Investors Attention and Stock Market Volatility

Transcription

1 Investors Attention and Stock Market Volatility Daniel Andrei Michael Hasler Princeton Workshop, Lausanne 2011 Attention and Volatility Andrei and Hasler Princeton Workshop / 15

2 Prerequisites Attention and Volatility Andrei and Hasler Princeton Workshop / 15

3 Prerequisites Consider the dividend process dδt δ t = f t dt + σ δ dz δ t : t T + Attention and Volatility Andrei and Hasler Princeton Workshop / 15

4 Prerequisites Consider the dividend process dδt δ t = f t dt + σ δ dz δ t : t T + Price of the short-term asset Price of the long-term asset Attention and Volatility Andrei and Hasler Princeton Workshop / 15

5 Prerequisites Consider the dividend process dδt δ t = f t dt + σ δ dz δ t : t T + Price of the short-term asset Price of the long-term asset Price of the stock Attention and Volatility Andrei and Hasler Princeton Workshop / 15

6 Motivation I Prices and Realizations of Dividend Claims: 1996:2-2009:08. Source: Binsbergen et al. (forthcoming, AER 2011). Attention and Volatility Andrei and Hasler Princeton Workshop / 15

7 Motivation II 0.8 S&P500 Volatility Focus on Economic News Q Q Q Q Q Q Q Q Attention and Volatility Andrei and Hasler Princeton Workshop / 15

8 Our Aim To show that the fluctuating investors attention explain the behavior of the short-term asset returns and of the market returns. Attention and Volatility Andrei and Hasler Princeton Workshop / 15

9 Our Aim To show that the fluctuating investors attention explain the behavior of the short-term asset returns and of the market returns. Our Model A pure exchange Lucas economy with an unobservable fundamental and a signal (flow of news). The attention is modeled as the correlation between the unobserved fundamental and the signal. Attention and Volatility Andrei and Hasler Princeton Workshop / 15

10 Outline I Model II Results III Conclusions Attention and Volatility Andrei and Hasler Princeton Workshop / 15

11 Model Outline I Model II Results III Conclusions Attention and Volatility Andrei and Hasler Princeton Workshop / 15

12 Model The risky asset is a claim to the dividend process δ: dδ t δ t = f t dt + σ δ dz δ t The dividend expected growth rate, f, is unobservable and behaves according to: ) df t = λ ( f ft dt + σ f dzt f The representative agent observes a signal, s, with the following dynamics ds t = Φ t dzt f + 1 Φ 2 t dzt s Attention and Volatility Andrei and Hasler Princeton Workshop / 15

13 Model The risky asset is a claim to the dividend process δ: dδ t δ t = f t dt + σ δ dz δ t The dividend expected growth rate, f, is unobservable and behaves according to: ) df t = λ ( f ft dt + σ f dzt f The representative agent observes a signal, s, with the following dynamics ds t = Φ t dzt f + 1 Φ 2 t dzt s Attention and Volatility Andrei and Hasler Princeton Workshop / 15

14 Model The risky asset is a claim to the dividend process δ: dδ t δ t = f t dt + σ δ dz δ t The dividend expected growth rate, f, is unobservable and behaves according to: ) df t = λ ( f ft dt + σ f dzt f The representative agent observes a signal, s, with the following dynamics ds t = Φ t dzt f + 1 Φ 2 t dzt s Attention and Volatility Andrei and Hasler Princeton Workshop / 15

15 Model Investors Attention: A Sample Path 1.3 Dividend dδ t δ t = f t dt + σ δ dz δ t Attention and Volatility Andrei and Hasler Princeton Workshop / 15

16 Model Investors Attention: A Sample Path Performance φ t = t dδu 0 e ω(t u) δ u 1.3 Dividend dδ t δ t = f t dt + σ δ dz δ t Attention and Volatility Andrei and Hasler Princeton Workshop / 15

17 Model Investors Attention: A Sample Path Attention Φ t Ψ Ψ (1 Ψ)e Λ(φ t f /ω) Performance φ t = t dδu 0 e ω(t u) δ u 1.3 Dividend dδ t δ t = f t dt + σ δ dz δ t Attention and Volatility Andrei and Hasler Princeton Workshop / 15

18 Model The dynamics of the post filtering state vector: dδ t δ t = ˆf t dt + (σ δ 0)dW t ) dˆf t = λ ( f ˆft dt + ) (ˆf t dφ t = ω ω φ t dγ t = ( σ 2 f ( γt σ δ σ f Φ t dt + (σ δ 0)dW t ( ) 1 Φ 2 t 2λγ t γ2 t σδ 2 ) dw t ) dt Attention and Volatility Andrei and Hasler Princeton Workshop / 15

19 Model GMM Estimation Parameter Value Std Error t-stat p-val σ δ f λ σ f ω Λ Ψ Attention and Volatility Andrei and Hasler Princeton Workshop / 15

20 Model Equilibrium We compute the equilibrium using the techniques from Karatzas, Lehoczky, and Shreve (1987) and Cox and Huang (1989). The state vector is not affine we perform an accurate quadratic approximation. After the approximation, we can use the theory of affine processes to compute the price of the risky asset: S t = E t t ξ s ξ t δ s ds The stock return volatility is computed by applying Itô s lemma: σ t = 1 S ( t diff xt T S t x t ) Attention and Volatility Andrei and Hasler Princeton Workshop / 15

21 Model Equilibrium We compute the equilibrium using the techniques from Karatzas, Lehoczky, and Shreve (1987) and Cox and Huang (1989). The state vector is not affine we perform an accurate quadratic approximation. After the approximation, we can use the theory of affine processes to compute the price of the risky asset: S t = E t t ξ s ξ t δ s ds The stock return volatility is computed by applying Itô s lemma: σ t = 1 S ( t diff xt T S t x t ) Attention and Volatility Andrei and Hasler Princeton Workshop / 15

22 Model Equilibrium We compute the equilibrium using the techniques from Karatzas, Lehoczky, and Shreve (1987) and Cox and Huang (1989). The state vector is not affine we perform an accurate quadratic approximation. After the approximation, we can use the theory of affine processes to compute the price of the risky asset: S t = E t t ξ s ξ t δ s ds The stock return volatility is computed by applying Itô s lemma: σ t = 1 S ( t diff xt T S t x t ) Attention and Volatility Andrei and Hasler Princeton Workshop / 15

23 Model Equilibrium We compute the equilibrium using the techniques from Karatzas, Lehoczky, and Shreve (1987) and Cox and Huang (1989). The state vector is not affine we perform an accurate quadratic approximation. After the approximation, we can use the theory of affine processes to compute the price of the risky asset: S t = E t t ξ s ξ t δ s ds The stock return volatility is computed by applying Itô s lemma: σ t = 1 S ( t diff xt T S t x t ) Attention and Volatility Andrei and Hasler Princeton Workshop / 15

24 Results Outline I Model II Results III Conclusions Attention and Volatility Andrei and Hasler Princeton Workshop / 15

25 Results Fundamental Volatility and Market Volatility Scatter Plot Linear Fit Market Volatility Fundamental s Volatility σ( ˆf) 10 2 Estimate Standard Error t Statistic P-Value R 2 α β Attention and Volatility Andrei and Hasler Princeton Workshop / 15

26 Results Fundamental Volatility and Market Volatility Scatter Plot Linear Fit Market Volatility Fundamental s Volatility σ( ˆf) 10 2 Estimate Standard Error t Statistic P-Value R 2 α β Attention and Volatility Andrei and Hasler Princeton Workshop / 15

27 Results Fundamental Volatility and Market Volatility Scatter Plot Linear Fit Market Volatility Fundamental s Volatility σ( ˆf) 10 2 Estimate Standard Error t Statistic P-Value R 2 α β Attention and Volatility Andrei and Hasler Princeton Workshop / 15

28 Results Estimate Standard Error t Statistic P-Value R 2 α β β Attention and Volatility Andrei and Hasler Princeton Workshop / 15 Investors Attention and Market Volatility Scatter Plot Quadratic Fit Market Volatility Attention Φ

29 Results Estimate Standard Error t Statistic P-Value R 2 α β β Attention and Volatility Andrei and Hasler Princeton Workshop / 15 Investors Attention and Market Volatility Scatter Plot Quadratic Fit Market Volatility Attention Φ

30 Results Investors Attention and Market Volatility Scatter Plot Quadratic Fit Market Volatility Attention Φ Estimate Standard Error t Statistic P-Value R 2 α β β Attention and Volatility Andrei and Hasler Princeton Workshop / 15

31 Results One Simulated Path 2.6 Short Term Asset s Price Short Term Asset s Dividend Time Attention and Volatility Andrei and Hasler Princeton Workshop / 15

32 Results Short Term Asset Vol / Market Vol 0.58 Scatter Plot Linear Fit 0.56 Volatility Ratio Attention Estimate t Statistic P-Value R 2 α β Attention and Volatility Andrei and Hasler Princeton Workshop / 15

33 Results Short Term Asset Vol / Market Vol 0.58 Scatter Plot Linear Fit 0.56 Volatility Ratio Attention Estimate t Statistic P-Value R 2 α β Attention and Volatility Andrei and Hasler Princeton Workshop / 15

34 Results Short Term Asset Vol / Market Vol 0.58 Scatter Plot Linear Fit 0.56 Volatility Ratio Attention Estimate t Statistic P-Value R 2 α β Attention and Volatility Andrei and Hasler Princeton Workshop / 15

35 Results CAPM: Short Term Asset Estimate t Statistic P-Value R 2 α β Return predictability: Market Returns Estimate t Statistic P-Value R 2 α β Return predictability: Short Term Asset Returns Estimate t Statistic P-Value R 2 α β Attention and Volatility Andrei and Hasler Princeton Workshop / 15

36 Results CAPM: Short Term Asset Estimate t Statistic P-Value R 2 α β Return predictability: Market Returns Estimate t Statistic P-Value R 2 α β Return predictability: Short Term Asset Returns Estimate t Statistic P-Value R 2 α β Attention and Volatility Andrei and Hasler Princeton Workshop / 15

37 Results CAPM: Short Term Asset Estimate t Statistic P-Value R 2 α β Return predictability: Market Returns Estimate t Statistic P-Value R 2 α β Return predictability: Short Term Asset Returns Estimate t Statistic P-Value R 2 α β Attention and Volatility Andrei and Hasler Princeton Workshop / 15

38 Conclusions Outline I Model II Results III Conclusions Attention and Volatility Andrei and Hasler Princeton Workshop / 15

39 Conclusions Conclusions In a pure exchange economy with an unobservable fundamental, fluctuating attention generates GARCH effects both for the market returns and for the short-term asset returns. The volatility is low when the attention is low and vice versa. The short term asset volatility increases more with the attention than the stock volatility. The short-term asset has a β lower than 1 and its returns are predictable, as recent empirical results suggest. Additional implications that we explore in subsequent work: comovement of asset returns, amplification of the difference of beliefs. Attention and Volatility Andrei and Hasler Princeton Workshop / 15