The Risk Channel of Unconventional Monetary Policy Dejanir Silva - PowerPoint PPT Presentation

The Risk Channel of Unconventional Monetary Policy Dejanir Silva UIUC - Finance March, 2017 0 /1 6

Dramatic change in central bank portfolio USDBillions 5,000.00 Composition FED BalanceSheet: 4,500.00 OtherAssets Agency and MBS Holdings 4,000.00 TreasuryHoldings 3,500.00 3,000.00 2,500.00 2,000.00 1,500.00 1,000.00 500.00 - 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 1 /1 6

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 / 1 6

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 / 1 6

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 / 1 6

What are the effects of unconventional monetary policy on financial markets and the real economy? 3 / 1 6

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 / 1 6

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 / 1 6

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 Aggregate risk Price of risky asset wealth of bankers aversion and investment 2)Limited Asset Market Participation 3 / 1 6

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 Aggregate risk Price of risky asset wealth of bankers aversion and investment 2)Limited Asset Market Participation • Passive traders who hold market portfolio 3 / 1 6

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 Aggregate risk Price of risky asset wealth of bankers aversion and investment 2)Limited Asset Market Participation • Passive traders who hold market portfolio Asset purchases Net supply of risk Price of risky asset by the CB to active traders during crises 3 / 1 6

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 endogenousvolatility • Stationary distribution: Probability of future crises falls 4/ 1 6

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/ 1 6

Firms • Linear technology: 𝑍 𝑢 = 𝐵𝐿 𝑢 6 / 1 6

Firms • Linear technology: 𝑍 𝑢 = 𝐵𝐿 𝑢 • Law of motion of capital: 𝑒𝐿 𝑢 = 𝑕 𝑢 𝑒𝑢 + 𝜏𝑒𝑎 𝑢 𝐿 𝑢 6 / 1 6

Firms • Linear technology: 𝑍 𝑢 = 𝐵𝐿 𝑢 • Law of motion of capital: 𝑒𝐿 𝑢 = 𝑕 𝑢 𝑒𝑢 + 𝜏𝑒𝑎 𝑢 𝐿 𝑢 • Problem of the firm ∞ 𝜌 𝑡 𝑇 𝑢 = max 𝐹 න 𝐵 − 𝜅 𝑕 𝑡 𝑒𝑡 (1) 𝜌 𝑢 𝑕 𝑢 where 𝜅 ′ > 0, 𝜅 ′′ > 0 . 6 / 1 6

Firms • Linear technology: 𝑍 𝑢 = 𝐵𝐿 𝑢 • Law of motion of capital: 𝑒𝐿 𝑢 = 𝑕 𝑢 𝑒𝑢 + 𝜏𝑒𝑎 𝑢 𝐿 𝑢 • Problem of the firm ∞ 𝜌 𝑡 𝑇 𝑢 = max 𝐹 න 𝐵 − 𝜅 𝑕 𝑡 𝑒𝑡 (1) 𝜌 𝑢 𝑕 𝑢 where 𝜅 ′ > 0, 𝜅 ′′ > 0 . • The SPD satisfies 𝑒𝜌 𝑢 = − 𝑠 𝑒𝑢 − 𝜃 𝑢 𝑒𝑎 𝑢 ณ ณ 𝑢 𝜌 𝑢 𝑗𝑜𝑢.𝑠𝑏𝑢𝑓 𝑛𝑙𝑢.𝑞𝑠𝑗𝑑𝑓 𝑝𝑔 𝑠𝑗𝑡𝑙 6 / 1 6

Active traders • Decision problem of active traders (bankers j = b , savers j = s ): V j = max U j ( c j ) (2) ( c j ,α j ) subject to n j , t ≥ 0 and . 𝑒𝑜 𝑘,𝑢 = 𝑠 𝑢 + 𝛽 𝑘,𝑢 (𝜈 𝑆,𝑢 − 𝑠 𝑢 ) − 𝑑 𝑘,𝑢 𝑒𝑢 + 𝛽 𝑘,𝑢 𝜏 𝑆,𝑢 𝑒𝑎 𝑢 𝑜 𝑘,𝑢 𝑜 𝑘,𝑢 7 / 1 6

Active traders • Decision problem of active traders (bankers j = b , savers j = s ): V j = max U j ( c j ) (2) ( c j ,α j ) subject to n j , t ≥ 0 and . 𝑒𝑜 𝑘,𝑢 − 𝑑 𝜈 𝑆,𝑢 − 𝑠 𝑘,𝑢 𝑢 = 𝑠 𝑢 + 𝛽 𝑘,𝑢 𝜏 𝑆,𝑢 𝑒𝑢 + 𝛽 𝑘,𝑢 𝜏 𝑆,𝑢 𝑒𝑎 𝑢 𝑜 𝑘,𝑢 𝜏 𝑆,𝑢 𝑜 𝑘,𝑢 ≡𝜏 𝑘 ,𝑢 ≡𝜏 𝑘 ,𝑢 𝜃 𝑢 7/ 1 6

Active traders • Decision problem of active traders (bankers j = b , savers j = s ): V j = max U j ( c j ) (2) ( c j ,α j ) subject to n j , t ≥ 0 and . 𝑒𝑜 𝑘,𝑢 𝑘,𝑢 𝜃 𝑢 − 𝑑 𝑘,𝑢 = 𝑠 𝑢 + 𝜏 𝑒𝑢 + 𝜏 𝑘,𝑢 𝑒𝑎 𝑢 𝑜 𝑘,𝑢 𝑜 𝑘,𝑢 • 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/ 1 6

Hand-to-mouth consumers and the Central Bank • Hand-to-mouth consumers: simply consume government transfers • Simplifying assumption (7) • Important is the presence of investors who don’t continuously rebalance their portfolio • Central bank is subject to No-Ponzi condition and . 𝑒𝑜 𝑑𝑐,𝑢 = 𝑠 𝑢 + 𝜏 𝑑𝑐,𝑢 𝜃 𝑢 − 𝑈 𝑢 (8) 𝑒𝑢 + 𝜏 𝑑𝑐,𝑢 𝑒𝑎 𝑢 𝑜 𝑑𝑐,𝑢 𝑜 𝑑𝑐,𝑢 ( 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 / 1 6

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 ( σ cb , 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/ 1 6

Market price of risk 𝑠 𝜏 + 𝜏 𝑟,𝑢 + ℎ 𝑢 𝜃 𝑢 = 𝛿 𝑢 𝜕 𝑢 • Aggregate risk aversion: −1 𝑦 𝑢 + 1 − 𝑦 𝑢 𝛿 𝑢 = 𝛿 𝑐 𝛿 𝑡 where 𝑦 is the share of wealth of low risk version agent. 𝑠 • Net supply of risk: 𝜕 𝑢 • Without a central bank, 𝜕 𝑢 𝑠 =1 • Hedging terms: ℎ 𝑢 • Average hedging demand for 1 0 / 1 6

Balance sheet recession A − ι ( g t ) ι ( g t ) = q t t q = t r + ( σ + σ ) η − µ t q , t S , t t Market price of risk Price of capital 1 0.95 0.8 0.9 0.6 0.85 log(q) η 0.4 0.8 0.2 0.75 0 0.7 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x x 1 1 / 1 6

Balance sheet recession A − ι ( g t ) i’ ( g t ) = q t q = t r + ( σ + σ ) η − µ t q , t S , t t Market price of risk Price of capital 1 0.95 0.8 0.9 0.6 0.85 log(q) η 0.4 0.8 0.2 0.75 0 0.7 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x Laissez-faire Centralbank x 1 1 / 1 6

Effect on Interest Rates Interest rate 3 Weak balance sheet of bankers: 2.5 • High aggregate risk aversion • Precautionary savings 2 r 1.5 1 0.5 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 1 2 / 1 6