Understanding Predictability (JPE, 2004)

Transcription

1 Understandng Predctablty (JPE, 2004) Lor Menzly, Tano Santos, and Petro Verones Presented by Peter Gross NYU October 27, 2009 Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

2 Introducton Market returns forecastable by dvdend yeld However, relaton not stable (such as n the 1990s) Prce dvdend rato does not forecast dvdend growth Combnaton of tme-varyng rsk tolerance and tme-varyng dvdend growth rates can solve ths problem Increase n dvdend growth leads to Increase n expected return (due to greater duraton rsk) Increase n prce dvdend rato Ths can weaken forecastng power of dvdend yeld for dvdend growth and expected returns Need to correct usual predctve regressons by addng n consumpton prce rato Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

3 Overvew 1 Model 2 Prce Consumpton Rato 3 PD Ratos, Expected Returns, and Dvdend Growth 4 Emprcal Evaluaton 5 Concluson Predctablty of Dvdend Growth Predctablty of Stock Returns Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

4 Model (1) - Agents Contnuous Tme, t 2 [0, ). One pershable consumpton good Representatve agent has preferences gven by: Z E e ρt log(c t 0 X t )dt C t s current consumpton, X t external habt level De ne the surplus rato as S t = C t C t X t Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

5 Model (2) - Consumpton Process The nverse surplus rato, Y t = 1 S t processes and log consumpton, c t follow the dy t = k(ȳ Y t )dt α(y t λ)(dc t E t [dc t ]) dc t = µ c dt + σ c db 1 t α > 0 ensures that postve nnovatons n consumpton growth wll lead to negatve nnovatons n the nverse surplus λ 1 ensures lower bound for nverse surplus rato k controls spead of mean reverson Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

6 Model (3) - Cash Flow Process n rsky nancal assets, payng Dt tme t n unts of consumpton good at =1 Other ncome cash ow D 0 t (labor ncome, government transfers,...) Consumpton shares are gven by st = D t, = 1, 2,..., n and governed Ct by ds t = φ ( s s t)dt + s t σ (s t )db 0 t σ (s t ) = v n st j v j j=0 Here, B t s a N dmensonal standard Brownan moton (N n + 1), and v s a vector of constants for each = 1, 2,..., n. Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

7 Model (4) - Cash Flow Process Log dvdends, δ t = log(d t), are governed by dδ t = µ D (s t)dt + σ D (s t )db 0 t s µ D (s t) = µ c + φ σ (s t )σ(s t ) s t σ D (s t ) = σ c + σ (s t ), σ c = (σ c, 0, 0,..., 0) Quantty of economc mportance s Cov(dδ t, dc t ) = σ 2 c + θ CF where θ CF = v 1 σ c Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

8 Prce Consumpton Rato (1) - Total Wealth Portfolo Prce/Consumpton rato of total wealth portfolo s gven by P TW t C t = 1 ρ ρ + kȳ St ρ + k If S t s at average, then everythng collapses to standard case Decrease n rsk averson (ncrease n S t ) pushes rato up The excess return s gven by dr TW t = µ TW µ TW σ TW R (S t ) = R (S t )dt + σ TW R (S t )dbt 1, where R (S t ) R = [1 + α(1 λs t )] σ TW 1 + kys t(1 λs t )α kys t + ρ σ c Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

9 Prce Consumpton Rato (2) - Fgure 1 Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

10 PD Ratos and Expected Returns (1) - No Habt Wthout habt persstence, the prce dvdend rato of th asset s: Pt Dt = 1 ρ + φ 1 + φ ρ s s t The expected excess return n turn s gven by E t [dr t ] = σ 2 c + θ CF n j=0 θ j CF sj t 1 + (φ /ρ)( s /s t) = b 0 + b 1(s t ) D t P t Perfect lnear relaton between expected returns and dvdend yeld. Increase n relatve share ncreases prce dvdend rato/expected return (more so f φ /ρ s small) Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

11 PD Ratos and Expected Returns (2) - Habt Wth habts n place, no closed form solutons avalable However, very good approxmatons (error around 0.1 per cent) can be obtaned: Pt Dt â0 + â1s t + â2 s s t + â3 s st S t E t [dr t ] ˆb 0(S t ) + ˆb 1 (S t ) D t P t E t [dδ t] ˆm 0(S t, s t ) + ˆm 1(S t ) P t D t + ˆb 2 (S t ) C t P t Intuton for ths: D t more senstve to relatve share changes and C Pt t Pt more senstve to surplus consumpton changes Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

12 Emprcal Evaluaton (1) - Data Quarterly dvdends, returns, and market equty from CRSP Sample: value-weghted ndustry portfolos Cash ows nclude both dvdends and share repurchases Per capta consumpton (NDS) from NIPA, de ated by PCE Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

13 Emprcal Evaluaton (2) - Calbraton of Preferences Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

14 Emprcal Evaluaton (3) - Calbraton of Cash Flows Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

15 Emprcal Evaluaton (4) - Predctablty of Dvdend Growth Cash ow predctve regressons: d t,t+τ = β o + β X X t + ɛ t,t+τ, τ = 1, 4, or 7 years X t s s st, P t Dt, or both PD rato s never sgn cant when market dvdends are used, and only weakly when ndustres are used The relatve share s a strong predctor of dvdend growth, wth R 2 up to 41 percent for market at the 7 year horzon In ndvdual regressons, relatve share s sgn cant predctor for 15 out of 20 ndustres, wth R 2 above 30 percent n 10 cases Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

16 Emprcal Evaluaton (5) - Predctablty of Stock Returns Augmented expected return regresson: r t,t+τ = β 0 + β D /P Dt Pt + β C /P C t Pt + ɛ t,t+τ, τ = 1, 4, or 7 years Wth market return, no sgn cance for consumpton prce rato, due to very slow mean reverson of market Wth ndustry returns, the consumpton prce rato becomes sgn cant f mean reverson of dvdends s quck R 2 for some ndustres jumps dramatcally (e.g., from 3 to 37 percent for mnng) when ths s ncluded Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

17 Emprcal Evaluaton (6) - Relaton between Dvdends and Return Predctablty Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18

18 Concluson An ncrease n dvdend growth ncreases both expected returns and prce dvdend ratos An ncrease n rsk averson ncreases expected returns whle decreasng prce dvdend ratos Ths makes dvdend yeld less relable forecaster of future returns By ncludng consumpton prce rato, one can decouple these two sources of return predctablty The extent to whch dvdends are predctable n uences predctablty of returns by the dvdend yeld Presented by Peter Gross (NYU) Understandng Predctablty October 27, / 18