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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
- Indicates 95% Confidence Interval
- Indicates 90% Confidence Interval
Table 4B: F-Statistics for the Granger Tests:
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Null Hypothesis: Large Returns does not Granger Cause Small Returns (90, 95 and 99%
Confidence Intervals are indicated)
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
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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
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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)
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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
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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 99% Confidence Interval
** - 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
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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
*** - Indicates 99% Confidence Interval
** - Indicates 95% Confidence Interval
* - Indicates 90% Confidence Interval
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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
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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
*** - Indicates 99% Confidence Interval
** - Indicates 95% Confidence Interval
* - Indicates 90% Confidence Interval
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
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*
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
*** - Indicates 99% Confidence Interval
** - Indicates 95% Confidence Interval
* - Indicates 90% Confidence Interval
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
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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:
Null Hypothesis: Large Returns does not Granger Cause Small Returns (90, 95 and 99%
Confidence Intervals are indicated)
Year SAMC SARA SAST SATO
2002
2003
2004
2005
2006
2007
2008
2009
2010
- Indicates 99% Confidence Interval
- Indicates 95% Confidence Interval
- Indicates 90% Confidence Interval
Table 8B: F-Statistics for the Granger Tests:
Null Hypothesis: Large Returns does not Granger Cause Small Returns (90, 95 and 99%
Confidence Intervals are indicated)
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
*** - Indicates 99% Confidence Interval
** - Indicates 95% Confidence Interval
* - Indicates 90% Confidence Interval
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
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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.
REFERENCES
Acharya, R. H., (2010). Security Speed of Adjustment and Market Quality: A Case of National Stock
Exchange of India, The IUP Journal of Applied Finance, 16(6) 54 – 65
Altay, E. (2004). Cross-autocorrelation between small and large cap portfolios in the German and
Turkish stock markets. Journal of Financial Management and Analysis, 17(2), 77-92
Brennan, M. J., Jegadeesh, N. & Swaminathan, B. (1993). Investment analysis and the adjustment of
stock prices to common information. Review of Financial Studies, 6, 799 –824.
Brisley, N., & Theobald M. (1996). A Simple Measure of Price Adjustment Coefficients: A Correction,
Journal of Finance, 51(1) 381 –382.
Chan, M. M. (2011). The Causal Relationship between Dual-listed A-shares and H-shares in China:
An Error Correction Model. Journal of Applied Economics and Business Research, 1, 53-63
Chang, EC, GR McQueen and JM Pinegar (1999). Cross-autocorrelation in Asian stock markets.
Pacific-Basin Finance Journal , 7, 471 –493.
Chen, C. X & Rhee S. G. (2010). Short sales and speed of price adjustment: Evidence from the Hong
Kong stock market. Journal of Banking & Finance, 34, 471 –483
Chiang, T. C., Nelling E., & Tan L. (2008). The speed of adjustment to information: Evidence from the
Chinese stock market, International Review of Economics and Finance 17 216 –229
Chordia, T. & Swaminathan, B. (2000). Trading volume and cross-autocorrelations in stock returns.
Journal of Finance 55, 913 –935.
Damodaran, A. (1993). A Simple Measure of Price Adjustment Coefficients, Journal of Finance, 48(1),
387 –400.
8/16/2019 Information Assimilation Among Indian Stocks Impact of Turnover and Firm Size
23/24
8/16/2019 Information Assimilation Among Indian Stocks Impact of Turnover and Firm Size
24/24
Poshakwale, S. & Theobald, M. (2004). Market Capitalization, Cross Correlations, the Lead/Lag
Structure and Microstructure Effects in the Indian Stock Market, Journal of International Financial
Markets, Institutions and Money , 14 (4), 385 – 400
Rutledge, R. W., Zhang, Z. & Karim, K. (2008) Is There a Size Effect in the Pricing of Stocks in the
Chinese Stock Markets?: The Case of Bull Versus Bear Markets, Asia-Pacific Finan Markets, 15, 117-
133
Safvenblad, P. (2000). Trading volume and autocorrelation: Empirical evidence from the Stockholm
Stock Exchange. Journal of Banking & Finance, 24, 1275-1287
Sims, C. (1980). Macroeconomics and Reality. Econometrica, 48(1) 1-48
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