Intermediary Asset Pricing

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1 Intermediary Asset Pricing Z. He and A. Krishnamurthy - AER (2012) Presented by Omar Rachedi 18 September 2013

2 Introduction Motivation How to account for risk premia? Standard models assume households determine risk premia World is not so risky for households Consumption smooth and low correlation with stocks Equity premium puzzle Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 1 / 15

3 Introduction Motivation How to account for risk premia? Standard models assume households determine risk premia World is not so risky for households Consumption smooth and low correlation with stocks Equity premium puzzle Recent crisis pinpoints banks as crucial sector in the economy Re-capitalizing the banking sector was a priority after the collapse of Lehmann Banks capital matters! Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 1 / 15

4 Introduction Contribution Model in which banks determine risk premia Banks face an equity capital constraint Risk premia depends on banks capital Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 2 / 15

5 Introduction Contribution Model in which banks determine risk premia Banks face an equity capital constraint Risk premia depends on banks capital The model can account for the level & dynamics risk premia Non-linearity: when the equity constraint binds very tough times When banks hits the constraint, the economy enters in a crisis A model of endogenous banking crisis Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 2 / 15

6 The Model Environment Infinite-horizon, continuous-time Lucas tree economy Two groups of agents: Households and Bankers Households: invest in equity of banks and risk-free bonds Bankers: run banks, invest in stocks and bonds subject to equity constraint Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 3 / 15

7 The Model Environment Infinite-horizon, continuous-time Lucas tree economy Two groups of agents: Households and Bankers Households: invest in equity of banks and risk-free bonds Bankers: run banks, invest in stocks and bonds subject to equity constraint Only Bankers can invest in stocks (exogenous mkt segmentation) Bankers stochastic discount factor determines risk premia Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 3 / 15

8 The Model Assets Stocks: Price p t and yields flow of dividends dd t D t = gdt + σdz t, given D 0 Total Return Stocks: dr t = D tdt + dp t P t Bonds: zero net supply and yields the interest rate r t Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 4 / 15

9 The Model Banks Unit mass of infinitely-lived identical bankers who manage banks [ ] Bankers maximize E e ρt u (c 0 t ) dt Each bankers runs a bank Bankers are randomly matched to households (one-period link) Households invest in H t equity of bank Bankers invest their full wealth w t in the bank Return on banks capital: dr t = r tdt + α I (dr t r tdt) α I > 1, banks are levered and borrow ( α I 1 ) (w t + H t) in the bonds mkt Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 5 / 15

10 The Model Capital Constraint Households can t invest in stocks Households can t invest more than mw t in the equity of banks H t mw t No constraint on debt positions. Banks can leverage as much as they want. Bankers budget constraint is dw t = c t dt + w t r t dt + α I w t (dr t r t dt) Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 6 / 15

11 The Model Households OLG of agents to keep simplicity Receives a labor income l D t Invest a minimum λ of his wealth w h t in bonds Given log utility, the problem is [ ] max α h α h t [0,1] t E t dr t r t dt 1 ( ) α h 2 [ ] 2 t Vart dr t r t dt s.t. α h t (1 λ) w h t H t mw t dw h t = ( ld t ρwt h ) dt + w h t r t dt + αt h (1 λ) wt h ( ) dr t r t dt Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 7 / 15

12 The Model Equilibrium Risk Premium Risk premium when Bankers have log utility [ ] dct E t [dr t ] r t dt = γcov t, dr t c t E t [dr t ] r t dt = α I tvar t [dr t ] Given x t = wt P t, α I,const t α I,unconst t ( ) = (1 λ) 1 x t 1 + m x t Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 8 / 15

13 Quantitative Analysis Calibration Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 9 / 15

14 Quantitative Analysis Risk Premium and Banks Capital Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 10 / 15

15 Quantitative Analysis Endogenous Crises Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 11 / 15

16 Quantitative Analysis Main Results Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 12 / 15

17 Quantitative Analysis Probability of Crisis Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 13 / 15

18 Quantitative Analysis Recovery Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 14 / 15

19 Conclusion Conclusion A model where banks capital determine risk premia Non-linearity: when the equity constraint binds very tough times When banks hits the constraint, the economy enters in a crisis A model of endogenous banking crisis New strand of literature that focus on special role banks capital New strand of literature that studies Occasionally Binding Constraints Z. He and A. Krishnamurthy - AER (2012) Intermediary Asset Pricing Presented by Omar Rachedi (UC3M) 15 / 15

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