information assimilation among indian stocks impact of turnover and firm size

8/16/2019 Information Assimilation Among Indian Stocks Impact of Turnover and Firm Size

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Information Assimilation among Indian stocks: Impact

of turnover and firm size

INTRODUCTION

The Indian Stock Market has been the centre focus in the financial world to gauge and measure the

financial health and stability of the nation. The efficiency of the stock market is measured by its ability

to assimilate information. The measurement of the speed of information assimilation has become an

area of great interest in modern finance research.

The Indian stock market has received much attention since the year 2000 from global investors and

portfolio managers. These transnational investments require assessment of Indian stock market

efficiency for making effective investment decisions. Thus estimating the speed with which information

is assimilated in the share prices has evolved as an important contemporary research area in finance.

The review of literature both across the countries as well as in India deliberated on the issues whether

firm size, trading volume and turnover influence the speed at which the stocks observe market wide

news. Chordia & Swaminathan (2000) proposed that the returns from portfolios consisting of shares

with a large volume can predict the returns of portfolios of low volume shares. Kuo et. al. (2004)

observed the similar results in the Taiwanese market though it is not as strong as that of the US

markets. In India Acharya (2010) used market capitalization as a basis for classifying the companies

Dr. P. Krishna PrasannaIIT

Madras

Anish S. MenonIIT

Madras

ABSTRACT

The efficiency of a stock market is determined by the ability of the shares traded in it

to assimilate information in the least possible time. This study investigates the speed

of information assimilation of different portfolio of shares constructed using the

shares traded in the Bombay Stock Exchange (BSE). The study covers a period of 9

years from 2002 to 2010. Large and small portfolios of 30 stocks each are constructed

with reference to both firm level (market capitalization) and market level (sharestraded, volume traded and turnover ratio) factors. The study uses a Vector Auto

Regression (VAR) model to examine whether the portfolios constructed from the

shares that are highly liquid, frequently traded and have a large market capitalization

(large portfolios) lead the portfolios in which the shares are illiquid, thinly traded and

have a small market capitalization (small portfolios). The results are further augmented

using Granger Causality tests. The study finds that in some years the large portfolios

lead the small portfolios. However overall it is observed that the large portfolios are

not able to explain the movements of returns of the small portfolios.

Keywords: Speed of Information Assimilation – Vector Auto Regression – Granger

Causality


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for estimating the speed of information adjustment. Using ARMA model he found no difference in the

speed of adjustment between small and large companies in India.

In the absence of a clear consensus about the market behavior, the discovery of a security’s intrinsic

value and its reaction to market news remains a challenge. This paper extends the previous researchand examine whether the much debated firm size and turnover has any influence up on the speed of

adjustment across the Indian firms. Various portfolios are constructed based on both firm level

(market capitalization) and market level (shares traded, volume traded and turnover ratio) factors.

The rest of the paper is organized as follows. Section 2 presents the review of literature. Section 3

explains the data and methodology used in the study. Section 4 presents the results and discussion

and concluding remarks are given in section 5.

LITERATURE REVIEW

Review across countries

Theobald and Yallup (2004) observed that the speed of assimilation of information in the share prices

is responsible for the underreactions and overreactions in the market. De Bondt and Thaler (1985,

1987) provide evidence for overreaction while Michaely et.al. (1995) show that the markets primarily

under react.

Cross autocorrelation and Vector Auto Regression (VAR) have been used to examine the speed of

information hypothesis. Chordia and Swaminathan (2000) constructed 16 portfolios based on size and

trading volume characteristics in the US market to test the impact of firm size and turnover upon thespeed of adjustment. Turnover was used as a measure of trading volume. They observed that initially

that both daily and weekly autocorrelation decreased with firm size which led them to infer that large

firms assimilated information faster than small firms in the speed. Another observation they made was

that portfolios with high trading volumes led those with low trading volumes. A VAR model was used

by them to prove that high volume portfolios lead low volume portfolios and not vice-versa. They

suggested that the trading volume is a major factor that determines how lead-lag patterns are formed

in the stock market.

Safvenblad (2000) observes that there is a high degree of autocorrelation between the shares and the

index created using these shares. The high level of positive autocorrelation is attributable to the thin

trading in the market.

Kanas (2004) using the Exponential General Autoregressive Conditional Heteroskedastic (EGARCH)

model and Cross Correlation Function test has observed that there is a lead-lag relationship

between portfolios in the UK market which is caused by the differences in market capitalization of the

portfolio with portfolios with a large market capitalization leading portfolios with smaller market

capitalization.

Altay (2004) uses the Iterative Seemingly Unrelated Regression (ITSUR) model to study the cross-

autocorrelation structure in the German and Turkish markets in two sub-periods. He finds that large


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cap portfolios lead small cap portfolios in the German market in both sub-periods. However in the

case of the Turkish market he finds that this relationship is evident only in one sub-period and not in

the second. This he attributes to the movements in the Asian markets as well as the financial crisis in

Turkey which might have caused this deviant behavior. Kayali and Akarim (2010) use a VAR model to

study the lead-lag relationship of different sized Exchange Traded Funds (ETFs) in Turkey where onefund is made up of the twenty top Turkish companies while the other is made up of the twenty five

most liquid Small and Medium Enterprises (SMEs) listed on the Istanbul Stock-Exchange and find that

the large ETF leads the small ETF.

Review in Asian Markets

Chang et.al. (1999) studied six Asian stock markets (Hong Kong, Japan, Singapore, South Korea,

Taiwan, and Thailand) along with the US market for evidence of cross-autocorrelation. They found

that the cross-autocorrelation exists within the countries studied in various levels with the US being

the strongest and weakest in Singapore, Taiwan, and Thailand. They also observed that cross-

autocorrelation is a phenomenon distinct to a market within a country and is not pervasive across

countries.

Lee and Rui (2000) studied the causal relationship between cross market returns between the

Shanghai A, Shanghai B, Shenzhen A and Shenzhen B shares. They found that there exists feedback

relationships between Shanghai A and Shenzhen B shares, Shanghai B and Shenzhen B shares

where in both cases the volume of the former is able to predict the latter. They also observed that US

share returns was able to predict Shanghai A and Shanghai B share returns. However the Hong Kong

market was unable to do so.

Chiang et.al . (2008) studied the speed of information adjustment hypothesis. They constructed

portfolios consisting of class A and class B shares in the Chinese market and used the VAR model on

them. They found that class A shares are able to adjust assimilate information faster than class B

shares and that class A shares show a quicker speed of adjustment of information that class B

shares.

Chen and Rhee (2010) used a dynamic unrestricted VAR to measure the effect of short sales on the

speed of information adjustment. They found that shortable stocks adjust faster to new information

than non-shortable stocks and that short selling contributes to overall market efficiency.

Chan (2011) uses the cointegration and error correction model to study the causal relationship

between the China A and China H shares. The H shares can be traded by both domestic and foreign

investors while the A shares are restricted to domestic investors only. They observe that there is both

short and long term relationship between both classes of shares. They also note that there is a causal

relationship from A-shares to H-shares but not vice-versa.

Kuo et. al. (2004) used a methodology based on Chordia and Swaminathan (2000) to study the lead

lag relationship of portfolio returns in the Taiwan Stock Market. Their results support the speed of


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information hypothesis though they observe that there is a degree of market inefficiency that exists in

the Taiwanese market.

Review in India

Poshakwale (1996) noted that the Indian market was weak form efficient. He observed that there wasinformation assimilation in the Indian stock market as there existed the ‘day of the week , effect in the

BSE wherein the standard deviations and returns on Monday were lesser than that on Friday because

the prices on Monday would have adjusted for the information of the three previous days.

Marisetty (2003) studied the Indian stock markets using the Brisley and Theobald (1996) corrected

Damodaran model and found that the Indian markets initially overreact before converging to their

intrinsic values. He also noted that compared to the western markets, Indian stock markets were

slower in assimilating market information. He attributes this to the secretive nature of investors with

access to private information in less developed markets who might not disclose it till there is acorrection in prices. He observed a very high degree of overreaction in the Indian market on the first

day which reduced with time. He also observed that market wide information is assimilated into share

prices much faster than firm specific information since the information is publicly available to all

market participants. He used the alternative autocovariance method and observed that the BSE-

SENSEX is more efficient in adjusting for information than the NIFTY which he says displays

overreaction.

Poshakwale and Theobald (2004) conducted a study of four Indian market indices which had different

market capitalization characteristics. They used five market variance estimators to calculate the speedof information adjustment. They found that information was assimilated faster in indices with higher

market capitalization than indices with lower market capitalization. They also observed that indices

with smaller market capitalization demonstrated a general trend of underreaction.

Deo et. al. (2008) use the VAR model and granger causality tests to examine the relationship

between trading volume and returns in the Indian, Hong Kong, Indonesian, Malaysian, Korean,

Japanese and Taiwanese markets. They found that there is no causal relationship between volume

and returns in the Indian market.

Sivakumar (2010) used a Generalized Conditional Auto Regressive Heteroskedasticity (GARCH)

model to analyze the intraday adjustment in the BSE. He noted that information that arrived in a very

small duration of time (five minutes) was given preference over information that arrived later and that

this information was completely adjusted in a period of half an hour.

Acharya (2010) used an Auto Regressive Moving Average (ARMA) model to observe the effects of

change in the market quality or structure on the speed of information adjustment in the securities. He

classified the companies on the basis of market capitalization for estimating the speed of information

adjustment. He found that there was no difference in the speed of adjustment between small and

large companies.


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Joshi (2011) used an ARMA (1,1) model as proposed by Theobald and Yallup (2004) to study the

speed of price adjustment coefficients on a daily, weekly and monthly basis. The ARMA model was

used to capture the speed of information adjustment co-efficient. He found that the there was an

increase in speed of adjustment of information during the period 2002- 2007 with respect to the period

1995-2001. He also observed that during the period 2002-2007 there were significant overreactionsas compared to the period 1995-2001 where there were both overreactions and underreactions. He

also observed that weekly and monthly studies show a lesser degree of over or underreaction and a

fuller adjustment of information as compared to daily studies.

DATA AND METHODOLOGY

Sample and portfolio construction

Portfolios were constructed from listed stocks of the Bombay Stock Exchange (BSE). The portfolios

were constructed based on the stocks traded in the BSE as on 10th October, 2011. For the year

ended 31st December, 2010 there were over six thousand stocks listed in the BSE. These stocks were

first filtered on the basis of the stocks traded continuously for the entire year. These stocks were then

arranged in the descending order of the annual average of four characteristics namely market

capitalization (Lo and Mackinlay, 1988), number of shares traded, Rupee turnover (Brennan et. al.,

1998) and turnover ratio (Chordia and Swaminathan, 2000) (turnover ratio is the ratio of shares traded

to shares outstanding) of the previous year. The portfolios were then created by taking the top thirty

and bottom thirty stocks in each category. Once the portfolio was created then its composition was

held constant for the entire following year. The procedure was repeated for all the years starting from

2002 to 2010. In this manner eight portfolios were created per year amounting to a total of seventy

two portfolios over the nine years period. It is observed that the large portfolio on each of criteria

constitutes the stocks included in the BSE index SENSEX.

Data Sources

The information pertaining to stocks such as the daily closing price, volume traded and number of

shares traded has been collected from the BSE website (www.bseindia.com). The data with regard to

market capitalization has been obtained from the (Centre for Monitoring Indian Economy) CMIE

Prowess database.

The returns were then calculated by taking the natural log of the first difference of the daily closing

price.

(1)

Where Rit is the return of the stock i at time t and P it is the closing price of the stock i at time t.

With first differencing the variables were stationary as has been confirmed by the Phillip Perron (PP)

Test and the Augmented Dickey Fuller (ADF) Test.

Empirical Model

http://www.bseindia.com/http://www.bseindia.com/


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The study is conducted in two parts. In part one the portfolios are analyzed for the entire period from

2002 to 2010 as a single dataset. To further explain the behavior of the portfolios the portfolios are

analyzed annually in the second part of the study. The models and methodology of analysis remains

the same in both cases.

Cross autocorrelation patterns are first examined to understand lead lag patterns across the

constructed large and small portfolios. Then Vector Auto Regression (VAR) model is used to estimate

the relationship between the large and small portfolios. In order to examine the causality between the

variables, the Granger Causality test is used.

Cross autocorrelation

Cross-autocorrelation is the lagged cross-correlation between two variables in a time series. Lo and

Mackinlay (1990) after their study of shares in the US market suggested that the size of the portfolios

play an important role in determining the lead-lag relationship between them with large portfolio

returns leading small portfolios. They further propose that the pattern of lead-lag in portfolios created

based on size cannot be explained only by non-synchronous or thin trading but must be attributable to

the information exchange between the large and the small stocks.

Vector Auto Regression

Sims (1980) introduced the Vector Auto Regression (VAR) model to study the linear

interdependencies between multiple time series. Chordia and Swaminathan (2000) used a bivariate

VAR to test whether the cross-autocorrelations have information separate from their own auto-

correlations and to examine whether the return of high volume stocks to help predict the returns of lowvolume stocks or otherwise.

To mathematically formalize the VAR, consider two portfolios L and S with ‘L’ being the large portfolio

and ‘S’ being the small portfolio. Then the bivariate VAR model will consist of two equations:

(2)

(3)

In the case of regression equation (3) if the lagged returns of portfolio L can predict the current returns

of portfolio S then the returns of portfolio L is said to granger cause the returns of portfolio S. In other

words if the joint test of ck coefficients are statistically significant while the bk coefficients are not then

we can say that the returns of high-volume portfolios granger cause the returns of low-volume

portfolio controlling for the predictive power of lagged returns of low-volume portfolio. The Akaike

Information Criterion (AIC) is used to determine the appropriate lag length for the VAR. Based on the

AIC the lag length of 4 days is considered appropriate. Adopting the methodology of Chordia and

Swaminathan (2000) if the sum of slope coefficients corresponding to returns of portfolio L (a and c) is


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greater than zero, then large portfolio returns are expected to lead small portfolios. This tests for the

sign of predictability and is hence a more stringent test (This methodology is used in part one of the

research for the entire dataset only). The granger causality test (see Granger, 1969) determines the

independence of cross-autocorrelations from portfolio autocorrelations.

RESULTS AND DISCUSSION

Part one: Entire dataset

Descriptive Statistics

Table 1 shows the descriptive statistics of the entire dataset as a whole. It can be observed that the

average returns of the small portfolios are higher than that of the big portfolios. There has been

extensive literature (see Rutledge et. al., 2008) studying the comparative returns of portfolios

constructed from small and large stocks. It has been found that small firms have significantly greater

excess returns than large firms (see Fama and French 1992, 1995, 1996). The present data also

supports the same observation.

Cross autocorrelations

Table 2 shows the first order autocorrelations and cross-autocorrelations between the large and small

portfolios. The hypothesis is that the returns of the large stocks will lead the returns of the small

stocks. For example the hypothesis states that the autocorrelation of SAMCt with its own lag SAMCt-1

should be lower than the cross-autocorrelation of SAMCt with LARGEt-1. However it is observed that

this phenomenon is not observed in any of the four criteria. It can be concluded that there is no

significant lead lag relationship between the small and large portfolios on the basis of the criteria

chosen over the entire period studied as a single dataset. This is consistent with Deo et.al (2008) and

Acharya (2010) where they observe that large stocks do not lead small stocks.


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Table 1: Descriptive Statistics for all years together (mean returns at effective rates) (Total

2241 observations)

MEAN MEDIAN STANDARD DEVIATION N

LAR

GE

SA

TO

SA

ST

SA

RA

SA

M

C

LAR

GE

SA

TO

SA

ST

SA

RA

SAM

C

LAR

GE

SA

TO

SA

ST

SAR

A

SA

MC

0.77

34

4.8

0

82.

42

77.

70

73

1.7

1

0.00

13

0.0

03

1

0.0

029

0.0

027

0.00

39

0.01

71

0.0

184

0.0

18

9

0.01

81

0.02

0230

LARGE: Large Portfolio

SATO: Small Portfolio based on Annual Average Rupee Turnover

SAST: Small Portfolio based on Annual Average Shares Traded

SAMC: Small Portfolio based on Annual Average Market Capitalization

Table 2: Autocorrelation and cross autocorrelation matrices

SAM

C t

LAR

GE t

SAR

A t

LAR

GEt

SAS

T t

LAR

GE t

SAT

O t

LAR

GE t

SAMC

t-1

0.26

80

0.06

67

SAR

A t-1

0.20

80

0.052

0

SAS

T t-1

0.20

50

0.03

64

SAT

O t-1

0.24

70

0.04

67

LARGE

t-1

0.01

77

0.08

70

LAR

GE t-

1

0.00

35

0.087

0

LAR

GE t-

1

0.01

33

0.08

70

LAR

GE t-

1

0.02

89

0.08

70

VAR model and granger causality tests

Table 3 shows the results of the VAR models and table 4A and 4B shows the results of the granger

causality tests.

The following VAR is estimated using the daily data from 1st January, 2002 to 31

st December, 2010.

(4)

(5)

Here r L,t is the return on the large and r S,t is the return on the small portfolio. High refers to ∑ or∑ while Low refers to ∑ or ∑ according to the dependent variable. H1 represents a 1 or c1 while L1 represents b1 or d1 which are the coefficients of the first order lags.


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Table 3: VAR

Daily Returns: Total observations 2241

PORTFOLIO L1 Low H1 High

R2

LARGE-0.004553

0.023038 0.090770***0.070404 0.0125

SAMC 0.261276*** 0.328454 -0.006902 0.020860 0.0784

LARGE 0.005636 0.035055 0.087781*** 0.066673 0.0152

SATO 0.248289*** 0.330577 -0.024675 -0.029495 0.0701

LARGE -0.009097 0.019171 0.091935*** 0.071790 0.0132

SAST 0.189451*** 0.354644 -0.012194 -0.027234 0.0582

LARGE -0.023552 0.026125 0.096109*** 0.070869 0.0155

SARA 0.195529*** 0.338711 -0.000041 -0.024011 0.0564

*** - 99% Confidence Interval

It is observed that the first order lags of the large portfolio and the first order lags of the small portfolio

are significant when the large portfolio and the small portfolio are the predicted variables respectively.

This is also in consonance with the autocorrelation and cross-autocorrelation observations. It is also

observed that the R2

is higher in the equations where the small portfolio returns are the dependent

variables. Small portfolio returns can therefore be better predicted which is in support of the

observations made by Chordia and Swaminathan (2000).

Table 4A shows the summary of the granger causality tests. Table 4B shows the F-statistics of the

tests. The null hypothesis is that the large portfolio returns does not granger the small portfolio

returns. As can be surmised from the autocorrelation and VAR results the large portfolios would not

granger cause the smaller portfolio returns. However it is observed that there is a weak causality in

the case of the portfolios constructed with the annual average number of shares traded as the

criterion. It is found that large portfolio returns do granger-cause small portfolio returns at a 10% level

of significance. In case of this portfolio there is no direct effect of price since it the volume traded and

not the value traded. However the quantity of shares traded also reflects the information with regard

to the shares and has an impact on prices also.The results are similar with weekly returns also.

Table 4A: Granger Results Summarized

Null Hypothesis: Large Returns does not Granger Cause Small Returns (90, 95 and 99%

Confidence Intervals are indicated)

SAMC SARA SAST SATO

- Indicates 99% Confidence Interval



Table 4B: F-Statistics for the Granger Tests:


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SAMC SARA SAST SATO

0.3394 0.2217 0.0946* 0.1912

*** - Indicates 99% Confidence Interval

** - Indicates 95% Confidence Interval* - Indicates 90% Confidence Interval

Part 2: Annual data

In order to further study the effect of large portfolio returns on the returns of small portfolios the data

was studied on an annual basis.

Descriptive statistics:

Table 5A presents the descriptive statistics of the dataset on an annual basis from 2002 to 2010. It isobserved that the mean returns of the small portfolios are higher than that of the large portfolios.

However in the year 2006 the large portfolio returns are higher than the small portfolio returns. The

standard deviations of the returns are not significant also. It is also observed that the portfolios

constructed based on Rupee turnover and market capitalization have yielded positive results

throughout the nine years while the portfolios based on shares traded and turnover ratio have yielded

the same negative returns. Table 5B shows the mean annualized returns while chart 1 is a graphical

representation of the same. The mean annualized returns of the small portfolios are higher than the

returns of the large portfolios on most occasions.

Cross autocorrelations

Table 6 shows the annual first order autocorrelation and cross-autocorrelation matrices. It is observed

that from 2002 to 2005 the cross autocorrelation of the lagged returns of the large portfolios on the

small portfolios is lesser than the autocorrelation of the returns of the small portfolios. However from

2006 onwards to 2010 except for 2008 it is found that the cross autocorrelation of the large portfolio

returns is larger than the autocorrelation of the small portfolios in one or more portfolios. In 2005 this

relationship is observed in the portfolio constructed with shares traded as the criterion. In 2006 this

relationship is observed in the portfolio created with turnover ratio as the criterion. In 2007 thephenomenon is observed in portfolios created with turnover ratio and shares traded as the basis. In

2009 we find the relationship is existent in the portfolio created with the shares traded factor while in

2010 it is found that the relationship is observed in the portfolio created with Rupee turnover as the

criterion. In the case of the averages of autocorrelations and cross autocorrelations which is a simple

average of all annual cross autocorrelations and autocorrelations it is observed that there is no set of

portfolios in any of the four criteria that demonstrates this phenomenon which is in consonance with

the observations made in part one of this study.

Table 5A: Descriptive Statistics


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Ye

ar

MEAN MEDIAN STANDARD DEVIATION N

LAR

GE

SA

TO

SA

ST

SA

RA

SA

MC

LAR

GE

SA

TO

SA

ST

SA

RA

SA

MC

LAR

GE

SA

TO

SA

ST

SA

RA

SA

MC

20

02 0.00

02

0.0

01

9

0.0

02

0.0

02

0.0

02

2

0.00

11

0.0

024

0.0

025

0.0

025

0.00

21

0.01

11

0.0

18

3

0.0

183

0.0

19

4

0.0

209

3

0

20

03 0.00

22

0.0

03

6

0.0

034

0.0

032

0.0

03

9

0.00

27

0.0

029

0.0

030

0.0

028

0.00

39

0.01

06

0.0

18

4

0.0

158

0.0

16

1

0.0

203

3

0

20

04

-

0.00

01

0.0

02

9

0.0

017

0.0

011

0.0

02

8

0.00

20

0.0

046

0.0

038

0.0

034

0.00

50

0.01

77

0.0

19

8

0.0

182

0.0

18

5

0.0

196

3

0

20

05

-

0.0001

0.0

029

0.0008

0.0019

0.0

031

0.0015

0.0047

0.0035

0.0035

0.0051

0.0137

0.0

174

0.0181

0.0

164

0.0208

3

0

20

06 0.00

06

0.0

00

5

-

0.0

004

-

0.0

004

0.0

00

7

0.00

28

0.0

015

0.0

023

0.0

019

0.00

26

0.01

66

0.0

16

1

0.0

196

0.0

18

4

0.0

173

3

0

20

07 0.00

09

0.0

02

7

0.0

007

0.0

007

0.0

04

2

0.00

10

0.0

036

0.0

025

0.0

024

0.00

56

0.01

41

0.0

14

4

0.0

138

0.0

13

1

0.0

156

3

0

20

08

-

0.00

35

0.0

04

3

0.0

069

0.0

057

0.0

04

0

-

0.00

40

0.0

018

0.0

035

0.0

028

0.00

20

0.02

72

0.0

23

5

0.0

266

0.0

24

4

0.0

256

3

0

2009 0.00

22

0.003

0

0.0

020

0.0

021

0.003

8

0.00

13

0.0

027

0.0

025

0.0

032

0.00

44

0.02

34

0.020

1

0.0

202

0.020

9

0.0

215

30

20

10

-

0.00

04

0.0

01

4

0.0

004

0.0

009

0.0

01

4

0.00

06

0.0

037

0.0

025

0.0

016

0.00

38

0.01

15

0.0

15

7

0.0

152

0.0

11

7

0.0

179

3

0

Table 5B: Mean annualized returns


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Chart 1: Mean annualized return

Mean annualized return

Year LARGE SATO SAST SARA SAMC

2002 0.0513 0.6073 0.6479 0.6479 0.7322

2003 0.7437 1.4822 1.3602 1.2441 1.6772

2004 -0.0250 1.0806 0.5368 0.3207 1.0287

2005 -0.0247 1.0626 0.2213 0.6073 1.1680

2006 0.1611 0.1325-

0.0948

-

0.09480.1903

2007 0.2499 0.9517 0.1895 0.1895 1.8276

2008 -0.5764 1.8612 4.3908 3.0250 1.6593

2009 0.7020 1.0646 0.6218 0.6614 1.5039

2010 -0.0955 0.4207 0.1056 0.2533 0.4207

-1.0000

0.0000

1.0000

2.0000

3.0000

4.0000

5.0000

1 2 3 4 5 6 7 8 9

LARGE

SATO

SAST

SARA

SAMC


13/24

Table 6: Annual autocorrelation and cross autocorrelation matrices

2002SAM

C t

LAR

GE t

SAR

A t

LAR

GEt

SAS

T t

LAR

GE t

SAT

O t

LAR

GE t

SAMC

t-1

0.23

90

0.05

43

SAR

A t-1

0.26

60

0.027

6

SAS

T t-1

0.24

50

0.04

40

SAT

O t-1

0.17

10

0.02

34

LARGE

t-10.14

25

0.06

70

LAR

GE t-

1

0.18

53

0.067

0

LAR

GE t-

1

0.16

93

0.06

70

LAR

GE t-

1

0.15

88

0.06

70

2003SAM

C t

LAR

GE t

SAR

A t

LAR

GEt

SAS

T t

LAR

GE t

SAT

O t

LAR

GE t

SAMC

t-1

0.15

00

0.08

20

SAR

A t-1

0.20

00

0.047

9

SAS

T t-1

0.18

60

0.06

86

SAT

O t-1

0.20

30

0.07

93

LARGEt-1

0.00

86

0.14

70

LAR

GE t-

1

0.05

58

0.147

0

LAR

GE t-

1

0.03

12

0.14

70

LAR

GE t-

1

0.02

87

0.14

70

2004SAM

C t

LAR

GE t

SAR

A t

LAR

GEt

SAS

T t

LAR

GE t

SAT

O t

LAR

GE t

SAMC

t-1

0.26

80

0.04

94

SAR

A t-1

0.22

70

0.048

0

SAS

T t-1

0.23

70

0.05

49

SAT

O t-1

0.24

30

0.07

04

LARGE

t-10.19

57

0.02

90

LAR

GE t-

1

0.14

82

0.029

0

LAR

GE t-

1

0.16

36

0.02

90

LAR

GE t-

1

0.13

36

0.02

90

2005SAMC t

LARGE t

SAR A t

LARGEt

SAST t

LARGE t

SATO t

LARGE t

SAMC

t-1

0.31

40

0.06

97

SAR

A t-1

0.23

20

0.108

5

SAS

T t-1

0.14

70

0.11

49

SAT

O t-1

0.27

90

0.13

11

LARGE

t-10.27

86

0.16

90

LAR

GE t-

1

0.21

28

0.169

0

LAR

GE t-

1

0.21

95#

0.16

90

LAR

GE t-

1

0.27

50

0.16

90

2006SAM

C t

LAR

GE t

SAR

A t

LAR

GEt

SAS

T t

LAR

GE t

SAT

O t

LAR

GE t

SAMCt-1 0.4430

-

0.0295

SAR A t-1 0.1550

-

0.0664

SAST t-1 0.2640

-

0.0462

SATO t-1 0.4160

-

0.0012

LARGE

t-10.32

67

0.06

10

LAR

GE t-

1

0.24

45#

0.061

0

LAR

GE t-

1

0.25

73

0.06

10

LAR

GE t-

1

0.31

70

0.06

10

2007SAM

C t

LAR

GE t

SAR

A t

LAR

GEt

SAS

T t

LAR

GE t

SAT

O t

LAR

GE t

SAMC

t-10.26

50

-

0.07

31

SAR

A t-10.09

60

-

0.071

3

SAS

T t-10.05

50

-

0.09

75

SAT

O t-10.21

10

-

0.06

45

LARGEt-1

0.1825

0.0530

LARGE t-

0.1159

#0.053

0LARGE t-

0.1142

#0.05

30LARGE t-

0.1525

0.0530


14/24

1 1 1

2008 SAMC t

LARGE t

SAR A t

LARGEt

SAST t

LARGE t

SATO t

LARGE t

SAMC

t-10.32

10

-

0.00

43

SAR

A t-10.20

60

-

0.007

5

SAS

T t-10.22

30

0.02

08

SAT

O t-10.31

90

0.00

40

LARGE

t-1

-

0.32

71

0.08

80

LAR

GE t-

1

-

0.28

40

0.088

0

LAR

GE t-

1

-

0.31

78

0.08

80

LAR

GE t-

1

-

0.37

03

0.08

80

2009SAM

C t

LAR

GE t

SAR

A t

LAR

GEt

SAS

T t

LAR

GE t

SAT

O t

LAR

GE t

SAMCt-1

0.3160

0.0654

SAR A t-1

0.1860

0.0147

SAST t-1

0.1380

0.0268

SATO t-1

0.1870

0.0544

LARGE

t-10.19

60

0.08

60

LAR

GE t-

1

0.18

49

0.086

0

LAR

GE t-

1

0.15

24#

0.08

60

LAR

GE t-

1

0.15

67

0.08

60

2010SAM

C t

LAR

GE t

SAR

A t

LAR

GEt

SAS

T t

LAR

GE t

SAT

O t

LAR

GE t

SAMC

t-10.04

00

-

0.08

95

SAR

A t-10.19

10

-

0.011

2

SAS

T t-10.15

90

-

0.03

04

SAT

O t-10.14

60

-

0.02

76

LARGE

t-10.07

62

0.00

40

LARGE t-

1

0.08

09

0.004

0

LARGE t-

1

0.13

00

0.00

40

LARGE t-

1

0.16

44#

0.00

40

AVERA

GE

SAM

C t

LAR

GE t

SAR

A t

LAR

GEt

SAS

T t

LAR

GE t

SAT

O t

LAR

GE t

SAMC

t-1

0.29

45

0.01

56

SAR

A t-1

0.21

99

0.011

3

SAS

T t-1

0.20

68

0.01

95

SAT

O t-1

0.27

19

0.03

37

LARGE

t-10.13

50

0.08

80

LAR

GE t-

1

0.11

80

0.088

0

LAR

GE t-

1

0.11

50

0.08

80

LAR

GE t-

1

0.12

71

0.08

80

# - Indicates that the cross-autocorrelation is higher than the autocorrelation.

Daily Returns – Large Portfolio and Small Portfolio (Market Capitalization)


15/24

YEARPORTFOLI

OLag a b c d

R

2

2002 LARGE 1 .04189 .0154116 0.0067

2-

.0681304.0205789

SAMC 1 -.0573863 .2586546***

0.0852

2-

.414211***.1427449*

2003 LARGE 1.1529419

*-.0066933 0.0222

2 .027244 -.018461

SAMC 1 -.2992721*.2518985**

*0.0363

2 .0353951 -.0044238

2004 LARGE 1-

.0442754.1166622 0.0450

2-

.1597911-.0666641

SAMC 1 .0242289.2803428**

*0.0894

2 -.1471138* .002294

2005 LARGE 1 .179769** .0095558 0.0412

2 -.11098 -.0019419

SAMC 1 .2370705** .2471618***

0.1246

2 -.0983724 .0313336

2006 LARGE 1 .075251 -.0296064 0.0182

2-

.0291044-.0825871

SAMC 1 .1128613.3872787**

*0.2092

2 -.0643326 .0361892

2007 LARGE 1 .0901513 -.0852155 0.0385

2 .075841

-

.1652675

**

SAMC 1 .0248723.2528456**

*0.0841

2 .1500412* -.0891225

2008 LARGE 1.1862981

*.1448102 0.0154

2 .0084374 -.0059608

SAMC 1 -.218727** .1348373 0.12722 .0457024 .1036935


16/24

VAR

VAR models are fitted for each bivariate set of portfolios in every year. In all there are thirty six models

for the nine years from 2002 to 2010. Tables 7A to 7D give the summary results of the VAR models.

Table 7A: Portfolios based on market capitalization:


** - Indicates 95% Confidence Interval

* - Indicates 90% Confidence Interval

Table 7B: Portfolios based on Rupee turnover:

Daily Returns –

Large Portfolio and Small Portfolio (Turnover (Rs.))

YEARPORTFOLI

OLag a b c d

R

2

2002 LARGE 1 .0842631 -.0191286 0.0063

2-

.0631822.0246926

SATO 1 .1573262 .1090004 0.0640

2

-

.3891653**

*

.2046748**

2003 LARGE 1.1455764

*-.0010004 0.0228

2 .0347597 -.0277329

SATO 1 -.2596961* .296883*** 0.0561

2 -.0262486 -.0092953

2004 LARGE 1-

.0647987

.1372219

*0.0476

2

-

.1483384

*

-.0701989

SATO 1 -.0775862.3092498**

*0.0795

2009 LARGE 1 .11182 -.0394965 0.0170

2-

.1158795.1459531

SAMC 1 .0143828 .254567*** 0.1269

2 -.0550513 .205723**

2010 LARGE 1 .057537

-

.0765956

*

0.0178

2 .0484424 .0366906

SAMC 1 .1261813 .0049023 0.0130

2 -.0605659 .0948833


17/24

2 -.154824* -.0012931

2005 LARGE 1.1374821

*.0721726 0.0469

2 -.131569* .0068587

SATO 1 .2118941** .2171869***

0.1097

2 -.0603503 -.0538309

2006 LARGE 1 .0661004 -.0076933 0.0132

2-

.0532463-.0547808

SATO 1 .10269.3569307**

*0.1899

2 -.1127689 .0806468

2007 LARGE 1 .093175 -.0913761 0.0276

2 .0414611

-

.1334684

*

SATO 1 .0436274 .1954432** 0.0479

2 .0236256 -.0367497

2008 LARGE 1 .215739**.2021954

*0.0196

2 -.016489 -.0741996

SATO 1-

.297102***.043984 0.1558

2 .039403 .1454712*

2009 LARGE 1 .1119233 -.037894 0.0136

2-

.0994999.1197284

SATO 1 .0740587 .0934784 0.0664

2 -.0820134.2337226**

*

2010 LARGE 1 .0259603 -.0382175 0.0063

2 .063389 .0140175SATO 1 .1709189* .0880764 0.0336

2 -.0187004 .0287904





18/24

Table 7C: Portfolios based on shares traded:

Daily Returns – Large Portfolio and Small Portfolio (Shares Traded)

YEAR

PORTFOLI

O Lag a b c d

R

2

2002 LARGE 1 .0545047 .006774 0.0069

2-

.0758038.0319095

SAST 1 .0183519.2444239**

*0.0902

2

-

.3800317**

*

.1385836*

2003 LARGE 1

.1552791

* -.0123898 0.0243

2 .0439014 -.0426902

SAST 1 -.2029391*.2741365**

*0.0480

2 -.040499 -.0035271

2004 LARGE 1-

.0860946.1657964* 0.0531

2-

.0946831-.1485452

SAST 1 -.0718381 .329027*** 0.1010

2-

.1978376**-.0302468

2005 LARGE 1.1533281

**.0561705 0.0460

2 -.131608* .0182117

SAST 1.2518696**

*.0650606 0.0684

2 -.1325075 .1360456**

2006 LARGE 1

.1432787

* -.1091708 0.0232

2-

.1133319.0786963

SAST 1 .2148684** .1354055* 0.0945

2 .0237308 .076634

2007 LARGE 1.1361858

*

-

.1670566*

*

0.0247

2-

.0232513-.0148682

SAST 1 .1270337* -.0075552 0.0187

2 -.0688208 .084656


19/24

2008 LARGE 1.2023422

**.1696881* 0.0208

2-

.0001907-.0290889

SAST 1-

.3494104**

*

-.0427535 0.1238

2 .0656573 .1920823**

2009 LARGE 1 .1367585 -.0795561 0.0119

2-

.0600011.0616223

SAST 1 .1136309 .0221299 0.0432

2 .025632 .1142788

2010 LARGE 1 .0202644 -.0327088 0.00782 .0886358 -.0358308

SAST 1 .1010542 .1218212* 0.0289

2 -.0125593 .0152155




Table 7D: Portfolios based on shares traded:

Daily Returns – Large Portfolio and Small Portfolio (Turnover Ratio)

YEAR PORTFOLI

O

Lag a b c d

R

2002 LARGE 1 .0720079 -.0081557 0.0072

2 -

.0761244.0348871

SARA 1.0649588

.2461886**

*

0.1031

2 -

.4058371**

*

.1501245*

2003 LARGE 1 .1797033

**-.0382114

0.0239

2 .0117566 -.0090884

SARA 1-.1315616

.2476227**

*

0.0499

2 -.1025275 .0491452

2004 LARGE 1 -

.0829847

.1552284

*

0.0534

2 -.0690737

-.1708499


20/24

*

SARA 1-.1041483

.3409354**

*

0.0971

2 -.1851606* -.0472238

2005 LARGE 1 .1586503**

.0481401 0.0436

2 -

.1058497-.0182309

SARA 1 .1513745* .179708** 0.0694

2 -.0466695 -.0064396

2006 LARGE 1.1961678

**

-

.1686844

**

0.0318

2 -

.1134728

.0851192

SARA 1 .3064976**

*-.0380906

0.0648

2 -.023803 .0849735

2007 LARGE 1 .1225738 -.1409933 0.0170

2 -

.0351395.0037

SARA 1 .0920102 .049194 0.0198

2 -.0723073 .061044

2008 LARGE 1 .1883887*

.14975 0.0154

2 -

.0114256-.0257205

SARA 1 -

.294758***-.0626683

0.0923

2 -.0045603 .1086158

2009 LARGE 1 .1556941

*-.106904

0.0154

2 -.074073 .0928244

SARA 1 .1284428* .0549088 0.06592 .016376 .150438*

2010 LARGE 1 .0221815 -.0344627 0.0059

2 .0419316 .045162

SARA 1 -.0080014 .168319 0.0495

2 -.0292998 .1322124




The lag lengths are selected using the Akaike Information Criterion (AIC). In most cases in the

equations where the small portfolio returns is the dependent variable the coefficient of the large


21/24

portfolio returns (c) as the dependent/endogenous variable is significant. This supports the

observations made in table 6 where the cross autocorrelations of the lagged returns of the large

portfolio with that of small portfolios is higher than the autocorrelation of the small portfolio returns.

The R2of equations where the small portfolio returns is the dependent variable is also higher than that

where the large portfolio returns are the dependent variables thus again confirming the observationmade in part one of this study that the small portfolio returns are better predicted. Table 8A and 8B

give the results of the annual granger causality tests

Table 8A: Granger Results Annual Summarized:



Year SAMC SARA SAST SATO

2002

2003

2004

2005

2006

2007

2008

2009

2010




Table 8B: F-Statistics for the Granger Tests:



Year SAMC SARA SAST SATO

2002 3.58483** 4.30061** 3.85058** 4.32185**

2003 1.73239 1.21453 1.65993 1.93754

2004 1.47470 2.42539* 2.55475* 1.73529

2005 2.65583* 1.59985 4.54125** 2.78357*

2006 1.37097 5.22800*** 2.85865* 2.12495

2007 1.68198 1.30429 1.81158 0.21592

2008 3.14951** 6.03167*** 9.05958*** 7.16240***

2009 0.26282 1.42984 1.21458 0.97977

2010 0.80874 0.08481 0.60801 1.65713




It is observed that the large returns are shown to granger-cause the small portfolio returns in three out

of nine years in case of the portfolios constructed using market capitalization as the criterion, four out

of nine years in case of the portfolios created using turnover ratio as the basis, five out of nine years

in case of the portfolios created using shares traded as the factor and three out of nine years in the

case of the portfolios created using Rupee turnover as the criterion. This confirms the observations


22/24

made by Chordia and Swaminathan (2000) though the relationship is not as strong as that in the US

and other developed markets. This also confirms the observations made by Deo et. al. (2008) and

Acharya (2010) that in the case of Indian markets there was no difference in the speed of adjustment

of information between large and small stocks.

CONCLUSION

This paper examines the speed of information hypothesis as proposed by Chordia and Swaminathan

(2000) with reference to the Indian market. The study covers a period of nine years. Autocorrelations

and cross autocorrelations have been studied for the various portfolios constructed.VAR and Granger

Causality tests have been used to study the relationship between the portfolio returns of the large

portfolios and small portfolios. It is observed that though there is a relationship between large and

small portfolios with the returns of large portfolios leading that of small portfolios, this phenomenon is

weak and not consistent across time and the criterion used to construct the portfolios. This is

confirmatory of the observations made in other studies that also observe similar behavior in

developing markets with different strengths though not as strong as developed markets.

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information assimilation among indian stocks impact of turnover and firm size

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