Why Does Return Predictability Concentrate in Bad Times? EFA 2015
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1 Why Does Return Predictability Concentrate in Bad Times? Julien Cujean Michael Hasler EFA 215
2 Empirical Fact Disagreement and the content of news predict stock returns Diether, Malloy, & Scherbina (22), Tetlock (27) Main Fact: This relation is concentrated in bad times Cen, Wei & Yang (214), Garcia (213) 1 / 8
3 Empirical Fact Disagreement and the content of news predict stock returns Diether, Malloy, & Scherbina (22), Tetlock (27) Main Fact: This relation is concentrated in bad times Cen, Wei & Yang (214), Garcia (213) 1 / 8
4 Our Explanation Main Idea: Countercyclical disagreement (Patton and Timmermann (21)) explains observed patterns of time-series predictability 2 / 8
5 Our Explanation Main Idea: Countercyclical disagreement (Patton and Timmermann (21)) explains observed patterns of time-series predictability If disagreement is countercyclical 2 / 8
6 Our Explanation Main Idea: Countercyclical disagreement (Patton and Timmermann (21)) explains observed patterns of time-series predictability If disagreement is countercyclical Predictability strengthens as economic conditions deteriorate 2 / 8
7 Our Explanation Main Idea: Countercyclical disagreement (Patton and Timmermann (21)) explains observed patterns of time-series predictability If disagreement is countercyclical Predictability strengthens as economic conditions deteriorate We build a model consistent with these facts 2 / 8
8 The Model The stock is a claim to the aggregate output: dδ t δ t = f t dt + σ δ dw t 3 / 8
9 The Model The stock is a claim to the aggregate output: dδ t δ t = f t dt + σ δ dw t Unobservable 3 / 8
10 The Model The stock is a claim to the aggregate output: dδ t δ t = f t dt + σ δ dw t Unobservable Agent A f is mean-reverting: df t = κ( f f t )dt + σ f dw f t 3 / 8
11 The Model The stock is a claim to the aggregate output: dδ t δ t = f t dt + σ δ dw t Unobservable Agent A f is mean-reverting: df t = κ( f f t )dt + σ f dw f t Agent B f is a 2-state Markov Chain: f t = {f h,f l } ( ) λ λ Λ = ψ ψ 3 / 8
12 The Model The stock is a claim to the aggregate output: dδ t δ t = f t dt + σ δ dw t Unobservable Estimate: ˆf A t = E A t (f t ) Agent A f is mean-reverting: df t = κ( f f t )dt + σ f dw f t Estimate: ˆf B t = E B t (f t ) Agent B f is a 2-state Markov Chain: f t = {f h,f l } ( ) λ λ Λ = ψ ψ 3 / 8
13 Estimation Parameter Symbol Value Mean-Reversion Speed f A κ.1911 Long-Term Mean f A f.63 High State f B f h.794 Low State f B f l.711 Intensity High to Low λ.322 Intensity Low to High ψ.3951 d f A t Agent A f is mean-reverting: = κ( f f t A )dt + γ dŵ t A σ δ 4 / 8
14 Estimation Parameter Symbol Value Mean-Reversion Speed f A κ.1911 Long-Term Mean f A f.63 High State f B f h.794 Low State f B f l.711 Intensity High to Low λ.322 Intensity Low to High ψ.3951 d f A t Agent A f is mean-reverting: = κ( f f t A )dt + γ dŵ t A σ δ Agent B f is a 2-state Markov Chain: d f t B = (λ + ψ)(f f t B )dt + 1 ( f t B f l )(f h σ f t B )dŵ t B δ 4 / 8
15 Term Structure of Disagreement Good (G), Normal (N), Bad (B) Times P( f t B ) f h f fm f l 5 Time Fundamental f 5 / 8
16 Term Structure of Disagreement Good (G), Normal (N), Bad (B) Times P( f t B ) f h f N fm f l 5 Time Fundamental f 5 / 8
17 Term Structure of Disagreement Good (G), Normal (N), Bad (B) Times P( f t B ) f h f N fm f l 5 Time Fundamental f 5 / 8
18 Term Structure of Disagreement Good (G), Normal (N), Bad (B) Times P( f t B ) f h f N fm f l 5 Time Fundamental f 5 / 8
19 Term Structure of Disagreement Good (G), Normal (N), Bad (B) Times P( f t B ) f h f N fm f l 5 Time Fundamental f Source: Patton and Timmermann (21) Dispersion / 8
20 Term Structure of Disagreement Good (G), Normal (N), Bad (B) Times P( f t B ) f h f N fm B f l Fundamental f Source: Patton and Timmermann (21) 5 Time Dispersion / 8
21 Term Structure of Disagreement Good (G), Normal (N), Bad (B) Times P( f t B ) f h f N fm B f l 5 Time Fundamental f Source: Patton and Timmermann (21) Dispersion / 8
22 Term Structure of Disagreement Good (G), Normal (N), Bad (B) Times P( f t B ) f h f N fm B f l 5 Time Fundamental f Source: Patton and Timmermann (21) Dispersion / 8
23 Term Structure of Disagreement Good (G), Normal (N), Bad (B) Times P( f t B ) f h f G N fm B f l Fundamental f Source: Patton and Timmermann (21) 5 Time Dispersion / 8
24 Term Structure of Disagreement Good (G), Normal (N), Bad (B) Times P( f t B ) f h f G N fm B f l Fundamental f Source: Patton and Timmermann (21) 5 Time Dispersion / 8
25 Term Structure of Disagreement Good (G), Normal (N), Bad (B) Times P( f t B ) f h f G N fm B f l Fundamental f Source: Patton and Timmermann (21) 5 Time Dispersion / 8
26 Impulse Response We compute the expected price response to a shock Ŵ today: E t (D t S u ) 6 / 8
27 Impulse Response We compute the expected price response to a shock Ŵ today: E t (D t S u ) Shock Ŵt time St time 6 / 8
28 Impulse Response We compute the expected price response to a shock Ŵ today: E t (D t S u ) Shock Ŵt time St time 6 / 8
29 Impulse Response We compute the expected price response to a shock Ŵ today: E t (D t S u ) Shock Ŵt time St t time 6 / 8
30 Impulse Response We compute the expected price response to a shock Ŵ today: E t (D t S u ) Shock Ŵt time St t time 6 / 8
31 Impulse Response We compute the expected price response to a shock Ŵ today: E t (D t S u ) Shock Ŵt time St t u time 6 / 8
32 Impulse Response We compute the expected price response to a shock Ŵ today: E t (D t S u ) Shock Ŵt D ts u time St t u time 6 / 8
33 Impulse Response We compute the expected price response to a shock Ŵ today: E t (D t S u ) Shock Ŵt time St D ts u t u time 6 / 8
34 Impulse Response We compute the expected price response to a shock Ŵ today: E t (D t S u ) Shock Ŵt time St D ts u t u time 6 / 8
35 Impulse Response We compute the expected price response to a shock Ŵ today: E t (D t S u ) Shock Ŵt time St D ts u t u 6 / 8
36 Impulse Response We compute the expected price response to a shock Ŵ today: E t (D t S u ) Shock Ŵt time E t(d ts u) St t u 6 / 8
37 Price Impulse Response 4 2 E PA t [Dt Su] 2 4 Normal Times Time u t 7 / 8
38 Price Impulse Response 4 2 E PA t [Dt Su] 2 4 Normal Times Bad Times Time u t 7 / 8
39 Price Impulse Response 4 2 E PA t [Dt Su] 2 4 Normal Times Bad Times Good Times Time u t 7 / 8
40 Serial Correlation Serial Correlation ρ(h) Good Times Normal Times Month Lag h Bad Times / 8
41 Serial Correlation Serial Correlation ρ(h) Good Times Normal Times Month Lag h Bad Times Source: Moskowitz, Ooi & Pedersen (212) t-stat / 8
42 Serial Correlation Serial Correlation ρ(h) Good Times Normal Times Month Lag h Bad Times / 8
43 Serial Correlation Serial Correlation ρ(h) Good Times Normal Times Month Lag h Bad Times β 2,h t-stat r e t /σ t 1 = α + β 1,h r e t h /σ t h 1 + β 2,h D t h r e t h /σ t h 1 + ɛ t / 8
44 Serial Correlation Serial Correlation ρ(h) Good Times Normal Times Month Lag h Bad Times Momentum crashes Daniel and Moskowitz (213), Baroso and Santa-Clara (214) 8 / 8
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