A Model of Monetary Policy and Risk Premia/media/others/events/2014/macrofinance...A Model of...

30
A Model of Monetary Policy and Risk Premia Itamar Drechsler Alexi Savov Philipp Schnabl NYU Stern and NBER NYU Stern, CEPR, and NBER Macro Finance Society Chicago, May 2014

Transcript of A Model of Monetary Policy and Risk Premia/media/others/events/2014/macrofinance...A Model of...

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A Model of

Monetary Policy and Risk Premia

Itamar Drechsler⇧ Alexi Savov⇧ Philipp Schnabl†

⇧NYU Stern and NBER †NYU Stern, CEPR, and NBER

Macro Finance SocietyChicago, May 2014

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Monetary policy and risk premia

1. Textbook model of monetary policy (e.g. New Keynesian)- nominal rate a↵ects real interest rate through sticky prices- largely silent on risk premia (can have indirect e↵ects given balancesheet constraints)

2. Yet lower nominal rates decrease risk premia- higher equity valuations, compressed credit spreads (“yield chasing”)- increased leverage by financial institutions

3. Today’s monetary policy directly targets risk premia- “Greenspan put”, Large-Scale Asset Purchases, “Operation Twist”

) We build a dynamic equilibrium asset pricing framework in whichmonetary policy a↵ects risk taking and risk premia

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Model overview

1. Central bank sets nominal rate to regulate economy’s e↵ective riskaversion by changing banks’ cost of leverage

2. Endowment economy, 2 agent types- low risk aversion: pool wealth as equity capital of “banks”- high risk aversion “depositors”- banks take leverage by issuing risk-free deposits- must hold fractional reserves against deposits

) imposes a cost on taking leverage- rationale: contain externalities due to deposit insurance/fire sales

- no nominal price rigidities

3. Central bank controls cost of holding reserves (= nominal rate)- when nominal rate falls, leverage becomes cheaper

) bank risk taking rises) risk premia and cost of capital fall

- we solve for reserve dynamics that implement nominal rate policy

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Essential mechanism

1. Nominal rate a↵ects banks’ external finance spread

= Fed Funds rate � risk-free bond rate- We obtain this via reserves, an asset-side cost- Also work out a liabilities-side channel where the nominal rate a↵ectsthe spread banks earn on deposits liabilities-side channel

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

Jul-80 Jul-83 Jul-86 Jul-89 Jul-92 Jul-95 Jul-98 Jul-01 Jul-04 Jul-07

Fed Funds rate

Fed Funds-TBill spread

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Related literature

1. “Credit view” of monetary policy: Bernanke and Gertler (1989); Kiyotaki andMoore (1997); Bernanke, Gertler, and Gilchrist (1999); Gertler and Kiyotaki(2010); Curdia and Woodford (2009); Adrian and Shin (2010); Brunnermeierand Sannikov (2013)

2. Bank lending channel: Bernanke and Blinder (1988); Kashyap and Stein (1994);Stein (1998); Stein (2012)

3. Government liabilities as a source of liquidity: Woodford (1990); Krishnamurthyand Vissing-Jorgensen (2012); Greenwood, Hanson, and Stein (2012)

4. Empirical studies of monetary policy and asset prices: Bernanke and Blinder(1992); Bernanke and Gertler (1995); Kashyap and Stein (2000); Bernanke andKuttner (2005); Gertler and Karadi (2013); Hanson and Stein (2014); Landier,Sraer, and Thesmar (2013); Sunderam (2013)

5. Asset pricing with heterogeneous agents: Dumas (1989); Wang (1996);Longsta↵ and Wang (2012)

6. Margins and asset prices: Gromb and Vayanos (2002); Geanakoplos (2003,2009); Brunnermeier and Pedersen (2009); Garleanu and Pedersen (2011)

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Setup

1. Aggregate endowment: dDt

/Dt

= µD

dt + �D

dB

t

2. Two agent types: A is risk tolerant, B is risk averse:

U

A = E0

⇥R10

f

A(Ct

,V A

t

) dt⇤

and U

B = E0

⇥R10

f

B(Ct

,V B

t

) dt⇤

- f i (Ct

,V i

t

) is Du�e-Epstein-Zin aggregator

- �A < �B creates demand for leverage (risk sharing)

3. State variable is the wealth share of A agents:

!t

=W

A

t

W

A

t

+W

B

t

- View !t

as risk-tolerant wealth pooled into bank capital

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Financial assets

1. Risky asset is a claim to D

t

with return process

dR

t

= µ (!t

) dt + � (!t

) dBt

2. Instantaneous risk-free bonds (deposits) pay r (!t

), the real rate

3. Banks must hold reserves in proportion to their deposits- w

S,t = risky asset portfolio share- w

M,t = reserves portfolio share

wM,t � max

h��2

t

(wS,t � 1) , 0

i

- scaling by �2t

is for analytical simplicity only- only central bank can create reserves (cannot be shorted)

4. Central bank adds/removes reserves from circulation bybuying/selling bonds, i.e. open market operations

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Central bank policy1. There are M

t

reserves. The central bank sets µM

and �M

in

dM

t

M

t

= µM

(!t

) dt + �M

(!t

) dBt

2. Each $ of reserves is worth ⇡t

consumption units. We take reservesas the numeraire, so ⇡

t

is the inverse price level.- For simplicity, we have the central bank choose dM

t

/Mt

so thatinflation is locally deterministic:

�d⇡t

⇡t

= i(!t

)dt

3. Define the nominal rate

n(!t

) = r(!t

) + i(!t

)

- n(!t

) is the central bank’s policy, which agents know

4. Central bank refunds its seignorage profits (⇡t

M

t

n

t

dt) to agents inproportion to their wealth

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Optimization

1. HJB equation for each agent type is:

0 = maxc,w

S

,wM

f (cW ,V )dt + E [dV (W ,!)]

subject to

w

M

� maxh��2 (w

S

� 1) , 0i

dW

W

=

r � c + w

S

(µ� r) + w

M

✓d⇡

⇡� r

| {z }= �n

+Gn

�dt + w

S

�dB

- �n is the excess return on reserves

- Gn is rate of seignorage payment per unit of wealth, G is the wealthshare of reserves

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Optimality conditions

1. Each agent’s value function has the form

V (W ,!) = ⇢1��

1�1/

✓W

1��

1� �

◆J (!)

1��1�

2. The FOC for consumption gives c⇤ = J

3. If �n < �B � �A, the portfolio FOCs give

w

A

S

=1

�A

µ� r

�2� �n +

✓1� �A

1� A

◆J

A

!

J

A

! (1� !)�!�

and w

A

s

> 1) raising n increases the cost of leverage) reduces risk taking wA

S

) increases risk premia (e↵ective risk aversion)

4. If �n � �B � �A, wA

S

= w

B

S

= 1 ) financial autarky

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Fed Funds and the external finance spread

1. There is no reserve requirement on Fed Funds, so the Fed Fundsrate is r + ��2

n

2. ��2n is the Fed Funds-risk-free bond (Tbill) spread- this is the premium banks pay for external funds- can rewrite banks’ FOC as an unconstrained portfolio choice:

w

A

S

=1

�A

µ�

Fed Funds ratez }| {(r + ��2

n)

�2+

✓1� �

1�

◆J

A

!

J

A

! (1� !)�!�

) Central bank regulates risk taking by influencing the external financespread through n

3. The same expression arises under the liabilities-side channelliabilities-side channel

Drechsler, Savov, and Schnabl (2014) 11/24

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Empirical relationship

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

Jul-80 Jul-83 Jul-86 Jul-89 Jul-92 Jul-95 Jul-98 Jul-01 Jul-04 Jul-07

Fed Funds rate

Fed Funds-TBill spread

20-week moving averages

1. 86% correlation2. Average spread is 57bps

- for comparison, Moody’s Baa-Aaa spread averages 1.07% in thisperiod

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Results

1. Solve HJB equations simultaneously for JA(!) and J

B(!)

2. Global solution by Chebyshev collocation

AAA

Risk aversion A �A 1.5Risk aversion B �B 15EIS A, B 3.5Endowment growth µ

D

0.02Endowment volatility �

D

0.02Time preference ⇢ 0.01Reserve requirement ��2

D

0.1Nominal rate 1 n1 0%Nominal rate 2 n2 5%

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Risk taking

w

A

S

w

B

S

0 0.2 0.4 0.6 0.8 10

2

4

6

8

10

ω

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

ω

n

1

= 0%n

2

= 5%

1. As the nominal rate increases, bank leverage falls and depositor risktaking increases

- increases e↵ective risk aversion of marginal investor

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The price of risk and the risk premium

µ� r

�µ� r

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

ω

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6 x 10−3

ω

n

1

= 0%n

2

= 5%

1. As nominal rate falls, the price of risk falls

2. Risk premium shrinks (“reaching for yield”)- e↵ect is larger for riskier assets

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Volatility

0 0.2 0.4 0.6 0.8 10.02

0.022

0.024

0.026

0.028

0.03

ω

n

1

= 0%n

2

= 5%

1. There is greater excess volatility at lower nominal rates due to morevolatile discount rates

- ! more volatile because leverage is higher- also risk premium more sensitive to ! variation

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The cost of capitalWealth-consumption ratio (P/D)

0 0.2 0.4 0.6 0.8 1120

140

160

180

200

220

ω

n

1

= 0%n

2

= 5%

1. Lower rates increase valuations for all !- e↵ect is largest for moderate !, where aggregate risksharing/leverage is at its peak

2. With production this leads to increased investment

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Production� (◆

t

)� �

0 0.2 0.4 0.6 0.8 10.01

0.011

0.012

0.013

0.014

0.015

0.016

!

1. Incorporate production and capital accumulation subject toadjustment costs (�):

dk

t

k

t

= [� (◆t

)� �] dt + �k

dB

t

2. FOC for investment is q�0(◆⇤) = 1- q

t

is the price of capital- lower nominal rate ! q

t

higher ! greater investment ◆

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The zero lower bound

1. When n = 0, there is no cost to taking leverage so banks are at theirunconstrained optimum

2. Because banks cannot be forced to take leverage, the nominal ratecannot go negative by no-arbitrage

- willing to hold large excess reserves as this is costless

3. Central bank can still raise asset prices by lowering expected future

nominal rates (forward guidance)

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Forward guidance

Nominal rate policies Ratio of risky asset prices

0 0.2 0.4 0.6 0.8 1−0.02

0

0.02

0.04

0.06

ω

0 0.2 0.4 0.6 0.8 11

1.02

1.04

1.06

1.08

1.1

ω

1. Forward guidance delays nominal rate hike from ! = 0.25 to ! = 0.3

2. Prices are higher under forward guidance even for ! ⌧ 0.25

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“Greenspan put”

Nominal rate policies Wealth-consumption ratio (P/D)

0 0.2 0.4 0.6 0.8 1−0.02

0

0.02

0.04

0.06

ω

0 0.2 0.4 0.6 0.8 1130

140

150

160

170

180

190

200

ω

1. Rates lowered in response to large negative shocks (! 0.3)- rates increased when ! is high to have same unconditional mean

2. Near ! = 0.3 valuations are flat in ! because central bank cuts ratesin response to negative shocks (as though investors own a put)

- but prices propped up by increasing leverage so further shocks causevaluations to fall more quickly

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“Greenspan put”

Risk premium (µ� r) Volatility (�)

0 0.2 0.4 0.6 0.8 14.5

5

5.5

6

x 10−3

ω

0 0.2 0.4 0.6 0.8 10.019

0.02

0.021

0.022

0.023

0.024

0.025

ω

1. Reduces risk premia near ! = 0.3

2. Volatility decreases for ! close to 0.3 due to policy

3. However, if ! declines further then volatility rises sharply becauseleverage has significantly increased

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Policy Shocks

Post-shock wealth share (!) Wealth-consumption ratio (P/D)

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

ω

0 0.2 0.4 0.6 0.8 1130

140

150

160

170

180

190

200

ω

1. Extend the model to incorporate unexpected shocks (a second statevariable)

2. Unexpected nominal rate increase causes ! to decrease

3. Total impact on valuations (red solid line) exceeds direct impact(dashed line) due to negative impact on ! (balance sheet e↵ect)

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Takeaway

1. Contemporary monetary policy targets risk premia, not just interestrates

2. An asset pricing framework for studying the relationship betweenmonetary policy and risk premia

3. Monetary policy ) external finance spread ) leverage ) riskpremia

4. Dynamic applications: forward guidance, “Greenspan put”

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Appendix

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Liabilities-side tradeo↵

1. Deposits pay a “low” rate due to household liquidity demand

2. But must be backed with greater collateral than non-deposit funding

) there is a tradeo↵ between deposit-taking and leverage- similar to tradeo↵ in Hanson, Shleifer, Stein, and Vishny (2014)

3. Nominal rate controls the spread earned on deposits- deposit rates are “sticky”, do not move one-to-one with the nominalrate (Driscoll and Judson 2013)

) Nominal rate governs the funding cost vs. leverage tradeo↵- banks’ FOC is the same as in the main model- higher nominal rate implies higher cost of taking leverage

BACK

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Reserves

Reserves share of wealth (G )

0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

ω

n

1

= 0%n

2

= 5%

1. Wealth share of reserves is very small at high nominal rates

2. Increases at low nominal rates- at zero nominal rate there is no cost to holding reserves

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Real interest raterisk-free rate (r)

0 0.2 0.4 0.6 0.8 10.014

0.016

0.018

0.02

0.022

0.024

0.026

ω

1. Real rate is lower under the higher nominal rate policy2. Increase in aggregate risk aversion increases precautionary savings

motive (as in a homogeneous economy)- i.e., depositors’ precautionary motive increases with their risky assetweight

- can be reversed under depositor liquidity preference (liabilities-sideversion) or with nominal price rigidities

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Wealth distribution

Stationary density of !

0 0.2 0.4 0.6 0.8 10

10

20

30

40

50

60

70

ω

1. For stationarity: introduce births/deaths- Wealth is distributed evenly to newly born

2. Lowering nominal rate increases the mean, variance, and left tail ofbank wealth share, due to greater risk taking

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Transmission of monetary policy

Bernanke and Blinder (AER 1992)918 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1992

0.2 - `-UNEMPLOYMENT RATE

0.0

-0.2 \ -

SECURITIES , -

-0.4

0-0.6 -/ DEPOSITS x

-0.8

-1.0 ~~~~~~~~~LOANS

-1.2 - -

-1.4 I I I I I I I I 4 8 12 16 20 24 HORIZON (MONTHS)

FIGURE 4. RESPONSES TO A SHOCK TO THE FUNDS RATE

sample begins in 1959:1, for comparability with the other results in this paper, and ends in 1978:12, when the Fed changed its definition and the format of its table. This endpoint, however, is not a problem for us, since we want to restrict ourselves to the pre-Volcker period anyway.40

We estimated three different VAR's, each including an indicator of monetary policy based on the funds rate, the unemployment rate, the log of the CPI, and the log levels of each of three bank balance-sheet vari- ables (deposits, securities, and loans) all de- flated by the CPI.41 As usual, six lags of each variable were used. From each esti- mated VAR, we calculated the implied im- pulse-response functions to a shock to the monetary indicator. Under the assumption that innovations to the indicators represent policy actions, the responses of the other five variables will trace out the dynamic

effects of such an action on the banking system and the economy.

The VAR coefficients themselves are not very interesting and so are not reported. Furthermore, since the shapes of the im- pulse-response functions are almost identi- cal regardless of whether the funds rate or the funds-rate-bond-rate spread is used as a policy measure, we show only the results using the funds rate. Figure 4 displays the responses to a one-standard-deviation (31- basis-point) shock to the funds rate over a horizon of 24 months.42

Tight money (a positive innovation in FUNDS) does indeed reduce the volume of deposits held by depository institutions, as we would expect. The effect starts immedi- ately, builds gradually, reaches its peak in about nine months, and appears to be per- manent.43 The other results bear in an in- teresting way on the money-versus-credit controversy. Naturally, bank assets fall along with bank liabilities; but the composition of the fall is noteworthy. For the first six 40The results were basically unchanged when we

used an alternative balance-sheet series which the Fed began publishing in 1973 and which is still being main- tained (see the Data Appendix).

41In alternative regressions, we used the balance- sheet variables in nominal terms. This made little dif- ference. Results were also similar when we differenced the data instead of using levels.

42The policy shocks themselves are transitory. They generally build for about four months and then die away rather quickly.

43Although the diagram stops at 24 months, we ran all the impulse-response functions out to 48 months.

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1. An increase in the nominal rate is followed by reduction in bankbalance sheets/leverage

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