Intermediary Leverage Cycles and Financial Stability Tobias Adrian and Nina Boyarchenko

Transcription

1 Intermediary Leverage Cycles and Financial Stability 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

2 Introduction Outline Introduction The Model Solution Distortions and Amplification Solvency Amplification T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

3 Introduction Questions about Financial Stability Policy Systemic distress of financial intermediaries raises questions about financial stability policies: How does capital regulation affect the tradeoff between the pricing of credit and the amount of systemic risk? How does macroprudential policy function in equilibrium? What are the welfare implications of capital regulation? We develop a theoretical framework to address these questions T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

4 Introduction Our Approach We use a standard macro model with a financial sector and add one key assumption: Funding constraints of financial intermediaries are risk based, so intermediaries have to hold more capital when the riskiness of their assets increases This assumption is empirically motivated and it allows us to capture stylized facts about: Procyclical leverage of intermediary balance sheets Procyclical share of intermediated credit Relationship between asset risk premia and intermediary leverage T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

5 The Model Outline Introduction The Model Solution Distortions and Amplification Solvency Amplification T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

6 The Model Economy Structure A t k ht Producers random dividend stream, A t,perunit 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 risk-free borrowing/lending T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

7 The Model Production Aggregate amount of capital K t evolves as Total output evolves as dk t = (I t λ k )K t dt Y t = A t K t Stochastic productivity of capital {A t = e at } t 0 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 T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

8 The Model Households Household preferences are: E [ + 0 ] e (ξt+ρht) log c t dt Liquidity preference shocks (as in Allen and Gale (1994) and Diamond and Dybvig (1983)) are exp ( ξ t ) dξ t = σ ξ ρ ξ,a dz at + σ ξ 1 ρ 2 ξ,a dz ξt Households do not have access to the investment technology dk ht = λ k k ht dt T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

9 The Model Households Optimization subject to [ + ] max E e (ξt+ρht) log c t dt {c t,k ht,b ht } 0 dw ht = r ft w ht dt + p kt A t k ht (dr kt r ft dt) + p bt A t b ht (dr bt r ft dt) c t dt and no-shorting constraints k ht 0 b ht 0 T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

10 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 (2012)) ( ) Φ (i t ) = φ φ1 i t 1 Intermediaries finance investment projects through inside equity and outside risky debt giving the budget constraint p kt A t k t = p bt A t b t + w t T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

11 The Model Intermediaries Risk Based Capital Constraint Risk based capital constraint (Danielsson, Shin, and Zigrand (2011)) 1 α dt k td (p kt A t ) 2 = w t Implies a time-varying leverage constraint θ t = p kta t k t w t = α 1 dt 1 2 d(pkt A t) p kt A t Note that the constraint is such that intermediary equity is proportional to the Value-at-Risk of total assets This will imply that default probabilities vary over time T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

12 The Model Risk-based Capital 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 2011 Annual Report T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

13 The Model Commercial Bank Lending Standards 60 ρ= VIX Credit Tightening Q2 91 Q2 93 Q2 95 Q2 97 Q2 99 Q2 01 Q2 03 Q2 05 Q2 07 Q2 09 Q T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

14 The Model Systemic Distress Solvency risk defined by Term structure of systemic distress τ D = inf t 0 {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 (NY Fed) Intermediary Leverage Cycles November 13, / 38

15 The Model Intermediaries Optimization Intermediary maximizes equity holder value to solve [ τd ] E e ρt w t dt max {k t,β t,i t} subject to the dynamic intermediary budget constraint dw t = k t p kt A t (dr kt + (Φ (i t ) i t /p kt ) dt) b t p bt A t dr bt and the risk based capital constraint 1 α dt k td (p kt A t ) 2 = w t 0 T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

16 The Model Equilibrium An equilibrium in this economy is a set of price processes {p kt, p bt, C bt } t 0, a set of household decisions {k ht, b ht, c t } t 0, and a set of intermediary decisions {k t, β t, i t, θ t } t 0 such that: 1 Taking the price processes and the intermediary decisions as given, the household s choices solve the household s optimization problem, subject to the household budget constraint. 2 Taking the price processes and the household decisions as given, the intermediary s choices solve the intermediary optimization problem, subject to the intermediary wealth evolution and the risk based capital constraint. 3 The capital market clears: 4 The risky bond market clears: 5 The risk-free debt market clears: 6 The goods market clears: K t = k t + k ht. b t = b ht. w ht = p kt A t k ht + p bt A t b ht. c t = A t (K t i t k t ). T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

17 The Model Related Literature Leverage Cycles: Geanakoplos (2003), Fostel and Geanakoplos (2008), Brunnermeier and Pedersen (2009) Amplification in Macroeconomy: Bernanke and Gertler (1989), Kiyotaki and Moore (1997) Financial Intermediaries and the Macroeconomy: Gertler and Kiyotaki (2012), Gertler, Kiyotaki, and Queralto (2011), He and Krishnamurthy (2012a,b), Brunnermeier and Sannikov (2011, 2012) T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

18 Solution Outline Introduction The Model Solution Distortions and Amplification Solvency Amplification T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

19 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 t θ t = 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 Risk-based capital constraint implies α 2 θ 2 t = σ 2 ka,t + σ2 kξ,t T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

20 Solution Volatility Risk y = x R 2 = Leverage Growth α Leverage Growth Volatility Lagged VIX T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

21 Solution Intermediary Balance Sheets Intermediated Credit Growth Total Credit Growth Intermediated Credit Growth y = x R 2 = 0.46 Total Credit Growth Leverage Growth α Leverage Growth Asset Growth Asset Growth Leverage Growth α Leverage Growth Equity Growth Equity Growth T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

22 Solution Optimal Household Choices Denote by π kt = (p kt A t k ht ) /w ht and π bt = (p bt A t b ht ) /w ht Lemma 3.1 The household s optimal consumption choice satisfies: ( ) c t = ρ h σ2 ξ 2 w ht. In the unconstrained region, the household s optimal portfolio choice is given by: [ πkt π bt ] ([ ] [ ]) 1 [ ] σka,t σ = kξ,t σka,t σ ba,t µrk,t r ft σ ba,t σ bξ,t σ kξ,t σ bξ,t µ Rb,t r ft [ ] [ ] 1 σka,t σ σ ba,t ρ ξ,a ξ σ kξ,t σ bξ,t 1 ρ 2. ξ,a T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

23 Solution Equilibrium Expected Returns Expected return to capital µ Rk,t r ft = ( σka,t 2 + ) 1 θ t ω t σ2 kξ,t 1 ω t }{{} compensation for own risk ( ) + σ ξ σ ka,t ρ ξ,a + σ kξ,t 1 ρ 2 ξ,a }{{} compensation for liquidity risk Expected return to intermediary debt µ Rb,t r ft = ( σba,t 2 + ) ω t (θ t 1) σ2 bξ,t 1 ω t } {{ } compensation for own risk ( ) + σ ξ σ ba,t ρ ξ,a + σ bξ,t 1 ρ 2 ξ,a }{{} compensation for liquidity risk + (σ ka,t σ ba,t + σ kξ,t σ bξ,t ) ω t (θ t 1) 1 ω t }{{} compensation for risk of correlated asset + (σ ka,t σ ba,t + σ kξ,t σ bξ,t ) 1 θ tω t 1 ω t }{{} compensation for risk of correlated asset T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

24 Solution Excess Returns Equity Return α Financial Sector Equity Return y = x R 2 = 0.17 Leverage Growth Lagged Leverage Growth Bond Return α Financial Sector Bond Return y = x R 2 = Leverage Growth Lagged Leverage Growth T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

25 Solution Equilibrium Prices of Risk I Shocks dŷ t = σa 1 (d log Y t E t [d log Y t ]) = dz at d ˆθ t = ( ( [ ]) σθa,t 2 + ) 1 σ2 2 dθt dθt θξ,t E t θ t θ t = σ θa,t σ 2 θa,t + σ2 θξ,t dz at + σ θξ,t σ 2 θa,t + σ2 θξ,t dz ξt. T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

26 Solution Equilibrium Prices of Risk II Price of risk of leverage η θt = (σ ka,t σ a ) σ 2 kξ,t ( 2θ ) tω t p kt β (1 ω t ) σ kξ,t + σ ξ 1 ρ 2 ξ,a Price of risk of leverage is always positive (Adrian, Etula, and Muir (2011)), and depends on leverage growth in a nonmonotonic fashion (Adrian, Moench, and Shin (2010) find a negative relationship) T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

27 Solution Equilibrium Prices of Risk III Realized Mean Return S1B5 S3B5 Mom10 S1B4 S2B3 S2B4 S3B4 S4B5 S1B3 S4B4 S1B2 S3B3 S3B2 Mom S4B3 S2B2 9 Mom 8 S5B5 S4B1 S5B2 S4B2 S5B4 S5B3 S5B1 S3B1 Mom Mom Mom 3 Mom 4 76 S2B1 Mom 5 Mom y 2 3yr 3 4yr 4 5yr 1 2yr S1B1 0 1yr S2B5 2 4 Mom Predicted Expected Return Figure: Source: Adrian, Etula, and Muir (2011) T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

28 Solution Equilibrium Prices of Risk IV Price of risk of output ( η yt = σ a + σ ξ ρ ξ,a σ ) ka,t σ a 1 ρ 2 σ ξ,a kξ,t Switches sign, consistent with insignificant estimates of price of output risk Usually becomes negative when exposure to liquidity shock is small More T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

29 Distortions and Amplification Outline Introduction The Model Solution Distortions and Amplification Solvency Amplification T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

30 Distortions and Amplification Solvency Term Structure of Systemic Risk Distress probability Distress probability 0 Horizon α T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

31 Distortions and Amplification Solvency Volatility Paradox Distress probability Distress probability Local volatility Price of leverage risk T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

32 Distortions and Amplification Amplification Constant Leverage Benchmark Constant expected output and consumption growth But lower level of output and consumption growth Constant investment and price of capital Liquidity shocks have no impact on real activity T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

33 Distortions and Amplification Amplification A Sample Path of the Economy Output 1 Financial Crisis Triggers Recession t Benign Financial Crisis Consumption Wealth 0.5 Leverage t t Return on debt t T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

34 Distortions and Amplification Amplification Household Welfare Welfare α T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

35 Distortions and Amplification Amplification Conclusion Dynamic, general equilibrium theory of financial intermediaries leverage cycle with endogenous amplification and endogenous systemic risk Conceptual basis for policies towards financial stability Systemic risk return tradeoff: tighter intermediary capital requirements tend to shift the term structure of systemic downward, at the cost of increased prices of risk today Model captures important stylized facts: 1 Procyclical intermediary leverage 2 Procyclicality of intermediated credit 3 Financial sector equity return and intermediary leverage growth 4 Exposure to intermediary leverage shocks as pricing factor T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

36 Distortions and Amplification Amplification Tobias Adrian, Emanuel Moench, and Hyun Song Shin. Financial Intermediation, Asset Prices, and Macroeconomic Dynamics. Federal Reserve Bank of New York Staff Reports No. 442, Tobias Adrian, Erkko Etula, and Tyler Muir. Financial Intermediaries and the Cross-Section of Asset Returns. Federal Reserve Bank of New York Staff Reports No. 464, Franklin Allen and Douglas Gale. Limited market participation and volatility of asset prices. American Economic Review, 84: , Ben Bernanke and Mark Gertler. Agency Costs, Net Worth, and Business Fluctuations. American Economic Review, 79(1):14 31, Markus K. Brunnermeier and Lasse Heje Pedersen. Market Liquidity and Funding Liquidity. Review of Financial Studies, 22(6): , Markus K. Brunnermeier and Yuliy Sannikov. The I Theory of Money. Unpublished working paper, Princeton University, Markus K. Brunnermeier and Yuliy Sannikov. A Macroeconomic Model with a Financial Sector. Unpublished working paper, Princeton University, T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

37 Distortions and Amplification Amplification Jon Danielsson, Hyun Song Shin, and Jean-Pierre Zigrand. Balance sheet capacity and endogenous risk. Working Paper, Douglas W. Diamond and Philip H. Dybvig. Bank runs, deposit insurance and liquidity. Journal of Political Economy, 93(1): , Ana Fostel and John Geanakoplos. Leverage Cycles and the Anxious Economy. American Economic Review, 98(4): , John Geanakoplos. Liquidity, 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 Econometric Society, Mark Gertler and Nobuhiro Kiyotaki. Banking, Liquidity, and Bank Runs in an Infinite Horizon Economy. Unpublished working papers, Princeton University, Mark Gertler, Nobuhiro Kiyotaki, and Albert Queralto. Financial Crises, Bank Risk Exposure, and Government Financial Policy. Unpublished working papers, Princeton University, Zhiguo He and Arvind Krishnamurthy. A model of capital and crises. Review of Economic Studies, 79(2): , 2012a. T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38

38 Distortions and Amplification Amplification Zhiguo He and Arvind Krishnamurthy. Intermediary asset pricing. American Economic Review, 2012b. Nobuhiro Kiyotaki and John Moore. Credit Cycles. Journal of Political Economy, 105(2): , T. Adrian, N. Boyarchenko (NY Fed) Intermediary Leverage Cycles November 13, / 38