Stress Testing U.S. Bank Holding Companies A Dynamic Panel Quantile Regression Approach Francisco Covas Ben Rump Egon Zakrajšek Division of Monetary Affairs Federal Reserve Board October 30, 2012 2 nd Conference of the Macro-prudential Research Network of the European System of Central Banks European Central Bank
The analysis and opinions expressed herein are solely those of the authors and do not represent the views of the Federal Reserve Board, the Federal Reserve System, or any of our colleagues.
MOTIVATION Macroprudential Supervision and Financial Stability U.S. Stress Tests (SCAP 2009, CCAR 2011, CCAR 2012) Simultaneous evaluation of capital adequacy plans of the 19 largest U.S. bank holding companies Consistency of macro scenarios across banks Multiple, independent estimates of losses, pre-provision net revenue and tier 1 common ratio under the adverse macro scenario Goal: To ensure U.S. banks hold sufficient high quality capital to absorb losses without triggering an excessive reduction in assets
TIER 1 COMMON RATIO FOR THE 19 CCAR BANKS Period: 2007:Q1 2012:Q2 Quarterly, NSA 14 SCAP CCAR 2011 CCAR 2012 12 10 8 6 2007 2008 2009 2010 2011 2012
BANK OPACITY AND STRESS TESTS Bank-specific results of the stress tests are released to the public The release of the results provides new information to market participants Banks are opaque and market participants do not know the economic value of banks portfolios (Flannery et al. [2010]) Event type studies find that banks with larger capital shortfalls experience more negative idiosyncratic returns (Peristiani et al. [2010]) For example, after the release of CCAR 2012 results banks with higher declines in tier 1 common ratios (T1CR) under stressed conditions experienced lower idiosyncratic returns
IDIOSYNCRATIC STOCK RETURNS FOR CCAR BANKS Two-day window after announcement of CCAR 2012 results 8 7 6 5 4 3 2 1 0-1 -2-3 RF BAC STT COF AXP USB WFC FITB BBT MET KEY STI JPM PNC β ^ = - t-stat = 4.0 2 R = 0.51 BK GS MS C -4 1 2 3 4 5 6 7 Decline in T1CR under stress conditions (percentage points)
OUR PAPER Evaluate the forecasting performance of top-down stress-testing models and construct density forecasts for T1CR 1. Top-down models are useful to benchmark aggregated results of stress tests 2. Can be used to evaluate banks capital adequacy plans under different macro scenarios Key features of our top-down stress testing approach: Fixed Effects Quantile Autoregression (FE-QAR): Variation in the coefficient on the lagged dependent variable allows for changes in the scale and shape of the conditional distribution - important feature that helps capturing the fat tails of credit losses The impact of macro variables on the dependent variable is time-varying (Schechtman et al. [2012])
Fixed Effects Quantile Autoregression Y it = variable forecasted for bank i in period t X it 1 = vector of portfolio shares for bank i in period t 1 Z t = macroeconomic factors in period t The FE-QAR(p) model: Q π (Y it Y it 1,...,Y it k,x it 1,Z t ) = p α(π)+η i + φ k (π)y it k +β(π) X it 1 +θ(π) Z t k=1 π (0,1) = π-quantile Qπ (Y it Y it 1,...,Y it k,x it 1,Z t ) = conditional quantile function ηi = fixed effect of bank i
DENSITY FORECASTS Use Monte Carlo simulation to generate density forecasts 1. Use the estimated coefficients and the trajectory of the macro variables to generate a forecast path 2. Use the individual forecast paths to calculate the evolution of T1CR 3. Generate many paths for each bank, using a different sequence of idiosyncratic shocks for each path (ensemble forecasts) 4. Aggregate the forecasts across all banks 5. Shocks across subcomponents of credit losses and revenue are correlated (based on the estimated covariance matrix) Compare the density forecasts with the ones generated using a dynamic linear model with fixed effects
DATA Merger-adjusted FR Y-9C Reports 1. Net charge-offs for eight major loan portfolios 2. Six subcomponents of pre-provision net revenue Included 15 BHCs (Includes most largest BHCs, 900 Obs.) Sample period: 1997:Q1 2011:Q4 Macroeconomic factors: 1. Slope of yield curve 2. Unemployment rate (4Q Change) 3. Real Gross Domestic Product (4Q Log Change) 4. CoreLogic house price index (4Q Log Change) 5. Price index for commercial real estate (4Q Log Change) 6. BBB-rated corporate bond spread
QUANTILE PROCESSES: PERSISTENCE Period: 1997:Q1 2011:Q4 Sum of autoregressive coefficients in RRE NCO model Sum of autoregressive coefficients in TI model FE-QAR Estimate 95% confidence interval 1.6 1.4 1.6 1.4 1.2 1.2 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 0.05 0.20 0.35 0.50 0.65 0.80 0.95 Quantile 0.05 0.20 0.35 0.50 0.65 0.80 0.95 Quantile
QUANTILE PROCESSES: MACRO VARIABLES Period: 1997:Q1 2011:Q4 House price growth in RRE NCO model Term spread in NIM model FE-QAR Estimate 0.01 0.20 95% confidence interval 0.00 0.15-0.01 0.10 0.05-0.02 0.00 0.05 0.20 0.35 0.50 0.65 0.80 0.95 Quantile -0.03 0.05 0.20 0.35 0.50 0.65 0.80 0.95 Quantile
FORECAST EVALUATION Pseudo out-of-sample forecasts for aggregate net charge-offs and pre-provision net revenue Period for out-of-sample forecasts is 2005:Q1 2011:Q4 Construct recursive 4-quarter-ahead forecasts (paper reports 1-, 2- and 3-quarters ahead as well) Path of macro variables and assets shares are taken as given Formal tests for the optimality of the density forecasts indicate that short-term forecasts have desirable statistical properties
DENSITY FORECASTS FOR NET CHARGE-OFFS Four-Quarter-Ahead: 2005:Q1 2011:Q4 Net charge-offs Quarterly FE-QAR 6.5 6.0 Net charge-offs Quarterly FE-OLS 6.5 6.0 Actual Forecasted median 5.5 5.0 5.5 5.0 4.5 4.5 4.0 4.0 3.5 3.5 3.0 3.0 2.5 2.5 2.0 2.0 1.5 1.5 0.5 0.5 2005 2006 2007 2008 2009 2010 2011 0.0 2005 2006 2007 2008 2009 2010 2011 0.0
DENSITY FORECASTS FOR PPNR Four-Quarter-Ahead: 2005:Q1 2011:Q4 FE-QAR Pre-provision net revenue Quarterly 4.0 FE-OLS Pre-provision net revenue Quarterly 4.0 Actual 3.5 3.5 Forecasted median 3.0 3.0 2.5 2.5 2.0 2.0 1.5 1.5 0.5 0.5 0.0 0.0-0.5-0.5 2005 2006 2007 2008 2009 2010 2011-2005 2006 2007 2008 2009 2010 2011 -
DENSITY FORECASTS FOR T1CR Ultimately, we are interested in constructing density forecasts for T1CR Use a simple capital calculator that takes as inputs the model projections for each revenue and loan loss subcomponents Use the CCAR 2012 adverse macro scenario to generate the density forecasts for aggregate net charge-offs, pre-provision net revenue and T1CR Due to the nonlinearities in loan losses and trading income the density forecast of T1CR has fatter left tails under the quantile model Thus, the quantile model generates higher capital shortfalls
PROJECTIONS FOR NET CHARGE-OFFS CCAR 2012 Projection Period: 2011:Q4 2013:Q4 Net charge-offs Quarterly FE-QAR 5.0 Net charge-offs Quarterly FE-OLS 5.0 Actual 4.5 4.5 Forecasted median 4.0 4.0 3.5 3.5 3.0 3.0 2.5 2.5 2.0 2.0 1.5 1.5 2007 2008 2009 2010 2011 2012 2013 0.5 2007 2008 2009 2010 2011 2012 2013 0.5
PROJECTIONS FOR PRE-PROVISION NET REVENUE CCAR 2012 Projection Period: 2011:Q4 2013:Q4 Pre-provision net revenue Quarterly 3.5 Pre-provision net revenue Quarterly 3.5 Actual 3.0 3.0 Forecasted median 2.5 2.5 2.0 2.0 1.5 1.5 0.5 0.5 0.0 0.0-0.5-0.5 2007 2008 2009 2010 2011 2012 2013-2007 2008 2009 2010 2011 2012 2013 -
DENSITY FORECASTS FOR TIER 1 COMMON RATIO Under CCAR 2012 Adverse Macro Scenario as of 2013:Q4 FE-OLS FE-QAR T1CR in 2011:Q3 Density 120 100 80 60 40 20 2 4 6 8 10 0 Tier 1 Common Ratio ()
FINANCIAL CRISIS IN 2008-2009 How would these models perform at the onset of the last financial crisis? Estimate both the quantile and linear models until the end of 2007 Project losses and revenues over the next two years, taking as given the realized values of the macro variables and portfolio shares Evaluate capital shortfalls using the density forecast for T1CR at the end of 2009:Q4
PROJECTIONS FOR NET CHARGE-OFFS Projection Period: 2008:Q1 2009:Q4 Net charge-offs Quarterly FE-QAR 5.0 Net charge-offs Quarterly FE-OLS 5.0 Actual 4.5 4.5 Forecasted median 4.0 4.0 3.5 3.5 3.0 3.0 2.5 2.5 2.0 2.0 1.5 1.5 2005 2006 2007 2008 2009 0.5 2005 2006 2007 2008 2009 0.5
PROJECTIONS FOR PRE-PROVISION NET REVENUE Projection Period: 2008:Q1 2009:Q4 Pre-provision net revenue Quarterly 3.5 Pre-provision net revenue Quarterly 3.5 Actual 3.0 3.0 Forecasted median 2.5 2.5 2.0 2.0 1.5 1.5 0.5 0.5 0.0 0.0-0.5-0.5 2005 2006 2007 2008 2009-2005 2006 2007 2008 2009 -
CAPITAL SHORTFALLS IN 2007:Q4 % Violations Expected Shortfall FE-QAR FE-OLS FE-QAR FE-OLS All banks 2.74 1.30 6.9 0.9 BAC 3.06 0.02 15.2 0.6 C 22.82 17.32 24.4 5.1 JPM 4.04 0 15.2 0 WFC 0.12 0 14.6 0 NOTE: Projection period: 2008:Q1 2009:Q4. Results are relative a tier 1 common target of 2 percent. Expected shortfall is in billions of dollars. Bank names: BAC = Bank of America Corporation; C = Citigroup, Inc.; JPM = JPMorgan Chase & Co.; and WFC = Wells Fargo & Company.
CONCLUSIONS Expand the existing top-down stress-testing methodologies in two dimensions: 1. Density forecasts 2. Quantile regressions Top-down model that can be used as a macroprudential tool: 1. Calibration of Macroeconomic scenarios for stress-testing 2. Identification of vulnerabilities during good times 3. Time-varying capital buffers 4. Restrictions on distributions Work in progress: incorporate BHCs with short-time series (need to use IV quantile regression)