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Banque Nationale De Belgique Sa — Technical Presentation (November 2010)
39 slides from Banque Nationale De Belgique Sa's technical presentation, November 2010
Slide 1: Self-Fulfilling Risk Panics
Self-Ful…lling Risk Panics Philippe Bacchetta University of Lausanne Cédric Tille Graduate Institute, Geneva Eric van Wincoop University of Virginia November 2010 Bacchetta-Tille-van Wincoop () Risk Panics November 2010 1 / 37
Slide 2: Stock Price and Risk
Stock Price 120.0 110.0 100.0 90.0 80.0 70.0 40.0 T T r T T T T T 01.01.07 01.06.07 01.11.07 01.04.08 01.09.08 01.02.09 01.07.09 01.12.09 01.05.10 Risk 30 80 70 30 20 10 ° T T T T r T T T 01.01.07 01.06.07 01.41.07 01.04.08 01.09.08 01.02.09 01.07.09 01.12.09 01.05.10
Slide 3: How can we explain such sharp Breaks?
How can we explain such sharp Breaks? Changes in fundamentals and news (Lehman Brothers, Greek crisis) are not large enough. Problems had been brewing for some time and were not suddenly revealed. A full year elapsed between the start of the crisis and the panic of the fall 2008. Assuming exogenous
Slide 4: Our Contribution: a Theory of Risk Panics
Our Contribution: a Theory of Risk Panics Self-ful…lling shifts in risk, de…ned as the variance of the future asset price. Key ingredient: the asset price depends on risk. Tomorrow’s asset price and risk depend on perceived risk on subsequent days. If risk is expected to move over time, prices will
Slide 5: Main Findings
Main Findings Multiplicity of equilibria: one with high risk and low asset price, one with low risk and high asset price. Two sources of multiplicity: "Static": contemporaneous interaction of risk, liquidity and wealth. "Dynamic": new aspect linked to self-ful…lling beliefs about future risk. Dual n
Slide 6: Related literature
Related literature Finance literature on market liquidity and leverage. Adrian and Shin (2008), Brunnermeier and Pedersen (2009), Danielsson et al. (2009), Gromb and Vayanos (2002,2008), He and Krishnamurthy (2008a, b), Kyle and Xiong (2001) and Xiong (2001). Notice that we do not rely on time-varyi
Slide 7: Outline of the Presentation
Outline of the Presentation Illustrate multiplicity of equilibria when there is a link between the asset price and risk. Include this in a simple mean-variance portfolio choice model, with bonds and risky equity. Extend to a general equilibrium setting, requiring approximations. Consider redistribut
Slide 8: The Key Mechanism
The Key Mechanism Simple linear relation between the current asset price and uncertainty about the future asset price (risk): Qt = λ0 λ1 Riskt = λ0 λ1 Vart (Qt +1 ) Take a sunspot variable that is extrinsic to the model. A key assumption is that it is persistent: St = ρSt 1 + εt εt has a symmetric d
Slide 9: Equilibria
Equilibria Fundamental equilibrium. The asset price is constant and there is no risk: Qt = λ0 . Notice V = 0. Sunspot equilibrium. The asset price is a¤ected by the sunspot: Qt = Q̃ V ( St ) 2 where: 1 Q̃ = λ0 λ1 V 2 ω 2 ; V = 4λ1 ρ2 σ2 >0 The persistence of the sunspot variable implies time-varying
Slide 10: Current and future risk
Current and future risk Any non-zero realization of St implies that the future asset price is more sensitive to future shocks, i.e. Riskt is higher. At the same time, Riskt +1 is higher: h i Riskt +1 = 4V 2 ρ2 σ2 ρ2 (St )2 + 2ρSt εt +1 + (εt +1 )2 + V 2 ω 2 and more volatile: h i 4 4 4 2 2 2 2 Vart
Slide 11: Intuition
Intuition The future asset price Qt +1 is a linear function of future risk Riskt +1 . This gives a mapping between current and future risk: Riskt = Vart (Qt +1 ) = λ21 Vart (Riskt +1 ) 2 As Vart (Riskt +1 ) = 4V ρ2 σ2 Riskt , one solution is zero risk (fundamental, V = λ1 = 0). The other solution is
Slide 12: Sunspot-like Equilibrium
Sunspot-like Equilibrium St can also have a fundamental role. Consider: Qt = λ0 λ1 Riskt + λ2 St The asset price is of the form: Qt = Q̃ + vSt V ( St ) 2 Fundamental equilibrium. V = 0; risk is constant; Riskt = λ22 σ2 . Sunspot like equilibrium. V > 0 (identical to previous) and risk is time-varyin
Slide 13: Fundamental and Sunspot-like Impact
Fundamental and Sunspot-like Impact Manuelli and Peck (1992): There are two ways that random fundamentals can in‡uence economic outcomes. First, randomness a¤ects resources which intrinsically a¤ects prices and allocation. Second, the randomness can endogenously a¤ect expectations or market psycholo
Slide 14: Introducing this in Portfolio Choice
Introducing this in Portfolio Choice A standard expected utility framework without portfolio constraint does not lead to a link between the asset price and risk. the only risk that matters then is asset payo¤ uncertainty. the asset price depends on the covariance of future asset payo¤ with the stoch
Slide 15: A Simple Mean-Variance Model
A Simple Mean-Variance Model Closed economy with in…nite horizon. Overlapping generations of agents that are born with wealth WI , constant across generations. Agents purchase a risk-free bond, with constant exogenous return R (we later consider a variable rate) and risky equity, that is a claim on
Slide 16: Portfolio Choice
Portfolio Choice Denote the portfolio share invested in the risky equity by αt . Agents maximize a mean-variance utility in terms of the portfolio return: Et Rtp+1 0.5γVart Rtp+1 ; Rtp+1 = αt RK ,t +1 + (1 αt ) R The optimal portfolio re‡ects the expected excess return on equity scaled by its varian
Slide 17: Equilibria with no Fundamental Role
Equilibria with no Fundamental Role Consider that S plays no fundamental role and the dividend is constant (m = 0). The asset price is of the form: Qt = Q̃ V ( St ) 2 Fundamental equilibrium implies no risk (V = 0): Qt = Q̃fund = Ā/ (R 1) The sunspot equilibrium entails time-varying risk and a low
Slide 18: Equilibria with Fundamental Role
Equilibria with Fundamental Role We now introduce a fundamental role for S (m > 0). The asset price is of the form: Qt = Q̃ + vSt V (St )2 The fundamental equilibrium entails constant risk (V = 0): 2 Āρ Āρ Qt = Q̃ + m St ; Vart (At +1 + Qt +1 ) = 1+ m2 σ2 R ρ R ρ The sunspot-like equilibrium entai
Slide 19: General Equilibrium Model
General Equilibrium Model The interest rate on the bond is endogenously determined by the clearing of the bond market. If the bond is in …xed supply, the clearing of both asset markets requires a constant portfolio share, pinning down the expected return and risk. Introduce a bond supply that is a f
Slide 20: Asset Market Clearing
Asset Market Clearing The clearing of the bond market is: (1 α t ) WI + WH υ + ηRt = 0 Combining with the clearing of the equity market, αt WI = Qt K , we get a the bond interest rate as a function of the asset price: Qt K + υ ηRt = WI + WH Bacchetta-Tille-van Wincoop () Risk Panics November 2010 20
Slide 21: Solving the Model
Solving the Model The endogenous interest rate leads to a non-linearity in the asset market clearing. The model is solved using a numerical solution. We conjecture a functional form for the log equity price that is quadratic in S: qt = q̃ + vSt V (St )2 A quadratic approximation of the asset market
Slide 22: Switching Equilibria
Switching Equilibria Introduce an exogenous Markov process that shifts the economy between states. Agents know the probabilities of switching, and expectations are computed taking the possibility of switching into account. Two states: a low risk state (denoted by 1) that converges to the fundamental
Slide 23: Figure 4 Switching Equilibria
Figure 4 Switching Equilibria* blue=low risk state; red=high risk state ~ Q v V V Q1 Q , 2 p1= p2 p1= p2 p1= p2 * This is based on the parameters of Figure 2. When p 1=p2=1, the high and low risk states correspond exactly to equilibria 1 and 2 in Figure 3.
Slide 24: Risk Panics
Risk Panics A panic is a switch from the low to the high risk state. It is characterized by: increase in risk, and the volatility of risk. decrease in the equity price. decrease in the portfolio share put in equity (lower leverage). decrease in the interest rate. Three key points are worth stressing
Slide 25: A Panic is not a Change in Fundamental
A Panic is not a Change in Fundamental The state variable S remains unchanged in a panic. Its role however changes, as it acquires a sunspot role that dominates its fundamental role. The state variable becomes the focal point for a self-ful…lling change in risk perceptions. A panic is distinct from
Slide 26: The Impact of the Panic depends on the Level of the Fundamental
The Impact of the Panic depends on the Level of the Fundamental The di¤erence of the asset price between the two states is: q2,t q1,t = q̃2 q̃1 + (v2 v1 )St (V2 V1 ) (St )2 | {z } >0 q2,t q1,t < 0. The more negative the fundamental, the bigger the asset price change, as well as the other impacts of
Slide 27: The Fundamental has a larger Price Impact after the Panic
The Fundamental has a larger Price Impact after the Panic After the panic the state variable S has a sunspot role. Changes in S now a¤ect the economy primarily through its role as a focal point for expectations. An improvement in the fundamental can lead to a quick recovery of asset markets (markets
Slide 28: Financial Shocks
Financial Shocks To bring the market closer to the current crisis, we introduce a …nancial shock, which is a redistribution of endowments between investors and households, leaving the total endowment unchanged. Interpreted as losses su¤ered by investors on risky securities. Allowing for a change in
Slide 29: Solution
Solution We conjecture a functional form for the log equity price that is quadratic in the state variable: qt = q̃ v θt V ( θ t )2 In addition to the dynamic multiplicity described above (which hinges on persistence of the state variable), there is a static multiplicity. Perceptions of higher risk l
Slide 30: Application to the Crisis
Application to the Crisis The model is too stylized to …nely match the crisis, but can it deliver the broad pattern? The distinct stages are of particular interest: moderate impact in the …rst year of the crisis, followed by severe disruptions in the wake of Lehman Brothers. We consider four success
Slide 31: Figure 8 Model Simulation
Figure 8 Model Simulation shaded area = high risk equilibrium; vertical lines = endowment shock Wealth of investors Equity Price Risk Equity Price Volatility Risk 8 7 6 5 4 3 2 1 0 0 2 4 6 8 10 12 14 16 Gross Interest Rate Leverage illiquidity The economy starts in the low risk equilibrium. At time
Slide 32: Extensions
Extensions Allow endowments to also include equity, so asset prices a¤ect wealth directly. High volatility equilibrium is ampli…ed. Open economy setting: capital ‡ows recently dominated by (de)leveraging. Preliminary results consistent with recent developments. Introducing an impact on the real econ
Slide 33: Conclusions
Conclusions Simple general equilibrium model of portfolio choice. Rich set of results regarding liquidity and risk: static and dynamic multiplicity. Multiple equilibria and sunspot phenomena that could explain many features of the recent …nancial crisis. Open avenues for much more future work. Bacch
Slide 34: APPENDIX SLIDES
APPENDIX SLIDES Bacchetta-Tille-van Wincoop () Risk Panics November 2010 34 / 37
Slide 35: Figure 1 Sunspot Equilibria
Figure 1 Sunspot Equilibria* v 4 3 ~ Equilibrium 2: Q 0.5; v 1.9;V 4.5 2 ~ 1 Equilibrium 1: Q 1.2; v 0;V 0 ~ 0 Q 0 0.5 1 1.5 2 Equilibrium 3: -1 ~ Q 0.34 ; v 0; -2 V 8.9 ~ -3 Equilibrium 4: Q 0.5; v 1.9;V 4.5 -4 -5 -6 *A 0.3; W 0.1; 1; 0.4; 0.4; 4;W 2;
Slide 36: Figure 2 Sunspot-Like Equilibria
Figure 2 Sunspot-Like Equilibria* v 4 3 ~ Equilibrium 2: Q 0.5; v 1.6;V 2.8 2 ~ 1 Equilibrium 1: Q 1.1; v 0.05;V 0.003 0 ~ ~ Q Q 0 0.5 1 1.5 2 -1 -2 ~ -3 Equilibrium 4: Q 0.48; v 2.1;V 6.7 -4 ~ Equilibrium 3: Q 0.39; v 1.4;V 8.7 -5 -6 *A 0.3; W 0.1; 1; 0.4;
Slide 37: Figure 5 Equilibria with Financial Shocks: No Persistence
Figure 5 Equilibria with Financial Shocks: No Persistence* v ~ Equilibrium 2: Q 0.18; v 3.1;V 15.0 ~ Equilibrium 1: Q 1.1; v 0.02;V 0.05 ~ Q * A 0.3; W 0.1; 1; 0.4; 0.4; 0; 4;WI 2; m 2; K 1
Slide 38: Figure 6 Sunspot and Sunspot-Like Equilibria with Financial Shocks
Figure 6 Sunspot and Sunspot-Like Equilibria with Financial Shocks* Panel A Sunspot-Like Equilibria Panel B Sunspot Equilibria v ~ Equilibrium 2: Q 0.79; v 0.75;V 2.3 v ~ ~ Equilibrium 2: Q 0.5; v 1.9;V 4.5 Equilibrium 1: Q 1.1; v 0.03;V 0.05 ~ Equilibrium 1: Q 1.1; v 0;V 0 ~
Slide 39: Time Line Simulation
Time Line Simulation 2 (Q1, 8 (Q3, 11 (Q2, 14 (Q1, period 2007) 2008) 2009) 2010) drop in wealth of switch to wealth leveraged switch back leveraged high risk institutions to low risk institutions state (risk restored to pre- state panic) crisis level
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