Return Predictability: Dividend Price Ratio versus Expected Returns - PowerPoint PPT Presentation

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

Objective Perhaps one of the best predictor of realized returns is Expected Returns (Institute) 08 May 2010 2 / 17

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 2010 2 / 17

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 2010 2 / 17

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 2010 2 / 17

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 2010 2 / 17

Definitions and Identity r t = ln ( P t + 1 + D t + 1 ) (1) P t (Institute) 08 May 2010 3 / 17

Definitions and Identity r t = ln ( P t + 1 + D t + 1 ) (1) P t pd t = P t (2) D t (Institute) 08 May 2010 3 / 17

Definitions and Identity r t = ln ( P t + 1 + D t + 1 ) (1) P t pd t = P t (2) D t ∆ d t + 1 = ln ( D t + 1 ) (3) D t (Institute) 08 May 2010 3 / 17

Definitions and Identity r t = ln ( P t + 1 + D t + 1 ) (1) P t pd t = P t (2) D t ∆ d t + 1 = ln ( D t + 1 ) (3) D t Campbell and Shiller Log-Linearized Identity (form 1,2 and 3): r t + 1 = κ + ρ pd t + 1 + ∆ d t + 1 − pd t exp ( pd ) pd = E [ log ( PD t )] , κ = log ( 1 + exp ( pd )) − ρ pd and ρ = 1 + exp ( pd ) ∞ κ 1 − ρ + ρ ∞ pd ∞ + ρ i − 1 ( ∆ d t + i − r t + i ) ∑ pd t = i = 1 (Institute) 08 May 2010 3 / 17

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 2010 4 / 17

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 Measurement Equation g t + ε d ∆ d t + 1 = γ 0 + � t + 1 pd t = A − B � µ t + B � g t 1 − ρ + γ 0 − δ 0 κ 1 1 A = 1 − ρ , B 1 = , B 2 = . 1 − ρδ 1 1 − ργ 1 (Institute) 08 May 2010 4 / 17

General Form of Model State Equation g t + ε g � g t + 1 = γ 1 � (4) t + 1 (Institute) 08 May 2010 5 / 17

General Form of Model State Equation g t + ε g � g t + 1 = γ 1 � (4) t + 1 Measurement Equation g t + ε d ∆ d t + 1 = γ 0 + � (5) t + 1 g t + δ 1 pd t − B 1 ε µ t + 1 + B 2 ε g pd t + 1 = ( 1 − δ 1 ) A − B 2 ( γ 1 − δ 1 ) � t + 1 (6) (Institute) 08 May 2010 5 / 17

General Form of Model State Equation g t + ε g � g t + 1 = γ 1 � (4) t + 1 Measurement Equation g t + ε d ∆ d t + 1 = γ 0 + � (5) t + 1 g t + δ 1 pd t − B 1 ε µ t + 1 + B 2 ε g pd t + 1 = ( 1 − δ 1 ) A − B 2 ( γ 1 − δ 1 ) � t + 1 (6) Θ = ( γ 0 , δ 0 , γ 1 , δ 1 , σ g , σ µ , σ D , ρ g µ , ρ gD , ρ µ D ) Θ = I 2 0 x R 3 + x l 3 c x R 2 I 2 I 3 0 ∈ ( − 1 , 1 ) c ∈ [ − 1 , 1 ] (Institute) 08 May 2010 5 / 17

Matrix Structure X t = FX t − 1 + R ε t Y t = M 0 + M 1 Y t − 1 + M 2 X t Kalman Equations η t = Y t − M 0 − M 1 Y t − 1 − M 2 X t | t − 1 M 2 P t | t − 1 M � S t = 2 P t | t − 1 M � 2 S − 1 = K t t X t | t = FX t − 1 | t − 1 + K t η t ( I − K t M 2 )( FP t − 1 | t − 1 F � + R Σ R � ) = P t | t (Institute) 08 May 2010 6 / 17

Matrix Structure X t = FX t − 1 + R ε t Y t = M 0 + M 1 Y t − 1 + M 2 X t Kalman Equations η t = Y t − M 0 − M 1 Y t − 1 − M 2 X t | t − 1 M 2 P t | t − 1 M � S t = 2 P t | t − 1 M � 2 S − 1 = K t t X t | t = FX t − 1 | t − 1 + K t η t ( I − K t M 2 )( FP t − 1 | t − 1 F � + R Σ R � ) = P t | t Log Likelihood: T T η � t S − 1 ∑ ∑ L = − log ( det ( S t )) − η t t t = 1 t = 1 (Institute) 08 May 2010 6 / 17

Optimization Results Parameter Coefficient Std error γ 0 0.0138 0.0108 δ 0 0.0524 0.016 γ 1 0.0717 0.1996 δ 1 0.9459 0.0401 σ g 0.0926 0.058 σ d 0.0139 0.0064 σ µ 0.0688 0.0772 ρ g µ 0.4802 0.4706 ρ µ D -0.3815 1.3919 Table: 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) rates and the corresponding price-dividend ratios. 08 May 2010 7 / 17

Predictive Regressions Univariate Regression r t = β 0 + β 1 µ t − 1 + ε t (7) r t = θ 0 + θ 1 PD t − 1 + v t (8) VAR p ∑ Y t = C + A i Y t − i i = 1 Y t = [ r t µ t − 1 ] � Y t = [ r t PD t − 1 ] � Measures of Predictive Accuracy - insample and out of sample. (Institute) 08 May 2010 8 / 17

Results of insample accuracy Periods β Std error t-ratio R-Squared 1 0.981 0.457 2.146 0.040 2 1.46 0.645 2.263 0.042 3 2.102 0.760 2.765 0.063 4 2.844 0.880 3.23 0.084 5 3.399 0.961 3.536 0.096 Periods β Std error t-ratio R-Squared 1 -0.088 0.042 -2.103 0.038 2 -0.134 0.059 -2.264 0.042 3 -0.196 0.069 -2.8 0.064 4 -0.262 0.081 -3.242 0.084 5 -0.311 0.088 -3.532 0.094 Table: Insample predictability with µ t − 1 . and pd t − 1 . (Institute) 08 May 2010 9 / 17

Out of Sample Forecast with lagged expected returns Horizon 1 Year 2 Year 3Year 4 Year 5 Year 1 0.0098 0.1791* 0.0472* 0.0012 0.00464 2 0.0222* 0.0657 0.0096 0.0027 0.03765 3 0.0006 0.0083 0.0007 0.0355* 0.09522* 4 0.00004** 0.0029 0.0037 0.0382 0.02861 5 0.0055 0.0052 0.0174 0.0038 0.07713 6 0.0010 0.00009** 0.0002** 0.0001** 0.00001** 7 0.0010 0.0071 0.0080 0.0043 0.00475 8 0.0010 0.02050 0.0221 0.0153 0.01522 Table: Out of Sample MSE. ( µ t − 1 ) The table reflects the out of sample predictability over the period 2001-2008 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 2010 10 / 17

Out of sample forecast using price dividend ratio Horizon 1 Year 2 Year 3Year 4 Year 5 Year 1 0.05945 0.24030* 0.04674* 0.00144 0.00331 2 0.08510* 0.10404 0.00959 0.00221 0.03303 3 0.02627 0.02403 0.00071 0.03323 0.08657 4 0.01417 0.01265 0.00352 0.03557* 0.02383 5 0.00046** 0.00074** 0.01641 0.00521 0.08753* 6 0.00691 0.00405 0.00022** 0.00001** 0.00014** 7 0.00639 0.01874 0.00826 0.00518 0.00677 8 0.01998 0.03771 0.02250 0.01678 0.01858 Table: Out of Sample MSE. The table reflects the out of sample predictability over the period 2001-2008 when returns are predicted by pd t − 1 . (Institute) 08 May 2010 11 / 17

Vector Autoregression P =1 P =2 P =3 R t µ t − 1 R t µ t − 1 R t µ t − 1 C 0.056 0.05959 0.0552 0.05994 0.04527 0.051 (0.021)* (0.002) (0)** (0.002) (0.018)* (0.036) R t − 1 0.042 0.00027 0.07501 0.00401 0.075 0.003 (0.691) (0.977) (0.47) (0.432) (0.48) (0.442) µ t − 1 0.594 0.92012 -0.36116 0.942 0.513 1.079 (0.215) (0)** (0.706) (0)** (0.736) (0)** R t − 2 -0.23105 -0.06505 -0.226 -0.0639 (0.026) (0)** (0.049) (0)** µ t − 2 1.30222 0.03875 0.127 -0.112 (0.203) (0.616) (0.952) (0.334) R t − 3 0.109 0.0199 (0.488) (0.046) µ t − 3 0.356 0.026 (0.786) (0.728) Adj R- Squared 0.0179 0.8398 0.0788 0.9355 0.0859 0.9503 Akaike 422.47 472.473 477.63 Schwartz 430.54 459.062 458.92 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 2010 12 / 17