The Risk Channel of Unconventional Monetary Policy

Transcription

1 The Risk Channel of Unconventional Monetary Policy Dejanir Silva UIUC - Finance March, /16

2 Dramatic change in central bank portfolio USDBillions 5, , , Composition FED BalanceSheet: Other Assets Agency and MBS Holdings Treasury Holdings 3, , , , , , /16

3 Stimulus and potential side effect Goal: stimulate economy Federal Reserve on objective of asset purchases... help to make broader financial conditions more accommodative through the purchase of longer-term securities. 2 / 16

4 Stimulus and potential side effect Goal: stimulate economy Federal Reserve on objective of asset purchases... help to make broader financial conditions more accommodative through the purchase of longer-term securities. Potential side effect: risk-taking BIS, commenting on central bank policy: Extraordinarily low interest rates and compressed risk premia once again pushed investors into riskier assets in their search for yield [...] 2 / 16

5 Stimulus and potential side effect Goal: stimulate economy Federal Reserve on objective of asset purchases... help to make broader financial conditions more accommodative through the purchase of longer-term securities. Potential side effect: risk-taking BIS, commenting on central bank policy: Extraordinarily low interest rates and compressed risk premia once again pushed investors into riskier assets in their search for yield [...] Policy evaluation: Integrated view: effects on the real economy and on financial risk-taking 2 / 16

6 What are the effects of unconventional monetary policy on financial markets and the real economy? 3 / 16

7 What are the effects of unconventional monetary policy on financial markets and the real economy? 1)Heterogeneous Risk-Aversion 2)Limited Asset Market Participation 3 / 16

8 What are the effects of unconventional monetary policy on financial markets and the real economy? 1)Heterogeneous Risk-Aversion Active traders: Savers more risk-averse than Bankers 2)Limited Asset Market Participation 3 / 16

9 What are the effects of unconventional monetary policy on financial markets and the real economy? 1)Heterogeneous Risk-Aversion Active traders: Savers more risk-averse than Bankers Drop in share of wealth of bankers Aggregate risk aversion Price of risky asset and investment 2)Limited Asset Market Participation 3 / 16

10 What are the effects of unconventional monetary policy on financial markets and the real economy? 1)Heterogeneous Risk-Aversion Active traders: Savers more risk-averse than Bankers Drop in share of wealth of bankers Aggregate risk aversion Price of risky asset and investment 2)Limited Asset Market Participation Passive traders who hold market portfolio 3 / 16

11 What are the effects of unconventional monetary policy on financial markets and the real economy? 1)Heterogeneous Risk-Aversion Active traders: Savers more risk-averse than Bankers Drop in share of wealth of bankers Aggregate risk aversion Price of risky asset and investment 2)Limited Asset Market Participation Passive traders who hold market portfolio Asset purchases by the CB Net supply of risk to active traders Price of risky asset during crises 3 / 16

12 Main findings 1) Output growth rate: Crises vs normal times Asset purchases rise in output growth during crises Expectation of less severe crises less output growth in normal times 2) Risk concentration and probability of crises Asset purchases fall in risk concentration and endogenous volatility Stationary distribution: Probability of future crises falls 4 / 16

13 Overview of the environment: Continuous-time. Two goods: consumption and capital. Firms produce final goods using capital Investment adjustment costs Active traders (bankers and savers) trade risky and risklessassets Heterogeneity: savers are more risk averse than bankers. Hand-to-mouth households consume government transfers Central bank issues riskless liabilities and buy risky assets Rebates the proceeds to hand-to-mouth consumers 5 / 16

14 Firms Linear technology: Y t = AK t 6 / 16

15 Firms Linear technology: Law of motion of capital: dk t K t Y t = AK t = g t dt + σdz t 6 / 16

16 Firms Linear technology: Law of motion of capital: Problem of the firm dk t K t Y t = AK t = g t dt + σdz t S t = max E න π s A ι g g t π s ds t (1) where ι > 0, ι > 0. 6 / 16

17 Firms Linear technology: Law of motion of capital: Problem of the firm dk t K t Y t = AK t = g t dt + σdz t S t = max E න π s A ι g g t π s ds t (1) where ι > 0, ι > 0. The SPD satisfies dπ t = ณr π t dt ณη t dz t t int.rate mkt.price of risk 6 / 16

18 Active traders Decision problem of active traders (bankers j = b, savers j = s ): V j = max U j (c j ) (c j,α j ) (2) subject to n j,t 0 and. dn j,t n j,t = r t + α j,t (μ R,t r t ) c j,t n j,t dt + α j,t σ R,t dz t 7 / 16

19 Active traders Decision problem of active traders (bankers j = b, savers j = s ): V j = max U j (c j ) (c j,α j ) (2) subject to n j,t 0 and. dn j,t n j,t = r t + α j,t σ R,t σ j,t μ R,t r t σ R,t η t c j,t n j,t dt + α j,tσ R,t dz t σ j,t 7/ 16

20 Active traders Decision problem of active traders (bankers j = b, savers j = s ): V j = max U j (c j ) (c j,α j ) (2) subject to n j,t 0 and. dn j,t n j,t = r t + σ j,t η t c j,t n j,t dt + σ j,t dz t Preferences: continuous-time EZ preferences EIS ψ > 1 and risk aversion γ j Savers are more risk averse than bankers: γ s > 1 >γ b Mortality risk stationary distribution 7/ 16

21 Hand-to-mouth consumers and the Central Bank Hand-to-mouth consumers: simply consume government transfers Simplifying assumption Important is the presence of investors who don t continuously rebalance their portfolio Central bank is subject to No-Ponzi condition and. dn cb,t n cb,t = r t + σ cb,t η t T t n cb,t dt + σ cb,t dz t (7) (8) (σ cb,t, T t ) determined by policy rules σ cb,t = σ cb (x t,w t ); T t = T (x t, w t ) where (x t, w t ) is the vector of state variables. 8 / 16

22 Two benchmarks 1) Homogeneous risk-aversion (γ b = γ s ): No risk concentration σ b,t = σ s,t Balanced growth path No variation in returns/growth rates No balance sheet recession 2) Full participation benchmark: No hand-to-mouth/passive traders. Fix initial (σcb, T ) and consider (σ, T ). Investors exactly offset policy change Neutrality result: no changes in consumption, prices, and investment Modigliani-Miller / Ricardian Equivalance type of result (see Wallace (1981)). 9/ 16

23 Market price of risk η t = γ t ω t r σ + σ q,t + h t Aggregate risk aversion: γ t = x t γ b + 1 x t γ s 1 where x is the share of wealth of low risk version agent. Net supply of risk: ω t r Without a central bank, ω t r =1 Hedging terms: h t Average hedging demand for 10 / 16

24 η log(q) Balance sheet recession q t = A ι(g t ) r t + (σ+ σ q,t )η t µ S,t t ι (g t ) = q t 1 Market price of risk 0.95 Price of capital x x 11 / 16

25 η log(q) Balance sheet recession q t = A ι(g t ) r t + (σ+ σ q,t )η t µ S,t i (g t ) = q t 1 Market price of risk 0.95 Price of capital x Laissez-faire Central bank x 11 / 16

26 r Effect on Interest Rates 3 Interest rate Weak balance sheet of bankers: High aggregate risk aversion Precautionary savings x / 16

27 r Effect on Interest Rates 3 Interest rate Weak balance sheet of bankers: High aggregate risk aversion Precautionary savings Effect of asset purchases: Precautionary savings Intertemporal substitution x / 16

28 σ / (σ+σ b q ) Myopic component Hedging component Myopic and Hedging Demands σ b,t = η t γ b myopic + 1 γ b σ γ ζ,t b hedging 15 Leverage 15 Myopic component 0 Hedging component x x x 1 13 / 16

29 σ - σ b s Myopic component Hedgind component UMP and Risk Concentration 0.8 Risk concentration σ b,t = 0.8 η t + 1 γ b σ γ b γ ζ,t b myopic hedging Myopic component 0 Hedging component x x / 16 x

30 σ -σ b s Endogenous volatility q x,t q w,t σ q,t = σ x,t + σ w,t σ x,t = x t (1 x t ) (σ b,t σ s,t ) q t q t 0.02 Endogenous Volatility 1.4 Risk Concentration σ q x x 14 / 16

31 σ - σ b s Endogenous volatility q x,t q w,t σ q,t = σ x,t + σ w,t σ x,t = x t (1 x t ) (σ b,t σ s,t ) q t q t 0.02 Endogenous Volatility 1.4 Risk Concentration σ q x Laissez-faire Central bank x 14 / 16

32 PDF probability UMP and Financial Stability g (%) number of std. deviations below the mean Laissez-faire Central bank 15 / 16

33 Thanks. 16 / 16