14
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. Shiller 3 (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

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Page 1: -035X An Indexed, Refereed & Peer Reviewed Journal of ... Feb18/29.pdf · Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education / Nishant P. Dhruv &

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

Page 2: -035X An Indexed, Refereed & Peer Reviewed Journal of ... Feb18/29.pdf · Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education / Nishant P. Dhruv &

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

13.50

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PR

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P/E Ratio of NIFTY (April 2004 to December 2016)

Page 3: -035X An Indexed, Refereed & Peer Reviewed Journal of ... Feb18/29.pdf · Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education / Nishant P. Dhruv &

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

Page 4: -035X An Indexed, Refereed & Peer Reviewed Journal of ... Feb18/29.pdf · Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education / Nishant P. Dhruv &

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:

Page 5: -035X An Indexed, Refereed & Peer Reviewed Journal of ... Feb18/29.pdf · Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education / Nishant P. Dhruv &

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

Page 6: -035X An Indexed, Refereed & Peer Reviewed Journal of ... Feb18/29.pdf · Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education / Nishant P. Dhruv &

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

Page 7: -035X An Indexed, Refereed & Peer Reviewed Journal of ... Feb18/29.pdf · Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education / Nishant P. Dhruv &

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

Page 8: -035X An Indexed, Refereed & Peer Reviewed Journal of ... Feb18/29.pdf · Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education / Nishant P. Dhruv &

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

Page 9: -035X An Indexed, Refereed & Peer Reviewed Journal of ... Feb18/29.pdf · Towards Excellence: An Indexed, Refereed & Peer Reviewed Journal of Higher Education / Nishant P. Dhruv &

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

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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.

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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

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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.

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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.

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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 | 268

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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