What Drives Bank Peformance?

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. What Drives Bank Peformance? Luca Guerrieri and James Collin Harkrader 2021-009 Please cite this paper as: Guerrieri, Luca, and James Collin Harkrader (2021). “What Drives Bank Peformance?,” FinanceandEconomicsDiscussionSeries2021-009. Washington: BoardofGovernorsofthe Federal Reserve System, https://doi.org/10.17016/FEDS.2021.009. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

What Drives Bank Performance? Luca Guerrieri∗ James Collin Harkrader †‡ January 19, 2021 Abstract Focusing on some key metrics of bank performance, such as revenues and loan charge-off rates, we estimate the fraction of the observed variation in these metrics that can be attributed to changes in economic conditions. Macroeconomic factors can explain the preponderance of the fluctuations in charge-off rates. By contrast, bank-specific, idiosyncratic factors account for a sizableshareofthevariationinbankrevenues. Theseresultspointtoimportanceofbank-specific business models as a driver of performance. JEL codes: E30, G21 Key words: Pre-provision net revenues, charge-off rates, macroeconomic factors, banking factors, principal components, backcasting. ∗Federal Reserve Board, 20th and C Streets NW, Washington, DC 20551; e-mail: Luca.Guerrieri@frb.gov †Federal Reserve Board, 20th and C Streets NW, Washington, DC 20551; e-mail: James.C.Harkrader@frb.gov ‡The authors work at the Board of Governors of the Federal Reserve System. We thank Michele Modugno for helpful comments. The material in this paper does not represent the views of the Board of Governors of the Federal Reserve System or any other person associated with the Federal Reserve System. 1

1 Introduction Economic theory teaches us to expect a link between macroeconomic fluctuations and the performance of financial intermediaries. We set out to investigate this link empirically. Focusing on some key metrics of bank performance, such as revenues and loan charge-off rates, we seek to understand what fraction of the observed variation in these metrics can be attributed to changes in economic conditions. Furthermore, we arealso interested insplittingthe remainderof thevariation between changes that affect the banking sector overall and changes driven by idiosyncratic factors specific to individual banks. The connection between macroeconomic performance and bank performance is at the center of stress tests, a standard supervisory tool used across the world. In practice, stress tests rely on only a few scenarios and are not usually tailored to capture bank-specific variation. To the extent that bank-specific variation is important, it becomes central to consider scenarios that can stress different business models. We find that macroeconomic factors can explain the preponderance of the fluctuations in loan charge-off rates. However, we find that bank-specific idiosyncratic factors explain a sizable share of the variation in bank revenues. Therefore, it would be important to consider scenarios specifically tailored to idiosyncratic bank risk when developing stress scenarios for revenues.1 Our analysis needs to resolve three problems. The first problem is to summarize statistically the state of the macroeconomy. We rely on a large dataset including 132 macroeconomic series, first assembled by Stock and Watson (2002) and later updated and expanded by McCracken and Ng(2015). Followingtheirlead, weuseprincipalcomponents(PCs)tocapturetheessentialsources of macroeconomic variation. The second problem is to pick measures of bank performance. We select pre-provision net revenue (PPNR) and charge-off rates, key performance measures monitored by bank analysts and bank supervisors.2 To distinguish between sources of variation in performance that are common acrossthebanking-sectorandbankspecificfactors,weuseapaneloflargebanksholdingcompanies that participated in the latest stress tests in the United States. Forourdecompositionweuseatwo-stepapproach. Inthefirststep, weregresstheperformance measures on the macro principal components, which gives us the fraction of the variation explained by macroeconomic fluctuations. The residuals from these first-step regressions embody the part 1OnepeculiarfeatureoftheU.S.stress-testsrunbytheFederalReserveisthatparticipatingbanksarerequired to submit scenarios that are tailored to their specific business model. For an analysis based on these scenarios, see for instance Arseneau (2017). 2PPNR refers to interest and non-interest income net of expenses prior to the inclusion of loss provisions and taxes. 2

of the performance measures driven by banking-wide and bank-specific variation. In the second step, we use another PC to capture banking-sector variation, with the remainder then attributed to bank-specific factors. The third problem is that the bank performance data start at different times for the various banks depending on when they became bank-holding companies. We rely again on Stock and Watson (2002) to impute or backcast the missing data, balancing the panel. Their procedure summarizes the variation common across banks to impute any unbalanced data. We extend their method to include an additional set of factors, our macro principal components. Considering this additional information is especially important for our analysis. Intuitively, excluding the macroeconomic variation from the backasting step would artificially reduce the fraction of the variation in bank performance driven by macroeconomic changes for the imputed values and for the overall dataset. Since our statistical procedure orthogonalizes the three sources of variation—macroeconomic, banking-sector, and idiosyncratic—we can use R-squares statistics from each regression to size the contribution of the three different sources to the variation in the bank performance measures. We find that only for 3 out 34 banks in our dataset, idiosyncratic bank factors explain slightly more thanhalfofthevariationincharge-offratesaccordingtoadjustedR-squaresstatistics. Bycontrast, for about one-third of the banks we consider, idiosyncratic factors account for more than half of the variation in PPNR. Asidefromourmainfindingsontheimportanceofbank-specificvariation,weprovideMATLAB routines that implement our extended backcasting procedure. This toolbox is generally applicable to balancing a dataset using both variation from complete series in the dataset and factors external to the dataset. When this additional external information is not relevant, our extended algorithm collapses to the algorithm proposed by Stock and Watson (2002).3 Moreover, our analysis contributes to the literature on charge-off rates and PPNR. There is a significant body of literature focused on modeling credit risk and, relatedly, charge-off rates, whereas the literature on modeling PPNR is much thinner.4 An exception is Lehnert and Hirtle (2015), which provides a top down econometric procedure, the CLASS model, for modeling all of the performance measures that accumulate to capital. Similarly, Hale, Krainer and Erin (2015), determine the optimal level of aggregation for modeling different bank performance measures. 3TheMATLABroutinesimplementingthealgorithmandreplicationscodeforthispaperareavailableathttps:// github.com/lucashare/backcasting. An online appendix available at http://www.lguerrieri.com/the_drivers_ of_bank_perform.pdf. 4For instance, for credit risk see McNeil, Frey and Embrechts (2015), Frye and Pelz (2008), Barth et al. (2018). 3

2 Data Our bank performance data rely on two commonly used measures, loan charge-offs and preprovision net revenue (PPNR). Charge-offs encompass losses declared on loans, which typically lag macroeconomic variables. We express charge-offs as rates relative to total loans and leases for each given bank, as is standard practice. PPNR is defined as the difference between, on one side, interest and non-interest income and, on the other side, interest and non-interest expenses. We express PPNR as a percent of average assets, a common empirical choice. In our application, we obtain PPNR and charge-off data from the FR Y-9C Release, a quarterly report for income and balance sheet data of bank holding companies (BHCs).5 We focus on the 34 BHCs that participated in the 2020 stress tests conducted by the Federal Reserve. Our sample ranges from the first quarter of 2002 to the third quarter of 2019. Table 1 lists the banks in the sample. As an example, Figure 1 shows annualized PPNR and charge-offs for two BHCs with comparable business models, JPMorgan Chase and Bank of America. The PPNR series show jagged and idiosyncratic movements. Bycontrast, charge-offseriesaremuchsmootherthanPPNRandgenerallymovemore closely with one another and with aggregate macroeconomics series. To calculate our macro PCs, we also use 132 macroeconomic time series from McCracken and Ng (2015). These series run from the second quarter of 1959 to the third quarter of 2020. They encompass a broad list of macroeconomic series on economic activity, factors of production, and interest rates. To extract the key fluctuations in these series, we take principal components. The test of Bai and Ng (2002) calls for 12 factors. 5Thedataareadjustedformergersandacquisitionsoffirmsalsosubjecttostatutoryreportinginthequarterin which they occur. 4

Table 1: Data Range Bank Abbreviation Data Start Data End ALLY FINANCIAL INC. ALLY 2009:2 2020:3 AMERICAN EXPRESS COMPANY AXP 2009:1 2020:3 BANK OF AMERICA CORPORATION BAC 2002:1 2020:3 BANK OF NEW YORK MELLON CORPORATION, THE BNYM 2007:3 2020:3 BARCLAYS US LLC BARC 2016:3 2020:3 BMO FINANCIAL CORP. BMO 2002:1 2020:3 BNP PARIBAS USA, INC. BNP 2016:3 2020:3 CAPITAL ONE FINANCIAL CORPORATION COF 2004:4 2020:3 CITIGROUP INC. C 2002:1 2020:3 CITIZENS FINANCIAL GROUP, INC. CFG 2002:1 2020:3 CREDIT SUISSE HOLDINGS, INC. CS 2016:3 2020:3 DB USA CORPORATION DB 2002:1 2020:3 DISCOVER FINANCIAL SERVICES DFS 2009:2 2020:3 FIFTH THIRD BANCORP FITB 2002:1 2020:3 GOLDMAN SACHS GROUP, INC., THE GS 2009:1 2020:3 HSBC NORTH AMERICA HOLDINGS INC. HSBC 2004:1 2020:3 HUNTINGTON BANCSHARES INCORPORATED HBAN 2002:1 2020:3 JPMORGAN CHASE & CO. JPM 2002:1 2020:3 KEYCORP KEY 2002:1 2020:3 MORGAN STANLEY MS 2009:1 2020:3 MUFG AMERICAS HOLDINGS CORPORATION MUFG 2002:1 2020:3 M&T BANK CORPORATION MTB 2002:1 2020:3 NORTHERN TRUST CORPORATION NTRS 2002:1 2020:3 PNC FINANCIAL SERVICES GROUP, INC., THE PNC 2002:1 2020:3 RBC US GROUP HOLDINGS LLC RBC 2018:2 2020:3 REGIONS FINANCIAL CORPORATION RF 2004:3 2020:3 SANTANDER HOLDINGS USA, INC. SAN 2012:1 2020:3 STATE STREET CORPORATION STT 2002:1 2020:3 TD GROUP US HOLDINGS LLC TD 2015:3 2020:3 TRUIST FINANCIAL CORPORATION TFC 2002:1 2020:3 U.S. BANCORP USB 2002:1 2020:3 UBS AMERICAS HOLDING LLC UBS 2016:3 2020:3 5

Figure 1: A First Look at the Data, Left: PPNR, Right: Charge-offs 3 2.5 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 )stessA egarevA fo %( RNPP 5 JPM PPNR BAC PPNR 4.5 4 3.5 3 2.5 2 1.5 1 0.5 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 )sesaeL dna snaoL latoT fo %( sffo-egrahC JPM Charge-offs BAC Charge-offs Source: Federal Reserve Y-9C Release. 3 Statistical Methods Wedescribefirstourprocedureforsizingtheimportanceofdifferenttypesoffactors—macroeconomic vs. banking-wide factors—in explaining the variation in the bank performance measures. We then describe how we backcast the missing data. 3.1 Data Decomposition To size the relative importance of different types of factors we use a two-step procedure. First, we estimate X = λ MF +(cid:15)MF (1) b,t b t b,t by ordinary least squares, where X represents, alternatively, charge-offs or PPNR rates, λ is b,t b vector of factor loadings, MF is a vector of macro principal components and (cid:15)MF represents t b,t variation in the performance measure orthogonal to the macro factors. We use the residuals from the first-step regression, (cid:15)MF, to extract one more principal comb,t ponent, CF , which we interpret as capturing banking-sector variation common across banks but t orthogonal to the variation captured by the macro principal components. We estimate the factor loadings γ in b (cid:15)MF = γ CF +(cid:15)CF (2) b,t b t b,t by ordinary least squares. The residuals from this regression, (cid:15)CF, is the bank-specific variation in b,t 6

the performance measures, i.e., the variation not explained by either the macro factors or the cross sectional factors. 3.2 Balancing the Dataset Were-purposethetwo-stepprocedureinSection3.1tobackcastthebankperformancemeasures thatdonotstartatthebeginningofthedatasetandthusbalanceourpanelofbanks. Instep1), we identify banks with a full sample of data. Using this data, we run regressions 1 and 2. We then use the estimated coefficients λˆ and γˆ to impute any missing values.6 In step 2), we re-estimate the b b coefficients λˆ and γˆ using the original data and the imputed data from step 1). We then re-impute the data that were missing in step 1) using these re-estimated coefficients. We repeat step 2) until the maximum difference in the missing data across iterations is smaller than a given tolerance, which we set at 10e−4. If we were to remove the regression of Equation 1, this procedure would collapses to that of Stock and Watson (2002). 4 Results We find that the macro factors explain a large portion of the variation in our performance measures across banks, although these factors seem to more consistently explain the variation in charge-offs than in PPNR. 4.1 Decomposing the Data Figure 2 shows the cumulative R-squares from the regressions of macro factors and banking factors on charge-offs and PPNR for each bank in our sample. The macro factors explain a large proportion of the variation in charge-offs across all of the banks, with R-squares exceeding 0.5 for all but one bank. Furthermore, the addition of the banking factor, on top of the the macro factors, leads to R-squares that exceed 0.9 for about two-thirds of the banks in our panel. By contrast, the same factors, explain a lower fraction of the variation in PPNR. About a third of the banks show R-squares below 0.5 and only a handful of banks tally R-Squares above 0.9. These differences are also evident in the lower panels of the figure, which report adjusted R-Squares. While the adjusted and standard R-Squares are close to each other for charge-offs the differences are more pronounced for PPNR, with one bank even showing a negative adjusted R-Square. Idiosyncratic, bank-specific variation is more prevalent in the case of PPNR than for charge-off rates. 6In the case of chargeoffs, if our estimates point to negative chargeoff rates, we use a floor of 0, instead. 7

Figure 2: Macro Factors Explain a Large Portion of the Variation in Charge-off Rates as Opposed to PPNR. Left: PPNR, Right: Charge-offs. R-Squares BTM MPJ YEK NABH CNP BTIF CAB CFT TTS BSU GFC SRTN OMB PXA GFUM YLLA SC PNB C SM FOC SG BD CBSH FR MYNB DT SFD NAS SBU CRAB CBR 1 Macro Factors Banking Factor 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 BTM MPJ YEK NABH CNP BTIF CAB CFT TTS BSU GFC SRTN OMB PXA GFUM YLLA SC PNB C SM FOC SG BD CBSH FR MYNB DT SFD NAS SBU CRAB CBR 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Adjusted R-squares BTM MPJ YEK NABH CNP BTIF CAB CFT TTS BSU GFC SRTN OMB PXA GFUM YLLA SC PNB C SM FOC SG BD CBSH FR MYNB DT SFD NAS SBU CRAB CBR 1 0.8 0.6 0.4 0.2 0 -0.2 BTM MPJ YEK NABH CNP BTIF CAB CFT TTS BSU GFC SRTN OMB PXA GFUM YLLA SC PNB C SM FOC SG BD CBSH FR MYNB DT SFD NAS SBU CRAB CBR 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 4.2 A Look at the Backcasts After evaluating the relative importance of different sets of factors, we turn to our ability to use these factors to impute missing data. We rely on a pseudo-out-of-sample exercise for which, as a representative example, we backcast the charge-off rates for one bankc, JPMorgan Chase based on a shortened sample that drops the first 50 quarterly observations, so that the observed sample for this pseudo-out-of-sample exercise runs from the third quarter of 2014 through the third quarter of 8

2020. The backast for our baseline model, shown by the dashed red line, hugs the observed data, the solid back line. To help evaluate the importance of the macro factors the figure also shows an alternative backcast based on a model that simply drops the macro factors and retains one banking factor, as in the baseline model. The figures shows clearly a deterioration in performance in a pseudo-out-of-sample sense, as can be gauged from the greater gap between the dashed green line, for the alternative backcast, and the solid black line (the observed data) than the analogously gap for the dashed red line (for the baseline backcast). As a second alternative, we consider increasing the number of banking factors to compensate for the exclusion of the macro factors. We use the test in Bai and Ng (2002) to determine the optimal number of banking factors, which calls for five factors. As can be seen from the figure, the dash-dotted blue line for this alternative backcast is closer to the observed data but not as close as our baseline backcast. Figure 3: Comparing Pseudo-Out-of-Sample Backcasts of Charge-off Rates, JPMorgan Chase 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 )sesaeL dna snaoL latoT fo %( sffo-egrahC POOS Backcast POOS Backcast (No Macro Factors, 1 Banking Factor) POOS Backcast (No Macro Factors, 5 Banking Factors) Observed Source: Authors’ calculations and Federal Reserve Y-9C Release. 5 Conclusion We decomposed the variation in a dataset of bank performance measures into the proportion explained by macroeconomic fluctuations and the proportion explained by one factor common across the banking sector, leaving the remainder for idiosyncratic, bank-specific variation. For our decomposition, we extended the backcasting procedure by allowing for factors drawn outside the unbalanced dataset of interest. 9

We found that macroeconomic factors and one banking factor can explain a large proportion of the variation in bank performance measures, as is the case for charge-off rates. However, the same factors only explain a smaller proportion of the variation of PPNR rates. We showed that external macro factors—allowed by our extension of Stock and Watson (2002)—produce superior backcasts in a pseudo-out-of-sample sense, closer to the observed data. Our results point to the importance of considering bank-specific, idiosyncratic factors when modelling PPNR rates. This finding is relevant for the design of stress-test scenarios. References Arseneau, David M. 2017. How Would US Banks Fare in a Negative Interest Rate Environment? Finance and Economics Discussion Series 2017-030r1 Board of Governors of the Federal Reserve System (U.S.). Bai, J. and S. Ng. 2002. “Determining the Number of Factors in Approximate Factor Models.” Econometrica pp. 191–221. Barth, James, Sumin Han, Sunghoon Joo, Kang-Bok Lee, Stevan Maglic and Xuan Shen. 2018. “Forecasting net charge-off rates of banks: What model works best?” Quantitative Finance and Economics 2:554–589. Frye, Jon and Eduard A. Pelz. 2008. BankCaR (Bank Capital-at-Risk): a credit risk model for U.S. commercial bank charge-offs. Technical report. Hale, Galina, John Krainer and McCarthy Erin. 2015. “Aggregation Level in Stress Testing Models.” Federal Reserve Bank of San Francisco Working Paper Series . Lehnert,AndreasandBeverlyHirtle.2015. “SupervisoryStressTests.”Annual Review of Financial Economics 7(1):339–355. McCracken, Michael W. and Serena Ng. 2015. “Fred-Md: A Monthly Database for Macroeconomic Research (2015-06-15).” FRB St. Louis Working Paper (2015-12). McNeil, Alexander J., Rudiger Frey and Paul Embrechts. 2015. Quantitative Risk Management, Concepts, Techniques and Tools. Princeton, New Jersey: Princeton University Press. Stock, JamesHandMarkWWatson.2002. “MacroeconomicForecastingUsingDiffusionIndexes.” Journal of Business and Economic Statistics 20(2):147–62. 10