rate but in unreported results have confirmed results based on a joint non-accrual and 90 days past due rate. 28 The interpretation of the effect accounting measures have on risk weights differs depending on the timing. A relationship with past portfolio performance shows the effect of reference data and most recent historic portfolio risk evidence. The effect of the contemporaneous delinquency and charge offs is showing the build in effect from the Basel formula, while the future portfolio performance over the next year serves as a type of back test of current risk weights. 14

15 In additional tests, we further attempt to mitigate any potential effects of endogeneity by lagging the loan performance and market indicators; the results are similar. 29 We do not include bank fixed effects in our specifications since we want to be able to capture whether banks with higher RWAs also have higher risk. A specification with bank fixed effects with controls for risk metrics could be used to identify banks that deviate significantly from the expected levels given their loan performance. We do however test not only the levels of risk weights but also the difference between Basel II/III and Basel I risk weights which controls for other unobserved characteristics. A caveat to our approach is that our evaluation is based on relative rankings. A conservative institution, which assigns higher AIRB parameters than necessary given the portfolio risk will impact the general alignment of banks' risk and risk weights across all banks. In such cases, the "misalignment" may not be directly interpretable as an inaccuracy on the part of the less conservative banks; rather, the conservative banks have affected the order of relative ranking. Note that a conservative bank in terms of risk weights may not appear conservative in terms of risk weighted asset capital ratio. Since capital is costly to obtain, in the long run we expect banks to aim at providing the most accurate possible risk parameters for their portfolio but the AIRB approach is not yet officially implemented in the US. 3. Results 3.1. Univariate Correlations We begin our analysis by considering how the various Basel risk measures are associated with each other and how the various controls, loan performance, and market indicators are associated with each other. Table 2 Panel A shows the pairwise correlations between the Basel risk measures. While all of the correlations are statistically significant (p-values below 0.10), we can see some initial indications that the AIRB measures are substantially different than the Basel I risk measures. The various AIRB measures are very highly correlated with one-another 29 As a further test, for the regressions of Basel risk measures on market based risk measures, we consider the instruments used in Flannery and Rangan (2008); unfortunately, these instruments have only limited statistical correlations with the market indicators in the first stage regressions. Nevertheless, the results of the second stage regressions are broadly consistent with those reported in the paper. The results of all the unreported specifications using lags and instruments are available from the authors upon request. 15

16 (between 74% and 91%) while the correlation of all of the AIRB measures with the Basel I measure is much lower (between 25% and 66%). Panel B highlights the correlations of business mix, loan performance, and market risk indicators. Several patterns emerge here. The negative correlation of shares of corporate and residential real estate shows that banks typically focus on one or the other segment. Most market measures are more correlated with the residential real estate share probably because the data covers the recent mortgage crisis. We see fairly high level of correlation between the various market measures but they are far from perfectly correlated (from just 14% between Moody s ratings and stock return volatility and 73% between stock return volatility and bond spreads). Similarly, the correlations between market risk measures and accounting risk measures vary widely. For example, past average non-accrual loans has a correlation with market measures ranging from negative 10% to positive 35%. This suggests that market perceptions of risk, may be volatile and depend on changing market sentiments, thus caution is needed in interpreting any of these measures as a comprehensive indicator of market perceived bank portfolio risk. An alternative explanation for these relatively low correlations might be the inherent backward looking nature of accounting measures as compared to the more forward looking nature of market measures, which are also less of a direct measure of portfolio risk unlike accounting loan performance Relation of Loan Performance and Basel Risk Measures Table 3 summarizes our univariate correlations between the different Basel risk measures and accounting based loan-performance measures and business mix, which is a naïve portfolio based risk measure assuming certain portfolios are on average riskier; we use rank-correlations to minimize the impact of differences in measures over time (i.e. there may be a drift in loan performance or Basel risk measures but our goal is to evaluate the alignment in the relative ranking). Statistically significant correlations (p-value below 0.10) are shown in bold. The relationship between Basel risk measures and weak loan performance appears very strong and the correlations are statistically significant in all cases while the strength of the correlations appears higher for the Basel AIRB measures compared the Basel I RWA/TA. We also find corporate share has a negative correlation with all of the AIRB measures while the residential real estate share has significant positive correlation with all the Basel risk measures, albeit 16

17 stronger for the AIRB measures. This might be explained with the recent mortgage crisis in the US and significant real estate related losses, which dominates the data. The results in table 3 provide preliminary support for our hypotheses that Basel AIRB risk weights are indeed risk sensitive and are more risk sensitive than Basel I risk weights. While we also find Basel I risk weights are correlated with risk, these tests do not control for business mix which we expect drives the correlations. For a more complete picture, we turn to our regression analysis. In table 4, we present results for our regression of Basel risk measures on loan performance measures. In specifications (1)-(4) BI RWA/TA is regressed on loan performance (Past Charge-Offs, Past Non-Accrual Loans, and Delinquency Rate), business mix (Corporate, Res RE, and Sovereign Shares), organizational controls (Log Assets and Traditional Bank). In specifications (5)-(8) AIRB RWA/TA is regressed on the same set of variables. For each RWA measure, we report results first for the base model excluding loan performance for each RWA measure (columns 1 and 5) and then in the adjacent columns include each loan performance measure in separate regressions given their high correlations (columns 2-4 and 6-8). The results suggest that for both the AIRB and the Basel I RWA measures business mix explains a large amount of variation in the RWA measures (76.1% and 68.4% of the variation respectively). In particular, we find that the real estate share of banking book business has a highly significant positive correlation with RWA measures in all cases. The sovereign share also has a negative correlation although this is insignificant for the AIRB RWA measure in most cases. Next, we consider whether our accounting risk measures are correlated with RWAs. In columns (6)-(8), we do in fact see very strong positive correlations between weak loan performance and AIRB RWA/TA and the adjusted R-squares are substantially higher in these columns relative to column (5). In contrast, we do not see a significant or even a positive association between weak loan performance and BI RWA/TA. This is consistent with our hypothesis that Basel AIRB risk weights are risk sensitive and BI risk weights are not. In table 5, we explore whether the strength of the association depends on the AIRB measure used. In particular we want to see whether the relation is stronger with banking book AIRB measures and more so when the PD based AIRB measure is used. Table 5 reports results of the same specification shown in table 4 with the Basel risk measure being AIRB BB RWA/Exposures in columns 1-3, AIRB BB ECL/Exposures in columns 4-6, and AIRB BB Avg 17

18 PD in columns 7-9. To the extent the relations are strong in each case, the difference is not obvious although we do see that the statistical association is significant at the 0.01 level in columns 7-9 for all thee loan performance measures where as that is not the case in columns 1-6 or in table 4 columns Source of Diverging Risk Sensitivity of Basel I vs BII/III AIRB Tables 4 and 5 document that AIRB risk weights are highly sensitive to loan performance whereas Basel I risk weights are not sensitive. This is likely driven by internal risk weights estimated under the AIRB approach being higher (lower) where actual risk outcomes are perceived to be worse (better). In effect, this means the difference in AIRB RWA/TA and BI RWA/TA should be driven by loan performance. We evaluate this question in two parts. First, we look at the fixed Basel I risk weights by portfolio in comparison to the average estimated AIRB risk weights by portfolio; we do this for the Res RE, Corporate, and Sovereign portfolios. Table 6 illustrates that the average AIRB estimated portfolio risk weights (portfolio Risk Weighted Assets divided by portfolio Exposure) are higher for the Res RE fixed weights by about 5.9% suggesting that the Basel I based risk weight is too low by about 5.9%. Similarly, table 6 suggests that the Basel I corporate risk weight is too high (by 66%) and that Basel I sovereign risk weight is to low (by 5%). The higher AIRB risk weights for Res RE is expected as Res RE is stressed during this period and higher AIRB loss estimates are expected. Similarly, the Basel I risk weight is 100% for corporates in general but not all corporate exposures, many of which are highly rated, default at a high rate. In terms of sovereigns, the OECD counties have zero risk weights under Basel I, but many OECD counties were stressed and faced the possibility of default over the sample period. Therefore, the average AIRB risk weights at the portfolio level appear more reflective of actual risk than the fixed Basel I risk weights. 30 Next, we look at univariate differences in the difference between AIRB RWA/TA and BI RWA/TA. Note that table 1 suggests that on average AIRB RWA/TA is about 4% higher than BI 30 The portfolio risk weights presented in table 6 for Basel I represent the risk weights for the general categories of loans. While, the Basel I risk weights are fixed by asset class there are also sub-classes for some asset classes where risk weights may be much higher or lower than the general category weights. For example although mortgages are treated as less risky than corporates there are mortgage products that receive not a 50% but a 100% risk weight. There are also exposures requiring a 200% risk weight. Therefore, the Basel I risk weights shown in table 6 should be seen as a convenient approximation of asset class risk weights. For more details on Basel I asset class risk weights see 18

19 RWA/TA. Table 7 panel A suggests that that for banks with above the median level of Res RE exposure, this difference is about 3.3%, for banks with above the median corporate exposure the difference is about -5.6%, and for banks with above the median sovereign exposure the difference is 5.9%. Therefore table 6 and panel A of table 7 collectively suggest that differences in portfolio risk weights and portfolio composition drive the difference between AIRB RWA/TA and BI RWA/TA. Therefore, it must be that these differences drive the increased risk sensitivity found in table 4 and 5 of AIRB risk weights. As a final test, we regress the difference AIRB RWA/TA BI RWA/TA on the same set of regressors used in tables 4 and 5. The results are shown in Table 7 panel B and suggest clearly that the difference in AIRB and Basel I risk measures come largely from sensitivity to loan performance. Notably, the adjusted R-squares in columns (2) - (4) are double to triple the adjusted R-square of in column (1). This is strong evidence that the implementation of AIRB risk weights corresponds to the intended risk sensitive capital framework across US AIRB banks Relation of Market Risk Measures and Basel Risk Measures We also explore the association between market based risk measures and Basel risk measures. Table 8 presents univariate rank correlations between the market risk measures and the various Basel risk measures. The correlations are usually negative and never positive and significant for BI RWA/TA. For the AIRB measures, the correlations are more often positive but not usually significant. Only for the AIRB Avg PD, are the correlations positive for all four market risk measures. Overall, table 8 presents preliminary evidence of a weak positive relation between market risk indicators and Basel AIRB risk indicators. In table 9, we present results of multivariate tests considering the association between Basel I RWA/TA and AIRB RWA/TA with our various market risk indicators. The results document a weak association between market and RWA measures. For BI RWA/TA, the association is always negative and never statistically significant. For AIRB RWA/TA, the association is positive only for Moody s Rating Weak and for Bond Spread and statistically significant only for Moody s Rating Weak. Overall, table 5 suggests a weak and non-robust positive relation between market risk measures and Basel AIRB risk weights and a lack of any relation between Basel I risk weights and market risk measures. 19