Comparing Di erent Regulatory Measures to Control Stock ... · to Control Stock Market Volatility:...

Comparing Different Regulatory Measures

to Control Stock Market Volatility:

A General Equilibrium Analysis

A. Buss B. Dumas R. Uppal G. VilkovINSEAD INSEAD, CEPR, NBER Edhec, CEPR Goethe U. Frankfurt

Journee of the Foundation BdF

04 June 2014

Buss, Dumas, Uppal, Vilkov Financial Regulation 04 June 2014 1 / 35

Outline

1 Motivation, Objective, and Contribution

2 The Model

3 The Real Effects of Financial Markets

4 Effects of Regulatory Measures

5 Conclusion


Outline


2 The ModelKey Features of Our ModelSome Details of the ModelCalibrating the Model



5 Conclusion


Two Major Themes of the Paper

Develop a model where financial markets influence real sector

I Specifically, can sentiment-prone investors affect real economy?

� investment,

� output,

� consumption

I Results: We show negative externalities due to sentiment-proneinvestors.


Two Major Themes of the Paper

Financial Regulation

I Which policy measure is most effective for regulating financialmarkets and reducing its negative externalities?

1 Tobin Tax

2 Short-sale constraint

3 Borrowing / Leverage constraint

I Results:

� Tobin tax and short-sale constraint are counter-effective.

� Borrowing / Leverage constraint seems to be promising.


Related Literature

I Our model is related to the literature on “investor sentiment”and “behavioral equilibrium theory.”

� Single non-Bayesian household: Barberis, Shleifer, and Vishny(1998) and Daniel, Hirshleifer, and Subrahmanyam (1998)

� Non-optimizing households: Hong and Stein (1999)

� Sentiment and production: Panageas (2005)

I Also, the literature on the remedies to the recent financial crisisis close to our work.

� Collateral restrictions: Geanakoplos and Fostel (2008) andGeanakoplos (2009).

� Credit constraints: Krishnamurthy (2003).

� Monetary tools: Ashcraft, Garleanu, and Pedersen (2010).


Outline





5 Conclusion


First Key Feature of Our Model:

Investors with Heterogeneous Beliefs

I Hansen (2007): “While introducing heterogeneity among investorswill complicate model solution, it has intriguing possibilities.”

I Stiglitz (2010) criticizes representative-investor models; statesimportance of heterogeneous investors as key challenge.

I Sargent (2008) in his presidential address to the American EconomicAssociation, discusses extensively the implications ofthe common beliefs assumption for policy.


Second Key Feature of Our Model:

Heterogeneous Beliefs with Endogenous Risk

I Model meets twin challenges set by Eichenbaum (2010).

I The twin challenges Eichenbaum (2010) posed are:

1 to model heterogeneity in beliefs and persistent disagreementbetween investors, and

2 financial market frictions with risk residing internally in thefinancial system rather than externally in the production system.

I The twin challenges are met here because in our model theheterogeneity of investor beliefs is a fluctuating, stochastic oneso that it constitutes an internal source of risk:

� sentiment is stochastic, and

� volatility of sentiment is stochastic;

thus, market alternates between periods of quiescence and agitation.


Third Key Feature of Our Model:

Market Incompleteness and Frictions

I Typically, general-equilibrium models assume complete financialmarkets, which simplifies the task of solving for equilibrium.

I However, once regulatory constraints are introduced, financialmarkets are not complete.

I We identify the equilibrium when markets are incomplete.


Outline





5 Conclusion


Model: Production I

I We assume that there exists a representative firm producing andpaying out a single consumption good.

I At each period t the firm uses the capital stock Kt to generateproduction Yt = Kt × Zt , where Zt denotes the stochastictechnology.

I The capital of the firm depreciates at the periodic rate δ, and afterinvestment It its law of motion can be described as

Kt+1 = (1− δ)Kt + It

I We assume that the change in the capital level is subject to

quadratic adjustment costs ξ2

(ItKt− δ)2

Kt


Model: Production II

I Investment It is chosen to maximize value of firm Pk,t for owner k:

PSk,t(Kt) = max

It ,...,IT−1

{Dt + Et

[T∑

τ=t+1

Mk,τ

Mk,tDτ

]}

I We assume that the value of the firm is maximized with respect tothe expectations of the rational investor.

� Carceles-Poveda and Coen-Pirani (2007) show that withconstant-returns-to-scale production, investors agree oninvestment decisions even in markets that are not complete.

� Even though markets are not complete, the pricing kernels ofthe two investors are similar, and so the investment choices theymake are also similar.


Model: Households/Investors

I Additive external habit (”catching up with the Joneses”):

maxEk

T∑t=0

βtk(ck,t − hk × Ct)

1−γk

1− γk, where

I hk is the habit factor; scaling last period’s aggregate consumption Ct

I γk > 0 controlling the investor’s risk appetite

I Ek is investor k’s cond. expectation (subjective probability measure)

I subject to budget equation

ck,t + θSk,tSk,t︸︷︷︸equity investment

+ θBk,tBk,t︸︷︷︸risk-free investment

= θSk,t−1 (Sk,t + Dt) + θBk,t−1


Model: Source of Uncertainty

Uncertainty in the economy is generated by a Hidden Markov Model.

Hidden Part

I Two unobservable fundamental states: ’Expansion’ or ’Recession’.

I Transition between the unobservable states follows a Markov process.

Observables

I While the state of the economy is unobservable for the investors,they observe

1 productivity realization Zt : ’high’ or ’low’

2 a public signal: ’positive’ or ’negative’


Model: Beliefs

I We assume that

� the realized technology level provides information about thecurrent state of the economy,

� while the signal is pure noise.

I Investors use the observations to form conditional state probabilitiesusing a nonlinear analog of the Kalman filter.

I One investor (“rational”) knows signal is pure noise.

I The other investor (“sentiment-prone”) believes incorrectly thatsignal also provides useful information; assigning weight w .


Regulatory Measures

1 Tobin tax κt affects the individual budget constraint:

ck,t +θSk,tSk,t +θBk,tBk,t +κt Sk,t∣∣θSk,t − θSk,t−1

∣∣ = θSk,t−1 (Sk,t + Dt) +θBk,t−1

Tax revenue is reimbursed to investors as a lump-sum transfer.

2 Short-sale constraint restricts the holdings of the risky asset to beabove a predefined limit ρ:

θSk,t ≥ ρ, ∀k , t.

3 Leverage constraint limits the amount of borrowing, or equivalently,investment in the risky asset, to be less than a specified level α:

θSk,t × Sk,t

θBk,t × Bk,t + θSk,t × Sk,t≤ α, ∀k, t,


Equilibrium

Equilibrium in this economy is defined as

I consumption policies, ck,t , that maximize lifetime expected utility

I portfolio policies, θ{B,S}k,t , that finance the optimal portfolio policy

I investment policy, It , that maximizes the value of the firm

I price processes for the financial assets, {Bt , St}, such that thefollowing markets clear at each state and date:

� markets for the stock and bond,

� market for consumption, and investment.


Outline





5 Conclusion


Calibration of the Model

I For the quantitative analysis we calibrate our model to match severalstylized facts of the U.S. macroeconomy and financial markets.

I For example, output and investment volatility as well as the leveredequity risk premium and its volatility.

I We solve model for 30 years, assuming each period in modelcorresponds to one year, with the last 15 years used as burn-in period.

I All statistics are based on 10,000 simulated paths of economy.

I We assume the two investors have homogeneous preferences.


Parameter Values

Description Variable ValueHidden Markov ChainAutocorrelation hidden states A1,1, A2,2 0.95Precision of technology B1,1 + B1,2,B2,3 + B2,4 0.95Probability of the initial state πk 0.5

Preferences and BeliefsSentiment of irrational Agent w 0.9Subject time preference ρk 0.9606Risk aversion γk 3Habit parameter hk 0.1

ProductionDepreciation δ 0.08Volatility of technology σT 4.90%Technology growth dT 0.60%Adjustment costs ξ 13


Financial and Business Cycle Statistics:

Model vs. U.S. Data

Description Variable Model DataMacroeconomic variablesOutput volatility σ(Y ) 3.99% 3.78%Normalized investment volatility σ(I ) 2.67% 2.39%Normalized consumption volatility σ(C ) 0.93% 0.40%Correlation between investment & output Cor(I ,Y ) 0.82 0.96Correlation between consumption & output Cor(C ,Y ) 0.95 0.76

Financial variablesRisk-free rate rf 2.30% 1.94%Interest rate volatility σ(rf ) 8.30% 5.44%Equity premium E [Rep] 3.30% 6.17%Equity premium volatility σ(Rep) 21.70% 19.40%Sharpe ratio E [Rep]/σ(Rep) 15% 32%


Outline





5 Conclusion


Effect of Sentiment on Financial Variables

Sentiment is measured by weight put on uninformative signal by “sentiment-prone” investor.

Volatility of Stock Returns

0 0.2 0.4 0.6 0.8 10.2

0.21

0.22

0.23

0.24

0.25

0.26

Sentiment

I Results for interest rate volatility are comparable.Buss, Dumas, Uppal, Vilkov Financial Regulation 04 June 2014 25 / 35

Effect of Sentiment on Investment Growth

Investment Growth

0 0.2 0.4 0.6 0.8 10.033

0.034

0.035

0.036

0.037

0.038

0.039

Sentiment


Effect of Sentiment on Investment Growth

Volatility of Investment Growth Rate

0 0.2 0.4 0.6 0.8 10.09

0.095

0.1

0.105

0.11

0.115

Sentiment

I Results for output / consumption are comparable.Buss, Dumas, Uppal, Vilkov Financial Regulation 04 June 2014 26 / 35

Outline





5 Conclusion


Effect of Regulatory Measures

I We illustrate the effects of regulatory measures using figures.

I Each plot has three lines:

� The red line depicts case when both investors learn rationally;

� The black line depicts case of excessive volatility due to“sentiment-prone” trading but without regulations;

� The blue line depicts case with a particular regulatory measurein the economy with excessive volatility.


Volatility of Stock Returns

Red: Both rational; Black: One sentiment-prone, no regulation; Blue: With regulation

0 0.005 0.01 0.015 0.020.2

0.22

0.24

0.26

0.28

0.3

Tobin tax−0.25 −0.2 −0.15 −0.1 −0.05 0

0.2

0.22

0.24

0.26

0.28

0.3

Short−sale constraint

1.522.533.540.2

0.22

0.24

0.26

0.28

0.3

Leverage constraint


Investment Growth


0 0.005 0.01 0.015 0.020.032

0.033

0.034

0.035

0.036

0.037

0.038

0.039

Tobin tax−0.25 −0.2 −0.15 −0.1 −0.05 0

0.032

0.033

0.034

0.035

0.036

0.037

0.038

0.039


1.522.533.540.032

0.033

0.034

0.035

0.036

0.037

0.038

0.039

Leverage constraint


Investment Growth Volatility


0 0.005 0.01 0.015 0.020.09

0.095

0.1

0.105

0.11

0.115

0.12

Tobin tax−0.25 −0.2 −0.15 −0.1 −0.05 0

0.09

0.095

0.1

0.105

0.11

0.115

0.12


1.522.533.540.09

0.095

0.1

0.105

0.11

0.115

0.12

Leverage constraint


Summary of Findings

Code:• Blue indicates positive effect (good)

• Red indicates negative effect (bad)

Quantity Tobin Short-sale LeverageTax Constraint Constraint

Financial MarketsFinancing costs Lower Lower LowerVolatility Higher Higher Lower

ProductionInvestment and output Reduced Reduced IncreasedVolatility Increased Increased Mixed

ConsumptionGrowth Lower Lower Much higherVolatility Higher Higher Lower


Outline





5 Conclusion


Conclusion

Real Effects of Financial Markets

I Study the impact of sentiment-prone investors on the real sector.

I Results: We demonstrate negative externalities due tosentiment-prone investors.

Financial Regulation

I We quantitatively assess the effectiveness of regulatorymeasures:

� Tobin financial transaction tax: Mostly negative ...

� Short-sale constraint: Mostly negative ...

� Leverage constraint: Promising ...


References

Ashcraft, A., N. Garleanu, and L. H. Pedersen, 2010, “Two Monetary Tools: Interest Rates and Haircuts,” NBERMacroeconomics Annual, 25, 143–180.

Barberis, N., A. Shleifer, and R. Vishny, 1998, “A Model of Investor Sentiment,” Journal of Financial Economics, 49(3),307–343.

Daniel, K., D. Hirshleifer, and A. Subrahmanyam, 1998, “Investor Psychology and Security Market Under- and Overreactions,”Journal of Finance, 53(6), 1839–1885.

Eichenbaum, M., 2010, “What Shortcomings in Macroeconomic Theory and Modelling have been Revealed by the FinancialCrisis and how should they be Addressed in the Future?,” Comments from an ECBpanel,http://faculty.wcas.northwestern.edu/ yona/research.html.

Geanakoplos, J., 2009, “The Leverage Cycle,” in NBER Macroeconomic Annual, ed. by Acemoglu, D., K. Rogoff, and M.Woodford, vol. 24, pp. 1–65. University of Chicago Press.

Geanakoplos, J., and A. Fostel, 2008, “Collateral Restrictions and Liquidity Under-Supply: A Simple Model,” Economic Theory,35, 441–467.

Hansen, L. P., 2007, “Beliefs, Doubts and Learning: Valuing Macroeconomic Risk,” American Economic Review, 97(2), 1–30.

Hong, H., and J. C. Stein, 1999, “A Unified Theory of Underreaction, Momentum Trading, and Overreaction in Asset Markets,”Journal of Finance, 54(6), 2143–2184.

Krishnamurthy, A., 2003, “Collateral Constraints and the Amplification Mechanism,” Journal of Economic Theory, 111(2),277–292.

Panageas, S., 2005, “The Neoclassical Theory of Investment in Speculative Markets,” Working Paper, University ofPennsylvania.

Sargent, T. J., 2008, “Evolution and Intelligent Design,” American Economic Review, 98(1), 5–37.

Stiglitz, J. E., 2010, “An Agenda for Reforming Economic Theory,” Slides for presentation at Cambridge INET Conference.


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