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

rt=ln(Pt+1+Dt+1 Pt ) (1)

(Institute) 08 May 2010 3 / 17

Definitions and Identity

rt=ln(Pt+1+Dt+1 Pt ) (1) pdt= Pt Dt (2)

(Institute) 08 May 2010 3 / 17

Definitions and Identity

rt=ln(Pt+1+Dt+1 Pt ) (1) pdt= Pt Dt (2) ∆dt+1= ln(Dt+1 Dt ) (3)

(Institute) 08 May 2010 3 / 17

Definitions and Identity

rt=ln(Pt+1+Dt+1 Pt ) (1) pdt= Pt Dt (2) ∆dt+1= ln(Dt+1 Dt ) (3) Campbell and Shiller Log-Linearized Identity (form 1,2 and 3): rt+1 = κ + ρpdt+1 + ∆dt+1 − pdt pd = E[log(PDt)], κ = log(1+ exp(pd)) − ρpd andρ = exp(pd) 1 + exp(pd) pdt = κ 1 − ρ + ρ∞pd∞ +

∞

∑

i=1

ρi−1(∆dt+i − rt+i)

(Institute) 08 May 2010 3 / 17

State Space Model

State Equation µt+1 − δ0 = δ1(µt − δ0) + εµ

t+1

gt+1 − γ0 = γ1(gt − γ0) + εg

t+1

(Institute) 08 May 2010 4 / 17

State Space Model

State Equation µt+1 − δ0 = δ1(µt − δ0) + εµ

t+1

gt+1 − γ0 = γ1(gt − γ0) + εg

t+1

Measurement Equation ∆dt+1 = γ0 + gt + εd

t+1

pdt = A − B µt + B gt A = κ 1 − ρ + γ0 − δ0 1 − ρ , B1 = 1 1 − ρδ1 , B2 = 1 1 − ργ1 .

(Institute) 08 May 2010 4 / 17

General Form of Model

State Equation

• gt+1 = γ1

gt + εg

t+1

(4)

(Institute) 08 May 2010 5 / 17

General Form of Model

State Equation

• gt+1 = γ1

gt + εg

t+1

(4) Measurement Equation ∆dt+1 = γ0 + gt + εd

t+1

(5) pdt+1 = (1 − δ1)A − B2(γ1 − δ1) gt + δ1pdt − B1εµ

t+1 + B2εg t+1 (6)

(Institute) 08 May 2010 5 / 17

General Form of Model

State Equation

• gt+1 = γ1

gt + εg

t+1

(4) Measurement Equation ∆dt+1 = γ0 + gt + εd

t+1

(5) pdt+1 = (1 − δ1)A − B2(γ1 − δ1) gt + δ1pdt − B1εµ

t+1 + B2εg t+1 (6)

Θ = (γ0, δ0, γ1, δ1, σg, σµ, σD, ρg µ, ρgD, ρµD) Θ = I2

0x R3 +x l3 cx R2

I 2

0 ∈ (−1, 1)

I 3

c ∈ [−1, 1]

(Institute) 08 May 2010 5 / 17

Matrix Structure

Xt = FXt−1 + Rεt Yt = M0 + M1Yt−1 + M2Xt Kalman Equations ηt = Yt − M0 − M1Yt−1 − M2Xt|t−1 St = M2Pt|t−1M

2

Kt = Pt|t−1M

2S−1 t

Xt|t = FXt−1|t−1 + Ktηt Pt|t = (I − KtM2)(FPt−1|t−1F + RΣR)

(Institute) 08 May 2010 6 / 17

Matrix Structure

Xt = FXt−1 + Rεt Yt = M0 + M1Yt−1 + M2Xt Kalman Equations ηt = Yt − M0 − M1Yt−1 − M2Xt|t−1 St = M2Pt|t−1M

2

Kt = Pt|t−1M

2S−1 t

Xt|t = FXt−1|t−1 + Ktηt Pt|t = (I − KtM2)(FPt−1|t−1F + RΣR) Log Likelihood: L = −

T

∑

t=1

log(det(St)) −

T

∑

t=1

η

tS−1 t

ηt

(Institute) 08 May 2010 6 / 17

Optimization Results

Parameter Coefficient Std error γ0 0.0138 0.0108 δ0 0.0524 0.016 γ1 0.0717 0.1996 δ1 0.9459 0.0401 σg 0.0926 0.058 σd 0.0139 0.0064 σµ 0.0688 0.0772 ρg µ 0.4802 0.4706 ρµD

• 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 rates and the corresponding price-dividend ratios.

(Institute) 08 May 2010 7 / 17

Predictive Regressions

Univariate Regression rt = β0 + β1µt−1 + εt (7) rt = θ0 + θ1PDt−1 + vt (8) VAR Yt = C +

p

∑

i=1

AiYt−i Yt = [rt µt−1] Yt = [rt PDt−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 µt−1. and pdt−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. (µt−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

• ver the period 2001-2008 when returns are predicted by pdt−1.

(Institute) 08 May 2010 11 / 17

Vector Autoregression

P =1 P =2 P =3 Rt µt−1 Rt µt−1 Rt µt−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) Rt−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) µt−1 0.594 0.92012

• 0.36116

0.942 0.513 1.079 (0.215) (0)** (0.706) (0)** (0.736) (0)** Rt−2

• 0.23105
• 0.06505
• 0.226
• 0.0639

(0.026) (0)** (0.049) (0)** µt−2 1.30222 0.03875 0.127

• 0.112

(0.203) (0.616) (0.952) (0.334) Rt−3 0.109 0.0199 (0.488) (0.046) µt−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 µt−1variable 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

Forecasting VAR with PD

Table: Results from VAR model with realized and expected dividend growth: Sample 1900-2008

P =1 P =2 P =3 Rt PDt−1 Rt PDt−1 Rt PDt−1 C 0.0517 3.217 0.0497 3.23576 0.04848 3.239 (0.015)** (0)** (0)** (0)** (0.001)** (0)** Rt−1 0.05274

• 0.276

0.0543

• 0.054

0.07822

• 0.0522

(0.617) (0.17) (0.609) (0.272) (0.464) (0.276) PDt−1 0.05966 0.551

• 0.0439

0.898

• 0.0785

1.1080 (0.039) (0.027) (0.331) (0) (0.649) (0) Rt−2

• 0.219

0.7024

• 0.2337

0.70758 (0.034) (0) (0.036) (0) PDt−2 0.0418 0.0977

• 0.015
• 0.121

(0.105) (0) (0.928) (0.326) Rt−3 0.1334

• 0.1499

(0.44) (0.25) PDt−3 0.00379 0.0008 (0.903) (0.975) Adj R-Squared 0.0299 0.4861 0.0764 0.9518 0.086 0.9546 Akaike 106.257 230.792 227.592 Schwartz 98.1831 217.381 208.882

Table:

VAR Results with pdt−1variable 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 13 / 17

Insample Forecast Accuracy

Horizons and VAR order µt−1 PDt−1 2 Years P = 1 0.220 0.234 P = 2 0.363 0.354 P = 3 0.420 0.443 3 Years P = 1 0.492 0.494 P = 2 0.601 0.599 P = 3 0.616 0.617 4 Year P = 1 0.551 0.548 P = 2 0.588 0.585 P = 3 0.602 0.606 5 Year P = 1 0.608 0.617 P =2 0.653 0.639 P = 3 0.653 0.651

Table:

In Sample R- Squared. The left column illustrates the number of years of accumulated returns with the corresponding VAR

• rder. The two other columns report the goodness of fit R-squared when µt−1and PDt−1are used as predictors.

(Institute) 08 May 2010 14 / 17

Out of sample forecast ability model :mu(t-1)

Period 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 = 3 1 0.0396 0.0233 0.0210 0.1231 0.0587 0.0555 0.0093 0.0522 0.0500 0.0031** 0.0016 0.0051 0.0021** 0.0005** 0.0024 2 0.0851 0.0718 0.0618 0.0030 0.0162 0.0368 0.0246 0.0096 0.0094 0.0118 0.0100 0.0048 0.0142 0.0473 0.0584 3 0.0211 0.0328 0.0482 0.0630 0.0612 0.0637 0.0726 0.0837 0.0406 0.1139 0.1309 0.1258 0.0339 0.1041 0.1172 4 0.0011 0.0007** 0.0071** 0.0026 0.0005** 0.0075 0.0000** 0.0029 0.0009** 0.0085 0.0057** 0.0020 0.4810 0.2757 0.2598 5 0.0008** 0.0067 0.0156 0.0009 0.0664 0.0511 0.0009 0.0235 0.0051 0.3164 0.1974 0.1703 0.0637 0.0068 0.0077** 6 0.0034 0.0104 0.0181 0.0002** 0.0101 0.0013** 0.2478 0.1517 0.2221 0.0288 0.0024 0.0000** 0.0460 0.0156 0.0272 7 0.0015 0.0000 0.0002 0.3435 0.2139 0.2481 0.0678 0.0005** 0.0030 0.0687 0.0578 0.0246 0.0913 0.0348 0.0321 8 0.2975 0.2314 0.2128 0.1232 0.0193 0.0107 0.0427 0.0242 0.0233 0.0411 0.0299 0.0267 0.0540 0.0123 0.0103 2 period Return 1 period Return 3 period Return 4 period Return 5 period Return

Mean Squared Error for out of sample forecasts. The predictor variable is µt−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 2010 15 / 17

Out of Sample Pd(t-1)

Period 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 = 3 1 0.0264 0.0195 0.0189 0.0833 0.0506 0.0505 0.0120 0.0521 0.0456 0.0010** 0.0034 0.0060 0.0050** 0.0033 0.0041** 2 0.0629 0.0693 0.0583 0.0154 0.0136 0.0406 0.0297 0.0039 0.0087 0.0063 0.0121 0.0044 0.0635 0.0495 0.0631 3 0.0342 0.0283 0.0479 0.1016 0.0389 0.0464 0.0811 0.0442 0.0505 0.0953 0.1264 0.1359 0.1003 0.0792 0.1198 4 0.0045 0.0009 0.0051 0.0001** 0.0019 0.0012 0.0003** 0.0021 0.0012** 0.0142 0.0084 0.0003 0.3276 0.3513 0.2604 5 0.0000 0.0023 0.0109 0.0055 0.0272 0.0198 0.0004 0.0010** 0.0224 0.3386 0.2252 0.1489 0.0296 0.0022** 0.0049 6 0.0073 0.0108 0.0113 0.0038 0.0081** 0.0002** 0.2375 0.1778 0.1436 0.0357 0.0020** 0.0000** 0.0161 0.0168 0.0281 7 0.0001** 0.0000** 0.0001** 0.2897 0.2499 0.2709 0.0625 0.0057 0.0025 0.0784 0.0616 0.0185 0.0475 0.0526 0.0359 8 0.2711 0.2428 0.2236 0.0955 0.0326 0.0168 0.0391 0.0456 0.0112 0.0477 0.0328 0.0233 0.0249 0.0247 0.0105 1 period Return 2 period Return 3 period Return 4 period Return 5 period Return

Mean Squared Error for out of sample forecasts .In the case where the predictor is pdt−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 2010 16 / 17

Conclusion

Evidence of Long Run Predictability for both Expected Returns and the Price Dividend Ratio

(Institute) 08 May 2010 17 / 17

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 2010 17 / 17

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 2010 17 / 17

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 2010 17 / 17

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 2010 17 / 17