Bank Capital Buffers in a Dynamic Model 1

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1 Bank Capital Buffers in a Dynamic Model 1 Jochen Mankart 1 Alex Michaelides 2 Spyros Pagratis 3 1 Deutsche Bundesbank 2 Imperial College London 3 Athens University of Economics and Business CRESSE 216, July 3 1 The views expressed in this presentation represent the authors personal opinions and do not necessarily reflect those of the Deutsche Bundesbank.

2 Basel III: status quo Global regulators embarked on most substantial regulatory overhaul of banking sector since Great Depression. Comprehensive Basel III reforms to be finalized in 216. Once fully phased in, banks subject to multiple requirements: Minimum capital: risk-weighted, leverage requirements. Capital buffers: capital conservation, countercyclical capital (CCyB), systemic buffer (SIBs). Liquidity: liquidity coverage ratio (LCR), net stable funding ratio (NSFR). Recovery and resolution regimes: bail-ins, cocos, loss-absorbing debt capacity.

3 Motivation Basel III will affect bank behavior and industry structure. Already dramatic change of balance sheets globally. But banks yet to feel full impact of regulatory implementation. Understand and realistically assess the impact of new regulations requires quantitative structural models. Gauge systamic risk by reproducing bank heterogeneity and cyclical behavior, as in the data.

4 Early evidence from the field Basten, Koch (215): CCyB affects composition of mortgage supply, with capital-constrained and specialized banks raising rates more. Aiyar et al. (214): Significantly negative effect of minimum capital requirements on cross-border lending. Drehmann, Gambacorta (212): CCyB slows down credit growth in booms, and credit contractions in downturns.

5 Growing literature on quantitative banking models DeNicolo, Gamba, Lucchetta (213), He, Krishnamurthy (213), Brunnermeier, Sannikov (214), Corbae, DErasmo (214), Martinez, Miera, Suarez (214), Klimenko, Pfeil, Rochet (215).

6 This paper We build a quantitative banking model to replicate cross sectional heterogeneity pro-cyclical lending counter-cyclical bank failures. Estimate the model using the Method of Simulated Moments. Use the model to evaluate how risk-weighted capital adequacy and a leverage requirements interact to affect bank behavior.

7 Our starting point Assets Liabilities loans L r L deposits D r D liquid assets S r S wholesale funds F g F equity E Banks choose dividends X t, new loans N t, liquid assets S t, and wholesale borrowing F t to maximize owners utility subject to: (unweighted) leverage constraint (L t + N t) + S t E t X t λ u = (1) (risk-weighted) capital adequacy constraint ω L (L t + N t) + ω S S t E t X t λ w = 16.66, (2) with ω L = 1 (ω S =.2) risk weight on loans (liquid assets) Aggregate and idiosyncratic shocks move loan write-offs, deposit growth and returns.

8 Model I: Balance sheet, equity and loan evolution Balance sheet constraint Evolution of loans Evolution of equity L t+ {}}{ L t + N t +S t = D t + F t + E t+ {}}{ E t X t (3) L t+1 = (1 ϑ w t+1 ) L t+ (4) E t+1 = E t+ + Π t+1 τπ t+1 I Πt+1 > (5) where L t loan stock, N t new loans (potentially negative), S t liquid assets, D t deposits, F t wholesale funds, E t equity, X t dividends, ϑ loan repayments, w t+1 loan write offs, Π t+1 profits, τ =.15 corporate tax rate, I Πt+1 > indicator function for positive profits.

9 Model II: Bank profits Π t+1 = (r L,t+1 ω t+1 ) L t+ + r S,t+1 S t r D,t+1 D t g N (N t, D t ) g F (F t, D t, E t+ ) cd t (6) g N (N t, D t ) adjustment (screening) cost for loans. g F cost of wholesale funding. c operating cost of running the bank.

10 Model III: Cost functions Cost of accessing wholesale funding markets: Loan adjustment costs: g F (F t, E t, D t ) = r Ft F t + φ F F 2 t D t φ E E 2 t D t (7) g N (N t, D t ) = I nt>φ N N 2 t D t + (1 I nt>)ψφ N N 2 t D t (8) with ψ = 1.3 capturing costly loan liquidation, and I nt> indicator function for positive new loans.

11 The bank s problem V C (L t, D t, E t ; w t, r t ) = with default decision subject to max X t,s t,f t,n t { (X t ) 1 γ 1 γ + E t [βv (L t+1, D t+1, E t+1 ; w t+1, r t+1, )]} V (L t, D t, E t ; w t, r t ) = max[v D, V C (L t, D t, E t ; w t, r t )] leverage (1) and capital adequacy (2) constraints, balance sheet constraint (3), loan evolution (4), equity evolution (5), profits (6).

12 Estimated parameters The 7 estimated parameters are Parameter Large banks Small banks Discount factor β.975 (.4).986 (.11) CRRA γ 1.31 (.4) 1.89 (.6) Operating cost c.11 (.2).96 (.1) Screening cost φ N.63 (.4).9 (.4) Cost wholesale funding φ F.92 (.2).81 (.3) Discount wholesale funding φ E.7(.4).7(.1) Consumption after exit c D 2e 5 (3e 4) 4e 5 (8e 4)

13 Moments Moments Big banks Small banks model data model data Mean failure rate (in %) Mean loans/assets Mean deposits/assets Mean equity/assets Mean profit/equity Mean dividends/equity Std. loans/assets Std. deposits/assets Std. equity/assets Std. profit/equity Std dividends/equity

14 The final 82 quarters in the life of a bank Write offs A: Exogenous shocks Deposit growth Equity B: Equity and loan states Loans Booms Recessions New loans C: New loans Liquid assets D: Liquid assets and wholesale funding Wholesale funding Profits 15 x E: Profits and dividends Time x Dividends Leverage F: Regulatory capital ratios 4 2 Lev. constraint,33.3 Cap. constraint, Time Capital adequacy

15 Cyclical properties of leverage and bank failures 25 Small banks Large banks.3.25 Small banks Large banks time Leverage time Bank failure Details failed banks

16 Cross sectional heterogeneity: Leverage Data Model

17 Taking stock We have a structural model of bank behavior Generates reasonable cross-sectional heterogeneity and time series behavior Use it to conduct counterfactual policy experiments

18 2 counterfactual experiments 1 (Unweighted) leverage limit (baseline λ u = 33.3) changed from 25 to Risk-weighted capital adequacy constraint (baseline λ u = 16.6) changed from 13 to 2. 3 Steady state comparison.

19 Experiment I: Capital adequacy constraint (1).8.75 Large banks Small banks A: Loan to assets.4.2 B: % change in agg loan supply C: Equity to assets.651 lower loan supply, since banks substitute into liquid assets D: % change in profit to equity ratio Tighter (risk-weighted) capital adequacy constraint leads to: 1 E: % change in equity buffers x 1 4 F: Failure rates 1

20 .8.4 Experiment Large I: bankscapital adequacy constraint (2).75 Small banks A: Loan to assets.2 B: % change in agg loan supply C: Equity to assets D: % change in profit to equity ratio E: % change in equity buffers x 1 4 F: Failure rates 1 Tighter (risk-weighted) capital adequacy 1 constraint leads to: an increase in equity, 3 a fall in RoE Capital adequacy limit Capital adequacy limit

21 Introduction Model C: Equity to Estimation assets Results Counterfactual D: % change in profit Conclusion to equity ratio Back up Experiment I: Capital adequacy constraint (3) E: % change in equity buffers x 1 4 F: Failure rates Capital adequacy limit Capital adequacy limit Tighter (risk-weighted) capital adequacy constraint leads to: 4 lower RoE which reduces incentives to accumulate equity in excess of regulatory minima. 5 increases failure rate.

22 Experiment II: Leverage constraint (1).8.75 Large banks Small banks A: Loan to assets.3.2 B: % change in agg loan supply C: Equity to assets Tighter leverage requirement leads to: increase in loan supply, since banks substitute into loans D: % change in profit to equity ratio E: % change in equity buffers 1 x 1 4 F: Failure rates

23 A: Loan to assets B: % change in agg loan supply.8.3 Large Experiment.75 Small II: banksleverage constraint.2 (2) C: Equity to assets D: % change in profit to equity ratio E: % change in equity buffers x 1 4 F: Failure rates Tighter leverage requirement leads to: 8 25 increase in equity, 3 6 almost unchanged RoE (numeratorand denominator go in 5 25same direction) Leverage limit Leverage limit 1

24 Introduction Model Estimation Results Counterfactual Conclusion Back up C: Equity to assets D: % change in profit to equity ratio.75 2 Experiment II: Leverage constraint 1 (3) E: % change in equity buffers 1 x 1 4 F: Failure rates Leverage limit Leverage limit Tighter leverage requirement leads to: 4 increase in equity buffer of large banks, mixed for small, 5 small fall in failure rate of large but small rise for small banks.

25 Conclusions We estimate a dynamic banking model to examine the interaction of risk-weighted capital adequacy and leverage requirements. Banks hold an equity buffer in excess of the regulatory minimum. Tighter risk-weighted capital requirements: 1 reduce loan supply, 2 lead to endogenous fall in bank profitability and charter value, 3 reduce bank incentives to accumulate equity buffers, and 4 increase the incidence of bank failure. Tighter leverage requirements: 1 increase loan supply, 2 preserve bank charter value and incentives to accumulate equity buffers in excess of regulatory minima, and 3 reduce the incidence of bank failure.

26 Leverage for failed and non-failed banks: data vs model Failed banks Non-failed banks 35 3 failed banks non failed banks Time to failure Quarters to failure 14 8 Data Model Back

27 Experiment I: Equity buffers and capital adequacy limit.55 A: Large banks.55 B: Small banks unweighted risk weighted Capital adequacy limit.2.15 unweighted risk weighted Capital adequacy limit Risk weighted constraint always tighter for large banks. Back

28 Experiment II: Equity buffers and leverage limit.55 A: Large banks.55 B: Small banks unweighted risk weighted Leverage limit.2 unweighted risk weighted Leverage limit Again, risk weighted constraint always tighter for large banks. Back