Return Predictability: Dividend Price Ratio versus Expected Returns

Transcription

1 Return Predictability: Dividend Price Ratio versus Expected Returns Rambaccussing, Dooruj Department of Economics University of Exeter 08 May 2010 (Institute) 08 May / 17

2 Objective Perhaps one of the best predictor of realized returns is Expected Returns (Institute) 08 May / 17

3 Objective Perhaps one of the best predictor of realized returns is Expected Returns In the literature one of the best predictors of returns remains Price Dividend Ratios (Cohrane 2008) (Institute) 08 May / 17

4 Objective Perhaps one of the best predictor of realized returns is Expected Returns In the literature one of the best predictors of returns remains Price Dividend Ratios (Cohrane 2008) Campbell and Shiller (1988) posit a relationship between expected returns and expected dividend growth. (Institute) 08 May / 17

5 Objective Perhaps one of the best predictor of realized returns is Expected Returns In the literature one of the best predictors of returns remains Price Dividend Ratios (Cohrane 2008) Campbell and Shiller (1988) posit a relationship between expected returns and expected dividend growth. If Dividend Growth is unpredictable, all variation in Price Dividend Ratio is caused by the returns and vice versa. (Institute) 08 May / 17

6 Objective Perhaps one of the best predictor of realized returns is Expected Returns In the literature one of the best predictors of returns remains Price Dividend Ratios (Cohrane 2008) Campbell and Shiller (1988) posit a relationship between expected returns and expected dividend growth. If Dividend Growth is unpredictable, all variation in Price Dividend Ratio is caused by the returns and vice versa. This study compares the decomposed series of expected returns and price Dividend Ratio as a Predictor of Returns (Institute) 08 May / 17

7 Definitions and Identity r t =ln( P t+1+d t+1 P t ) (1) (Institute) 08 May / 17

8 Definitions and Identity r t =ln( P t+1+d t+1 P t ) (1) pd t = P t D t (2) (Institute) 08 May / 17

9 Definitions and Identity r t =ln( P t+1+d t+1 P t ) (1) pd t = P t D t (2) d t+1 = ln( D t+1 D t ) (3) (Institute) 08 May / 17

10 Definitions and Identity r t =ln( P t+1+d t+1 P t ) (1) pd t = P t D t (2) d t+1 = ln( D t+1 D t ) (3) Campbell and Shiller Log-Linearized Identity (form 1,2 and 3): r t+1 = κ + ρpd t+1 + d t+1 pd t pd = E [log(pd t )], κ = log(1 + exp(pd)) ρpd andρ = pd t = κ 1 ρ + ρ pd + i=1 ρ i 1 ( d t+i r t+i ) exp(pd) 1 + exp(pd) (Institute) 08 May / 17

11 State Space Model State Equation µ t+1 δ 0 = δ 1 (µ t δ 0 ) + ε µ t+1 g t+1 γ 0 = γ 1 (g t γ 0 ) + ε g t+1 (Institute) 08 May / 17

12 State Space Model State Equation µ t+1 δ 0 = δ 1 (µ t δ 0 ) + ε µ t+1 Measurement Equation g t+1 γ 0 = γ 1 (g t γ 0 ) + ε g t+1 d t+1 = γ 0 + ĝ t + ε d t+1 A = pd t = A B µ t + Bĝ t κ 1 ρ + γ 0 δ 0 1 ρ, B 1 = 1 1 ρδ 1, B 2 = 1 1 ργ 1. (Institute) 08 May / 17

13 General Form of Model State Equation ĝ t+1 = γ 1 ĝ t + ε g t+1 (4) (Institute) 08 May / 17

14 General Form of Model State Equation ĝ t+1 = γ 1 ĝ t + ε g t+1 (4) Measurement Equation d t+1 = γ 0 + ĝ t + ε d t+1 (5) pd t+1 = (1 δ 1 )A B 2 (γ 1 δ 1 )ĝ t + δ 1 pd t B 1 ε µ t+1 + B 2ε g t+1 (6) (Institute) 08 May / 17

15 General Form of Model State Equation ĝ t+1 = γ 1 ĝ t + ε g t+1 (4) Measurement Equation d t+1 = γ 0 + ĝ t + ε d t+1 (5) pd t+1 = (1 δ 1 )A B 2 (γ 1 δ 1 )ĝ t + δ 1 pd t B 1 ε µ t+1 + B 2ε g t+1 (6) Θ = (γ 0, δ 0, γ 1, δ 1, σ g, σ µ, σ D, ρ g µ, ρ gd, ρ µd ) Θ = I 2 0x R 3 +x l 3 c x R 2 I 2 0 ( 1, 1) I 3 c [ 1, 1] (Institute) 08 May / 17

16 Matrix Structure X t = FX t 1 + Rε t Kalman Equations Y t = M 0 + M 1 Y t 1 + M 2 X t η t = Y t M 0 M 1 Y t 1 M 2 X t t 1 S t = M 2 P t t 1 M 2 K t = P t t 1 M 2S t 1 X t t = FX t 1 t 1 + K t η t P t t = (I K t M 2 )(FP t 1 t 1 F + RΣR ) (Institute) 08 May / 17

17 Matrix Structure X t = FX t 1 + Rε t Kalman Equations Log Likelihood: Y t = M 0 + M 1 Y t 1 + M 2 X t η t = Y t M 0 M 1 Y t 1 M 2 X t t 1 S t = M 2 P t t 1 M 2 K t = P t t 1 M 2S t 1 X t t = FX t 1 t 1 + K t η t P t t = (I K t M 2 )(FP t 1 t 1 F + RΣR ) L = T t=1 log(det(s t )) T t=1 η t S t 1 η t (Institute) 08 May / 17

18 Estimation Results: The Estimate and S.E column reports the estimation results and the associated standard error from the net present value model given by equations 4,5 and 6.through optimization of the likelihood function using data between 1900 and 2008 on dividend growth (Institute) 08 May / 17 Optimization Results Parameter Coeffi cient Std error γ δ γ δ σ g σ d σ µ ρ g µ ρ µd Table:

19 Predictive Regressions Univariate Regression r t = β 0 + β 1 µ t 1 + ε t (7) VAR r t = θ 0 + θ 1 PD t 1 + v t (8) Y t = [r t µ t 1 ] Y t = [r t PD t 1 ] Y t = C + p i=1 A i Y t i Measures of Predictive Accuracy - insample and out of sample. (Institute) 08 May / 17

20 Results of insample accuracy Periods β Std error t-ratio R-Squared Periods β Std error t-ratio R-Squared Table: Insample predictability with µ t 1. and pd t 1. (Institute) 08 May / 17

21 Out of Sample Forecast with lagged expected returns Horizon 1 Year 2 Year 3Year 4 Year 5 Year * * * * * ** ** ** ** ** Table: Out of Sample MSE. (µ t 1 )The table reflects the out of sample predictability over the period for different horizon returns from 1 year to 5 years when returns are predicted by the filtered returns series.* represents the period where the mean squared error is highest ** represents the lowest mean squared error. (Institute) 08 May / 17

22 Out of sample forecast using price dividend ratio Horizon 1 Year 2 Year 3Year 4 Year 5 Year * * * * ** ** * ** ** ** Table: Out of Sample MSE. The table reflects the out of sample predictability over the period when returns are predicted by pd t 1. (Institute) 08 May / 17

23 Vector Autoregression P =1 P =2 P =3 R t µ t 1 R t µ t 1 R t µ t 1 C (0.021)* (0.002) (0)** (0.002) (0.018)* (0.036) R t (0.691) (0.977) (0.47) (0.432) (0.48) (0.442) µ t (0.215) (0)** (0.706) (0)** (0.736) (0)** R t (0.026) (0)** (0.049) (0)** µ t (0.203) (0.616) (0.952) (0.334) R t (0.488) (0.046) µ t (0.786) (0.728) Adj R- Squared Akaike Schwartz Table: VAR Results with µ t 1 variable as a predictor variable P refers to the number of lags in the VAR model. ** statistical significance at the 1 % level; * denotes significance at the 5 % level. The figures inside the brackets refer to the p-values (Institute) 08 May / 17

24 Forecasting VAR with PD Table: Results from VAR model with realized and expected dividend growth: Sample P =1 P =2 P =3 R t PD t 1 R t PD t 1 R t PD t 1 C (0.015)** (0)** (0)** (0)** (0.001)** (0)** R t (0.617) (0.17) (0.609) (0.272) (0.464) (0.276) PD t (0.039) (0.027) (0.331) (0) (0.649) (0) R t (0.034) (0) (0.036) (0) PD t (0.105) (0) (0.928) (0.326) R t (0.44) (0.25) PD t (0.903) (0.975) Adj R-Squared Akaike Schwartz Table: VAR Results with pd t 1 variable as a predictor variable P refers to the number of lags in the VAR model. ** statistical significance at the 1 % level; * denotes significance at the 5 % level. The figures inside the brackets refer to the p-values (Institute) 08 May / 17

25 Insample Forecast Accuracy Horizons and VAR order µ t 1 PD t 1 2 Years P = P = P = Years P = P = P = Year P = P = P = Year P = P = P = Table: In Sample R- Squared. The left column illustrates the number of years of accumulated returns with the corresponding VAR order. The two other columns report the goodness of fit R-squared when µ t 1 and PD t 1 are used as predictors. (Institute) 08 May / 17

26 Out of sample forecast ability model :mu(t-1) Period 1 period Return 2 period Return 3 period Return 4 period Return 5 period Return Year P = 1 P = 2 P = 3 P = 1 P = 2 P = 3 P = 1 P = 2 P = 3 P = 1 P = 2 P = 3 P = 1 P = 2 P = ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** Mean Squared Error for out of sample forecasts. The predictor variable is µ t 1. * illustrates the recursive mean squared error which is largest. ** illustrates the mean squared error which is lowest. P relates to the order of the VAR model. (Institute) 08 May / 17

27 Out of Sample Pd(t-1) Period 1 period Return 2 period Return 3 period Return 4 period Return 5 period Return Year P = 1 P = 2 P = 3 P = 1 P = 2 P = 3 P = 1 P = 2 P = 3 P = 1 P = 2 P = 3 P = 1 P = 2 P = ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** Mean Squared Error for out of sample forecasts.in the case where the predictor is pd t 1.* illustrates the recursive mean squared error which is largest. ** illustrates the mean squared error which is lowest. P relates to the order of the VAR model. (Institute) 08 May / 17

28 Conclusion Evidence of Long Run Predictability for both Expected Returns and the Price Dividend Ratio (Institute) 08 May / 17

29 Conclusion Evidence of Long Run Predictability for both Expected Returns and the Price Dividend Ratio Price Dividend Ratio is marginally a better Predictor than Expected returns. (Institute) 08 May / 17

30 Conclusion Evidence of Long Run Predictability for both Expected Returns and the Price Dividend Ratio Price Dividend Ratio is marginally a better Predictor than Expected returns. Both Series are persistent. (Institute) 08 May / 17

31 Conclusion Evidence of Long Run Predictability for both Expected Returns and the Price Dividend Ratio Price Dividend Ratio is marginally a better Predictor than Expected returns. Both Series are persistent. There may be a small amount of information present in Dividend Growth that makes the Price Dividend Ratio a marginally better predictor than expected returns. (Institute) 08 May / 17

32 Conclusion Evidence of Long Run Predictability for both Expected Returns and the Price Dividend Ratio Price Dividend Ratio is marginally a better Predictor than Expected returns. Both Series are persistent. There may be a small amount of information present in Dividend Growth that makes the Price Dividend Ratio a marginally better predictor than expected returns. Behavioural biasses? (Institute) 08 May / 17