Uncertainty about Government Policy and Stock Prices...Uncertainty about Government Policy and Stock Prices Luboˇs P´astorˇ and Pietro Veronesi Booth School of Business University

Uncertainty about Government Policy

and Stock Prices

Lubos Pastor

and

Pietro Veronesi

Booth School of Business

University of Chicago

NBER, CEPR

May 2010

What We Do

• We analyze how changes in government policy affect stock prices

What We Do


• We develop a general equilibrium model featuring

– Government with economic and political motives

What We Do


• We develop a general equilibrium model featuring

– Government with economic and political motives

– Uncertainty about government policy

1. Policy uncertainty

2. Political uncertainty

What We Find

• Government changes its policy after downturns in profitability

What We Find


• Policy changes increase volatility, risk premia, correlations

What We Find



• Stock prices fall at announcements of policy changes, on average

What We Find




– Prices rise if the old policy was sufficiently unproductive,but they fall on average (in expectation)

What We Find





– Expected stock price drop at the announcement is large

∗ when policy/political uncertainty is large

∗ when policy change is induced by a short or shallow downturn

– Distribution of announcement returns is left-skewed

What We Find





– Expected stock price drop at the announcement is large

∗ when policy/political uncertainty is large

∗ when policy change is induced by a short or shallow downturn

– Distribution of announcement returns is left-skewed

• Prices rise at announcements of policy decisions, on average

What We Find (cont’d)

• Government’s ability to change policy

– can imply a higher or lower level of stock prices

– amplifies stock price declines around policy changes

What We Find (cont’d)

• Government’s ability to change policy

– can imply a higher or lower level of stock prices


• Uncertainty about government policy reduces investment

Model

• Finite horizon [0, T ], continuum of equity-financed firms i ∈ [0, 1]

• Firm i’s profitability:

dΠit = (µ + gt) dt + σdZt + σ1dZi,t

gt = impact of government policy on average profitability

Model

• Finite horizon [0, T ], continuum of equity-financed firms i ∈ [0, 1]

• Firm i’s profitability:

dΠit = (µ + gt) dt + σdZt + σ1dZi,t

gt = impact of government policy on average profitability

• Government can change policy at a given time τ , 0 < τ < T

⇒ gt is a step function:

∗ Policy change ⇒ gt changes from gold to gnew

∗ No policy change ⇒ gt stays at gold

Policy Uncertainty

• Key assumption: gt is unknown to all agents

Policy Uncertainty

• Key assumption: gt is unknown to all agents

• Prior distribution is the same for both old and new policies:

gold ∼ N0, σ2

g

gnew ∼ N0, σ2

g

• Define σg ≡ policy uncertainty

– Uncertainty about government policy’s impact on profitability

Objective Functions

• Firms are owned by investors who maximize expected utility:

u (WT ) =W

1−γT

1 − γ

where γ > 1 and WT denotes total capital of all firms at time T

Objective Functions

• Firms are owned by investors who maximize expected utility:

u (WT ) =W

1−γT

1 − γ

where γ > 1 and WT denotes total capital of all firms at time T

• Government is “quasi-benevolent”: it solves

max

Eτ

W1−γT

1 − γ|no policy change

, Eτ

CW1−γT

1 − γ|policy change

C = political cost incurred by government if policy is changed

(C > 1 ⇒ cost; C < 1 ⇒ benefit)

Political Uncertainty

• Government knows C but investors don’t

Political Uncertainty

• Government knows C but investors don’t

• Investors perceive C as random, lognormal with mean E[C] = 1:

c = log (C) ∼ N

−

1

2σ2c , σ2

c

• Define σc ≡ political uncertainty

– Uncertainty about whether government policy will change

– Introduces an element of surprise into policy changes

Learning

• Government & investors learn about gt in a Bayesian fashionby observing profitability of each firm

Learning

• Government & investors learn about gt in a Bayesian fashionby observing profitability of each firm

• Proposition 1: The posterior beliefs are

gt ∼ Ngt, σ

2t

where ∀t ≤ τ ,

dgt = σ2tσ

−1dZt; σ2

t =1

1σ2

g

+ 1σ2t

• A policy change resets beliefs about gt from the posteriorN

(

gτ , σ2τ

)

to the prior N(

0, σ2g

)

; learning continues after time τ

Optimal Changes in Government Policy

• Government changes its policy at time τ iff

Eτ

CW1−γT

1 − γ| policy change

> Eτ

W1−γT

1 − γ| no policy change

Optimal Changes in Government Policy

• Government changes its policy at time τ iff

Eτ

CW1−γT

1 − γ| policy change

> Eτ

W1−γT

1 − γ| no policy change

• Proposition 2: A policy change occurs iff

gτ < g(c)

where

g(c) = −

(

σ2g − σ2

τ

)

(γ − 1) (T − τ )

2−

c

(T − τ ) (γ − 1)

• Investors don’t know c ⇒ cannot fully anticipate a policy change

Policy Changes Tend to Occur After Downturns

• Threshold g(c) is typically negative

• For the posterior mean to be negative while the prior mean is zero,realized profitability must be unexpectedly low

⇒ Policy changes tend to occur after “downturns”

Policy Changes Tend to Occur After Downturns

• Threshold g(c) is typically negative

• For the posterior mean to be negative while the prior mean is zero,realized profitability must be unexpectedly low

⇒ Policy changes tend to occur after “downturns”

• Example: Average across many paths simulated from our model

Table 1: Parameter Choices

σg σc µ σ σi T τ γ

0.02 0.10 0.10 0.05 0.10 20 10 5

0 2 4 6 8 10 12 14 16 18 20−3

−2

−1

0

1

2

3

Time

Pro

fita

bility (

%)

Panel A. Policy Change

Realized Profitability

Expected Profitability

Threshold

0 2 4 6 8 10 12 14 16 18 20−3

−2

−1

0

1

2

3

Time

Pro

fita

bility (

%)

Panel B. No Policy Change



Threshold

Figure 1. Profitability dynamics and the policy decision.

0 5 10 15 20−5

−4

−3

−2

−1

0

1

Time

Pro

fita

bili

ty (

%)

Panel A. σ c = 0, σ

g = 1%



Threshold

0 5 10 15 20−5

−4

−3

−2

−1

0

1

Time

Pro

fita

bili

ty (

%)

Panel B. σ c = 20%, σ

g = 1%



Threshold

0 5 10 15 20−5

−4

−3

−2

−1

0

1

Time

Pro

fita

bili

ty (

%)

Panel C. σ c = 0, σ

g = 3%

0 5 10 15 20−5

−4

−3

−2

−1

0

1

Time

Pro

fita

bili

ty (

%)

Panel D. σ c = 20%, σ

g = 3%

Figure 2. Profitability dynamics conditional on a policy change:

The roles of policy uncertainty and political uncertainty.

Stock Prices

• Firm i’s stock is a claim on the firm’s liquidating dividend BiT

• Market value of stock i is given by

M it = Et

πT

πtBi

T

• Complete markets ⇒ State price density is uniquely given by

πt =1

λEt

W

−γT

,

where total wealth WT is the sum of all BiT ’s

• Risk-free rate = 0

Stock Price Reaction to the Announcement of a Policy Change

• Proposition 3: Closed-form solution for stock return atthe announcement of a policy change, R(gτ )



• Proposition 4: R(gτ ) < 0 iff gτ > g∗, where

g∗ = −σ2

g − σ2τ

(T − τ )

γ −

1

2

< 0

– Cash flow versus discount rate effects



• Proposition 4: R(gτ ) < 0 iff gτ > g∗, where

g∗ = −σ2

g − σ2τ

(T − τ )

γ −

1

2

< 0

– Cash flow versus discount rate effects

• P2 + P4 ⇒ Policy change occurs and stock prices fall iff

g∗ < gτ < g(c)

– The interval is expected to be below zero since g∗ < g(0) < 0

0

50

100

150

200

g∗ g(0)gτ 0

Fre

quency d

istr

ibutio

n

Panel A.

0

50

100

150

200

g∗ g(0)gτ 0

Panel B.

0

50

100

150

200

g∗ g(0) gτ 0

Fre

quency d

istr

ibutio

n

Panel C.

0

50

100

150

200

g∗ g(0) gτ0

Panel D.

Figure 3. Probability of a policy change, as perceived by investors just before τ .

Expected Return at the Announcement of a Policy Change

• EAR = Expected return at the announcement of a policy change

• Proposition 5: EAR is negative (E {R(gτ )} < 0)




– Positive announcement returns tend to be small becausethey occur when the policy change is anticipated

– Negative announcement returns tend to be large becausethey occur when the policy change comes as a surprise






– Some utility-increasing policy changes reduce stock prices







– Investors expect government to derive a political benefit froma policy change: E(C|policy change) < E(C) = 1







– Investors expect government to derive a political benefit froma policy change: E(C|policy change) < E(C) = 1

• EAR is more negative when policy/political uncertainty is large

0 2 4 6 8 10 12 14 16 18 20−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

σc (%)

Retu

rn (

%)

σg = 1%

σg = 2%

σg = 3%

Figure 4. Expected announcement return.

Determinants of the Announcement Return

• We relate the announcement return to the length and depth

of the downturns that induce policy changes

Determinants of the Announcement Return

• We relate the announcement return to the length and depth

of the downturns that induce policy changes

• Let t0 mark the beginning of a downturn: gt0 = 0

LENGTH = τ − t0

DEPTH =gτ

Std(gτ ). . . number of std dev’s by which gt drops

• Note that

gτ |gt0 = 0 ∼ N (0, Std(gτ )) , where Std(gτ ) =√√√√σ2

t0− σ2

τ

−2.5 −2 −1.5 −1 −0.5 0 0.5−20

−15

−10

−5

0

Depth

Re

turn

(%

)

Panel A. Announcement Return

−2.5 −2 −1.5 −1 −0.5 0 0.50

0.2

0.4

0.6

0.8

1

Depth

Pro

ba

bili

ty

Panel B. Probability of a Policy Change

Length = 10

Length = 5

Length = 1

Length = 10

Length = 5

Length = 1

Figure 5. Announcement return and the downturn length and depth.

−2 −1 0 1 2−15

−10

−5

0

Depth

Retu

rn (

%)

Panel A. Announcement Return, σg = 1%

−2 −1 0 1 20

0.2

0.4

0.6

0.8

1

Depth

Pro

babili

ty

Panel C. Probability of a Policy Change, σg = 1%

−5 −4 −3 −2 −1 0−30

−25

−20

−15

−10

−5

0

Depth

Retu

rn (

%)

Panel B. Announcement Return, σg = 3%

−5 −4 −3 −2 −1 00

0.2

0.4

0.6

0.8

1

Depth

Pro

babili

ty

Panel D. Probability of a Policy Change, σg = 3%

Length = 10

Length = 5

Length = 1

Figure 6. Announcement return and the downturn length and depth:

The role of policy uncertainty.

0 2 4 6 8 10 12 14 16 18 20−6

−5

−4

−3

−2

−1

0

σc (%)

Re

turn

(%

)

Panel A. Expected Announcement Return. Length = 5 years

σg = 1%

σg = 2%

σg = 3%

0 2 4 6 8 10 12 14 16 18 20−20

−15

−10

−5

0

σc (%)

Re

turn

(%

)

Panel B. Expected Announcement Return. Length = 1 years

σg = 1%

σg = 2%

σg = 3%

Figure 7. Expected announcement return and the downturn length.

−20 −15 −10 −5 00

10

20

30

40

50

Return (%)

Fre

qu

en

cy D

istr

ibu

tion

Panel A. σc = 10%

−20 −15 −10 −5 00

10

20

30

40

Return (%)

Fre

qu

en

cy D

istr

ibu

tion

Panel B. σc = 20%

σg = 1 %

σg = 2 %

σg = 3 %

σg = 1 %

σg = 2 %

σg = 3 %

Figure 8. Probability distribution of stock returns on the day of the announcement

of a policy change.

Expected Return at the Announcement of a Policy Decision

• Expected jump in stock prices at time τ is generally positive

Expected Return at the Announcement of a Policy Decision

• Expected jump in stock prices at time τ is generally positive

– It is negative iff g∗ < gτ < g∗∗, where

g∗∗ = −γ

2(T − τ )

σ2

g − σ2τ

< 0

• Investors demand a premium for facing jumps in SDF

E(

JM,τ

)

= −Cov(

Jπ,τ , JM,τ

)

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

σc (%)

Re

turn

(%

)

Panel A. Expected Return at Announcement of a Policy Decision

0 2 4 6 8 10 12 14 16 18 20−5

−4

−3

−2

−1

0

σc (%)

Re

turn

(%

)

Panel B. Expected Return at Announcement of Policy Change

σg = 1%

σg = 2%

σg = 3%

0 2 4 6 8 10 12 14 16 18 200

1

2

3

4

5

σc (%)

Re

turn

(%

)

Panel C. Expected Return at Announcement of No Policy Change

σg = 1%

σg = 2%

σg = 3%

σg = 1%

σg = 2%

σg = 3%

Figure 9. Expected return at the announcement of a policy decision.

Dynamics of Stock Returns

• We derive closed-form solutions for the dynamics of

– the stochastic discount factor

– expected return of each stock

– volatility of stock returns

– correlations between stocks

9 9.5 10 10.5 1110

15

20

25

30

Time

Pe

rce

nt

pe

r ye

ar

Panel C. Return Volatility

σg=1%

σg=2%

σg=3%

9 9.5 10 10.5 1120

40

60

80

100

Time

Pe

rce

nt

Panel D. Correlation

σg=1%

σg=2%

σg=3%

9 9.5 10 10.5 1120

40

60

80

100

120

Time

Pe

rce

nt

pe

r ye

ar

Panel A. SDF Volatility

σg=1%

σg=2%

σg=3%

9 9.5 10 10.5 110

5

10

15

20

25

30

Time

Pe

rce

nt

pe

r ye

ar

Panel B. Expected Return

σg=1%

σg=2%

σg=3%

Figure 10. Properties of returns around policy changes.

Price Dynamics When Policy Changes Are Precluded

• We compare model-implied stock prices with their counterpartsin the hypothetical scenario in which policy changes are precluded

• We find that the government’s ability to change policy

– can increase or decrease market values


9 9.5 10 10.5 112

2.1

2.2

2.3

2.4

2.5Panel A. Market Value, Length = 1

Time

Policy change allowed

Policy change precluded

9 9.5 10 10.5 1112

13

14

15

16

17

18Panel C. Volatility, Length = 1

Time

Pe

rce

nt

pe

r ye

ar

9 9.5 10 10.5 112.25

2.3

2.35

2.4

2.45

2.5Panel B. Market Value, Length = 5

Time

9 9.5 10 10.5 1110

12

14

16

18Panel D. Volatility, Length = 5

Time

Pe

rce

nt

pe

r ye

ar

Figure 11. The level and volatility of stock prices around policy changes.

Extension: Endogenous Timing of Policy Change

• We extend the model by endogenizing the timing of policy change

– No closed-form solutions; solve numerically

• Government can change policy at any time τ ∈ [1, 2, . . . , 19]

• Each year i, a new value of Ci is drawn; Ci are iid

• Value function reflects option value of waiting

• We find our results continue to hold when τ is endogenous

0 5 10 15 20

−4

−3

−2

−1

0Panel A. Announcement Return

σc (%)

Pe

rce

nt

σg = 1%

σg = 2%

σg = 3%

5 10 15 20−10

−8

−6

−4

−2

0Panel B. Announcement Return

Policy Announcement Date

Pe

rce

nt

σg = 1%

σg = 2%

σg = 3%

−1 −0.5 0 0.5 110

12

14

16

18

20Panel C. Return Volatility

Time Relative to Policy Announcement Date

Pe

rce

nt

pe

r ye

ar

σg = 1%

σg = 2%

σg = 3%

−1 −0.5 0 0.5 120

30

40

50

60

70Panel D. Correlation

Time Relative to Policy Announcement Date

Pe

rce

nt

σg = 1%

σg = 2%

σg = 3%

Figure 12. Endogenous timing of a policy change.

Extension: Investment Adjustment

• We extend the model by allowing firms to disinvest

• At time τ , each firm can disinvest and switch capital into cash

• Firms make investment decisions at the same time as governmentmakes the policy decision

Extension: Investment Adjustment

• We extend the model by allowing firms to disinvest

• At time τ , each firm can disinvest and switch capital into cash

• Firms make investment decisions at the same time as governmentmakes the policy decision

• Proposition 7: In Nash equilibrium, a fraction ατ ∈ [0, 1] offirms continue investing. The government changes its policy iff

gτ < g (c, ατ )

• We solve the problem numerically

– The threshold g (c, ατ ) depends on ατ , which depends on gτ

Extension: Investment Adjustment (cont’d)

• For parameter values in Table 1, the equilibrium has ατ = 1(no disinvestment), so all results continue to hold

– To obtain disinvestment, we reduce µ from 10% to 2%

Extension: Investment Adjustment (cont’d)

• For parameter values in Table 1, the equilibrium has ατ = 1(no disinvestment), so all results continue to hold

– To obtain disinvestment, we reduce µ from 10% to 2%

• We find:

– Both policy and political uncertainty reduce investment

– Our key asset pricing results continue to hold

0 5 10 15 20−1.5

−1

−0.5

0

σc (%)

Retu

rn (

%)

Panel B. Announcement Return

σg = 1%

σg = 2%

σg = 3%

0 5 10 15 2070

75

80

85

90

95

100

σc (%)

α (

%)

Panel A. Equilibrium α

σg = 1%

σg = 2%

σg = 3%

9 9.5 10 10.5 1110

15

20

25

Time

Perc

ent per

year

Panel C. Return Volatility

σg=1%

σg=2%

σg=3%

9 9.5 10 10.5 1120

40

60

80

100

Time

Perc

ent

Panel D. Correlation

σg=1%

σg=2%

σg=3%

Figure 13. Investment adjustment.

Conclusions: Key Empirical Predictions

• Stock returns at announcements of policy changes should benegative, on average

– Especially when policy/political uncertainty is high, or whenpolicy change is induced by a short or shallow downturn

– Distribution of announcement returns should be left-skewed

• Stock returns at announcements of policy decisions should bepositive, on average

• Policy changes should increase volatilities, risk premia, andcorrelations

Documents

Uncertainty about Government Policy and Stock Prices...Uncertainty about Government Policy and Stock Prices Luboˇs P´astorˇ and Pietro Veronesi Booth School of Business University