modeling the random walk hypothesis for select industries listed in bse

International Journal of Management (IJM), ISSN 0976 6502(Print), ISSN 0976 - 6510(Online),

Volume 6, Issue 1, January (2015), pp. 527-535 IAEME

527 G.S. David Sam Jayakumar & A.Sulthan, Modeling the Random Walk Hypothesis for Select Industries

Listed in BSE (ICAM 2015)

MODELING THE RANDOM WALK HYPOTHESIS FOR

SELECT INDUSTRIES LISTED IN BSE

Dr. G.S. David Sam Jayakumar

Assistant Professor, Jamal Institute of Management, Tiruchirappalli

A. Sulthan

Research scholar, Jamal Institute of Management, Tiruchirappalli

ABSTRACT

The objectives of any professional investor is to carefully watch the volatility return of

measure industries and companies. Among the various techniques of the volatility, random walk

hypothesis tests the return of industries pure random or non random. This study made an attempt to

study on random walk hypothesis with top Indian industries. The study was conducted for log return

of industries from October 2011 to June 2014. various factors were carefully analyzed and

interpreted. The finding and suggestions were made on the basis of giving a suggestion to the

investors.

INTRODUCTION AND RELATED WORK

The empirical evidence in the random- walk literature existed before the theory was

established. That is so say empirical results were discovered first and then an attempt was made to

develop a theory that could possibly explain the results. After these initial occurrences, more results

and more theory were uncovered. This has led then to a diversity of theories. Which are generically

called the random walk theory. Worthington, Andrew C. & Higgs, Helen (2004)tests for random

walks and weak-form market efficiency in European equity markets. Daily returns for sixteen

developed markets (Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy,

Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and the United Kingdom) and four

INTERNATIONAL JOURNAL OF MANAGEMENT (IJM)

ISSN 0976-6502 (Print)

ISSN 0976-6510 (Online)

Volume 6, Issue 1, January (2015), pp. 527-535

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emerging markets (Czech Republic, Hungary, Poland and Russia) are examined for random walks

using a Augmented Dickey-Fuller (ADF). Ali F. Darrat and Maosen Zhong (2000) investigate, with

new daily data, whether prices in the two Chinese stock exchanges (Shanghai and Shenzhen) follow

a random-walk process as required by market efficiency. Srinivasan (2010) examined the random

walk hypothesis to determine the validity of weak-form efficiency for two major stock markets in

India. Similarly, Kabir Hassan, Al-Sultan (2003) explained unlike previous studies in stock market

efficiency literature on KSE, examines the weak-form efficiency by taking into consideration the

institution - al features of the KSE. On the other hand,Faiq Mahmood et.al (2006)endeavored to

examine the efficiency of Chinese stock market and how the global financial crisis influences the

efficiency of Chinese stock market. Hin Yu Chung (2006) also examined the random walk

hypothesis to determine the validity of weak-form efficiency for two major stock markets in China.

This study also provides evidence on the existence of the day-of-the-week effect on Chinese stock

market. Bizhan Abedini (2009) explored some evidence whether Kuala Lumpur Stock Exchange

(KLSE) is efficient in the weak form or not for the period January 2006 to June 2008 using daily

General Index. The methods used for the study are Autocorrelation Function test (ACF), Runs tests,

Variance ratio test and Unit root test (Augmented Dickey-Fuller Test (ADF)). Ankit Agarwal (2006)

tells us that the efficient market hypothesis has been and continues to be one of the most contentious

issues in finance..Nikolay Angelov (2009) explained that the development of capital markets in

transition and emerging market economies is a very important prerequisite for fostering their growth

as it allows the available funds to be channeled easily to their best investment uses. Kian-Ping Lim

(2000)provided a systematic review of the weak-form market efficiency literature that examines

return predictability from past price changes, with an exclusive focus on the stock markets. Korkmaz

(2001) explained in his study, that the efficiency concept was emphasized. Weak Form Market

Efficiency of Efficient Market Hypothesis was tested in Istanbul Stock Exchange (ISE). Ibrahim

Awad (2009) examined the efficiency of the Palestine Security Exchange (PSE) at the weak-level for

35 stocks listed in the market by using daily observations of the PSE indices: Alquds index, general

index, and sector indices. Parametric and nonparametric tests for examining the randomness of the

PSE stock prices were utilized. The parametric tests include serial correlation test, and Augmented

Dickey-Fuller (ADF) unit root tests.

METHODOLOGY AND TECHNIQUES OF DATA ANALYSIS

The objectives of any professional investor is to carefully watch the volatility return of

measure industries and companies. Among the various techniques in measuring the volatility.

Random walk hypothesis tests the return industries pure random or non random. This is study is

attempt to study on random walk hypothesis of top Indian industries. The study was conducted for

log return of industries from October 2011to June 2014.The monthly data of following industries

Automobile, Health Care, PSU, Capital Goods, Bank, Consumer Durable, FMCG, IT, Power, Metal,

Oil & Gas are considered. The analysis was conducted at different stages In Stage-1Multivariate test

of Normality for security returns was promoted and in Second stage, summary statistics for industry

returns and selection of optimal lag length are formulated, Stage-3 Augmented dickey-filler test is

used on industrial returns for understanding the random walk of the industrial return with ADF

regression equation.





MULTIVARIATE NORMALITY TESTS

Multivariate normality tests check a given set of data for similarity to the multivariate

normal distribution. The null hypothesis is that the data set is similar to the normal distribution,

therefore a sufficiently small p-value indicates non-normal data. Multivariate normality tests include

the Cox-Small test and Smith and Jain's adaptation of the Friedman-Rafsky test. Mardia's test is

based on multivariate extensions of skewness and kurtosis measures. Under the null hypothesis of

multivariate normality, the statistic A will have approximately a chi-squared

distribution with (1/6)*k(k + 1)(k + 2) degrees of freedom, and B will be approximately standard

normal N(0,1).Mardia's kurtosis statistic is skewed and converges very slowly to the limiting normal

distribution. For medium size samples (50 n





TABLE-2: SUMMARY STATISTICS FOR INDUSTRY RETURNS Industry

Name Mean

Standard

Deviation C.V Skewness Ex.kurtosis

AUTOMOBILE 0.0565792 1.29719 22.9270 0.175903 1.08326

HEALTHCARE 0.0723178 0.861176 11.9082 -0.185413 0.794022

PSU -0.0423310 1.14071 26.9473 -0.0875869 0.691177

CAPITALGOODS -0.0205306 1.55488 75.7348 -0.0348614 0.846336

BANK 0.0380047 1.60244 42.1642 0.196942 1.71437

CONSUMER

DURABLE 0.0529387 1.52398 28.7876 -0.351868 2.73797

FMCG 0.0902287 1.06559 11.8099 0.0585206 1.76327

IT 0.0654255 1.41274 21.5932 -0.461118 8.40083

POWER -0.0555093 1.25673 22.6401 -0.239719 0.930730

METAL -0.0432414 1.69574 39.2158 0.217300 1.18240

OIL &GAS 0.00843248 1.29422 153.481 0.0292861 0.276246

TABLE-3: SELECTION OF OPTIMAL LAG LENGTH

INDUSTRY

NAME

LOG

LIKELYHOOD MINIMUM AIC NO. OF LAGS

AUTOMOBILE -1649.60702 3.357578 3

HEALTHCARE -1235.14655 2.516034 3

PSU -1502.91225 3.075964 11

CAPITALGOODS -1823.76358 3.707134 1

BANK -1858.58515 3.777838 1

CONSUMER DURABLE -1813.54191 3.686380 1

FMCG -1462.33178 2.973262 1

IT -1726.96985 3.516690 4

POWER -1619.64059 3.294702 2

METAL -1907.98357 3.894383 9

OIL GAS -1641.41990 3.353137 9

TABLE- 4:AUGMENTED DICKEY-FULLER TEST FOR INDUSTRIAL RETURNS

INDUSTRY NAME NO. OF LAGS TAU- STATISTIC P-VALUE

AUTOMOBILE 3 -16.2014





TABLE-5: AUGEMENTED DICKEY- FULLER REGRESSION OF AUTOMOBILE

INDUSTRY

DEPENDENT VARIABLE (Yt) INDEPENDENT

VARIABLE CO-EFFICIENT

STANDARD

ERROR T-RATIO P- VALUE

Yt-1 -0.954715 0.0589279 -16.20 0.000

Yt-1 0.0525487 0.0507943 1.035 0.3011

Yt-2 0.0840064 0.0426575 1.969 0.0492

Yt-3 0.0132796 0.0317385 0.4184 0.6757

TABLE-6: AUGEMENTED DICKEY- FULLER REGRESSION OF HEALTH CARE

INDUSTRY


VARIABLE CO-EFFICIENT

STANDARD

ERROR T-RATIO P- VALUE

Yt-1 -0.932412 0.0590844 -15.78 0.000

Yt-1 0.0449442 0.0506426 0.8875 0.3750

Yt-2 0.0572486 0.0422931 1.354 0.1762

Yt-3 -0.0293119 0.0316401 -0.9264 0.3545

TABLE-7: AUGEMENTED DICKEY- FULLER REGRESSION OF PSU INDUSTRY


VARIABLE CO-EFFICIENT STANDARDERROR T-RATIO P- VALUE

Yt-1 -0.927421 0.100902 -9.191 0.000

Yt-1 0.0548600 0.0963860 0.5692 0.5694

Yt-2 0.111401 0.0924200 1.205 0.2283

Yt-3 0.0332749 0.0883061 0.3768 0.7064

Yt-4 0.0228120 0.0828515 0.2753 0.7831

Yt-5 -0.0134660 0.0774038 -0.1740 0.8619

Yt-6 -0.0365102 0.0709886 -0.5143 0.6072

Yt-7 0.00462035 0.0642714 0.07189 0.9427

Yt-8 -0.0274312 0.0573316 -0.4785 0.6324

Yt-9 0.0678314 0.0496639 1.366 0.1723

Yt-10 0.0753571 0.0422990 1.782 0.0751

Yt-11 -0.00269448 0.0320442 -0.08409 0.9330

TABLE-8: AUGEMENTED DICKEY- FULLER REGRESSION OF CAPITAL GOODS

INDUSTRY



Yt-1 -0.865620 0.0417141 -20.75 0.000

Yt-1 -8.55909e-05 0.0317015 -0.002700 0.9978





TABLE-9: AUGEMENTED DICKEY- FULLER REGRESSION OF BANKING INDUSTRY

DEPENDENT VARIABLE (Yt)

INDEPENDENT


Yt-1 -0.920905 0.0421715 -21.84 0.000

Yt-1 0.0389763 0.0316758 1.230 0.2188

TABLE-10: AUGEMENTED DICKEY- FULLER REGRESSION OF CONSUMER GOODS

INDUSTRY



Yt-1 -0.963386 0.0431395 -22.33 0.000

Yt-1 0.0386268 0.0316752 1.219 0.2230

TABLE-11: AUGEMENTED DICKEY- FULLER REGRESSION OF FMCG INDUSTRY



Yt-1 -0.949519 -0.0438541 21.65 0.000

Yt-1 -0.00859111 0.0316886 -0.2711 0.7864

TABLE-12: AUGEMENTED DICKEY- FULLER REGRESSION OF IT INDUSTRY



Yt-1 -0.933471 0.0696107 -13.41 0.000

Yt-1 -0.0123527 0.0626152 -0.1973 0.8436

Yt-2 -0.0569377 0.0536147 -1.062 0.2885

Yt-3 -0.0863471 0.0435286 -1.984 0.0476

Yt-4 -0.0232004 0.0317325 -0.7311 0.4649

TABLE-13: AUGEMENTED DICKEY- FULLER REGRESSION OF POWER INDUSTRY


VARIABLE CO-EFFICIENT STANDARD ERROR T-RATIO P- VALUE

Yt-1 -0.897502 0.0509804 -17.60 0.000

Yt-1 -0.0223555 0.0430953 -0.5187 0.6041

Yt-2 0.0333378 0.0317127 1.051 0.2934





TABLE-14: AUGEMENTED DICKEY- FULLER REGRESSION OF METAL INDUSTRY

DEPENDENT VARIABLE (Yt)

INDEPENDENT


Yt-1 -0.837903 0.0958598 -8.741 0.000

Yt-1 -0.133425 0.0919120 -1.452 0.1469

Yt-2 -0.0580228 0.0868697 -0.6679 0.5043

Yt-3 -0.106771 0.0813799 -1.312 0.1898

Yt-4 -0.153140 0.0748676 -2.045 0.0411

Yt-5 -0.142044 0.0681419 -2.085 0.0374

Yt-6 -0.164812 0.0605182 -2.723 0.0066

Yt-7 -0.114785 0.0526939 -2.178 0.0296

Yt-8 -0.110444 0.0443702 -2.489 0.0130

Yt-9 -0.0291774 0.0318417 -0.9163 0.3597

TABLE-15: AUGEMENTED DICKEY- FULLER REGRESSION OF OIL & GAS

INDUSTRY


VARIABLE CO EFFICIENT STANDARDERROR T-RATIO P- VALUE

Yt-1 -1.04475 0.107867 -9.686 0.000

Yt-1 0.0463984 0.102453 0.4529 0.6507

Yt-2 0.0713329 0.0955918 0.7462 0.4557

Yt-3 -0.0153071 0.0888546 -0.1723 0.8633

Yt-4 -0.0637455 0.0817805 -0.7795 0.4359

Yt-5 -0.0656524 0.0737200 -0.8906 0.3734

Yt-6 -0.0426841 0.0646261 -0.6605 0.5091

Yt-7 -0.0602768 0.0548418 -1.099 0.2720

Yt-8 -0.104721 0.0450953 -2.322 0.0204

Yt-9 -0.00959004 0.0320666 -0.2991 0.7650

DISCUSSION

Table-1 visualises the result of Mardia Multi-Variate test of normality such as Mardias

Skewness test, MardiasKutosis test and HenzeZirklertest. The test was applied for the returns of top

securities listed in BSE. The result of the test confirms that the security returns of securities are

departed from Multi-Variate normality and the returns are non-normally distributed. Hence, the

researcher assumed that the returns of securities are non-normally distributed. Table-2 exhibits the

descriptive statistics of security returns of Automobile Companies. Among the top 5 companies in

automobile industrythe Mean Returns of Bajaj Auto Ltd., and Tata Motors Ltd., are same followed

by Hero Motor Corp., and Maruti Suzuki Ltd., respectively. As for as Maruti Suzuki is concerned the

Standard Deviation of returns are less compared to the remaining companies. This shows the security

returns of Maruti Suzuki Ltd., is less volatile and highly consistent. Finally the Uni-Variate

Skewness, Kurtosis, Sharpe-Wilk Statistics and Anderson-Darling Statistics confirms that the returns

of automobile companies are departed from UniVariate normality and it follows the non-normal

distribution. Table-3Exhibit the selection of optimal lags length for the result of top industries listed





in BSE.The minimum AIC ( Akaike Information criteria). So the optimal lag length for the return of

automobile industries. The followed by the lag length for Health care, PSU, Capital goods are the 11,

1 respectively. Finally the return of PSU industry is have the lag length of 11 days and if is greater

combined to remember industries. Table-4 Exhibit the unit root test are Augmented Dickey-Filler

test which explains accepted or rejected are random walk hypothesis. The TAU statistics of the

Dickey-Filler test for all the industry statistical perform on present level. Hence reject the Null

hypothesis of random walk and accepted the Alternative hypothesis. Which reviews the all industry

do not follow a random walk is having a pattern. Table-5 to Table-15 Visualize the Augmented

Dickey-Filler test for selected industries. In order to perform ADF refers in researcher Yt is

dependent variable in independent variable Yt-1, Yt-2, Yt-3 and etc.., respectively. The shows

the first and endured result in the industries return. Yt-1, Yt-2 , Yt-3 in the return lags of the industry

returns. The result compare that Yt-1, Yt-2, Yt-3 is that of 1 % and 5 % significant level. The

comparison rejects random walk hypothesis for all selected return of industries. The following

suggestions were given to the investor:The return of auto mobile industry is high in all the years.

Which reveals that accordingly to the augmented dickey-filler test, if the investors invest their funds

in the auto mobile industry. They can achieve a maximum possible returns while compared to the

other industries. Moreover the returns of PSU, metal , oil & gas industry are greater when compared

to other industries in over all period basis. The returns earned from oil &gas, metal, PSU industries

follows the above maximum yielding industries. After analyzing the top 10 companies data, the

following recommendations were suggested to investors to invest and cautions to invest the market

share respectively. We find that the following industries is less risk because the unsystematic risk or

marketable risk is less for securities. This shows the random walk hypothesis risk of the following

industries is less compared to non-marketable risk of the industry. The are automobile, health care,

PSU, capital goods, bank, consumer durable, FMCG, IT, power, metal, oil &gas. So investors will

made investment in this industries it avoid risk of loss of securities.

CONCLUSION

Based on the analysis, the researcher comes to a concrete conclusion. This study deals with

the Random walk hypothesis the top industries listed in BSE. At first the researcher observe the

returns of the industries are not normally distributed and its having a different pattern. More over the

researcher emphasis the investors to look into the average returns of the security and also the

industries involved before investing their funds. If the invest observe the industries they can use the

returns of auto mobile industry is play a vital role. Followed by metal, oil & gas, banking industries.

Finally the random walk hypothesis is the most important of an investors whether he/she may be a

individual institutional investor. According to result of the analysis the researcher recommends the

investors to invest their funds in auto mobile, metal, PSU, oil & gas, banking industries. Then only

they can earn a maximum return with the nominal risk.

REFERENCE

[1] Ali F.Darrat and Maosen Zhong (2000) On Testing the Random-Walk Hypothesis: A Model-Comparison Approach Volume 35, Issue 3, pages 105124.





[2] Ankit Agarwal (2006).Testing weak form of Market efficiency by application of simple technical trading rules on the Indian stock market, Dissertation.

[3] Kantesha Sanningammanavara and Kiran Kumar K V, Economic Indicators and Stock Market Performance - An Empirical Case of India, International Journal of Management

(IJM), Volume 5, Issue 8, 2014, pp. 107 - 114, ISSN Print: 0976-6502, ISSN Online:

0976-6510.

[4] Bizhan Abedini(2009).An Evaluation of Efficiency of Kuala Lumpur Stock Exchange, Interdisciplinary Journal of Contemporary Research in Business, August 2009, vol 1, no4.

[5] Darrat, A. F., and Zhong, M. (2000): On testing the random-walk hypothesis: a model-comparison approach. The Financial Review, vol. 35, no. 3, 105-124.

[6] Dickey, D. A., and Fuller, W. A. (1981): Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, vol. 49, 1057- 1072.

[7] Faiq Mahmood, Xia Xinping, Humera Shahid, Muhammad Usman(2006) Global Financial Crisis: Chinese Stock Market Efficiency, ISSN 2229 3795, Asian Journal of management

research.

[8] Kabir M. Hassan, Waleed S. Al-Sultan, and Jamal A. Al-Saleem (2003) Stock Market Efficiency in the Gulf Cooperation Council Countries (GCC): The Case of Kuwait Stock

Exchange. Scientific journal of administrative development, Vol 1 No 1, I.A.D.

[9] P. Srinivasan (2010), Testing Weak-Form Efficiency of Indian Stock Markets, APJRBM Volume 1, Issue 2, November ISSN 2229-4104.

[10] Worthington, Andrew C. & Higgs, Helen (2004) Random walks and market efficiency in European equity markets. Global Journal of Finance and Economics, 1(1), pp. 59-78.

modeling the random walk hypothesis for select industries listed in bse

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