Policies and Systemic Risk Tobias Adrian and Nina Boyarchenko The views presented here are the authors and are not representative of the views of the Federal Reserve Bank of New York or of the Federal Reserve System
Introduction Motivation for Regulation shortages are key characteristics of the financial crises stress is caused by: Short-term wholesale funding of non-traditional, illiquid assets Mismanagement of contingent liquidity risk Uncertainty about counterparties and collateral disruptions Basel III regulation promotes resilience to liquidity shocks by addressing two objectives: Enhance resilience to short-term funding shocks by requiring FIs to hold a minimum pool of liquid assets (LCR) Improve longer term liquidity management by requiring activity funded with core or stable funding (NSFR) [not finalized] T. Adrian, N. Boyarchenko Regulation 2
Introduction Ratio of Unstable Liabilities to Liquid Assets Fraction of liabilities that runs at a 3 day horizon under stress Liquid assets haircutted to account for illiquidity Haircuts are from the LCR, plot from Dong and Zhou (214) T. Adrian, N. Boyarchenko Regulation 3
Introduction Our Approach We use a standard macro model with a financial sector We add two key assumptions: Financial intermediaries have to hold liquidity against liabilities regulation is risk based as in Adrian and Boyarchenko (212) Framework allows us to study the equilibrium implications of liquidity requirements on the quantity and price of credit Framework also features systemic financial crises T. Adrian, N. Boyarchenko Regulation 4
Introduction Preview of Results Within the context of our model, liquidity requirements are a preferable prudential policy tool relative to capital requirements Tightening liquidity requirements lowers the likelihood of systemic distress, without impairing consumption growth requirements trade off consumption growth and distress risk T. Adrian, N. Boyarchenko Regulation 5
The Model Economic Structure A t k ht Producers random dividend stream, A t, per unit of project financed by direct borrowing from intermediaries and households i t A t k t Intermediaries financed by households against capital investments C bt b ht Households solve portfolio choice problem between holding intermediary debt, physical capital and riskfree borrowing/lending T. Adrian, N. Boyarchenko Regulation 6
The Model Intermediaries Balance Sheet Assets Liabilities Productive capital (A t p kt k t ) Risky debt (A t p bt b t ) Risk-free debt (A t T t ) Inside equity (w t ) T. Adrian, N. Boyarchenko Regulation 7
The Model Production Total output evolves as Y t = A t K t Stochastic productivity of capital {A t = e at } t da t = ādt + σ a dz at p kt A t denotes the price of one unit of capital in terms of the consumption good Aggregate amount of capital K t evolves as dk t = (I t λ k )K t dt T. Adrian, N. Boyarchenko Regulation 8
The Model Intermediaries Financial intermediaries create new capital dk t = (Φ(i t ) λ k ) k t dt Investment carries quadratic adjustment costs (Brunnermeier and Sannikov (212)) ( ) Φ (i t ) = φ 1 + φ1 i t 1 Intermediaries finance investment projects through inside equity and outside risky debt giving the budget constraint T t A t + p kt A t k t = p bt A t b t + w t T. Adrian, N. Boyarchenko Regulation 9
The Model Intermediaries Risk Based Constraint Risk based capital constraint (Danielsson, Shin, and Zigrand (211)) 1 α dt k td (p kt A t ) 2 w t Implies a time-varying leverage constraint θ kt = p kta t k t w t α 1 dt 1 2 d(pkt A t) p kt A t Equity is proportional to the Value-at-Risk of assets implying time varying default probabilities T. Adrian, N. Boyarchenko Regulation 1
The Model Risk-based Constraints VaR is the potential loss in value of inventory positions due to adverse market movements over a defined time horizon with a specified confidence level. We typically employ a one-day time horizon with a 95% confidence level. Source: Goldman Sachs 211 Annual Report T. Adrian, N. Boyarchenko Regulation 11
The Model Commercial Bank Tightening Standards 6 ρ=.6813 1 4 5 VIX Credit Tightening 2 Q2 91 Q2 93 Q2 95 Q2 97 Q2 99 Q2 1 Q2 3 Q2 5 Q2 7 Q2 9 Q2 11 5 T. Adrian, N. Boyarchenko Regulation 12
Intermediated.5 The Model 1 Procyclicality induced by Risk based Constraint Leverage Growth Leverage Growth 4 2 2 4 Total Credit Growth 5 5 5 y =.86 +.56x R 2 =.56 5 5 Equity Growth 5 1.5.5 1 Debt Growth Intermediated Leverage Growth Leverage Growth.1.5.5.1.15 Total Credit Growth 1.5.5 1 1.5.5 1 Equity Growth 1.5.5 1 1.5.5 1 Debt Growth Source: Adrian and Boyarchenko (212) T. Adrian, N. Boyarchenko Regulation 13
The Model Systemic Risk Return Tradeoff 1 Welfare Distress probability.8.6 2 4 6 8 1 α 2 Source: Adrian and Boyarchenko (212) T. Adrian, N. Boyarchenko Regulation 14
The Model Intermediaries Constraint constraint (similar to Basel III s liquidity coverage ratio) Requires intermediaries to hold cash in proportion to outstanding debt where The constraint can be rewritten as 1 + θ bt θ }{{ kt Λ } θ }{{} bt cash/equity debt/equity θ bt = p bta t b t w t θ bt 1 1 Λ (θ kt 1) = Λ(θ kt 1) Intermediaries are required to hold cash to buffer potential short term funding needs T. Adrian, N. Boyarchenko Regulation 15
The Model Intermediaries Optimization Intermediary are myopic mean-variance optimizers solving [ ] dwt max E t γ [ ] θ t,θ bt,i t 2 V dwt t, subject to the dynamic intermediary budget constraint dw t w t w t w t = θ t (dr kt r ft dt) θ bt (dr bt r ft dt) + r ft dt, the risk-based capital constraint constraint θt 1 1 d (pkt A t ) 2 α, dt p kt A t and the liquidity constraint θ bt Λ(θ kt 1) T. Adrian, N. Boyarchenko Regulation 16
The Model Systemic Distress Distress occurs when Term structure of systemic distress τ D = inf t {w t ωp kt A t K t } δ t (T ) = P (τ D T (w t, θ t )) In distress Management changes Intermediary leverage reduced to θ 1 by defaulting on debt Intermediary instantaneously restarts with wealth w τ + D = θ τ D θ w τ D T. Adrian, N. Boyarchenko Regulation 17
The Model Systemic Distress and Regulation 1 Distress probability.8.6 6 month 1 year 5 year 8 1 2 4 6 8 1 α Source: Adrian and Boyarchenko (212) T. Adrian, N. Boyarchenko Regulation 18
The Model Households Household preferences are: E [ + ] e (ξt+ρht) log c t dt preference shocks (as in Allen and Gale (1994) and Diamond and Dybvig (1983)) are exp ( ξ t ) dξ t = σ ξ dz ξt Households do not have access to the investment technology dk ht = λ k k ht dt T. Adrian, N. Boyarchenko Regulation 19
Solution Market Structure Market Intermediaries Households Total k t k ht K t Consumption i t k t A t c t A t K t Risky Debt b t b ht Risk-Free Debt T t A t T ht A t BA t T. Adrian, N. Boyarchenko Regulation 2
Solution Equilibrium An equilibrium in this economy is: A set of price processes {p kt, p bt, r ft } t A set of household decisions {k ht, b ht, c t } t A set of intermediary decisions {k t, ρ t, i t, θ t, θ bt } t Such that: 1 Household s optimize 2 Intermediary s optimize 3 The capital market clears 4 The risky bond market clears 5 The risk-free debt market clears 6 The goods market clears T. Adrian, N. Boyarchenko Regulation 21
Solution Solution Strategy Equilibrium is characterized by two state variables, leverage θ t and relative intermediary net worth ω t ω t = Represent state dynamics as w t w t + w ht = w t p kt A t K t dω t ω t dθ kt θ kt = µ ωt dt + σ ωa,t dz at + σ ωξ,t dz ξt = µ θt dt + σ θa,t dz at + σ θξ,t dz ξt Numerical solution T. Adrian, N. Boyarchenko Regulation 22
Solution Roadmap Examine the trade-off between requirements and capital requirements requirements and supply of risk-free debt Varying the tightness of liquidity and capital regulation affects the risk-taking behavior of intermediaries the intermediaries leverage cycle endogenous volatility amplification endogenous systemic risk Varying the supply of risk-free debt affects the equilibrium risk-free rate and thus the equilibrium cost of issuing risky debt T. Adrian, N. Boyarchenko Regulation 23
Welfare Trading off and Regulation T. Adrian, N. Boyarchenko Regulation 24
Conclusion Conclusion Impact of liquidity and capital requirements in general equilibrium The model features Procyclical financial intermediary leverage cycle Endogenous volatility Endogenous systemic risk Within the context of our model, liquidity requirements are a preferable prudential policy tool relative to capital requirements Tightening liquidity requirements lowers the likelihood of systemic distress, without impairing consumption growth In contrast, capital requirements trade off consumption growth and distress probabilities T. Adrian, N. Boyarchenko Regulation 25
Conclusion Related Literature Regulation: Goodhart, Kashyap, Tsomocos, and Vardoulakis (212), Perotti and Suarez (211), Calomiris and Heider (213) Leverage Cycles: Geanakoplos (23), Fostel and Geanakoplos (28), Brunnermeier and Pedersen (29) Amplification in Macroeconomy: Bernanke and Gertler (1989), Kiyotaki and Moore (1997) Financial Intermediaries and the Macroeconomy: Gertler and Kiyotaki (212), Gertler, Kiyotaki, and Queralto (211), He and Krishnamurthy (212, 213), Brunnermeier and Sannikov (211, 212) T. Adrian, N. Boyarchenko Regulation 26
Conclusion Tobias Adrian and Nina Boyarchenko. Intermediary Leverage Cycles and Financial Stability. Federal Reserve Bank of New York Staff Report No. 567, 212. Franklin Allen and Douglas Gale. Limited market participation and volatility of asset prices. American Economic Review, 84:933 955, 1994. Ben Bernanke and Mark Gertler. Agency Costs, Net Worth, and Business Fluctuations. American Economic Review, 79(1):14 31, 1989. Markus K. Brunnermeier and Lasse Heje Pedersen. Market and Funding. Review of Financial Studies, 22(6):221 2238, 29. Markus K. Brunnermeier and Yuliy Sannikov. The I Theory of Money. Unpublished working paper, Princeton University, 211. Markus K. Brunnermeier and Yuliy Sannikov. A Macroeconomic Model with a Financial Sector. Unpublished working paper, Princeton University, 212. Charles Calomiris and Florian Heider. A Theory of Regulation. Unpublished working paper, 213. Jon Danielsson, Hyun Song Shin, and Jean-Pierre Zigrand. Balance sheet capacity and endogenous risk. Working Paper, 211. T. Adrian, N. Boyarchenko Regulation 27
Conclusion Douglas W. Diamond and Philip H. Dybvig. Bank runs, deposit insurance and liquidity. Journal of Political Economy, 93(1):41 419, 1983. Ana Fostel and John Geanakoplos. Leverage Cycles and the Anxious Economy. American Economic Review, 98(4):1211 1244, 28. John Geanakoplos., Default, and Crashes: Endogenous Contracts in General Equilibrium. In M. Dewatripont, L.P. Hansen, and S.J. Turnovsky, editors, Advances in Economics and Econometrics II, pages 17 25. Econometric Society, 23. Mark Gertler and Nobuhiro Kiyotaki. Banking,, and Bank Runs in an Infinite Horizon Economy. Unpublished working papers, Princeton University, 212. Mark Gertler, Nobuhiro Kiyotaki, and Albert Queralto. Financial Crises, Bank Risk Exposure, and Government Financial Policy. Unpublished working papers, Princeton University, 211. Charles A.E. Goodhart, Anil K. Kashyap, Dimitrios P. Tsomocos, and Alexandros P. Vardoulakis. Financial Regulation in General Equilibrium. NBER Working Paper No. 1799, 212. T. Adrian, N. Boyarchenko Regulation 28
Conclusion Zhiguo He and Arvind Krishnamurthy. A Model of and Crises. Review of Economic Studies, 79(2):735 777, 212. Zhiguo He and Arvind Krishnamurthy. Intermediary Asset Pricing. American Economic Review, 13(2):732 77, 213. Nobuhiro Kiyotaki and John Moore. Credit Cycles. Journal of Political Economy, 15(2):211 248, 1997. Enrico Perotti and Javier Suarez. A Pigovian Approach to Regulation. International Journal of Central Banking, 7(4):3 41, 211. T. Adrian, N. Boyarchenko Regulation 29
Conclusion Intermediaries binding Constraints.5 1.5 1 1.3.1.8.6.3.1.8.6.8.6.8.6 2 3 4 5.6.8 2 4 T. Adrian, N. Boyarchenko Regulation 3
Conclusion Risk Free Rate.5.3.1 2 3 4 5.1.95.9.85.5.3.1.6.8.1.95.9.85.8.6 2 4.98.97.96.95.94.93 T. Adrian, N. Boyarchenko Regulation 31
Conclusion Households Risky Assets.5.3.1 2 3 4 5 3 2.5 2 1.5 1.5.5.3.1.6.8 4.5 4 3.5 3 2.5 2 1.5 1.5.8.6 2 4 5 4 3 2 1 T. Adrian, N. Boyarchenko Regulation 32
Conclusion Household Welfare.5 High.5 High.3.1.3.1 2 3 4 5 Low.6.8 Low High.8.6 2 3 4 5 Low T. Adrian, N. Boyarchenko Regulation 33
Conclusion Debt-to-equity Ratios.5.3.1 12 1 8 6 4 2.5.3.1 2 15 1 5 2 3 4 5.6.8 25.8 2.6 15 1 5 2 3 4 5 T. Adrian, N. Boyarchenko Regulation 34
Conclusion Distress probability.5.5.35.3.1.3.1.3.1.3 5.15.1.5 2 3 4 5.6.8.8.18.6.16.14.12.1.8 2 3 4 5.6 T. Adrian, N. Boyarchenko Regulation 35
Conclusion Local Volatility.5.5 4.3.1.15.1.3.1 2.18.16.14.12.1 2 3 4 5.6.8.8.6.18.16.14 2 3 4 5 T. Adrian, N. Boyarchenko Regulation 36
Conclusion Exposures of Return to to Fundamental Shocks σ ka σ kξ 2 3 4 5.12.1.8.6.4.2 2 3 4 5.1.15 σ ka σ kξ.8.6.15.1.5.8.6.1.12.14 2 3 4 5 2 3 4 5 σ ka σ kξ.6.8.1.5.6.8.5.1.15 T. Adrian, N. Boyarchenko Regulation 37
Conclusion Consumption Growth.5 High.5 High.3.1.3.1 2 3 4 5 Low.6.8 Low High.8.6 2 3 4 5 Low T. Adrian, N. Boyarchenko Regulation 38