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

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Dramatic change in central bank portfolio

• 500.00

1,000.00 1,500.00 2,000.00 2,500.00 3,000.00 4,000.00 4,500.00 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

USDBillions

5,000.00

Composition FED BalanceSheet:

OtherAssets Agency and MBS Holdings TreasuryHoldings

3,500.00

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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.”

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 [...]”

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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

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What are the effects of unconventional monetary policy on financial markets and the real economy?

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What are the effects of unconventional monetary policy on financial markets and the real economy?

1)Heterogeneous Risk-Aversion 2)Limited Asset Market Participation

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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

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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

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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

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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

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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

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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

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Firms

• Linear technology:

𝑍

𝑢 = 𝐵𝐿𝑢

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Firms

• Linear technology:
• Law of motion of capital:

𝑍

𝑢 = 𝐵𝐿𝑢

𝑒𝐿𝑢 𝐿𝑢 = 𝑕𝑢𝑒𝑢 + 𝜏𝑒𝑎𝑢

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Firms

• Linear technology:
• Law of motion of capital:
• Problem of the firm

(1)

where 𝜅′ > 0, 𝜅′′ > 0.

𝑇𝑢 = max

𝑕

𝐹 න

𝑢 ∞ 𝜌𝑡

𝜌𝑢 𝐵 − 𝜅 𝑕𝑡 𝑒𝑡 𝑍

𝑢 = 𝐵𝐿𝑢

𝑒𝐿𝑢 𝐿𝑢 = 𝑕𝑢𝑒𝑢 + 𝜏𝑒𝑎𝑢

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Firms

• Linear technology:
• Law of motion of capital:
• Problem of the firm

(1)

where 𝜅′ > 0, 𝜅′′ > 0.

𝑇𝑢 = max

𝑕

𝐹 න

𝑢 ∞ 𝜌𝑡

𝜌𝑢 𝐵 − 𝜅 𝑕𝑡 𝑒𝑡

• The SPD satisfies

𝑒𝜌𝑢 𝜌𝑢 = − ณ 𝑠

𝑢 𝑗𝑜𝑢.𝑠𝑏𝑢𝑓

𝑒𝑢 − ณ 𝜃𝑢

𝑛𝑙𝑢.𝑞𝑠𝑗𝑑𝑓 𝑝𝑔 𝑠𝑗𝑡𝑙

𝑒𝑎𝑢 𝑍

𝑢 = 𝐵𝐿𝑢

𝑒𝐿𝑢 𝐿𝑢 = 𝑕𝑢𝑒𝑢 + 𝜏𝑒𝑎𝑢

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Active traders

• Decision problem of active traders (bankers j = b, savers j = s ):

Vj = max Uj (cj )

(cj,αj)

(2) subject to nj,t ≥ 0 and .

𝑒𝑜𝑘,𝑢 𝑜𝑘,𝑢 = 𝑠𝑢 + 𝛽𝑘,𝑢(𝜈𝑆,𝑢 − 𝑠𝑢) − 𝑑

𝑘,𝑢

𝑜𝑘,𝑢 𝑒𝑢 + 𝛽𝑘,𝑢𝜏𝑆,𝑢𝑒𝑎𝑢

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Active traders

• Decision problem of active traders (bankers j = b, savers j = s ):

Vj = max Uj (cj )

(cj,αj)

(2) subject to nj,t ≥ 0 and .

𝑒𝑜𝑘,𝑢 𝑜𝑘,𝑢 = 𝑠𝑢 + 𝛽𝑘,𝑢𝜏𝑆,𝑢

≡𝜏𝑘,𝑢

𝜈𝑆,𝑢 − 𝑠

𝑢

𝜏𝑆,𝑢 − 𝑑

𝑘,𝑢

𝑜𝑘,𝑢

𝜃𝑢

𝑒𝑢 + 𝛽𝑘,𝑢𝜏𝑆,𝑢

≡𝜏𝑘,𝑢

𝑒𝑎𝑢

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Active traders

• Decision problem of active traders (bankers j = b, savers j = s ):

Vj = max Uj (cj )

(cj,αj)

(2) subject to nj,t ≥ 0 and .

𝑒𝑜𝑘,𝑢 𝑜𝑘,𝑢 = 𝑠𝑢 + 𝜏

𝑘,𝑢𝜃𝑢 − 𝑑 𝑘,𝑢

𝑜𝑘,𝑢 𝑒𝑢 + 𝜏

𝑘,𝑢𝑒𝑎𝑢

• Preferences: continuous-time EZ preferences
• EIS ψ

> 1 and risk aversion γj

• Savers are more risk averse than bankers: γs > 1 >γb
• Mortality risk ⇒ stationary distribution

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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 (7)

• Central bank is subject to No-Ponzi condition and

. (8) (σcb,t, Tt ) determined by policy rules σcb,t = σcb (xt,wt); Tt = T (xt, wt)

where (xt, wt ) is the vector of state variables.

𝑒𝑜𝑑𝑐,𝑢 𝑜𝑑𝑐,𝑢 = 𝑠𝑢 + 𝜏𝑑𝑐,𝑢𝜃𝑢 − 𝑈𝑢 𝑜𝑑𝑐,𝑢 𝑒𝑢 + 𝜏𝑑𝑐,𝑢𝑒𝑎𝑢

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Two benchmarks

1) Homogeneous risk-aversion (γb = γs):

• No risk concentration

σb,t = σs,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)).

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Market price of risk

𝜃𝑢 = 𝛿𝑢 𝜕𝑢

𝑠 𝜏 + 𝜏𝑟,𝑢 + ℎ𝑢

𝛿𝑢 = 𝑦𝑢 𝛿𝑐 + 1 − 𝑦𝑢 𝛿𝑡

−1

• Aggregate risk aversion:

where 𝑦 is the share of wealth of low risk version agent.

• Net supply of risk: 𝜕𝑢

𝑠

• Without a central bank, 𝜕𝑢

𝑠=1

• Hedging terms: ℎ𝑢
• Average hedging demand for

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Balance sheet recession

t

q = A −ι(gt)

t

r + (σ+ σ )η −µ

q,t t S,t t

ι (gt) = qt

0.2 0.8 1 0.4 0.6 x 0.7 0.75 0.8 0.85 0.9 0.95

log(q)

Price of capital 0.2 0.8 1 0.4 0.6 x 0.2 0.4 0.6 0.8 1

η

Market price of risk

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Balance sheet recession

t

q = A −ι(gt)

t

r + (σ+ σ )η −µ

q,t t S,t

i’(gt) = qt

0.2 0.4 0.6 0.8 1 x 0.7 0.75 0.8 0.85 0.9 0.95

log(q)

Price of capital 0.2 0.8 1 0.4 0.6 x 0.2 0.4 0.6 0.8 1

η

Market price of risk Centralbank Laissez-faire

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Effect on Interest Rates

0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6

x

0.5 1 1.5 2 2.5 3

r Interest rate

Weak balance sheet of bankers:

• High aggregate risk aversion
• Precautionary savings

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Effect on Interest Rates

0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6

x

0.5 1 1.5 2 2.5 3

r Interest rate

Weak balance sheet of bankers:

• High aggregate risk aversion
• Precautionary savings

Effect of asset purchases:

• Precautionary savings
• Intertemporal substitution

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Myopic and Hedging Demands

• 3

1 5 10 15

b q

σ / (σ+σ ) Leverage

5 10 15

Myopic component Myopic component

• 2.5
• 2
• 1.5
• 1
• 0.5

Hedging component Hedgingcomponent

• 3.5

0.2 0.4 0.6 0.8

x

0.2 0.4 0.6 0.8

x

1 0.2 0.4 0.6 0.8

x

1

𝜏𝑐,𝑢 = 𝜃𝑢 𝛿𝑐

𝑛𝑧𝑝𝑞𝑗𝑑

+ 1 − 𝛿𝑐 𝛿𝑐 𝜏𝜂,𝑢

ℎ𝑓𝑒𝑕𝑗𝑜𝑕

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UMP and Risk Concentration

1 0.2 0.4 0.6 0.8

x

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

σ - σb

s

Risk concentration

1 0.2 0.4 0.6 0.8

x

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Myopic component Myopic component

0.2 0.4 0.6 0.8 1

x

• 0.25
• 0.2
• 0.15
• 0.1
• 0.05

Hedgind component Hedging component

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𝜏𝑐,𝑢 = 𝜃𝑢 𝛿𝑐

𝑛𝑧𝑝𝑞𝑗𝑑

+ 1 − 𝛿𝑐 𝛿𝑐 𝜏𝜂,𝑢

ℎ𝑓𝑒𝑕𝑗𝑜𝑕

Endogenous volatility

qt qx,t qw,t qt σq,t = σx,t + σw,t σx,t = xt (1 − xt ) (σb,t − σs,t )

0.2 0.8 1 0.4 0.6

x

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

σ

q

Endogenous Volatility

0.2 0.8 1 0.4 0.6

x

0.2 0.4 0.6 0.8 1 1.2 1.4

σ -σ

b s

Risk Concentration

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Endogenous volatility

qt qx,t qw,t qt σq,t = σx,t + σw,t σx,t = xt (1 − xt ) (σb,t − σs,t )

0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002 0.02

σ

q

Endogenous Volatility

0.2 0.4 0.6 0.8 1 1.2 1.4

σ - σb s Risk Concentration

0.2 0.4 0.6

x

0.8 1

Laissez-faire

0.2 0.4 0.6 0.8 1

Central bank x

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UMP and Financial Stability

0.5 1 1.5 2 2.5 3 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

probability

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

g(%) PDF number of std. deviations below the mean

Laissez-faire Central bank

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Thanks.

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