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Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education /
Nishant P. Dhruv & Dr. Parul P. Bhati / Page 255-268
FEB, 2018. VOL.10. SPECIAL ISSUE FOR ICGS-2018 www.ascgujarat.org Page | 255
A STUDY ON EFFECT OF P/E RATIO ON STOCK RETURNS
Nishant P. Dhruv
&
Dr. Parul P. Bhati
Abstract This paper enunciates the research in the field of finance to assist the investors for better
investment decision. The rational for the study is to facilitate the investors to know the effect
of price-to-earning ratio on stock market which eventually help them to take informed
investment decision thereby reducing their exposure of risk. The purpose of the paper is to
determine empirically whether the investment performance of stocks is related to price-to-
earnings ratio.
The objective of the study is to measure the effect of price-to-eanring ratio on stock returns.
For this purpose, monthly data of all the variables were taken for the study during the period
April 1994 to December 2016. The purpose of the study is to find out the effect of
macroeconomic variables and price-to-earning ratio on stock returns. For this purpose,
various econometric tests were carried out which includes Correlogram, Unit Root test,
Cointegration test, Vector Error Correction Estimates (VECM), Vector Auto Regressive
(VAR), Normality test, Heteroscedasticity test and Serial Correlation test. To understand the
effect of macroeconomic variables and price-to-earning ratio on stock returns in long and
short run, the researcher has used Vector Error Correction Estimates (VECM) and Vector
Auto Regressive (VAR) models. After the series of testing, we found no association of
macroeconomic variables and price-to-earning ratio with stock returns in long run. But, there
is association of macroeconomic and price-to-earning ratio with stock return in short run.
The individual coefficients of exchange rate and foreign institutional investment have
significant effect.
Keywords: Indian stock market performance, Time Series, Unit root, Cointegration test,
Vector Auto Regressive model, Price-earnings ratio, Vector Error Correction Estimates,
Heteroscedasticity Test, Normality test, Serial Correlation Test, Correlogram
Background of the study: When trying to decipher which valuation, method is appropriate to use to value a stock, for
the first time, most investors quickly discover the overwhelming number of valuation
techniques available to them today. There are the various valuations methods such as
discounted cash flow method, earning per share, dividend yield, price-to-book value, price-
to-sales value, price-to-cash flow, capital asset pricing model, price-to-earnings ratio, and
many others. The question arises which valuation method one should use? Appropriately, no
method is best suited for every situation. Each stock is different, and each industry sector has
distinctive properties that may require varying valuation approaches. The professionals and
academicians have been trying to find out a reliable tool to identify the right stock for
investment. Robert J. Shiller3 (the Yale economist, 1996) wrote, ''The simplest and most
ISSN No. 0974-035X
An Indexed, Refereed & Peer Reviewed Journal of Higher Education
Towards Excellence UGC-HUMAN RESOURCE DEVELOPMENT CENTRE,
GUJARAT UNIVERSITY, AHMEDABAD, INDIA
Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education /
Nishant P. Dhruv & Dr. Parul P. Bhati / Page 255-268
FEB, 2018. VOL.10. SPECIAL ISSUE FOR ICGS-2018 www.ascgujarat.org Page | 256
widely used ratio to predict the market is the price earnings ratio.'' Many stock pickers used
P/E ratio as the first measure of a share's prospects. Even the disclosure guidelines prescribed
by SEBI for fresh issue of shares ensures due weight of the price-to-earnings ratio. Monica
Singhania4 studied the various determinants of equity share prices concerning Indian Stock
market. The regression method was used to find out relationships between Market price of
equity and book value, dividend per share, earnings per share, growth, price-to-earnings ratio
and dividend yield. Result of analysis indicates that price-earnings ratio, earning per share are
the variables which contributed the most in determining share prices followed by book value,
dividend per share and yield. Hence, it shows that P/E phenomenon exists in the Indian stock
market.
The earlier empirical research also indicate that low price-to-earning securities tend to
outperform high price-to-earning securities. Hence, the prices of securities are biased, and a
price-to-earnings ratio is an indicator of this bias. The paper also attempts to determine
empirically whether the performance of equity shares is related to their P/E ratios.
In the recent past, the concern has increased that the stock market may be headed for a
downturn because firms’ share prices have become very high relative to their earnings.
According to Shen Pu5, many analysts who hold this view, point out that, in the past, high
price-earnings ratios have usually been followed by slow growth in stock prices. On the other
hand, few analyst3 disagree as they believe that history is no longer a true reflection because
fundamental changes in the economy have made stocks more attractive to investors, which
justifies a higher price-earnings ratio.
NIFTY Price-to-Earnings Ratio:
Figure 1 Price-to-Earnings Ratio of NIFTY (Source: www.nseindia.com)
Nifty P/E ratio measures the average P/E ratio of the Nifty 50 companies covered by the
Nifty Index. PE ratio also known as "price multiple" or "earnings multiple." Craytheon
mentioned that if P/E is 17, it means Nifty is 17 times its earnings. Nifty is considered to be
in oversold range when Nifty PE value is below 14, and it is considered to be in overvalued
range when Nifty PE is near or above 22. The market quickly bounces back from the
oversold region because intelligent investors start buying stocks looking to snatch up bargains
11.00
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PR
ICE-
TO-E
AR
NIN
G R
ATI
O
P/E Ratio of NIFTY (April 2004 to December 2016)
Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education /
Nishant P. Dhruv & Dr. Parul P. Bhati / Page 255-268
FEB, 2018. VOL.10. SPECIAL ISSUE FOR ICGS-2018 www.ascgujarat.org Page | 257
and they do the exact opposite when Nifty P/E is in the overbought region. Further, the
research carried out by the independent research firm Craytheon, explained how dangerous it
is to remain invested in an expensive market. Since the commencement of NSE, whenever
Nifty’s Price-Earnings ratio exceeded 22, the average return from Indian equities in the
subsequent three years became negative.
Table 1 Nifty Price-to-Earnings Ratio and Return in Subsequent Years
Nifty’s PE Subsequent three-year
returns (%)
Less than 14 152.10
14-16 112.36
16-18 79.14
18-20 51.18
20-22 21.18
22-24 -14.98
24-26 -32.92
26-28 -36.60
28-30 -40.17
So, based on the above evidence, it can be concluded that a passive long-term investor should
buy stocks when P/E reaches 15-16 and stop buying stocks when P/E goes above 22.
The earlier empirical research indicate that low price-to-earning securities tend to outperform
high price-to-earning securities. Hence, the prices of securities are biased, and a price-to-
earnings ratio is an indicator of this bias. The paper primarily attempts to determine
empirically whether the performance of equity shares is related to their P/E ratios.
In the recent past, the concern has increased that the stock market may be headed for a
downturn because firms’ share prices have become very high relative to their earnings.
Analysts who hold this view, point out that, in the past, high price-earnings ratios have
usually followed by slow growth in stock prices. On the other hand, several analysts disagree
as they believe that history is no longer a true reflection because fundamental changes in the
economy have made stocks more attractive to investors, which justifies a higher price-
earnings ratio.
Review of Literature According to one view, lower the P/E ratio, the better it is for investors, as there are chances
of higher appreciation. Nicholson was first to demonstrate the P/E effect. He published a
three-page paper in which he included two studies. Data were procured from the statistical
industry summaries prepared by Studley Shupert & Co. In the first study, he considered 100
mainly industrial stocks over period from 1939 to 1959. He described that the lowest P/E
quintile stock, rebalanced every five years, have delivered an investor 14.7 times his original
investment at the end of 20 years as compared to 4.7 times for the highest P/E quintile stock.
In the second study, he covered 29 Chemical Common stocks with prices and P/E ratios for
Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education /
Nishant P. Dhruv & Dr. Parul P. Bhati / Page 255-268
FEB, 2018. VOL.10. SPECIAL ISSUE FOR ICGS-2018 www.ascgujarat.org Page | 258
the years 1937 to 1954. The 50% lowest P/E ratios averaged over 50% more appreciation
than the 50% highest P/E ratios.
Nicholson extended his work by looking at the earnings of 189 companies between 1937 and
1962. Dividing companies into five groups by P/E ratios (P/E less than or equal to 10, P/E
between 10 to 12, P/E between 12 to 15, P/E between 15 to 20, P/E greater than 20). After
that, he calculated mean price appreciation for each group. He found that the average price
appreciation over seven years were 131% (12.71 % per annum) for companies with a P/E
below ten, decreasing almost monotonically to71% (7.97% per annum) for those with P/E
over 20. He concluded the purchase of the common stocks may logically seek the greater
productivity represented by stocks with lower rather than higher P/E ratios.
Further, Basu Sanjay described the relationship between common stocks and price-earnings
ratio. In his research, he has considered 14-year period and establish that low P/E ratio
portfolio earned 6% more per year than a high P/E portfolio. The stocks are ordered
according to E/P ratio and divided into five equally weighted portfolios and re-ranked in
January and rebalanced annually in April. The data was collected from NYSE and must have
60 months of data before it included in one of the five portfolios. He concluded that low P/E
and high return relationship strictly increases from quintiles two to five. Average returns per
annum were 9.34% for the highest P/E, with beta of 1.11, compared to 16.30% for the lowest
P/E of 0.99. Basu recognized that the low P/E portfolios seem to have, on average, earned
higher return than the high P/E securities.
Sultan Singh, Himani Sharma, and Kapil Choudhary tested the semi-strong efficient market
hypothesis in Indian equity market by determining empirically whether the investment
performance of common stocks is related to the investment strategies based on their P/E
(Price-Earnings ratio) and B/M (Book value to Market value ratio) ratios. S&P CNX 500
index has chosen for data analysis. Securities ranked according to the highest P/E ratio to the
lowest P/E ratio. Five portfolios were formed based on P/E ratio. The continuously
compounded returns of the portfolios were calculated assuming initial investment in each of
their respective securities. Sharpe, Treynor, and Jensen measures had been calculated to
compare performance of the portfolios. The similar steps performed on portfolios ranked
based on B/M ratio. Author concluded that low P/E portfolios have earned the higher return
than the high P/E portfolios and the high B/M portfolios have earned the higher return than
the low B/M portfolios.
Research Objectives A lot of literatures have discussed on price multiples. The most of the research work has
been made based on earnings and cash flow. Penman proved that the description of P/E
ratio reconciles the standard growth interpretation of the P/E with the transitory earnings.
However, a very less literature on price multiples are available for developing market
including India.
Specific Objectives:
1. To empirically test short run and long-run causality of P/E ratio on stock returns.
2. To develop econometric model considering the variables significantly affecting stock
returns and to use it for forecasting.
Hypothesis:
Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education /
Nishant P. Dhruv & Dr. Parul P. Bhati / Page 255-268
FEB, 2018. VOL.10. SPECIAL ISSUE FOR ICGS-2018 www.ascgujarat.org Page | 259
1. There does not exists long-run relationship between P/E ratio and stock returns which will
be tested using Vector Error Correction Model.
2. There does not exists short-run relationship between P/E ratio and stock returns which
will be tested using Vector Auto-Regressive Model.
Research Methodology:
Based on the empirical research, in this study, it is proposed to understand the effect of price-
to-earning ratio in long and short run on stock returns.
Sample Size
The universe of the study consists of all the securities listed on exchanges like BSE, NSE and
other regional exchange. Because the number of such securities are large, it may be beyond
the capacity of individual researcher to pursue the study on one hundred percent enumerative
basis. Hence, the study has been carried out by a representative index. Further, to determine
whether the investment performance of equity shares is affected by their price-earnings ratio
or not, the price-to-earning ratio of SENSEX selected for the study to understand the effect
on stock returns.
Data Collection
To accomplish the research objective, the secondary data collected from the stock exchanges
and relevant online research magazines & websites.
Period of Study
The monthly data has been analyzed for the duration between April 1994 to December 2016
for 22 years and six months.
Methodology
Vector Error Correction Estimates (VECM) and Vector Auto Regressive Model (VAR)
applies to a category of multiple time series models. The model is used to forecast the long
and short run effect of price-earning-ratio on stock returns. Both models were based on the
presence of cointegrating vectors found in Johansen Cointegration model. Further, the
reliability of the model should tested through normality test of residuals, heteroscedasticity
test of residuals and serial correlation test.
Results The Vector Error Correction Model (VECM) test is to identify the long-run association
between Sensex and Price-Earning ratio.
Vector Error Correction Estimates:
Table 2 Vector Error Correction Estimates
Vector Error Correction Estimates
Date: 11/17/17 Time: 13:00
Sample (adjusted): 1994M07 2016M12
Included observations: 270 after adjustments
Standard errors in ( ) & t-statistics in [ ]
Cointegrating Eq: CointEq1
LSENSEX(-1) 1.000000
Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education /
Nishant P. Dhruv & Dr. Parul P. Bhati / Page 255-268
FEB, 2018. VOL.10. SPECIAL ISSUE FOR ICGS-2018 www.ascgujarat.org Page | 260
LPE(-1) -9.078931
(1.73460)
[-5.23403]
C 17.38027
Error Correction:
D(LSENSEX
) D(LPE)
CointEq1 0.005619 0.008842
(0.00165) (0.00180)
[ 3.39806] [ 4.91584]
D(LSENSEX(-1)) 0.323758 -0.151171
(0.11424) (0.12426)
[ 2.83400] [-1.21653]
D(LSENSEX(-2)) -0.075797 0.087579
(0.11448) (0.12452)
[-0.66212] [ 0.70333]
D(LPE(-1)) -0.099275 0.357368
(0.10281) (0.11183)
[-0.96558] [ 3.19551]
D(LPE(-2)) 0.130497 -0.038772
(0.10253) (0.11153)
[ 1.27272] [-0.34764]
C 0.005158 -0.002013
(0.00376) (0.00409)
[ 1.37108] [-0.49194]
R-squared 0.098632 0.147066
Adj. R-squared 0.081561 0.130912
Sum sq. resids 0.902568 1.067902
S.E. equation 0.058471 0.063601
F-statistic 5.777649 9.103946
Log likelihood 386.5126 363.8046
Akaike AIC -2.818612 -2.650404
Schwarz SC -2.738647 -2.570439
Mean dependent 0.006862 -0.003432
S.D. dependent 0.061012 0.068223
Determinant resid covariance (dof
adj.) 3.88E-06
Determinant resid covariance 3.70E-06
Log likelihood 922.0668
Akaike information criterion -6.726421
Schwarz criterion -6.539836
Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education /
Nishant P. Dhruv & Dr. Parul P. Bhati / Page 255-268
FEB, 2018. VOL.10. SPECIAL ISSUE FOR ICGS-2018 www.ascgujarat.org Page | 261
Dependent Variable: D(LSENSEX)
Method: Least Squares
Date: 11/17/17 Time: 13:01
Sample (adjusted): 1994M07 2016M12
Included observations: 270 after adjustments
D(LSENSEX) = C(1)*( LSENSEX(-1) - 9.0789305026*LPE(-1) +
17.3802736354 ) + C(2)*D(LSENSEX(-1)) +
C(3)*D(LSENSEX(-2)) +
C(4)*D(LPE(-1)) + C(5)*D(LPE(-2)) + C(6)
Coefficient Std. Error t-Statistic Prob.
C(1) 0.005619 0.001654 3.398059 0.0008
C(2) 0.323758 0.114241 2.833998 0.0050
C(3) -0.075797 0.114477 -0.662116 0.5085
C(4) -0.099275 0.102813 -0.965582 0.3351
C(5) 0.130497 0.102534 1.272717 0.2042
C(6) 0.005158 0.003762 1.371079 0.1715
R-squared 0.098632 Mean dependent var 0.006862
Adjusted R-squared 0.081561 S.D. dependent var 0.061012
S.E. of regression 0.058471 Akaike info criterion -2.818612
Sum squared resid 0.902568 Schwarz criterion -2.738647
Log-likelihood 386.5126
Hannan-Quinn
criteria. -2.786501
F-statistic 5.777649 Durbin-Watson stat 1.999594
Prob(F-statistic) 0.000044
Here, C1 is significant as the p-value is 0.08% which is lower than 5% but at the same time,
its coefficient must be negative. Here, the role of the coefficient is to correct the error. So, to
correct the error, the coefficient should be negative, and as in the table mentioned above, the
coefficient is positive which rather increases the error. Further, R-squared is only 9.86%
which is very low compared to the minimum significance level of 70%.
Vector Autoregressive Model (VAR):
Table 3 Vector Auto Regressive Model
Vector Autoregression Estimates
Date: 11/17/17 Time: 13:01
Sample (adjusted): 1994M06 2016M12
Included observations: 271 after adjustments
Standard errors in ( ) & t-statistics in [ ]
LSENSEX LPE
LSENSEX(-1) 1.274318 -0.132264
(0.10677) (0.11654)
[ 11.9348] [-1.13492]
LSENSEX(-2) -0.273402 0.137938
Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education /
Nishant P. Dhruv & Dr. Parul P. Bhati / Page 255-268
FEB, 2018. VOL.10. SPECIAL ISSUE FOR ICGS-2018 www.ascgujarat.org Page | 262
(0.10645) (0.11619)
[-2.56829] [ 1.18716]
LPE(-1) -0.079848 1.282035
(0.09711) (0.10600)
[-0.82223] [ 12.0952]
LPE(-2) 0.037864 -0.350053
(0.09526) (0.10397)
[ 0.39749] [-3.36681]
C 0.119109 0.145927
(0.05310) (0.05796)
[ 2.24316] [ 2.51788]
R-squared 0.994610 0.931420
Adj. R-squared 0.994529 0.930389
Sum sq. resids 0.928042 1.105599
S.E. equation 0.059067 0.064470
F-statistic 12271.24 903.1693
Log-likelihood 384.6736 360.9523
Akaike AIC -2.802020 -2.626954
Schwarz SC -2.735560 -2.560494
Mean dependent 9.032466 2.909189
S.D. dependent 0.798563 0.244353
Determinant resid covariance (dof
adj.) 4.07E-06
Determinant resid covariance 3.92E-06
Log-likelihood 917.7636
Akaike information criterion -6.699362
Schwarz criterion -6.566443
Dependent Variable: LSENSEX
Method: Least Squares
Date: 11/17/17 Time: 13:02
Sample (adjusted): 1994M06 2016M12
Included observations: 271 after adjustments
LSENSEX = C(1)*LSENSEX(-1) + C(2)*LSENSEX(-2) +
C(3)*LPE(-1) + C(4)
*LPE(-2) + C(5)
Coefficient Std. Error t-Statistic Prob.
C(1) 1.274318 0.106773 11.93485 0.0000
C(2) -0.273402 0.106453 -2.568286 0.0108
C(3) -0.079848 0.097112 -0.822229 0.4117
C(4) 0.037864 0.095258 0.397492 0.6913
C(5) 0.119109 0.053099 2.243160 0.0257
Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education /
Nishant P. Dhruv & Dr. Parul P. Bhati / Page 255-268
FEB, 2018. VOL.10. SPECIAL ISSUE FOR ICGS-2018 www.ascgujarat.org Page | 263
R-squared 0.994610 Mean dependent var 9.032466
Adjusted R-squared 0.994529 S.D. dependent var 0.798563
S.E. of regression 0.059067 Akaike info criterion -2.802020
Sum squared resid 0.928042 Schwarz criterion -2.735560
Log likelihood 384.6736 Hannan-Quinn criter. -2.775335
F-statistic 12271.24 Durbin-Watson stat 2.005918
Prob(F-statistic) 0.000000
The coefficients C(1), C(2) & C(5) are significant as the p-value is less than 5%. In Vector
Autoregressive Model error correction is not required, i.e., the positive or negative values of
coefficients are immaterial which was the case in Vector Error Correction Model. The R-
squared and Durbin-Watson Statistics provides good model, but the value of coefficients C(3)
and C(4) is insignificant. Since, the coefficient C(4), is insignificant, we dropped it, and we
tested the model once again to see the fitness of the model. The result is specified as
mentioned below:
Dependent Variable: LSENSEX
Method: Least Squares
Date: 11/17/17 Time: 13:03
Sample (adjusted): 1994M06 2016M12
Included observations: 271 after adjustments
LSENSEX = C(1)*LSENSEX(-1) + C(2)*LSENSEX(-2) +
C(3)*LPE(-1) + C(5)
Coefficient Std. Error t-Statistic Prob.
C(1) 1.238932 0.058856 21.05008 0.0000
C(2) -0.238186 0.058924 -4.042282 0.0001
C(3) -0.041693 0.014706 -2.835208 0.0049
C(5) 0.120171 0.052948 2.269595 0.0240
R-squared 0.994607 Mean dependent var 9.032466
Adjusted R-squared 0.994546 S.D. dependent var 0.798563
S.E. of regression 0.058974 Akaike info criterion -2.808806
Sum squared resid 0.928593 Schwarz criterion -2.755638
Log-likelihood 384.5932
Hannan-Quinn
criteria. -2.787458
F-statistic 16413.36 Durbin-Watson stat 2.008991
Prob(F-statistic) 0.000000
The result depicts that all coefficients are significant. The high R-squared is 99.46 %, and
Durbin-Watson statistics is 2.008 which is quite good. It means that one-month lag, two-
month lag of price-to-earning ratio has its impact in the current month. So, the Sensex and
price-to-earning ratio have short-term association.
Testing of Residuals:
The purpose of testing residuals is that as far as possible, the difference between actual and
theoretical value must be equal to zero. Here, the phenomena (theoretical value) doesn’t have
any equation rather we frame the equation, or it is also known as observed value. So, in
general, the equation should completely explain the phenomena which is not possible. So, the
Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education /
Nishant P. Dhruv & Dr. Parul P. Bhati / Page 255-268
FEB, 2018. VOL.10. SPECIAL ISSUE FOR ICGS-2018 www.ascgujarat.org Page | 264
allowable error (residual) component need to test for the reliability of the prediction. The
following tests generated:
Testing of Normality of Residuals:
0
10
20
30
40
50
60
-0.2 -0.1 0.0 0.1 0.2
Series: Residuals
Sample 1994M06 2016M12
Observations 271
Mean -1.65e-15
Median 0.005599
Maximum 0.177056
Minimum -0.274206
Std. Dev. 0.058645
Skewness -0.446074
Kurtosis 4.628632
Jarque-Bera 38.93784
Probability 0.000000
Figure 2 Normality of Residuals
The above graph depicts that the chances of larger error and smaller error. So, in the above
case, the residuals are normally distributed which were necessary for the reliability of the
Vector Autoregressive Model (VAR) to forecast in short-run.
Test for Serial Correlation in Residuals:
Breusch-Godfrey Serial Correlation LM Test and Q-Statistics for Residuals. The serial
correlation in residuals should test the reliability of the model. For this, the Breusch-Godfrey
Serial Correlation LM test and Q-statistic test for residuals used in the study. If the residuals
correlated with each other than the model applied for forecasting the relationship between
price-to-earning ratio and Sensex would not stand reliable.
Table 4 Breusch-Godfrey Serial Correlation LM Test
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 1.037226 Prob. F(2,265) 0.3559
Obs*R-squared 2.104944 Prob. Chi-Square(2) 0.3491
Test Equation:
Dependent Variable: RESID
Method: Least Squares
Date: 11/17/17 Time: 13:06
Sample: 1994M06 2016M12
Included observations: 271
Presample missing value lagged residuals set to zero.
Variable Coefficient Std. Error t-Statistic Prob.
Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education /
Nishant P. Dhruv & Dr. Parul P. Bhati / Page 255-268
FEB, 2018. VOL.10. SPECIAL ISSUE FOR ICGS-2018 www.ascgujarat.org Page | 265
C(1) 1.033829 0.796104 1.298610 0.1952
C(2) -1.035332 0.797186 -1.298734 0.1952
C(3) 0.051470 0.043532 1.182354 0.2381
C(5) -0.143696 0.126925 -1.132127 0.2586
RESID(-1) -1.098581 0.838736 -1.309805 0.1914
RESID(-2) -0.224712 0.210834 -1.065827 0.2875
R-squared 0.007767 Mean dependent var -1.65E-15
Adjusted R-squared -0.010954 S.D. dependent var 0.058645
S.E. of regression 0.058965 Akaike info criterion -2.801843
Sum squared resid 0.921381 Schwarz criterion -2.722092
Log-likelihood 385.6498
Hannan-Quinn
criteria. -2.769822
F-statistic 0.414891 Durbin-Watson stat 1.993889
Prob(F-statistic) 0.838245
The null hypothesis in LM statistics, don’t have serial correlation. In the above table,
observed R squared has corresponding p-value 34.91% which is more than 5%. So, we
cannot reject the null hypothesis. It means the model mentioned above is free from serial
correlations.
Test for Heteroscedasticity in Residuals:
Table 5 Heteroscedasticity Test
Heteroskedasticity Test: ARCH
F-statistic 1.051868 Prob. F(1,268) 0.3060
Obs*R-squared 1.055575 Prob. Chi-Square(1) 0.3042
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 11/17/17 Time: 13:06
Sample (adjusted): 1994M07 2016M12
Included observations: 270 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.003159 0.000446 7.079003 0.0000
RESID^2(-1) 0.061972 0.060425 1.025606 0.3060
R-squared 0.003910 Mean dependent var 0.003372
Adjusted R-squared 0.000193 S.D. dependent var 0.006490
S.E. of regression 0.006489 Akaike info criterion -7.229895
Sum squared resid 0.011286 Schwarz criterion -7.203240
Log-likelihood 978.0358 Hannan-Quinn criteria. -7.219191
Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education /
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F-statistic 1.051868 Durbin-Watson stat 1.992545
Prob(F-statistic) 0.306002
Here, the null hypothesis is that residuals have homoscedasticity whereas the alternative
hypothesis is that residuals have heteroscedasticity. In the above table, the corresponding p
values of observed R-squared is 30.42% which is higher than the 5%. Hence, we cannot
reject null hypothesis, which means that residuals have homoscedasticity. If all the random
variables of residuals in the sequence or variables have the same variance, then the notion is
called homoscedasticity.
Forecasting ability of the model
9.2
9.6
10.0
10.4
10.8
11.2
I II III IV I II III IV
2015 2016
LSENSEXF ± 2 S.E.
Forecast: LSENSEXF
Actual: LSENSEX
Forecast sample: 2015M01 2016M12
Included observations: 24
Root Mean Squared Error 0.095829
Mean Absolute Error 0.080678
Mean Abs. Percent Error 0.793500
Theil Inequality Coefficient 0.004682
Bias Proportion 0.625312
Variance Proportion 0.056148
Covariance Proportion 0.318540
Figure 3 Forecasting the Effect of Price-Earning Ratio on Stock Returns
The author here used dynamic forecasting method to forecast Sensex based on equations
developed. In the forecast analysis, the bias number should be as small as possible because it
says how much mean of actual series differ from mean of forecast series. Also, variance
should be small as this number measure the proportion of variance difference from actual to
forecasted values. The remaining error which is unsystematic forecasting error should
measured by covariance proportion which should be approximately one as covariance
proportion is summation of biased and variance proportion. Thus, most of the mean squared
error should be concentrated in covariance proportion while bias and variance proportion
should be as small as possible for a forecast to be good and reliable. From above we can see
that Theils Inequality Coefficient is 0.0046 which is very small and thus we can say that
forecast is good. Also, variance is 0.056 which is also very small, and most of the error
concentrated in covariance proportion which is 0.31 thus forecast can be said good and
reliable.
Conclusion The principal objective is to empirically test short run and long-run causality of price-to-
earning ratio on stock returns. This causality in long run and short run measured with the help
of Vector Error Correction Estimates and Vector Auto-Regressive models.
Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education /
Nishant P. Dhruv & Dr. Parul P. Bhati / Page 255-268
FEB, 2018. VOL.10. SPECIAL ISSUE FOR ICGS-2018 www.ascgujarat.org Page | 267
The hypothesis is that there does not exists long-run relationship between price-to-earing
ratio and stock returns. Based on the study, we can conclude that price-to-earning ratio,
considered, for the study were stationary at level 1 so the series was stationery for order 1.
For testing, long-run relationship presence of cointegration among the variables tested. The
study found that there existed one cointegrating vector between price-to-earning ratio and
stock returns. The Vector Error Correction Estimates (VECM) test was applied, and the p-
value of the coefficient C(1) is significant as the p-value is 0.08% which is lower than 5%,
but at the same time, its coefficient must be negative. Here, the role of the coefficient is to
correct the error. So, to correct the error, the coefficient should be negative, but the test
showcased positive coefficient which increased the error in the model and can’t be consider
reliable. It can further confirmed from R-squared whose value were only 9.86% which were
insignificant. Hence, the price-earning ratio do not affect stock market returns in long run,
and therefore we accept the null hypothesis.
The second hypothesis was that there does not exists short-run relationship between price-to-
earning ratio and stock returns. The short-run relationship was tested using Vector Auto-
Regressive Model (VAR). The study reveals high R-squared 99.46% which is quite good.
The Durbin-Watson statistics 2.00 which suggests the absence of autocorrelation. The study
suggests that one-month lag, two-month lag of Price-to-earning ratio has its impact in the
current month. So, the price-to-earning ratio affects stock market returns in short run. Theils
dynamic forecasting method was used for forecasting which has Inequality Coefficient
0.0046 which is very small and thus we can say that forecast is good. Also, variance is 0.056
which is also very small, and most of the error concentrated in covariance proportion which
is 0.31 thus forecast can be said good and reliable.
References
1. Shah, Ajay, and Susan Thomas. "Securities markets." India Development Report (1997):
167-192.
2. Campbell, John Y., and Robert J. Shiller. Valuation ratios and the long-run stock market
outlook: an update. No. w8221. National Bureau of economic research, 2001
3. Singhania, Monica. "Determinants of equity prices: A study of selected Indian
Companies." The IUP Journal of Applied Finance 12.9 (2006): 39-51.
4. Shen, Pu. "The P/E ratio and stock market performance." Economic Review-Federal
reserve bank of Kansas City 85.4 (2000): 23.
5. Ahmed, Ehsan, J. Barkley Rosser Jr, and Jamshed Y. Uppal. "Emerging markets and
stock market bubbles: Nonlinear speculation?" Emerging Markets Finance and
Trade 46.4 (2010): 23-40. Available from:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.360.8248&rep=rep1&type=pdf
6. Gupta, L. C., P. K. Jain, and C. P. Gupta. "Indian stock market P/E ratios." Soc Cap Mark
Res Dev. ISBN (1998): 81-900513.
7. Vijayakumar, A. "Effect of Financial Performance on Share Prices in the Indian
Corporate Sector: An Empirical Study." Management and Labour Studies 35.3 (2010):
369-381.
8. Kane, Alex, Alan J. Marcus, and Jaesun Noh. "The P/E multiple and market
volatility." Financial Analysts Journal (1996): 16-24.
Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education /
Nishant P. Dhruv & Dr. Parul P. Bhati / Page 255-268
FEB, 2018. VOL.10. SPECIAL ISSUE FOR ICGS-2018 www.ascgujarat.org Page | 268
9. Basu, Sanjoy. "The relationship between earnings' yield, market value and return for
NYSE common stocks: Further evidence." Journal of financial economics 12.1 (1983):
129-156.
10. Bodhanwala, Ruzbeh J. "An Empirical Study on Analysing How Fund Managers in India
Analyse Financial Reports with Special Focus." Advances in Research in Business and
Finance 6 (2005): 33.
Nishant P. Dhruv
HOD – MBA & Integrated MBA
Atmiya Institute of Technology &
Science
Rajkot, Gujarat – India
+91 85111 20309
Dr. Parul P. Bhati
Deputy Director
Gujarat Technological University
Ahmedabad, Gujarat – India ,
+91 98255 14064