Consistency in Risk Weights for Corporate Exposures Under the Standardized Approach
In December 2017, the Basel Committee published the final elements of the revised Basel III capital framework, which included important enhancements to the risk sensitivity of the standardized approach. For corporate exposures in jurisdictions that allow the use of external ratings, banks can assign risk weights that vary with the external rating of the exposure and are generally lower than 100 percent. Corporate exposures that are not externally rated will continue to receive a 100-percent risk weight. For jurisdictions that do not allow the use of external ratings, banks can assign a 65-percent risk weight for corporate exposures classified as investment grade using banks’ own internal models. However, the revised Basel standardized approach only allows a bank to categorize a corporate as investment grade if the entity (or its parent company) has securities outstanding on a recognized securities exchange (the “securities-listing requirement”).
Recently, some jurisdictions that permit the use of external ratings—most notably the European Union—are allowing banks to assign a risk weight of 65 percent to unrated corporates with an internal rating equivalent to an investment-grade rating, and without requiring the securities listing requirement. This research note examines the consistency of risk weights to the same exposure across banks that lend to firms incorporated in the United States and examines the impact of requiring the corporate entity to have securities listed on a recognized exchange. The securities-listing requirement significantly reduces the number of high-quality corporates that can qualify as investment grade and therefore receive a lower 65-percent risk weight. This is a particularly important issue for exposures to mutual funds and pension funds that do not need to be publicly listed, as well as for private corporate entities.
We use data on estimates of corporate entities’ probability of default from 12 large banks to assess the relevance and impact of the securities-listing requirement (proxied as entities with equity listed on a recognized stock exchange) and the assigned risk weighting. We assess the accuracy of risk weights using more than 36,000 observations of probability of default for 12,342 unique entities. Based on banks’ determinations of the probability of default of each entity and Credit Benchmark’s (CB) 21-point scale, we find that banks’ investment-grade rating assignments to the same entity are generally consistent. This is true regardless of whether the corporate entity meets the securities listing requirement using the proxy approach noted above. Specifically, the difference in average risk weights on corporate exposures between the most and least conservative banks is 7 percent for publicly traded firms and 5 percent for privately held ones. Although there is more disagreement for firms that are publicly listed, the 2-percentage-point difference is not statistically different from zero at standard significance levels. Furthermore, these differences are largely driven by a few outlier banks and are much lower when comparing banks at the top and bottom of the interquartile range.
In summary, we show that using banks’ own internal ratings to distinguish between investment-grade and non-investment-grade obligors without the securities-listing requirement would significantly expand and enhance the risk sensitivity of the standardized approach for corporate entities. It would also result in little variation in risk weights across banks for the same entity.
Risk-weighted assets became a key component of banks’ regulatory capital ratios since the introduction of the Basel I Accord in 1988. In the United States, six of the eight capital requirements measure the adequacy of bank capital relative to risk-weighted assets. The total common equity tier 1 capital requirement of large banks, the most loss-absorbing form of capital, ranges between 7 and 13.6 percent of risk-weighted assets, depending on the performance of banks in the stress tests and their systemic footprint. Importantly, for the banks subject to the stress tests (roughly those with more than $100 billion in total assets), risk-weighted assets calculated under the standardized approach result in the most binding risk-based capital requirement. Therefore, the calculation of risk-weighted assets under the standardized approach often results in the most binding capital requirement for the largest U.S. banks.
Currently, corporate exposures receive a risk weight of 100 percent under the standardized approach in the United States. The recently finalized Basel III standardized approach includes several important changes to the internationally agreed-upon capital framework, including an enhancement of the risk-sensitivity of the standardized approach that will be taking effect in January 2023. More precisely, the revised capital framework allows banks to prescribe risk weights based on the intrinsic risk of the asset and allows for some flexibility in terms of permissible approaches.
For jurisdictions that do not allow the use of external ratings for regulatory purposes, banks will be able to assign a risk weight of 65 percent for investment-grade exposures that have securities outstanding on a recognized securities exchange. For all other corporate exposures, the risk weight remains at 100 percent. For jurisdictions that allow the use of external ratings, exposures to corporates are assigned a risk weight that varies with the external rating of the borrower and across five distinct risk-weight buckets ranging from 20 percent to 150 percent. Unrated exposures would be assigned a risk weight of 100 percent.
Our objective in the note is to assess the variability of risk weights under the Basel III revised standardized approach using data on banks’ own PD and CB’s mapping between PDs and a common 21-point rating scale. Using banks’ own internal ratings to prescribe a risk weight to a corporate exposure has the advantage of expanding the additional risk-sensitivity of the standardized approach to the entire corporate portfolio, and not restricting the assessment to entities with a public rating.
We follow the approaches suggested by Firestone and Rezende (2016) and Plosser and Santos (2014) to assess the consistency of banks’ own internal ratings for the same borrower. These papers analyze the variability of PD estimates for the same borrower across banks. Our analysis directly assesses the variability in risk weights for the same borrower across banks. This is more direct and answers the question of what the more granular approach would imply in terms of variability of risk-weighted assets across banks. The first step of the analysis is to map the PD of each bank to a rating grade using CB’s rating scale. Next, we assign a risk weight to the rating grade following the Basel III revisions to the standardized approach risk weights. We then use linear regressions to determine how much of the variation in the resulting assigned risk weights is systematic (a bank’s assessment of all of its obligors) relative to idiosyncratic (a bank’s assessment of just an individual obligor).
And finally, CB also provides a “Credit Consensus Rating” (CCR) for each entity in their sample using the obligor-level data on the PD from banks. In brief, CB calculates an average probability of default from each bank for the same entity and maps the average PD using CB’s own 21-point scale. The credit consensus rating developed by CB could also be useful in adopting the revisions to the Basel IV standardized approach, because it would allow banks and supervisors to examine where each bank’s own internal rating ranks relative to the consensus rating. The CCR could also be used as a fallback for banks that are still developing their own internal rating systems.
Description of the Sample
This empirical analysis uses obligor-level data from CB. The sample includes banks headquartered in the United States or with a significant exposure to U.S. firms and is current as of April 2021. The unit of observation in the analysis is a bank-entity pair, and the 12 banks and 12,342 unique entities result in a sample with more than 36,000 observations.
CB’s dataset includes the PD of each entity and a mapping between the PD and a 21-point scale. PDs subject to a guarantee or PD substitutions are excluded from the sample. CB’s 21-point rating scale and the corresponding ranges for the probability of default are presented in columns 1 through 3 of Exhibit 1. For example, an entity with a PD of 20 basis points would be assigned a “bbb+” rating score. The risk weights assigned to each rating category based on the revised standardized approach to determine risk weights are also shown in Exhibit 1. Column 4 reports the risk weights using the investment-grade split (for jurisdictions that do not allow the use of external ratings).
Exhibit 1: Mapping of PDs to Credit Benchmark’s Rating Categories
The empirical analysis includes two types of entities in banks’ wholesale portfolios: corporates and funds (i.e., loans to obligors that are mutual or investment funds). As shown in Exhibit 2, corporates account for 27 percent of the sample, while funds account for 73 percent. The shares are little changed when each bank-entity pair counts as a separate observation as reported in the last column of Exhibit 2. About 26 percent of corporate entities are publicly traded; however, almost none of the funds in the sample are publicly traded and therefore those exposures would likely not benefit from the lower risk weight prescribed to investment-grade exposures in the Basel III end-game package.
Exhibit 2: Percentage of Bank-Entity Pairs That Are Public
Exhibit 3: Number of Banks per Entity
Exhibit 3 shows the distribution of the number of banks that report data for the same entity. CB’s CCR covers entities with at least 3 contributing banks (“Consensus”) and entities with 2 contributing banks (“Implied”). For the latter, CB combines the PD of each entity with additional information based on the industry, region, and credit risk bucket to further refine the implied rating. On average, the sample has 3 banks reporting the PD of each entity. About 13 percent of the sample includes entities with 5 or more banks contributing the data. Nearly 50 percent of the sample included entities with only 2 contributors.
Exhibit 4: Consensus Ratings Across Credit Risk Categories
Exhibit 4 reports the distribution of entities across credit ratings using CB’s mapping between each entity’s probability of default and the corresponding credit rating. The ratings buckets in Exhibit 4 are segmented, following the more granular analysis proposed by the revised Basel III standardized approach for jurisdictions that permit the use of external credit ratings. About 75 percent of the entities in our sample are investment grade, as represented by the sum of the three leftmost bars. In addition, nearly 87 percent of funds are investment grade, compared to only 42 percent of corporate entities.
An implicit assumption of the empirical analysis is that the mapping between PDs to credit risk scales is quite similar across banks and closely approximates the CB mapping. In practice, that will not be the case. Most banks calibrate their own internal scales that map PD estimates to credit risk categories. However, individual scales and their granularity are limited by portfolios managed by the banks. The CB scale used in this analysis is derived from the scales of individual banks and offers a flexible mapping to exactly 21 categories, following the industry standard. CB’s analysis of banks’ internal scales finds a close alignment in the two approaches of mapping PD estimates to credit risk categories. We do not expect the resulting differences in risk weights to be material.
Exhibit 5: Agreement on Risk Weights on the Same Entity
Exhibit 5 summarizes the difference in ratings across entity types using a pairwise comparison. More precisely, we calculate the agreement between each pairwise combination of banks to a given entity. For example, an entity with six banks contributing a PD generates 15 pairwise contributions. We define each pairwise combination as “agree” if both banks assign an investment grade rating and “disagree” otherwise. To avoid overweighting entities with a larger number of banks, we first calculate the average agreement level across banks for the same entity, and then we average those results across all entities.
Exhibit 6: Agreement on Risk Weights on the Same Entity by Exposure Type
In our sample, banks agree with the attribution of the investment-grade rating for 92 percent of observations. That is, for the 8 percent of bank-entity pairs with a disagreement, the difference in the risk weight would be 35 percent. (The only possible difference is when a loan is rated investment grade by one bank and so gets a risk weight of 65 percent, and below-investment grade by another bank and so gets a risk weight of 100 percent.) Exhibit 6 splits the difference in assigned risk weights across traditional corporates and investment funds. The banks in our sample agree with the attribution of the credit rating above or below investment grade for 82 percent of traditional corporate exposures. The share of agreement is little changed when only publicly traded corporates are included. There is even greater agreement with the attribution of the risk weight to investment fund-exposures across banks, as it increases to 96 percent. In the next section, we investigate to what extent differences in risk weights are systematic versus idiosyncratic.
Our analysis has discussed the differences in rating assignments across banks at the entity level. As shown in the Exhibits 5 and 6 above, there would be some differences in the assignment of risk weights across banks if banks are allowed to use their own investment grade ratings irrespective of whether the securities listing requirement is imposed or not. However, most of the reported differences in risk weight to the same entity across banks are probably idiosyncratic (a bank’s assessment of an individual entity) and may cancel themselves out at the aggregate level when a bank assesses all its obligors.
To help discern between systematic and idiosyncratic differences, this section outlines an empirical strategy to assess systematic differences in risk weights across entities. We consider two sets of empirical specifications. The first regresses the level of risk weight attached to each entity on a set of bank dummy variables to estimate the systematic variation in risk weights across banks. The second specification investigates the deviation of each bank’s risk weight relative to the one obtained using the consensus rating. The level regressions are our baseline and follow the Federal Reserve Board’s methodology used by Firestone and Rezende (2016). The second approach demonstrates that the results are similar using CB’s consensus rating.
To assess systemic differences in bank risk weights, we follow the approach used by Firestone and Rezende (2016) and regress the hypothetical risk weight assigned by each bank on a set of entity and bank dummy variables:
where yij is the hypothetical risk weight of entity i by bank j, yi and δj are entity and bank dummy variables, and ∈ij represents the unobserved error term. We then run two sets of regressions. In one case, the dependent variable takes the value of either 65 percent or 100 percent, which corresponds to the risk weights of corporate exposures when the use of external ratings is not allowed. The second regression uses a more granular set of risk weights (five instead of two) following the jurisdictions that permit the use of external ratings. The regression analysis does not control for bank-specific characteristics besides the bank dummy variables. The objective of the analysis is to measure the variability in risk-weighted assets when banks use their own internal ratings to determine the risk weight of their exposures under the standardized approach.
The regression analysis includes entity-specific characteristics, represented with a dummy variable for each entity. We will also report results for relevant subsamples of the data, namely across the various portfolios included in the wholesale portfolio, and separately for publicly traded and privately held entities. We estimate robust standard errors and cluster observations at the entity level.
The focus of the analysis is on the coefficients on the bank dummies, represented by the vector δj . The estimated coefficients capture the systematic difference in bank j ’s risk weight assigned to each entity under the revised Basel III standardized approach. The data contain observations from 12 banks, and the vector δj is therefore composed of 11 dummy variables. (The bank with the median dummy coefficient represents the reference bank, and the value of the dummy variable is set to zero.) Moreover, the regression analysis includes 12,342 entity dummy variables represented by the vector yi, which ensures the individual contributions are adjusted for each entity’s average risk weight.
And finally, the dependent variable can only take two values. However, we are interested in the average systematic bias across banks, which can be a fraction of the risk weight and is therefore a continuous variable. For this reason, we still use a linear regression for estimating the model. The results are then ordered based on the value of coefficients. The order of banks’ dummy coefficient estimates can differ between specifications, so Bank 1 can be a different bank across the various specifications. This protects the confidentiality of the contributing banks.
Distance to Consensus Credit Rating Specification
The second regression specification analyzes the difference in the risk weight assigned to each entity relative to the risk weight obtained using the consensus credit rating. The problem can be reformulated as distance from mean, as presented by Berg and Koziol (2017), who use the following regression:
where ỹij is defined as the difference in the risk weight assigned to entity i by bank j relative to the consensus rating of entity i: ỹij =yij – ȳi. This measures systematic differences from the consensus rating and offers a different perspective on the results. This specification also gives a direct way to assess the variability of risk weights relative to the risk weight that corresponds to the consensus credit rating.
Before delving into the results, let’s look at how the regression analysis presents a way to distinguish between systematic and idiosyncratic variation in risk weights. For example, a case of systematic variation would be to assume Bank 1 assigns a risk weight of 65 percent for two entities, while Bank 2 assigns a risk weight of 100 percent to the same two entities. In addition, the consensus rating for each of the two entities would correspond to a risk weight of 65 percent. This means that the distance to consensus for both entities is zero for Bank 1 and 35 percent for Bank 2. The fixed effect of Bank 1 would then be zero, the fixed effect of Bank 2 would equal 35 percent, and the error term of the regression would be zero across all bank-entity pairs.
By contrast, a case of idiosyncratic variation would be to assume Bank 1 assigns a risk weight of 65 percent to the first entity and 100 percent to the second entity, while Bank 2 does the reverse. The risk weight that corresponds to the consensus rating would still be equal to 65 percent. In this case, the fixed effects of Banks 1 and 2 would be the same and equal to 17.5, and the error term would be equal to –17.5 and 17.5 for Bank 1 and 17.5 and –17.5 for Bank 2. The regression results discussed in the next section generalize this intuition to the 18 contribution banks. Therefore, the difference between the highest and the lowest fixed effect is a measure of the degree in systematic variation in risk weights. Idiosyncratic differences in risk weights are less important, because those do not result in material differences in capital requirements since they cancel out across loans.
We present two sets of results, one for each regression model (see Exhibits 8 and 9 in the Appendix). Exhibit 8 shows the estimated bank dummy variables when the dependent variable is the hypothetical risk weight of an entity that has a relationship with more than one bank in our sample. Column 1 shows the results using the full sample. Six of the 11 bank dummies are statistically different from zero at the 5-percent level. The size of the differences ranges between –2.1 percent and 3.5 percent. Therefore, the difference in average risk weights between the most pessimistic and the most optimistic banks is 5.6 percentage points. The difference in risk weight falls to 1.0 percent when comparing the third-lowest and the ninth-highest banks (interquartile range). The R-squared of the regression is 3.0 percent, which is relatively small. As a result, almost all the variation in risk weights appears to be driven by idiosyncratic factors.
The remaining columns in Exhibit 8 report the changes in the results across different subsamples. For corporate entities, the average risk weight is 85 percent. Six of the 11 bank dummies are statistically different from zero at the 5-percent level. The difference in average risk weights varies between –1.8 percent and 3.5 percent. The R-squared of the regression is 4.1 percent—still small, but slightly higher relative to the overall sample. The average difference in risk weights is the highest for funds, ranging from –3.5 percent to 6.7 percent. However, only one of the 11 bank dummies is statistically different from zero. The R-squared of the regression is 4.4 percent.
The last two columns in Exhibit 8 show the variation in the differences in risk weights when the entity is either a public or a private corporation. This is related to the requirement that for a bank to use its own investment-grade rating, the borrower must also have outstanding securities on a recognizable exchange. Column 4 shows the results for publicly traded firms and column 5 for private firms. As shown in Exhibit 7, the difference in average risk weights between the most conservative and the most optimistic banks is 7.3 and 5.2 percentage points for public and private entities, respectively. The results indicate that there is actually more disagreement across publicly traded firms, contrary to the logic of requiring firms to be publicly listed to qualify for the lower risk weight. However, a test of the difference in the two coefficients indicates the two values are not statistically different from each other at the 5-percent level. Therefore, whether a firm is public or private does not appear to be an important driver of systematic differences in risk weights. The difference in risk weight of public (private) corporates falls to 4.5 (2.1) percent when comparing the third-lowest and the ninth-highest banks (interquartile range).
Exhibit 7: Average Difference in Risk Weights on the Same Corporate Entity
Exhibit 8 reports the systematic variation in the distance to the consensus credit rating. The degree of systematic variation in risk weights is lower in this case, since the difference in the average risk weights between the most optimistic and pessimistic banks drops from 5.6 percent to 4.2 percent in the full sample. There is also almost no difference between the results for corporate entities. However, the sample with public corporates shows higher variability in average risk weights relative to the sample that includes only private corporates. And finally, the difference in average risk weights for funds between the most conservative and the most optimistic banks drops from 10.2 to 4.7 percent. Overall, across the two model specifications, the systematic variation in risk weights appears to be modest.
In this note, we have shown that the systematic variation in risk weights under the revised standardized approach for corporate exposures (including investment funds) would be modest. This is particularly true where banks can use their own internal ratings to distinguish between investment-grade and non-investment-grade entities. The systematic variation in risk weights for publicly traded exposures is also not statistically different from the one observed for privately held entities. Therefore, the requirement that investment-grade exposures also need to have securities traded on a recognized exchange is unnecessary.
Berg, Tobias, and Philipp Koziol, 2017, “An Analysis of the Consistency of Banks’ Internal Ratings,” Journal of Banking & Finance, Vol. 78, pp. 27–41. delivery.php (ssrn.com)
Firestone, Simon, and Marcelo Rezende, 2016, “Are Banks’ Internal Risk Parameters Consistent? Evidence from Syndicated Loans,” Journal of Financial Services Research, Vol. 50, pp. 211–242. 201384pap.pdf (federalreserve.gov)
Plosser, Matthew C., and João A. C. Santos, 2014, “Banks’ Incentives and the Quality of Internal Risk Models,” Federal Reserve Bank of New York Staff Reports, No. 704. sr704.pdf (newyorkfed.org)
Exhibit 8: Accuracy of Banks’ Own Internal Ratings Using the Level Specification
This table presents the results of estimating Equation 1 using ordinary least squares. The dependent variable equals the risk weight of 65 or 100 percent. Bank dummy variables are ordered from lowest to highest, and the order is not consistent across specifications. The reported standard errors (in brackets) are clustered at entity level. ***, **, * denote two-tailed statistical significance at the 1-, 5-, and 10-percent levels.
Exhibit 9: Accuracy of Banks’ Own Internal Ratings Using the Distance to Consensus Specification:
This table presents the results of estimating Equation 2 using ordinary least squares. The dependent variable equals the risk weight of 65 or 100 percent less the risk weight associated with the consensus rating. Bank dummy variables are ordered from lowest to highest, and the order is not consistent across specifications. The reported standard errors (in brackets) are clustered at entity level. ***, **, * denote two-tailed statistical significance at the 1-, 5-, and 10-percent levels.
 Basel Committee on Banking Supervision (BCBS), Basel III: Finalising post-crisis reforms (Dec. 2017), https://www.bis.org/bcbs/publ/d424.pdf [hereafter “Basel”].
 BCBS, An assessment of the long-term economic impact of stronger capital and liquidity requirements (Aug. 2010), https://www.bis.org/publ/bcbs173.pdf; Ingo Fender and Ulf Lewrick, BIS Working Papers No 591, Adding it all up: the macroeconomic impact of Basel III and outstanding reform issues, Bank for International Settlements, Monetary and Economic Department (Nov. 2016), https://www.bis.org/publ/work591.pdf.
 The six risk-based requirements include the common equity tier 1 capital, tier 1 capital, and total capital requirements under both the standardized and advanced approaches. The two non-risk-based requirements are the tier 1 capital and the supplementary leverage ratio.
 See “Federal Reserve Board announces individual large bank capital requirements, which will be effective on October 1” (August 10, 2020), available at https://www.federalreserve.gov/newsevents/pressreleases/bcreg20200810a.htm.
 Some of the very largest banks are bound by the enhanced supplementary leverage ratio but we expect this situation is temporary given the large size of the Federal Reserve’s balance sheet.
 Significant exposure is defined as banks with more than 1,000 U.S. entities in April 2021. The 12 banks include 2 Category I banks, 6 Category III banks, and 4 Category IV banks. A prior version of this analysis also included banks below Category IV. We have excluded those banks in this draft because it is unlikely the Basel III end-game revisions will apply to them in the U.S.
 Alternatively, we could define “agree” as when all banks lending to a given entity assign the same rating above or below investment grade. In that case, the percentage of banks that “agree” on the rating for the same entity declines from 92 percent to 86 percent.
 See Stepankova, Barbora (2020), “Consistency of Banks’ Internal Probability of Default Estimates,” IES Working Papers 44/2020, IES FSV, Charles University. Available at http://ies.fsv.cuni.cz/sci/publication/show/id/6356/lang/en
 This includes the variation explained by the dummy variable assigned to each obligor.