V. Harshitha Moulya Research Scholar Department of Business Administration Mangalore University Mangalore 
Dr T. Mallikarjunappa Professor Department of Business Administration Mangalore University Mangalore 
The excess market return earned by investors over the riskfree rate is termed as equity premium. Mehra and Prescott (1985) found a very high equity premium of 6% for the US market, which was very puzzling for various reasons. Several theories have guided the curiosity of this puzzle attributable to the consumption behaviour pattern and habits formation of individual investors. We used aggregate ratios of firms’ dividends and earnings as a proxy for investors’ consumption behaviour to estimate the equity premium for a crosssectional portfolio of firms using insample and outsample data. We found that, though, the dividendprice and earningsprice ratios acted as best insample predictors of excess equity returns. The estimated riskpremium varied across the crosssection of firms.
Keywords: Equity Premium, Excess RiskPremium, DividendPrice, EarningsPrice, EarningsYield, DividendYield, Firm Size, BM ratio.
The rational expectation framework proposed that the riskaverse representative agents in the general equilibrium always tried to maximise their expected value of the discounted stream of cashflows generated through an expected utility model (Lucas, 1978). It iscriticised as it failed to account for the large return differentials in the expected stock returns over the riskfree rate in the US market documented by Mehra and Prescott (1985). They estimated a large equity premium of 6.18% and the riskfree rate of 0.8% visàvis the historically observed premium of 0.35% for the US market, which was termed as the equity premium puzzle.The rationalists attributed the large equity premium to macroeconomic factors viz., the deferred consumption by riskaverse investors (John Y. Campbell & Cochrane, 1999; Weil, 1989) whereas the behaviourists proposed that the behaviour of individual investors viz., theexternal habit formation (Constantinides, 1990), and the behaviour of representative agent according to the prospect theory (Benartzi & Thaler, 1995) caused anomalous equity premium. Studies by(Campbell & Cochrane, 2000; Fama & French, 1988; Welch & Goyal, 2008) used the aggregate dividends and earnings of firms as a proxy for market consumption to estimate equity premium. In our study, we used aggregate dividends ratios and earnings ratios viz., dividendprice ratio, dividendyield ratio, earningsprice ratio and earningsyield ratio, for estimating the excess equity returns for the Indian market using the data of the NSE listed firms. The study is different in three things, viz.,  1) we used the bestfit linear model for estimation of equity returns and adjusted for the nonlinearity using a bestfit conditionalvariance model, 2) portfoliobased estimation of excess equity returns, and 3) we used insample and outsample estimations for the robustness of estimation models. We found that the estimated excess risk premium varied across the crosssection of firms. Both the dividendprice and earningsprice ratios estimated the insample equity premium; the outsample estimations were not better failing to prove the robustness of the estimation models. This paper is structured to discuss the literature review, theoretical framework for the selection of variables and hypothesised relationship between variables in section 2; data and methodology in section 3; discussion of results in section 4; and findings and conclusion in section 5.
The equity premium is the extra risk premium earned by investors by making an investment in a portfolio of risky securities over risk free securities. Mehra and Prescott (1985) found a large equity premium of 68% visàvis the historically observed equity premium of 0.35% for the US market, which was puzzling. A few studies tried to explain the equity premium puzzle by proposing new theories. The rationalist theory of Weil (1989)attributed the substantial equity premium to the deferred consumption behaviour of riskaverse investors attempting to generate higher per capita consumption growth rate over the rate offered by the riskfree Treasury bills. He suggested the equity premium puzzle transformed into the riskfree rate puzzle as the riskaverse investors under Lucas (1978) framework deferred their consumption by saving more even when the riskfree rate of returns offered was meagre. Campbell and Cochrane (1999) caused anomalous equity premium. Studies by (Campbell & Cochrane, 2000; Fama & French, 1988; Welch & Goyal, 2008) used the aggregate explained that the equity premium puzzle through a consumptionbased model where the aggregate consumption behaviour of representative agents perfectly correlated with the business cycle. The procyclical consumption declined towards the habit during the business trough, and the countercyclical equity premium puzzle increased due to the crosssectional variations in the wealth distribution of the heterogeneous representative agents. The behaviourist theory of Constantinides (1990) explained the equity premium puzzle and the riskfree rate puzzle through the model of ‘habitformation’ of the representative agents, where riskaverse agents didn’t consider the effect the current consumption on future preferences, but their utility depended on the levels of past consumption. The model failed to explain the consumption behaviour of wealthy investors, pension funds and endowments at the aggregate market level (Benartzi & Thaler, 1995). The duo proposed that investors behaved according to the prospect theory (Kahneman & Tversky, 1979), where, the riskaverse investors demanded a higher premium for assuming a higher variability in the securities returns due to their high sensitivity to losses. Thus, the highly riskaverse investors demand higher riskpremium as compensation for undertaking investments in the highlyrisky securities.
Mehra and Prescott (1985) used the real S&P index return and the estimated realinterest rate for the estimation of the equity premium. The security risk used in the estimation model was measured as a covariance of security returns with the per capita consumption, aproxy for consumption stream of investors under the rational utility framework. Welch (2000) surveyed finance professionals regarding estimation of the equity premium and found that there was neither a proper explanation for high values of equity premium nor any consensus on how to forecast equity premium. Thus there is an overlap of techniques used for estimation of expected stock returns and the excess equity returns, i.e. the equity premium. The seminal literature on the estimation of stock returns viz., the Capital Asset Pricing Model (CAPM) (Black, 1972; Lintner, 1965; Sharpe, 1964)established a linear relationship between the expected returns on securities and the market risk, where, the market risk is measured by beta in the general equilibrium model. The CAPM proposed that beta alone explained the expected stock returns given that markets are efficient. If the efficient markets hypothesis were to hold, the stocks were to be priced rationally, then the systemic differences in stock returns are attributed to the differences in risk. The market capitalisation of firm (Banz, 1981), the earningsprice (EP) ratio (Basu, 1983; Chan, Hamao, & Lakonishok, 1991) and the book equity to market equity (BM) ratio (Chan, Jegadeesh, & Lakonishok, 1995; Fama & French, 1992, 1993, 1996, 2006, 2012) along with the market beta significantly contributed for explaining the crosssectional variation of expected stock returns. Campbell and Cochrane(2000) used the consumptionbased model (Campbell & Cochrane, 1999) and the CAPM (Black, 1972; Lintner, 1965; Sharpe, 1964) to explain the timevarying expected returns using the dividendprice ratio as a proxy for market consumption. They found that, though, both the models estimated conditional asset returns, however, the portfoliobased models better approximated the unconditional asset returns. Campbell and Cochrane (1999, 2000) observed that changes in dividend explained more than half of the variation in stock returns and, variations in the aggregate dividendprice ratio is due to variations in aggregated expected excess returns. Berk (1995) found a strong correlation between expected stock return and dividendyield, along with other nonsystemic firm variables, failed the CAPM to account for crosssectional differences in expected stock returns. Fama and French (2002) suggested that any variable that is cointegrated with stock price can be used to estimate expected stock return, but the ratios should be meanreverting and stationary. They observed multicollinearity between the dividendprice ratio and earningsprice ratio. Their study found that estimation of expected returns using the firm’s fundamentals outperformed any other estimation on the ground of lower standard error and Sharpe ratio. Dimson, Marsh, and Staunton (2008)decomposed the equity risk premium into three components viz., the level of dividends, the growth in dividends and the effects of stock prices on dividendprice ratio. Fama and French(1988) used dividend yields for the estimation of expected stock returns. Fama and French(2002), Welch and Goyal(2008) used aggregate earnings and dividends ratios (dividendprice, dividendyield, earningsprice, and earningsyield ratios) for estimation of excess riskpremium; the theoretical arguments on asset pricing proposed that an average estimated stock return is the sum of the average dividend yield and the average rate of capital gain. These studies have predominantly used linear estimation technique for the expected equity premium. The dividendyield ratio and the dividendprice ratio were found to be the dominant predictors of future returns using artificial neural networks (Wong, Hassan, & Feroz, 2007; Welch & Goyal, 2008). Welch and Goyal(2008) accounted for the nonlinearity in the predictor variables viz., dividends ratios. Claus and Thomas (2001) and Gebhardt, Hvidkjaer, and Swaminathan (2005)used valuation models involving dividends and earnings ratios to estimate unconditional expected returns. Siegel (1992) and Siegel and Thaler (1997) acknowledged that the standard asset pricing models could not explain the higher equity premium. Damodaran (2009, 2012) noted that the variation in expected equity premium visàvis the actual historical equity premium of about 3% to 12% is due to the choice of different estimation periods, differences in riskfree rates and market indices, and differences in the way returns are averaged over time. The literature analysis identifies that there is an overlap of estimation techniques used for expected stock returns, and equity premium, and no proper consensus on the estimation technique for equity premium. Previous studies have predominantly used linear estimation techniques and valuation models for estimation of conditional and unconditional expected returns. It is found that dividends ratios acted as powerful predictors of expected stock returns. However, the timedependent, nonlinear and nonstationary dividends ratios contradict the proposition of stationary and meanreverting predictor variables resulting in sparse estimation. Thus there is a strong need for studies to explore robust estimation techniques for equity premium. In our study, we perform a linear estimation of equity premium after adjusting for the timedependent characteristics of the predictor variables by using the bestfit conditional and unconditional estimation models. We test for the robustness of the models by testing their outsample performance. We use the portfoliobased estimation of equity premium for crosssectional portfolios formed based on EP ratio, Firm size and the BM ratio rather than using firmlevel data.
We have used the monthly data of NSE listed firms, i.e. NSE 500 firms in the study. The period considered in the study is between 2004 and 2015. We formed different crosssectional portfolios for the estimation of the equity premium.
The NSE 500 firms have been categorised into different crosssectional portfolios, sorted based on EP ratio, BM ratio and the market capitalisation of the firms. The annual averages of the ratios were cumulated and ranked in descending order. The top 10 percent and the bottom 10 percent of firms under each category are considered for the analysis. Thus, we have considered six portfolios of 50 stocks each viz., EP High (top 10% EP firms), EP Low (Bottom 50 EP firms), Growth firms (top 10% BM firms), Value firms (Bottom 50 BM firms), MK High (top 50 market cap firms), and MK Low (bottom 10% market cap firms).
We collected the monthly closing prices of NSE 500 stocks, their EP ratio, market capitalisation and the BM ratio from the CMIE Prowess database. The CCIL 90 days Treasurybill index is used as a proxy for the riskfree rate. The Tbill index data is downloaded from the CCIL website, the sister website of the NSE. The variables used for regression are explained in Table 1.
Notation 
Formula 
Description 

Variables 

Where = stock price of an ith stock at the time ‘t’, N = No. of stocks in the portfolio 
Equalweighted portfolio price at time ‘t.’ 

(1) 
Lag price of the equalweighted portfolio at time ‘t’ 

_{ } 
Where = dividends of the ith stock at the time ‘t’; 
Aggregate dividends of all the stock in the portfolio at time ‘t’ 

_{ } 
Where = earnings per share of the ith stock at the time ‘t’; 
Aggregate earnings of all the stocks in the portfolio at time ‘t’ 

Where, r_{t} = riskfree rate of riskfree portfolio at time ‘t’ 
Riskfree return at time ‘t’ of the portfolio of riskfree treasury bills 

(1) 
The riskfree rate at time ‘t1’ ofthe portfolio of riskfree treasury bills 

_{ } 
Where p_{it} = price of the ith stock at time t; n = no. of outstanding stocks of the ith stock; 
The market capitalisation of the equalweighted portfolio at time ‘t’ 

Dependent Variable 

The equity premium is the difference between the return onthe portfolio of risky securities (capital gain + dividends) over the portfolio of riskfree treasury bills. 

Predictor Variables 

Dividendprice is the ratio of an aggregate dividend of the portfolio to a total market capitalisation of the portfolio at time ‘t’ 

Dividendyield is measured as the ratio of an aggregate dividend of the portfolio at the time ‘t’ to the total market capitalisation of the portfolio at the time ‘t1’ 

Earningsprice is the ratio of aggregate earnings of the portfolio to the total market capitalisation of the portfolio at the time ‘t’ 

Earningsyield is measured as the ratio of aggregate earnings of the portfolio at the time ‘t’ to the total market capitalisation of the portfolio at time ‘t1’

We have used Wong, Hassan, and Feroz (2007) and Welch and Goyal (2008)method for the estimation of equity premium using the dividends ratios and earnings ratios as predictor variables. We carried out both the insample and outsample estimations for the robustness of the model by dividing the dataset two viz., the insample (70%, i.e. 2004 to 2013 data) and outofsample data (30%, i.e. 2013 – 2015 data). We used OLS multiple regression techniques for mean estimation and the ARMAGARCH estimation for conditional meanvariance estimations, for taking care of serial correlation and heteroscedasticity problems in the residuals. The base model is represented mathematically in (1). The ARMA (P, Q) GARCH (p,q) representations are given in (2) and (3).
In the insample estimation, we have done the conditional mean forecasting of equity premium using the multiple OLS regression with bestfit ARMAGARCH model for adjusting for the nonlinearity in residuals viz., serial correlation and the heteroscedasticity problems. The OLS regression estimates provide the degree of the linear relationship of the equity premium with the predictor variables. The estimates are unbiased if the residuals of the model satisfy the properties of CLRM (Classical Linear Regression Model), i.e. BLUE (Best Linear Unbiased Estimators). The presence of significant autocorrelation and heteroscedasticity in the residuals violate the assumption of i.i.d. (identical independent distribution). We also checked the series for nonstationarity and multicollinearity issues. The nonstationary series produce spurious regression estimates. In order to test for the nonstationarity of the dependent and independent variables, we used the unit root tests (eviews version 8) viz., the ADF (Augmented DickeyFuller) test and the PP (PhilipPeron Fisher Chisquare) tests, for testing the null hypothesis that the series has a unit root (nonstationary). The null hypothesis is rejected at 5% level of significance if the ADF and PP statistics are higher than the respective critical values. We performed the VIF test (Variance Inflation Factor) for testing the multicollinearity of the predictor variables in the general estimation model (1) across each portfolio. If VIF > 10, then there is no multicollinearity among independent variables. We took EQPM as the dependent variable, and the computed EP, EY, DP and DY ratios are taken as independent variables for carrying out the OLS multipleregression. The residual diagnostics tests of the residuals of the OLS regression showed autocorrelation and heteroscedasticity problems. We fitted the bestfit ARMAGARCH model, which was selected based on the SIC (Schwarz Information Criteria) for the conditional meanvariance estimation of the equity premium.
The outofsample forecasting is done using the nstep ahead conditional forecasting of the equity premium using the insample estimates. The robustness of the bestfit insample model is ascertained by computing RMSE (Root Mean Squared Error), MAE (Mean Absolute Error) and MAPE (Mean Absolute Percentage Error) values for both insample and outsample data. The RMSE, MAE and MAPE predict the forecast accuracy of the estimation model. They are computed using (4), (5) and (6).
The forecast accuracy measures for both insample and outsample data are compared for robustness. A robust estimation model should produce accurate estimates for the outsample data
Table 2 provides the summary statistics of the variables for crosssectional portfolios. The aggregate earnings and dividends ratios viz., EP, EY, DP and EY for all the portfolios are found to be nonnormally distributed (skewness ≠ 0 and kurtosis ≠ 3). The estimated average equity premium is ranging from 0.7% – 0.8% for the portfolios. The estimated average equity premium is more for BM Low (0.81%) and MK Low (0.80%) and less for BM High (0.71%) and MK High (0.71%) portfolios, implying higher riskpremium for small size (MK Low) and value portfolios (BM Low). The findings support the size effect and value effect (Banz, 1981; Basu, 1983; Chan, Hamao, & Lakonishok, 1991; Chan, Jegadeesh, & Lakonishok, 1995; Fama & French, 1992, 1993, 1996, 2006, 2012)
Portfolio 
Mean 
Median 
Std. Dev 
Variance 
Max 
Min 
Kurtosis 
Skewness 
Count 
BM High 

EQPM 
0.7176 
0.7614 
0.2520 
0.0635 
1.1841 
0.0000 
0.7712 
0.4032 
125 
EP 
0.1112 
0.1203 
0.0495 
0.0025 
0.2685 
0.0335 
0.0348 
0.4302 
125 
EY 
0.1103 
0.1193 
0.0499 
0.0025 
0.2579 
0.0000 
0.0566 
0.3181 
125 
DP 
0.0315 
0.0282 
0.0223 
0.0005 
0.0867 
0.0000 
0.9551 
0.3972 
125 
DY 
0.0314 
0.0279 
0.0225 
0.0005 
0.0867 
0.0000 
0.9707 
0.4069 
125 
BM Low 

EQPM 
0.8140 
0.8566 
0.1843 
0.0340 
1.1660 
0.0000 
1.6972 
0.7869 
125 
EP 
0.2400 
0.2337 
0.0769 
0.0059 
0.4538 
0.0986 
0.4561 
0.6612 
125 
EY 
0.2391 
0.2328 
0.0780 
0.0061 
0.4538 
0.0000 
0.6339 
0.4022 
125 
DP 
0.0358 
0.0180 
0.0330 
0.0011 
0.1319 
0.0001 
0.1212 
1.1940 
125 
DY 
0.0352 
0.0184 
0.0328 
0.0011 
0.1320 
0.0000 
0.3794 
1.2863 
125 
EP High 

EQPM 
0.7321 
0.7750 
0.2047 
0.0419 
1.1337 
0.0000 
0.1610 
0.4093 
125 
EP 
0.0741 
0.0707 
0.0303 
0.0009 
0.1850 
0.0205 
2.0352 
1.2518 
125 
EY 
0.0737 
0.0684 
0.0308 
0.0010 
0.1828 
0.0000 
1.9682 
1.1199 
125 
DP 
0.0213 
0.0229 
0.0111 
0.0001 
0.0469 
0.0009 
1.1079 
0.1201 
125 
DY 
0.0213 
0.0226 
0.0112 
0.0001 
0.0454 
0.0000 
1.1256 
0.1154 
125 
EP Low 

EQPM 
0.7927 
0.8661 
0.2246 
0.0504 
1.1542 
0.0000 
0.1112 
0.7065 
125 
EP 
0.1492 
0.1566 
0.0924 
0.0085 
0.4976 
0.0255 
1.4396 
0.8249 
125 
EY 
0.1497 
0.1560 
0.0936 
0.0088 
0.4724 
0.0000 
0.3419 
0.6390 
125 
DP 
0.0296 
0.0147 
0.0363 
0.0013 
0.1440 
0.0001 
2.2605 
1.8538 
125 
DY 
0.0294 
0.0148 
0.0367 
0.0013 
0.1505 
0.0000 
2.6869 
1.9485 
125 
MK High 

EQPM 
0.7178 
0.7627 
0.1749 
0.0306 
1.0441 
0.0000 
0.9063 
0.6048 
125 
EP 
0.1746 
0.1552 
0.0640 
0.0041 
0.3752 
0.0725 
0.5154 
0.9683 
125 
EY 
0.1739 
0.1583 
0.0650 
0.0042 
0.3410 
0.0000 
0.1770 
0.7329 
125 
DP 
0.0199 
0.0123 
0.0146 
0.0002 
0.0708 
0.0020 
1.7769 
1.4060 
125 
DY 
0.0197 
0.0129 
0.0144 
0.0002 
0.0705 
0.0000 
1.7834 
1.4021 
125 
MK Low 

EQPM 
0.8003 
0.8481 
0.2824 
0.0798 
1.2852 
0.0000 
0.8257 
0.3260 
125 
EP 
0.1053 
0.1075 
0.0681 
0.0046 
0.2526 
0.0083 
1.0650 
0.2991 
125 
EY 
0.1052 
0.0979 
0.0693 
0.0048 
0.2530 
0.0000 
1.0563 
0.3059 
125 
DP 
0.0597 
0.0287 
0.0672 
0.0045 
0.2746 
0.0000 
1.1758 
1.5231 
125 
DY 
0.0599 
0.0294 
0.0685 
0.0047 
0.2891 
0.0000 
1.5910 
1.6081 
125 
Table 3 provides the results for the stationarity of the insample data. It is observed that the pvalues of the ADF test and the PPFisher test are significant at 5% level of significance, i.e. p<< 0.05, the nullhypothesis of unitroot (nonstationary) is rejected. Therefore, the series is stationary at level.





Method 
Statistic 
Prob.** 
Crosssections 
Observations 
Null: Unit root (assumes common unit root process) 

Levin, Lin & Chu t* 
0.40258 
0.6564 
30 
2916 
Null: Unit root (assumes individual unit root process) 

Im, Pesaran and Shin Wstat 
1.79004 
0.0367 
30 
2916 
ADF  Fisher Chisquare 
85.7878 
0.0161 
30 
2916 
PP  Fisher Chisquare 
156.913 
0.0000 
30 
2940 





Table 4 describes the results for multicollinearity of the predictor variables. It is observed that the VIF >> 10 for all the variables of the estimation model for all the portfolio. Therefore, there is no problem with multicollinearity among predictor variables.
OLS Model/Portfolio 
Variables 
VIF 
BM High 
EP_BMHIGH 
60.20005 
EY_BMHIGH 
57.73873 

DP_BMHIGH 
102.9117 

DY_BMHIGH 
103.3876 

BM Low 
DP_BMLOW 
65.50051 
DY_BMLOW 
66.38482 

EP_BMLOW 
53.64268 

EY_BMLOW 
50.38351 

EP High 
DP_EPHIGH 
93.5656 
DY_EPHIGH 
93.44293 

EP_EPHIGH 
71.22695 

EY_EPHIGH 
67.53738 

EP Low 
DP_EPLOW 
89.83399 
DY_EPLOW 
88.97493 

EP_EPLOW 
88.21873 

EY_EPLOW 
83.54424 

MK High 
DP_MKHIGH 
102.3738 
DY_MKHIGH 
104.9051 

EP_MKHIGH 
45.94443 

EY_MKHIGH 
45.95151 

MK Low 
DP_MKLOW 
17.96127 
DY_MKLOW 
16.95436 

EP_MKLOW 
98.53914 

EY_MKLOW 
95.96268 
Table 5 shows the estimates of the OLS multipleregression model for the insample data. The bestfit ARMAGARCH estimation technique is used for conditional meanvariance estimation of the equity premium. We found, AR (2) for BMHigh and MKHigh portfolios; AR(1)GARCH(0,1) for BMLow and EPHigh portfolios; and AR (1) for EPLow and MKLow portfolios, respectively, as the bestfit conditional mean and conditional meanvariance equations. The adjusted R2 were 0.97 (BMHigh), 0.81 (BMLow), 0.82 (EPHigh), 0.92 (EPLow), 0.89 (MKHigh) and 0.95 (MKLow). The adjusted R2 of 0.97 implies that 97% of the variation in the equity premium is explained by the predictor variables (estimation model) for BMHigh portfolios. The residual diagnostic tests showed no heteroscedasticity and no ARCH effects. The DW statistics showed serial correlations in the residuals, as DW ≠ 2 for all portfolios. The Fstatistic is significant for all estimation models. The results showed that all the estimated coefficients are significant at 5% level of significance for BMHigh (except intercept), EPHigh, EPLow, MKHigh and MKLow portfolios. However, for BMLow portfolio, the variation in dividendprice and dividendyield ratios didn’t significantly influence the change in equity premium as the coefficient estimates were not significant at 5% level. It is observed that priceratios are negatively associated with equity premium, and yieldratios are positively associated with equity premium for all portfolios (except MKLow, where, DP is positively associated with equity premium). This implies that a decrease in dividends and earnings at a time‘t’ reduces the equity premium available for shareholders. However, equity premium increases as the dividendyield and earningsyield ratios increase for all the stocks.
Bestfit OLS Model 
Variable 
Coefficient 
SE 
tstat/ zstat 
pvalue 
Adj. R^{2} 
Fstat 
DW 
BM HIGH 

AR(2) 
DP 
7.622 
1.337 
5.702 
0.000 
0.975 
579.862 
1.906 
DY 
8.317 
1.233 
6.743 
0.000 

EP 
1.995 
0.335 
5.960 
0.000 

EY 
1.985 
0.263 
7.556 
0.000 

C 
1.408 
1.438 
0.979 
0.330 

AR(1) 
0.527 
0.070 
7.573 
0.000 

AR(2) 
0.462 
0.069 
6.684 
0.000 

BM Low 

AR(1)  GARCH (0,1) 
DP 
1.580 
1.353 
1.168 
0.243 
0.805 
2.675 

DY 
2.031 
1.784 
1.138 
0.255 

EP 
1.336 
0.140 
9.536 
0.000 

EY 
1.501 
0.175 
8.561 
0.000 

C 
0.820 
0.150 
5.447 
0.000 

AR(1) 
0.953 
0.044 
21.565 
0.000 

RESID(1)^2 
0.602 
0.223 
2.700 
0.007 

EP High 

AR(1)  GARCH (0,1) 
DP 
10.563 
1.556 
6.786 
0.000 
0.820 
2.348 

DY 
11.973 
1.326 
9.032 
0.000 

EP 
2.751 
0.452 
6.084 
0.000 

EY 
2.495 
0.509 
4.907 
0.000 

C 
0.860 
0.177 
4.849 
0.000 

AR(1) 
0.974 
0.020 
49.202 
0.000 

RESID(1)^2 
0.959 
0.287 
3.344 
0.001 

EP Low 

AR (1) 
DP 
2.588 
1.144 
2.261 
0.026 
0.928 
251.116 
2.375 
DY 
3.574 
1.072 
3.336 
0.001 

EP 
2.454 
0.273 
8.995 
0.000 

EY 
2.983 
0.287 
10.394 
0.000 

C 
0.702 
0.062 
11.358 
0.000 

AR(1) 
0.867 
0.040 
21.785 
0.000 

MK High 

AR (2)

DP 
14.370 
2.604 
5.517 
0.000 
0.898 
141.518 
2.267 
DY 
15.566 
2.611 
5.962 
0.000 

EP 
0.885 
0.180 
4.925 
0.000 

EY 
1.043 
0.182 
5.732 
0.000 

C 
0.730 
0.092 
7.946 
0.000 

AR(1) 
0.483 
0.082 
5.863 
0.000 

AR(2) 
0.445 
0.079 
5.656 
0.000 




MK Low 

AR (1) 
DP 
0.544 
0.257 
2.113 
0.037 
0.955 
417.138 
2.605 
DY 
0.680 
0.257 
2.652 
0.009 

EP 
3.625 
0.524 
6.920 
0.000 

EY 
4.847 
0.458 
10.593 
0.000 

C 
0.601 
0.076 
7.896 
0.000 

AR(1) 
0.871 
0.046 
19.043 
0.000 
Notes: Column 1 shows the type of bestfit ARMAGARCH model used. Column 2 represents the estimated variables. Column 3 shows the coefficients of the estimation. Column 4 shows the standard error of the estimates. Column 5 shows the tstatistic/ zstatistic value of the estimates. The tests are done for the statistical significance of the estimates. Column 6 shows the pvalue of the estimates. The pvalue < 0.05 implies that the estimates are highly significant at 5% level. Column 7 shows the adjusted R2, which shows the goodnessoffit of the model. Column 8 shows the Fstatistic value of the regression, which is a proxy for the significance of the regression (higher Fstatistic). Column 9 shows the DurbinWatson value for serialcorrelation in the residuals. DW =2 implies there is no autocorrelation in residuals.
Table 6shows the forecast accuracy measures for insample and outsample estimations. The predictor variables performed well in insample estimation for BMHigh, BMLow, MKHigh portfolios as the forecast errors measured by RMSE, MAE and MAPE were less (<< 10%) compared to that of EP High, EPLow and MKLow portfolios, where RMSE and MAPE were greater. (For EPHigh, RMSE= 12%, MAPE = 17%; EPLow, RMSE = 10%, MAPE=14%; MKLow, RMSE = 10%, MAPE=14% respectively). The outsample measures viz., RMSE and MAE are greater for BMLow, EPLow, MKHigh and MKLow portfolios indicating the poor outsample performance of the estimation models. However, the dividends and earningsratios acted as best insample and outsample predictors for EPHigh portfolio.
Portfolio 
ARMAGARCH type 
Insample estimation 
Outsample estimation 


Obs. 
RMSE 
MAE 
MAPE 
Obs. 
RMSE 
MAE 
MAPE 

BM High 
AR (2) 
96 
6.575% 
5.098% 
11.148% 
26 
42.549% 
3.457% 
3.464% 

BM Low 
AR(1)  GARCH (0,1) 
98 
8.510% 
6.261% 
9.375% 
28 
9.831% 
7.727% 
7.588% 

EP High 
AR(1)  GARCH (0,1) 
98 
12.428% 
9.538% 
17.177% 
26 
6.001% 
5.301% 
5.328% 

EP Low 
AR (1) 
98 
10.481% 
8.987% 
14.054% 
26 
14.890% 
13.815% 
13.738% 

MK High 
AR (2) 
97 
7.137% 
6.027% 
9.65% 
26 
10.533% 
8.866% 
9.727% 

MK Low 
AR (1) 
98 
10.054% 
8.641% 
14.919% 
26 
16.190% 
14.144% 
13.678% 
The standard financial models failed to account for the large return differentials in the expected stock returns over the riskfree rate, leading to the puzzle of equity premium documented by Mehra and Prescott (1985). The proponents of market efficiency attributed the higher riskpremium to the macroeconomic consumption of representative agents, measured by aggregate dividends and earnings of firms (Campbell and Cochrane, 2000; Fama and French, 1988; Goyal and Welch, 2008). In our study, we estimated crosssectional equity premiums using aggregate dividends and earnings ratios. The equity premium varies accordingly with firm characteristics, riskfree rates and predictor variables (Damodaran, 2009; 2012). Therefore, we used the crosssectional portfolios formed based on market capitalisation (firm size), BM ratio and EP ratios. The OLS multivariate regression techniques, along with the bestfit ARMAGARCH model, were used for the estimation of conditional meanvariance equations of the expected equity premiums for insample and outsample data. We found that both dividendsratios and earningsratios acted as best insample predictors for all portfolios except the Value (BMLow) portfolio. The dividends ratios didn’t significantly estimate the equity premium for BMLow portfolio, and the results are incongruent with the findings of Goyal and Welch (2008) that timevarying dividendratios predicted themselves better than predicting equity premium. The poor outsample estimation shows that, though the aggregate dividends and earnings partly explained the crosssectional equity premiums, they acted as weaker predictors given their random walk behaviour (Goyal and Welch, 2008). Thus, our estimation techniques don’t contribute to providing any solid explanation for the anomalous behaviour of equity premium nor the uncertainty surrounding the predictability of the expected equity premium. Thus, there is a need for further research to explore robust techniques involving behavioural variables along with firm variables reflecting the economic behaviour to explain the behaviour of excess equity returns better.
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