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Chapter IV
Investment in Indian Stock
Market: Return Based Study
4.1
Indexes and Testing Tools
In this chapter, ample light will be thrown on the returns of the
stock market and the volatility in the markets. For the better results of
the study, we have taken 3 periods for analysis. We have gathered the
stock market data for the given three periods.
•
Boom : Period prior to recession -: 01 Jan 2006 – 31 Dec 2007
•
Recession: Period of recession-: 01 Jan 2008- 31 Dec 2009
•
Recovery: Period after recession-: 01 Jan 2010- 31 Dec 2011
Although the recession started knocking the doors somewhere in
2007 but the effect of recession started to be marked in 2008 and further.
So in this study, we have taken these three periods for getting the better
results. In this study, we have chosen the different indices to know the
effect of recession on returns in the different sectors.
•
S&P CNX Nifty
•
Bank CNX
•
FMCG Indices
•
Finance
•
Realty
4.2
For S&P CNX Nifty
The S&P CNX Nifty is the main index of the National Stock
Exchange of India Ltd. (NSE). The behavior of a portfolio of blue chip
companies, the largest and most liquid Indian securities, has been
observed by the index. It includes 50 of the approximately 1430
companies listed on the NSE, represents around 65% of its float-adjusted
market capitalization and is a real reflection of the Indian stock market.
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The S&P CNX Nifty includes 21 sectors of the Indian economy
and proposes investment managers' exposure to the Indian market in one
of the efficient portfolios. The trading has been started in the Index since
April 1996 and is well matched for benchmarking, index funds and
index based derivatives.
4.2.1 Partnership
India Index Services and Products Ltd. (IISL), is owned and
managed by the index S&P CNX Nifty, which is a joint venture of the
NSE and CRISIL. IISL is India’s first specialized company concentrated
upon the index as a core product. IISL has a licensing and marketing
agreement with Standard & Poors, who are leaders worldwide in
providing index services.
4.2.2 Highlights
The S&P CNX Nifty comprises 50 stock, float-adjusted marketcapitalization weighted index for India, reporting for 21 varied sectors
of the economy. It is used for several purposes, such as benchmarking
fund portfolios, index based derivatives and index funds. The S&P CNX
Nifty is evolved from economic research and is made for them
interested in investing and trading in Indian equities.
4.2.2.1 Representation of Market
About 65% of the total float-adjusted market capitalization of the
National Stock Exchange (NSE) represents the S&P CNX Nifty stocks.
4.2.2.2 Diversification
The S&P CNX Nifty is a diversified index, exactly reflecting the
whole market. The reward-to-risk ratio of S&P CNX Nifty is higher
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than that of other major indices, rendering similar returns but at
minimum risk.
4.2.2.3 Liquidity
The best measure of the liquidity of a stock market is its impact
cost. It exactly reflects the costs faced when actually trading on an
index. For a stock to qualify for including in the S&P CNX Nifty, it has
to reliably have market impact cost below 0.50 %, when doing S&P
CNX Nifty trades of Rupees (Rs) 20 million. For a portfolio size of Rs
20 million the current impact cost of the S&P CNX Nifty is 0.13%.
Index portfolios, due to the liquidity of the S&P CNX Nifty
constituent stocks of the NSE and as compared to other indices, the S&P
CNX Nifty has higher correlations with typical investment portfolios in
India. These were the two factors which allows for effective hedging of
the Index.
4.2.3 Index Family
4.2.3.1 S&P CNX Defty.
The S&P CNX Defty is a U.S. dollar-denominated index based on
the S&P CNX Nifty. This index was created to give a benchmark of
Indian stocks to international investors, rendering them with an
instrument for measuring returns on their equity investment in dollar
terms. This assures that the risk arising out of currency fluctuation is
covered through the S&P CNX Defty.
4.2.3.2 Eligibility Criteria
Selection of the index set is based on the following criteria:
•
Liquidity (Impact Cost)
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•
Float-Adjusted Market Capitalization
•
Float
•
Domicile
•
Eligible Securities
•
Other Variables
4.2.3.2.1 Liquidity.
To get include in the index, the security should have traded at an
average impact cost of 0.50 % or less during the last six months, for
90% of the observations. Impact cost is the cost of completing the
transaction in a security in proportion to its index weight, measured by
market capitalization at any point of time. This is the percentage markup
experienced while buying/selling the desired quantity of a security as
compared to its ideal price -- (best buy + best sell)/2.
4.2.3.2.2 Float-Adjusted Market Capitalization.
Companies which are eligible to get included in the S&P CNX
Nifty must have at least twice the float-adjusted market capitalization of
the current smallest index constituent.
4.3.2.3 Float.
Companies to get eligible to be included in the S&P CNX Nifty
should have at least 10% of its stock available to investors (float). For
this purpose, float is stocks which are not kept by the promoters and
related entities (where identifiable) of such companies.
4.2.3.2.4 Domicile.
The company must reside in India and trade on the NSE.
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4.2.3.2.5 Eligible Securities.
All common shares listed on the NSE (which are of equity and
not of preference shares) are eligible to get included in the S&P CNX
Nifty index. Stocks that provide a guaranteed fixed return are not
eligible like convertible stock, bonds, warrants, rights, and preferred.
4.2.3.2.6 Other Variables
For inclusion in the index, a company which comes out with an
IPO will be eligible if it meets the normal eligibility criteria for the
index -- impact cost, float-adjusted market capitalization and float -- for
a three-month period instead of a six-month period.
4.2.4 Timing of Changes
The index is reviewed half yearly, and a six-week notice is given
to the market before making any modification to the index constituents.
4.2.4.1 Additions.
Based on the float adjusted market capitalization criteria, the
complete list of eligible securities is accumulated. After that, the
liquidity (impact cost) and float adjustment filters are applied to them,
respectively. The companies which ranked the top, constitute the
replacement pool. The top stocks, in terms of size (float-adjusted market
capitalization) are, then, recognized for inclusion in the index from the
replacement pool.
4.2.4.2 Deletions.
Stocks may be removed due to mergers, acquisitions or spin-offs.
Otherwise, as noted above, a new eligible stock list is drawn up to
review against the current constituents twice a year. If this new list
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warrants changes in the existing constituent list, then the smallest
existing constituents will be declined in favor of the new additions.
4.2.5 Index Construction
4.2.5.1 Approaches
The S&P CNX Nifty is calculated using a float-adjusted, market
capitalization weighted methodology*, wherein the level of the index
indicates the total market value of all the stocks in the index relative to a
particular base period. The methodology is also taken into consideration
the constituent changes in the index and corporate actions such as stock
splits, rights issuance, etc., without affecting the index value.
From the beginning of June 26, 2009, the S&P CNX Nifty was
being calculated using float-adjusted market capitalization weighted
method, wherein the level of index indicated the float-adjusted market
capitalization of all stocks in the Index.
4.2.6 Index Maintenance
4.2.6.1 Rebalancing
Index maintenance plays an important role in assuring the stability
of the index, as well as in meeting its purpose of being a consistent
benchmark of the Indian equity markets. IISL has formed an Index
Policy Committee, which is engaged in the policy and guidelines for
managing the S&P CNX Nifty. The Index Maintenance Subcommittee
makes all the decisions related to the additions and deletions of
companies in the index. Changes in the index level indicate changes in
the market capitalization of the index which are stimulated by stock
price movements in the market. They do not indicate changes in the
market capitalization of the index, or of the individual stocks, that are
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happened by corporate actions such as dividend payments, stock splits,
and distributions to shareholders, mergers, or acquisitions. When a stock
is replaced by another stock in the index, the index divisor is adjusted so
that the modification in index market value that results from the addition
and deletion does not affect the index level.
4.2.6.2 Calculation Frequency.
The index is computed real-time on all the days on which
National Stock Exchange of India is open.
4.2.7 Currency of Calculation
For the S&P CNX Nifty, all prices are indicated in Indian rupee.
4.2.8 Base Date
The base period for the S&P CNX Nifty index is November 3,
1995, which points the completion of one year of operations of NSE's
Capital Market Segment. The base value of the index has been decided
at 1000, and a base capital of Rs 2.06 trillion.
4.2.9 Index Governance
4.2.9.1 Index Committee
A professional team at IISL, a company started by NSE and
CRISIL, deals the S&P CNX Nifty. The three-tier governance structure
consisting of the board of directors of IISL, the Index Policy Committee,
and the Index Maintenance Subcommittee. IISL has appointed the Index
Policy Committee, which is engaged in the policy and guidelines for
managing the S&P CNX Nifty. In the index all the decisions related to
the additions and deletions of companies are made by the Index
Maintenance Sub-committee. The S&P CNX Nifty fully provides
professionally implemented rules governing index revisions, corporate
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actions, etc. These rules are carefully considered, using Indian market
conditions, to fit in with the operational problems of index funds and
index arbitrageurs.
In this study, the help of some of the symbols has been taken to
make the study easy and compact.
R1 → Boom: Period prior to recession -: 01 Jan 2006 – 31 Dec 2007
R2 → Recession: Period of recession-: 01 Jan 2008- 31 Dec 2009
R3 → Recovery: Period after recession-: 01 Jan 2010- 31 Dec 2011
In the study of daily average returns for all the three periods given
below are the t-test symbols
H0:µ1 = µ2 or µ2 = µ3 or µ1 = µ3
H1:µ1 ≠ µ2 or µ2 ≠ µ3 or µ1 ≠ µ3
Where:
H0 = the null hypothesis: Significance value (p value) > 0.05
H1 = Significance value (p value) < 0.05
µ1 = Daily average return for sectoral wise indices for the period of
Boom (2006-07).
µ2 = Daily average return for sectoral wise indices for the period of
recession (2008-09).
µ3 = Daily average return for sectoral wise indices for the period of
recovery (2010-11).
In the study of volatility of returns through Leven’s Test, the
given below are the symbols
H0:v1 = v2 or v2 = v3 or v1 = v3
H1:v1 ≠ v2 or v2 ≠ v3 or v1 ≠ v3
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Where:
H0 = the null hypothesis: Significance value (p value) > 0.05
H1 = Significance value (p value) < 0.05
v1
= Volatility of daily sectoral index return for the period of Boom
(2006-07).
v2
= Volatility of daily sectoral index return for the period of
Recession (2008-09).
v3 = Volatility of daily sectoral index return for the period of
Recovery (2010-11).
Levene’s Test and T Test have been applied on all five selected
indexes. We will follow our customary steps to the return based analysis
of all five selected indexes:1.
Write the null and alternative hypotheses first:
H0: µ 1 = µ 2 or µ2 = µ3 or µ1 = µ3
H1: µ1 ≠ µ2 or µ2 ≠ µ3 or µ1 ≠ µ3
where µ is the mean return on all the selected indexes during the
period prior to the recession and period of recession and period of
recovery.
2.
Specify the α level: α = .05
3.
The appropriate statistical test we will use is the independent
sample t- test.
4.
The t value is calculated by SPSS software
Levene’s Test In statistics, Levene's Test is an inferential statistic
used to assess the equality of variances for a variable calculated for two
or more groups. Some common statistical procedures assume that
variances of the populations from which different samples are drawn are
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equal. Levene's Test assesses this assumption. It tests the null hypothesis
that the population variances are equal (called homogeneity of variance
or homoscedasticity). If the resulting P-value of Levene's test is less
than some critical value (typically 0.05), the obtained differences in
sample variances are unlikely to have occurred based on random sampling
from a population with equal variances. Thus, the null hypothesis of
equal variances is rejected and it is concluded that there is a difference
between the variances in the population.
Some of the procedures typically assuming homoscedasticity, for
which one can use Levene's Test, include analysis of variance and t-tests.
Levene's Test is often used before a comparison of means. When
Levene's Test shows significance, one should switch over to generalized
tests, free from homoscedasticity assumptions.
Levene's Test may also be used as a main test, for answering a
stand-alone question whether two sub-samples in a given population
have equal or different variances.
T-Test - A T-test is any statistical hypothesis test in which the test
statistic follows a Student's t distribution if the null hypothesis is
supported. It can be used to determine if two sets of data are significantly
different from each other, and are most commonly applied when the test
statistic would follow a normal distribution if the value of a scaling term
in the test statistic were known. When the scaling term is unknown and
is replaced by an estimate based on the data, the test statistic (under
certain conditions) follows a Student's t distribution.
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4.2.10 Return Based Analysis of S&P CNX Nifty
Results of T-Test and Leven’s TestWe have used SPSS software to perform the T- Test and Leven’s
Test. The results have two main parts: descriptive statistics and
inferential statistics. First, the descriptive statistics:
Table 4.1: Group Statistics for S&P CNX Nifty R1v/s R2
Group Statistics
Factor
values
N
Mean
Std.
Deviation
Std. Error
R1
498
.0015506
.01626111
.00072868
R2
489
-.0003389
.02511229
.00113562
Daily Lognormal
Returns on S&P CNX
Nifty
In the above table the result of the output shows that there are 498
observations in R1 (N) and they have an average of .0015506 with a
standard deviation of .016. There are 489 observations in R2 (N) and
they have on average of -.0003389 with a standard deviation of
0.2511229. To understand the daily return of the selected indices of the
stock market we have calculated the lognormal returns for the whole
study period (January 2006 to December 2011). The formula Ln(rtrt1)/100 is used to calculate the daily lognormal return for the
representative indices for the stock market.
Where,
Ln = lognormal returns
rt1 = previous day closing returns
The last column gives the standard error of the mean for each of
the two groups. Standard error mean of I column is .00072868
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(.016261111/ square root of 498). Standard error mean of II column is
.00113562 (.02511229/square root of 489)
The second part of the output gives the inferential statistics:
Table 4.2: Sample Test for S&P CNX Nifty R1v/sR2
Independent Samples Test
Daily
Lognormal
Returns on
S&P CNX
Nifty
Levene’s
Test for
quality of
Variances
F
Sig.
t-test for Equality of Means
t
df
Fig.
Mean
Std. Error
(2-tale) Difference Difference
95% Confidence
Interval of the
Difference
Lower
Equal
variances
assumed
Equal
variances not
assumed
48.741 .000 1.406
985
1.400 833.786
Upper
.160
.00188957 .00134427 -.000748 .00452752
.162
.00188957 .00134929 -.000759 .00453798
In the above table the columns labeled "Levene's Test for Equality
of Variances" tell us whether an assumption of the t-test has been met.
The t-test assumes that the variability of each group is approximately
equal. The column labeled "Sig." under the heading "Levene's Test for
Equality of Variances” gives the significance (p value) of Levene's Test
is .000. If this value is less than or equal to α level for the test (usually
.05), then reject the null hypothesis stating that the variability of the two
groups is equal, indicating that the variances are unequal. If the p value
is less than or equal to the α level, then one should use the bottom row
of the output (the row labeled "Equal variances not assumed.") If the p
value is greater than α level, then one should use the middle row of the
output (the row labeled "Equal variances assumed.") In this observation
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.000 is smaller than α, so we will assume that the variances are not equal
and we will use the bottom row of the output.
The column labeled "t" gives the observed or calculated t value.
In this example, assuming not equal variances, the t value is 1.400. (We
can ignore the sign of t for a two tailed t-test.) The column labeled "df"
gives the degrees of freedom associated with the t test. In this example,
there are 833.786 degrees of freedom.
The column labeled "Sig. (2-tailed)" gives the two-tailed p value
associated with the test. In this example, the p value is .162.
Decide if we can reject H0: As the decision rule is given by: If sig
value or p > α, then reject H0. Here sig or p value .162 is not less than
.05, so we fail to reject H0. That implies that we failed to observe a
difference between mean and sample values.
The daily mean return on S&P CNX Nifty during the period prior
to the recession (2006-07) was 0.15%, whereas the average daily returns
for the period under recession were -0.03%. The results of the
independent sample test indicated that there was no significant
difference, at the 5% level of significance, between the average daily
returns generated during the two periods. Whereas, Levene’s Test values
for the difference in variance of daily stock returns were highly
significant at the 1% level of significance, indicating that the volatility
of daily index returns differed considerably during bullish and bearish
market conditions. Volatility in daily index returns during recession was
2.51%, which was significantly higher than the volatility during the
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period prior to the recession. These results go with the general perception
that the markets are more volatile during recession.
The independent sample t test has been applied to test the equality
of daily mean returns on index and Levene’s Test for testing the
difference in volatility to test the following hypothesis:
1.
H0: µ1= µ2
H1: µ1≠µ2
H0: 0.15% = (-).03%
H1: 0.15% ≠ (-).03%
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value is > .05 it is (0.16) so our null hypothesis (H0)
becomes true (H1) false stating that there is no significant
difference between the mean sample values.
2.
Ho: V1=V2
H1: V1≠V2
H0: 1.6% = 2.5%
H1: 1.6% ≠ 2.5%
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 → H0 True, H1 rejected
Here sig value (.000) is < (.05), hence our null hypothesis H0
rejected and H1 accepted. It depicts that there is significant
difference between variances and markets are volatile in recession
period.
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Table 4.3: Group Statistics for S&P CNX Nifty R1 v/s R3
Group Statistics
Factor
Values
N
Mean
Std.
Deviation
Std. Error
Mean
R1
498
.0015506
.01626111
.00072868
R3
499
-.0002355
.01182847
.00052952
Daily Lognormal
Returns on S&P
CNX Nifty
In the above table the result of the above output shows that there
are 498 observations in R1 (N) and they have an average of .0015506
with a standard deviation of .016. There are 499 observations in R3 (N)
and they have on average of -.0002355 with a standard deviation of
0.01182847.
The last column gives the standard error of the mean for each of
the two groups. Standard error mean of I column is .00072868
(.016261111/ square root of 498). Standard error mean of II column is
.00052952 (.01182847/square root of 499).
The second part of the
output gives the inferential statistics:
Table 4.4: Sample Test for S&P CNX Nifty R1 v/s R3
Independent Samples Test
Daily
Lognormal
Returns on S
& P CNX Nifty
Levene’s Test
for Equality of
Variances
F
Equal variances
13.219
assumed
Equal variances
not assumed
Sig.
t-test for Equality of Means
t
.000 1.984
df
995
Sig.
Mean Std. Error
(2Difference Difference
tailed)
95% Confidence
Interval of the
Difference
Lower
Upper
.048 .00178618 .00090048 .00001914 .00355323
1.983 907.840 .048 .00178618 -00090075 .00001838 .00355399
In the above table the columns labeled "Levene's Test for Equality
of Variances" tell us whether an assumption of the T-Test has been met.
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The T-Test assumes that the variability of each group is approximately
equal. The column labeled "Sig." under the heading "Levene's Test for
Equality of Variances” gives the significance (p value) of Levene's Test
is .000. If this value is less than or equal to α level for the test (usually
.05), then reject the null hypothesis stating that the variability of the two
groups is equal, indicating that the variances are unequal. If the p value
is less than or equal to the α level, then one should use the bottom row
of the output (the row labeled "Equal variances not assumed.") If the p
value is greater than α level, then one should use the middle row of the
output (the row labeled "Equal variances assumed.") In this observation
.000 is smaller than α, so we will assume that the variances are not equal
and we will use the bottom row of the output.
The column labeled "t" gives the observed or calculated t value.
In this example, assuming not equal variances, the t value is 1.983. (We
can ignore the sign of t for a two tailed t-test.) The column labeled "df"
gives the degrees of freedom associated with the T- Test and there are
907.840 degrees of freedom.
The column labeled "Sig. (2-tailed)" gives the two-tailed p value
associated with the test. In this example, the p value is .048.
Decide if we can reject H0: As the decision rule is given by: If sig
value or p > α, then reject H0 or sig value or p < α, then accept H1. Here
sig or p value .048 is less than .05, so we will reject H0. That implies
that there is significant difference between mean and sample values.
The daily mean return on S&P CNX Nifty during the period prior
to the recession (2006-07) was 0.15%, whereas the average daily returns
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for the period under recovery (2010-11) were -0.02%. The results of the
independent sample test indicated that there was no significant difference,
at the 5% level of significance, between the average daily returns
generated during the two periods. Whereas, Levene’s Test values for the
difference in variance of daily stock returns were highly significant at
the 1% level of significance, indicating that the volatility of daily index
returns differs considerably during bullish and bearish market conditions.
Volatility in daily index returns during recovery was 1.1%, which was
significantly lower than the volatility during the period prior to the
recession. These results go with the general perception that the markets
are more volatile during recession.
Independent sample T Test has been applied to test the equality of
daily mean returns on index and Levene’s Test for testing the difference
in volatility to test the following hypothesis:
1.
H0: µ1= µ3
H1: µ1≠µ3
H0: 0.15% = (-).02%
H1: 0.15% ≠ (-).02%
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value is < .05 it is (0.048) so our null hypothesis (H0)
rejected and (H1) accepted stating that there is significant
difference between the mean sample values.
2.
Ho: V1=V3
H1: V1≠V3
H0: 1.6% = 1.1%
95
H1: 1.6% ≠ 1.1%
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (.000) is < (.05), hence our null hypothesis H0
rejected and H1 accepted. It depicts that there is a significant difference
between variances and markets which are volatile in recession period
Table 4.5: Group Statistics for S&P CNX Nifty R2 v/s R3
Group Statistics
Daily Lognormal
Returns on S&P
CNX Nifty
Factor
Values
N
Mean
Std.
Deviation
Std. Error
Mean
R2
489
-.0003389
.02511229
.00113562
R3
499
-.0002355
.01182847
.00052952
In the above table the result of the above output shows that there
are 489 observations in R2 (N) and they have an average of - .0003389
with a standard deviation of .02511229. There are 499 observations in
R3 (N) and they have an average of -.0002355 with a standard deviation
of 0.01182847.
The last column gives the standard error of the mean for each of
the two groups. Standard error mean of I column is .00113562
(.02511229/square root of 489). Standard error mean of II column is
.00052952 (.01182847/square root of 499). The second part of the
output gives the inferential statistics:
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Table 4.6: Sample Test for S&P CNX Nifty R2 v/s R3
Independent Samples Test
Daily
Lognormal
Returns on S
& P CNX
Nifty
Levene’s
Test for
Equality of
Variances
F
Sig.
t-test for Equality of Means
T
Equal variances
106.929 .000 -.083
assumed
Equal variances
not assumed
df
986
Sig.
Mean Std. Error
(2Difference Difference
tailed)
95% Confidence
Interval of the
Difference
Lower
Upper
.934
.00010339 .00124494
-.002546 .00233965
-.083 691.247 .934
.00010339 .00125300
-.002564 .00235676
In the above table the columns labeled "Levene's Test for Equality
of Variances" indicate whether an assumption of the t-test has been met.
The t-test assumes that the variability of each group is approximately
equal. The column labeled "Sig." under the heading "Levene's Test for
Equality of Variances” gives the significance (p value) of Levene's Test
is .000. If this value is less than or equal to α level for the test (usually
.05), then reject the null hypothesis stating that the variability of the two
groups is equal, indicating that the variances are unequal. If the p value
is less than or equal to the α level, then one should use the bottom row
of the output (the row labeled "Equal variances not assumed.") If the p
value is greater than α level, then one should use the middle row of the
output (the row labeled "Equal variances assumed.") In this observation
.000 is smaller than α, so we will assume that the variances are not equal
and we will use the bottom row of the output.
The column labeled "t" gives the observed or calculated t value.
In this example, assuming not equal variances, the t value is .083. (We
can ignore the sign of t for a two tailed t-test.) The column labeled "df"
gives the degrees of freedom associated with the T Test and there are
691.247 degrees of freedom.
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The column labeled "Sig. (2-tailed)" gives the two-tailed p value
associated with the test. In this example, the p value is .934.
Decide if we can reject H0: As the decision rule is given by: If sig
value or p > α, then reject H0 or sig value or p < α, then accept H1. Here
sig or p value .934 is greater than .05, so we will accept H0. That implies
that there is no significant difference between mean and sample values.
The daily mean return on S&P CNX Nifty during the period of
recession (2008-09) was -0.03%, whereas the average daily returns for
the period during recovery (2010-11) were -0.02%. The results of the
independent sample test indicated that there was no significant
difference, at the 5% level of significance, between the average daily
returns generated during the two periods. Whereas, Levene’s Test values
for the difference in variance of daily stock returns which were highly
significant at the 1% level of significance, indicating that the volatility
of daily index returns differed considerably during bullish and bearish
market conditions. Volatility in daily index returns during recovery was
1.18%, which was significantly lower than the volatility during the
period during recession. These results go with the general perception
that the markets are more volatile during recession.
Independent sample T Test has been applied to test the equality of
daily mean returns on index and Levene’s Test for testing the difference
in volatility to test the following hypothesis:
1.
H0: µ2 = µ3
H1: µ2 ≠ µ3
H0: (-) 0.03% = (-).02%
H1: (-) 0.03% ≠ (-).02%
98
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value is > .05 it is (0.934) so our null hypothesis (H0)
accepted and (H1) rejected stating that there is no significant
difference between the mean sample values.
2.
Ho: V2 = V3
H1: V2 ≠ V3
H0: 2.5% = 1.1%
H1: 2.5% ≠ 1.1%
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (.000) is < (.05), hence our null hypothesis H0
rejected and H1 accepted. It depicts that there is a significant
difference between variances and volatility does exist in markets
during the recession period as compared to recovery or boom.
4.3
For Bank Index
The CNX Bank Index is an index consisting of the most liquid
and huge capitalized Indian Banking stocks. It renders investors and
market intermediaries with a benchmark that includes the capital market
performance of the Indian banks. The Index contains 12 stocks from the
banking sector, which has been traded on the National Stock Exchange
(NSE).
99
Table 4.7: Portfolio Characteristics for Bank Index
Methodology:
No. of Constituents:
Launch Date:
Base Date:
Base Value:
Calculation Frequency:
Index Rebalancing:
Index PE:
Free Float Market Capitalization
12
September 15, 2011
January 01, 2000
1000
Real-time Daily
Semi-Annually
15.35
Source: www.nseindia.com
CNX Bank Index is calculated using free float market capitalization
method, wherein the level of the index indicates the total free float
market value of all the stocks in the index relative to particular base
market capitalization value. CNX Bank Index can be utilized for several
purposes such as benchmarking fund portfolios, launching of index
funds, ETF’s and structured products.
4.3.1 Index Methodology
4.3.1.1 Eligibility Criteria for Selection of Constituent Stocks
•
To get included in the bank index the companies must rank within
the top 500 companies ranked by average free-float market
capitalisation and aggregate turnover for the last six months.
•
Companies should constitute a part of the Banking sector.
•
In the last six months, the company’s trading frequency should be
at least 90%.
•
The company should have accounted a positive net worth.
•
The company should have an investable weight factor (IWF) of at
least 10%.
•
The company should have a listing history of 6 months. A
company which comes out with an IPO will be eligible for
100
inclusion in the index, if it fulfils the normal eligibility criteria for
the index for a 3 month period instead of a 6 month period.
•
Final selection of 12 companies shall be done based on the freefloat market capitalization of the companies.
4.3.2 Index Re-Balancing:
Index is re-balanced on half yearly basis. The cut-off date is
January 31 and July 31 of each year, i.e. for semi-annual review of
indices, average data for six months ending the cut-off data is taken into
consideration. Six weeks prior notice is given to market from the date of
modification.
4.3.3 Index Governance:
A professional team at IISL deals CNX Bank Index. The threetier governance structure comprises the Board of Directors of IISL, the
Index Policy Committee, and the Index Maintenance Sub-Committee.
Graph 4.1: Index performance for Bank
Source: www.nseindia.com
The above graph of CNX Bank Index shows that in the year 2008
index was at the level of 10000 and it was at the peak in the last of 2010.
The bank showed the dip in the year 2009. After 2008 index had been
showing the downfall till 2009.
101
Graph 4.2: 1 Year Performance Comparison of Sector Indices
Source: www.nseindia.com
The above graph shows that banking and media sector gave good
returns as compared to the other sectors. IT sector showed negative
returns while energy and metal sector gave less returns as compared to
auto, finance, FMCG and PSU bank sectors.
Table 4.8: Top 10 Constituents by Weightage
Company’s Name
ICICI Bank Ltd.
HDFC Bank Ltd.
State Bank of India
Axis Bank Ltd.
Kotak Mahindra Bank Ltd.
Indusind Bank Ltd.
Bank of Baroda
Yes Bank Ltd.
Punjab National Bank
Canara Bank
Weight (%)
29.02
27.34
13.60
8.08
5.38
3.72
3.22
2.71
2.56
1.57
Source: http://www.nseindia.com/content/indices/ind_cnx_bank.pdf
102
The above table shows that in Bank index the highest weightage
was given to the ICICI bank, HDFC bank. While public sector bank SBI
had given the weightage of 13.60% in the index.
4.3.4 Return Based Analysis of Bank Index
Table 4.9: Group Statistics for Bank Index R1 v/s R2
Group Statistics
Factor
Values
N
Mean
Std.
Deviation
Std. Error
Mean
R1
498
.0015509
.02007969
.00089979
R2
489
-.0001807
.03151807
.00142530
Daily Lognormal
Returns on Bank
CNX
The above table shows that there are 498 observations in R1 (N)
and they have an average of .0015509 with a standard deviation of
.02007969. There are 489 observations in R2 (N) and they have an
average of -.0001807 with a standard deviation of 0.03151807.
The last column gives the standard error of the mean for each of
the two groups. Standard error mean of I column is .00089979
(.02007969/square root of 498) Standard error mean of II column is
.00142530 (.03151807/square root of 489). The second part of the table
gives the inferential statistics:
Table 4.10: Sample Test for Bank Index R1 v/s R2
Independent Samples Test
Daily
Lognormal
Returns on
Bank CNX
Levene’s Test
for Equality of
Variances
F
Equal variances
64.832
assumed
Equal variances
not assumed
Sig.
t-test for Equality of Means
t
df
Sig.
Mean
Std. Error
(2-tailed) Difference Difference
95% Confidence Interval of
the Difference
Lower
Upper
.000 1.031 985
.303
.00173153
.00167907
-.001563
.00502649
825.
711
.305
.00173153
.00168556
-.001577
.00504001
1.027
103
In the above table the column labeled "Sig." under the heading
"Levene's Test for Equality of Variances” gives the significance
(p value) of Levene's Test is .000. In this observation .000 is smaller
than α, so we will assume that the variances are not equal and we will
use the bottom row of the output.
The column labeled "t" gives the observed or calculated t value.
In this example, assuming not equal variances, the t value is 1.027. (We
can ignore the sign of t for a two tailed t-test.) The column labeled "df"
gives the degrees of freedom associated with the t test and there are
825.711 degrees of freedom.
The column labeled "Sig. (2-tailed)" gives the two-tailed p value
associated with the test. In this example, the p value is .305.
Decide if we can reject H0: As the decision rule is given by: If sig
value or p > α, then reject H0 or sig value or p < α, then accept H1. Here
sig or p value .305 is more than .05, so we will accept H0. That implies
that there is no significant difference between mean and sample values.
The daily mean return on Bank index during the period prior to
the recession (2006-07) was 0.15%, whereas the average daily returns
for the period under recession were -0.01%. The results of the
independent sample test indicated that there was no significant
difference, at 5% level of significance, between the average daily returns
generated during the two periods. Whereas, Levene’s Test values for
difference in variance of daily stock returns were highly significant at
1% level of significance, indicating that the volatility of daily index
returns differed considerably during bullish and bearish market
104
conditions. Volatility in daily index returns during recession was 3.15%,
which was significantly higher than the volatility during the period prior
to the recession. These results go with the general perception that the
markets are more volatile during recession.
Independent sample t test has been applied to test the equality of
daily mean returns on Bank index and Levene’s Test for testing the
difference in volatility to test the following hypothesis:
1.
H0: µ1= µ2
H1: µ1≠µ2
H0: 0.15% = (-).01%
H1: 0.15% ≠ (-).01%
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value is > .05 it is (0.30) so our null hypothesis (H0)
becomes true (H1) false stating that there is no significant
difference between the mean sample values.
2.
Ho: V1=V2
H1: V1≠V2
H0: 2.00% = 3.15%
H1: 2.00% ≠ 3.15%
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (.000) is < (.05), hence our null hypothesis H0
rejected and H1 accepted. It depicts that there is significant
difference between variances and markets are volatile in recession
period.
105
Table 4.11: Group Statistics for Bank Index R1 v/s R3
Group Statistics
Daily Lognormal
Returns on Bank
CNX
Factor
Values
N
Mean
Std.
Deviation
Std. Error
Mean
R1
498
.0015509
.02007969
.00089979
R3
499
-.0002505
.01565607
.00070086
The above table shows that there are 498 observations in R1 (N)
and they have an average of .0015509 with a standard deviation of
.02007969. There are 499 observations in R3 (N) and they have an
average of -.0002505 with a standard deviation of 0.01565607.
The last column gives the standard error of the mean for each of
the two groups. Standard error mean of I column is .00089979
(.02007969/square root of 498). Standard error mean of II column is
.00070086 (.01565607/square root of 499)
. The second part of the
table gives the inferential statistics:
Table 4.12: Sample Test for Bank Index R1 v/s R3
Independent Samples Test
Levene’s Test
for Equality
Daily Lognormal of Variances
Returns on Bank
CNX
F
Sig.
Equal variances
assumed
Equal variances
not assumed
13.278
t-test for Equality of Means
t
.000 1.580
Df
995
1.579 938.316
Sig.
Mean Std. Error
(2-tailed) difference Difference
95% Confidence Interval
of the Difference
Lower
Upper
.114
.00180134 .00114026
-.000436
.00403893
.115
.00180134 .00114054
-.000437
.00403965
In the above table the column labeled "Sig." under the heading
"Levene's Test for Equality of Variances” gives the significance
106
(p value) of Levene's Test is .000. In this observation .000 is smaller
than α, so we will assume that the variances are not equal and we will
use the bottom row of the output.
The column labeled "t" gives the observed or calculated t value.
In this example, assuming not equal variances, the t value is 1.579. (We
can ignore the sign of t for a two tailed t-test.) The column labeled "df"
gives the degrees of freedom associated with the t test and there are
938.315 degrees of freedom.
The column labeled "Sig. (2-tailed)" gives the two-tailed p value
associated with the test. In this example, the p value is .115.
Decide if we can reject H0: As the decision rule is given by: If sig
value or p > α, then reject H0 or sig value or p < α, then accept H1. Here
sig or p value.115 is more than .05, so we will accept H0. That implies
that there is no significant difference between mean and sample values.
The daily mean return on Bank Index during the period prior to
the recession (2006-07) was 0.15%, whereas the average daily returns
for the period under recovery (2010-11) were -0.02%. The results of the
independent sample test indicated that there was no significant
difference, at 5% level of significance, between the average daily returns
generated during the two periods. Whereas, Levene’s Test values for
difference in variance of daily stock returns were highly significant at
1% level of significance, indicating that the volatility of daily index
returns differed considerably during bullish and bearish market
conditions. Volatility in daily index returns during recovery was 1.5%,
which was significantly lower than the volatility during the period prior
107
to recession. These results go with the general perception that the
markets are more volatile during the period prior to recession and in the
period of recession as compared to the recovery period.
Independent sample t test has been applied to test the equality of
daily mean returns on index and Levene’s Test for testing the difference
in volatility to test the following hypothesis:
1.
H0: µ1= µ3
H1: µ1≠µ3
H0: 0.15% = (-).02%
H1: 0.15% ≠ (-).02%
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value is (0.11) > .05 it is so our null hypothesis (H0)
accepted and (H1) rejected stating that there is no significant
difference between the mean sample value.
2.
Ho: V1=V3
H1: V1≠V3
H0: 2.00% = 1.5%
H1: 2.00% ≠ 1.5%
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (.000) is < (.05), hence our null hypothesis H0
rejected and H1 accepted. It depicts that there is significant
difference between variances and markets are volatile in recession
and boom period
108
Table 4.13: Group Statistics for Bank Index R2 v/s R3
Group Statistics
Daily
Lognormal
Returns on
Bank CNX
Factor
Values
N
Mean
Std.
Deviation
Std. Error
Mean
R2
489
-.0001807
.03151807
.00142530
R3
499
-.0002505
.01565607
.00070086
The above table shows that there are 489 observations in R2 (N)
and they have an average of -.0001807 with a standard deviation of
.03151807. There are 499 observations in R3 (N) and they have on
average of -.0002505 with a standard deviation of 0.01565607.
The last column gives the standard error of the mean for each of
the two groups. Standard error mean of I column is .00142530
(.03151807/square root of 489). Standard error mean of II column is
.00070086 (.01565607/square root of 499). The second part of the table
gives the inferential statistics:
Table 4.14: Sample Test for Bank Index R2 v/s R3
Independent Samples Test
Daily Lognormal
Returns on Bank
CNX
Levene’s Test
for Equality of
Variances
F
Equal variances
assumed
Equal variances
not assumed
Sig.
t-test for Equality of Means
t
128.686 .000 .044
df
986
.044 711.749
Sig.
Mean
Std. Error
(2-tailed) Difference Difference
95% Confidence
Interval of the
Difference
Lower
Upper
.965
.00006981 .00157860
-.003028
.00316762
.965
.00006981 .00158829
-.003048
.00318811
109
In the above table the column labeled "Sig." under the heading
"Levene's Test for Equality of Variances” gives the significance (p
value) of Levene's Test is .000. In this observation .000 is smaller than
α, so we will assume that the variances are not equal and we will use the
bottom row of the output.
The column labeled "t" gives the observed or calculated t value.
In this example, assuming not equal variances, the t value is .044. (We
can ignore the sign of t for a two tailed t-test.) The column labeled "df"
gives the degrees of freedom associated with the t test and there are
711.749 degrees of freedom.
The column labeled "Sig. (2-tailed)" gives the two-tailed p value
associated with the test. In this example, the p value is .965.
Decide if we can reject H0: As the decision rule is given by: If sig
value or p > α, then reject H0 or sig value or p < α, then accept H1. Here
sig or p value .965 is greater than .05, so we will accept H0. That implies
that there is no significant difference between mean and sample values.
The daily mean return on Bank Index during the period of the
recession (2008-09) was -0.01%, whereas the average daily returns for
the period during recovery (2010-11) were -0.02%. The results of the
independent sample test indicated that there was no significant
difference, at 5% level of significance, between the average daily returns
generated during the two periods. Whereas, Levene’s Test values for
difference in variance of daily stock returns were highly significant at
1% level of significance, indicating that the volatility of daily index
returns differed considerably during bullish and bearish market
110
conditions. Volatility in daily index returns during recovery was 1.5%,
which was significantly lower than the volatility during the period
during recession. These results go with the general perception that the
markets are more volatile during recession.
Independent sample t test has been applied to test the equality of
daily mean returns on index and Levene’s Test for testing the difference
in volatility to test the following hypothesis:
1.
H0: µ2 = µ3
H1: µ2 ≠ µ3
H0: (-) 0.01% = (-).02%
H1: (-) 0.01% ≠ (-).02%
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value is > .05 it is (0.965) so our null hypothesis (H0)
accepted and (H1) rejected stating that there is no significant
difference between the mean sample values.
2.
Ho: V2 = V3
H1: V2 ≠ V3
H0: 3.1% = 1.5%
H1: 3.1% ≠ 1.5%
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (.000) is < (.05), hence our null hypothesis H0
rejected and H1 accepted. It depicts that there is significant
difference between variances and volatility does exist in markets
during the recession period as compared to recovery or boom.
111
4.4
For FMCG Sector
The CNX FMCG Index is made to demonstrate the behavior and
performance of FMCGs (Fast Moving Consumer Goods) which are nondurable, mass consumption products and available off the shelf. The
CNX FMCG Index consisted of 15 stocks from FMCG sector listed on
the National Stock Exchange (NSE). CNX FMCG Index is calculated
using free float market capitalization method, wherein the level of the
index indicates the total free float market value of all the stocks in the
index relative to particular base market capitalization value. CNX
FMCG Index can be utilized for several purposes such as benchmarking
of fund portfolios, launching of index funds, ETF’s and structured
products.
4.4.1 Index Methodology
4.4.1.1 Eligibility Criteria for Selection of Constituent Stocks
•
To get included in the FMCG index the companies must rank
within the top 500 companies ranked by average free-float market
capitalisation and aggregate turnover for the last six months.
•
Companies should constitute a part of the FMCG sector.
•
In the last six months, the company’s trading frequency should be
at least 90%.
•
The company should have accounted a positive net worth.
•
The company should have reported an investable weight factor
(IWF) of at least 10%.
•
The company should have a listing history of 6 months. A
company which comes out with an IPO will be eligible for
inclusion in the index, if it fulfils the normal eligibility criteria for
the index for a 3 month period instead of a 6 month period.
112
•
Final selection of 15 companies shall be made based on the freefloat market capitalization of the companies.
4.4.2 Index Re-Balancing
Index is re-balanced on half yearly basis. The cut-off date is
January 31 and July 31 of each year, i.e. for semi-annual review of
indices, average data for six months ending the cut-off data is taken into
consideration. Six weeks prior notice is given to market from the date of
modification.
4.4.3 Index Governance
A professional team at IISL deals with the CNX FMCG Index.
The three-tier governance structure comprises of the Board of Directors
of IISL, the Index Policy Committee, and the Index Maintenance SubCommittee.
Graph 4.3: Index Performance for CNX FMCG Index
As on December 31, 2012
Source: www.nseindia.com
The above graph shows that the FMCG index had been
continuously increasing since its inception. Even at the time of recession
also it did not show much downfall.
113
Table 4.15: Portfolio Characteristics for FMCG Index
Methodology:
Free Float Market Capitalization
No. of Constituents:
10
Launch Date:
September 22 , 1999
Base Date:
December 01,1995
Base Value:
1000
Calculation Frequency:
Real-time Daily
Index Rebalancing:
Semi-Annually
Index PE:
35.33
Source: www.nseindia.com
Table 4.16: Top 10 Constituents by Weightage for FMCG Index
Company’s Name
Weight (%)
ITC Ltd.
53.47
Hindustan Unilever Ltd.
18.42
United Spirits Ltd.
5.91
Colgate Palmolive (India) Ltd.
3.57
Glaxo Smithkline Consumer Healthcare Ltd.
3.11
Godrej Consumer Products Ltd.
2.63
Dabur India Ltd.
2.41
Tata Global beverages Ltd.
2.19
United Breweries Ltd.
2.11
Marico Ltd.
1.71
Source: www.nseindia.com
The above table shows that more than 50% weightage was given
to the ITC Ltd. in the FMCG index. Hindustan Unilever had weightage
of 18.42%. Balance has divided into other companies.
114
4.4.4 Return Based Analysis of FMCG Index
Table 4.17: Group Statistics for CNX FMCG Index R1 v/s R2
Group Statistics
Factor
Values
N
Mean
Std.
Deviation
Std. Error
Mean
R1
498
.0007337
.01587573
.00071141
R2
489
.0002656
.01833503
.00082914
Daily
Lognormal
Returns on
FMCG CNX
The above table shows that there are 498 observations in R1 (N)
and they have an average of .0007337 with a standard deviation of
.01587573. There are 489 observations in R2 (N) and they have an
average of .0002656 with a standard deviation of 0.01833503.
The last column gives the standard error of the mean for each of
the two groups. Standard error mean of I column is .00071141
(.01587573/square root of 498). Standard error mean of II column is
.00082914 (.01833503/square root of 489). The second part of the table
gives the inferential statistics:
Table 4.18: Sample Test for CNX FMCG Index R1 v/s R2
Independent Samples Test
Levene’s Test
for Equality
Daily Lognormal of Variances
Returns on
FMCG CNX
F
Sig.
Equal variances
assumed
Equal variances
not assumed
4.753
.029
t-test for Equality of Means
T
.429
df
995
.428 960.083
Sig.
Mean
(2-tailed) Difference
Std. Error
Difference
95% Confidence Interval
of the Difference
Lower
Upper
.668
.00046813
.00109108
-.001673
.00260925
.668
.00046813
.00109251
-.001676
.00261211
115
In the above table the column labeled "Sig." under the heading
"Levene's Test for Equality of Variances” gives the significance
(p value) of Levene's Test is .029. In this observation .029 is smaller
than α, so we will assume that the variances are not equal and we will
use the bottom row of the output.
The column labeled "t" gives the observed or calculated t value.
In this example, assuming not equal variances, the t value is .428. (We
can ignore the sign of t for a two tailed t-test.) The column labeled "df"
gives the degrees of freedom associated with the t test and there are
960.083 degrees of freedom.
The column labeled "Sig. (2-tailed)" gives the two-tailed p value
associated with the test. In this example, the p value is .668.
Decide if we can reject H0: As the decision rule is given by: If sig
value or p > α, then accept H0 or sig value or p< α, then accept H1. Here
sig or p value .668 is greater than .05, so we will accept H0. That implies
that there is no significant difference between mean and sample values.
The daily mean return on FMCG index during the period prior to
the recession (2006-07) was 0.07% , whereas the average daily returns
for the period under recession was 0.02% the results of the independent
sample test indicated that there was no significant difference, at 5% level
of significance, between the average daily returns generated during the
two periods. Whereas, Levene’s Test values for difference in variance of
daily stock returns were highly significant at 1% level of significance,
indicating that the volatility of daily index returns differed considerably
during bullish and bearish market conditions. Volatility in daily index
116
returns during recession was 1.8 %, which was significantly higher than
the volatility during the period prior to recession. These results go with
the general perception that the markets are more volatile during
recession.
Independent sample t test has been applied to test the equality of
daily mean returns on Bank index and Levene’s Test for testing the
difference in volatility to test the following hypothesis:
1.
H0: µ1= µ2
H1: µ1≠µ2
H0: 0.07 % = 0.02 %
H1: 0.07 % ≠ 0.02%
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value is > .05 it is (0.668) so our null hypothesis (H0)
becomes true (H1) false stating that there is no significant
difference between the mean sample values.
2.
Ho: V1=V2
H1: V1≠V2
H0: 1.5 % = 1.8 %
H1: 1.5 % ≠ 1.8 %
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (.029) is < (.05), hence our null hypothesis H0
rejected and H1 accepted. It depicts that there is significant
difference between variances and markets are volatile in recession
period.
117
Table 4.19: Group Statistics for CNX FMCG Index R1 v/s R3
Group Statistics
Daily Lognormal
Returns on
FMCG CNX
Factor
Values
N
Mean
Std.
Deviation
Std. Error
Mean
R1
498
.0007337
.01587573
.00071141
R3
499
.0006993
.01022843
.00045789
The above table shows that there are 498 observations in R1 (N)
and they have an average of .0007337 with a standard deviation of
.01587573. There are 499 observations in R3 (N) and they have on
average of .0006993 with a standard deviation of 0.01022843.
The last column gives the standard error of the mean for each of
the two groups. Standard error mean of I column is .00071141
(.01587573/square root of 498). Standard error mean of II column is
.00045789 (.01022843/square root of 499)
The second part of the table gives the inferential statistics:
Table 4.20: Sample Test for CNX FMCG Index R1 v/s R3
Independent Samples Test
Daily
Lognormal
Returns on
FMCG CNX
Equal variances
assumed
Equal variances
not assumed
Levene’s Test
for Equality of
Variance
F
44.740
Sig.
.000
t-test for Equality of Means
T
df
Sig.
Mean
(2-tailed) Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
.041
995
.968
.00003440
.00084568
-.001625
.00169391
.041
848.713
.968
.00003440
.00084603
-.001626
.00169495
In the above table the column labeled "Sig." under the heading
"Levene's Test for Equality of Variances” gives the significance
118
(p value) of Levene's Test is .000. In this observation .000 is smaller
than α, so we will assume that the variances are not equal and we will
use the bottom row of the output.
The column labeled "t" gives the observed or calculated t value.
In this example, assuming not equal variances, the t value is .041. (We
can ignore the sign of t for a two tailed t-test.) The column labeled "df"
gives the degrees of freedom associated with the t test and there are
848.713 degrees of freedom.
The column labeled "Sig. (2-tailed)" gives the two-tailed p value
associated with the test. In this example, the p value is .968.
Decide if we can reject H0: As the decision rule is given by: If sig
value or p>α, then accept H0 or sig value or p < α, then accept H1. Here
sig or p value .968 is greater than .05, so we will accept H0. That implies
that there is no significant difference between mean and sample values.
The daily mean return on FMCG Index during the period prior to
the recession (2006-07) was 0.07 %, whereas the average daily returns
for the period under recovery (2010-11) were 0.06 %. The results of the
independent sample test indicated that there was no significant difference,
at 5% level of significance, between the average daily returns generated
during the two periods. Whereas, Levene’s Test values for difference in
variance of daily stock returns were highly significant at 1% level of
significance, indicating that the volatility of daily index returns differed
considerably during bullish and bearish market conditions. Volatility in
daily index returns during recovery was 1.0%, which was significantly
lower than the volatility during the period prior to recession. These
119
results go with the general perception that the markets are more volatile
during recession.
Independent sample t test has been applied to test the equality of
daily mean returns on index and Levene’s Test for testing the difference
in volatility to test the following hypothesis:
1.
H0: µ1= µ3
H1: µ1≠µ3
H0: 0.07 % = 0.06 %
H1: 0.07 % ≠ 0.06 %
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value is > .05 it is (0.968) so our null hypothesis (H0)
accepted and (H1) rejected stating that there is no significant
difference between the mean sample values.
2.
Ho: V1=V3
H1: V1≠V3
H0: 1.5 % = 1.0 %
H1: 1.5 % ≠ 1.0 %
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (.000) is < (.05), hence our null hypothesis H0
rejected and H1 accepted. It depicts that there is significant
difference between variances and markets are volatile in recession
period
120
Table 4.21: Group Statistics for CNX FMCG Index R2 v/s R3
Group Statistics
Factor
Values
N
Mean
Std.
Deviation
Std. Error
Mean
R2
489
.0002656
.01833503
.00082914
R3
499
.0006993
.01022843
.00045789
Daily Lognormal
Returns on FMCG
CNX
The above table shows that there are 489 observations in R2 (N)
and they have an average of .0002656 with a standard deviation of
.01833503. There are 499 observations in R3 (N) and they have an
average of .0006993 with a standard deviation of 0.01022843.
The last column gives the standard error of the mean for each of
the two groups. Standard error mean of I column is .00082914
(.01833503/square root of 489). Standard error mean of II column is
.00045789 (.01022843/square root of 499).The second part of the table
gives the inferential statistics:
Table 4.22: Sample Test for CNX FMCG Index R2 v/s R3
Independent Samples Test
Daily
Lognormal
Returns on
FMCG CNX
Equal variances
assumed
Equal variances
not assumed
Levene’s Test
for Equality of
Variances
F
71.674
Sig.
.000
t-test for Equality of Means
t
-.460
df
986
-.458 761.627
Sig.
Mean
(2-tailed) Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
.645
.00043374
.00094214
-.002283
.00141510
.647
.00043374
.00094717
-.002293
.00142564
In the above table the column labeled "Sig." under the heading
"Levene's Test for Equality of Variances” gives the significance
121
(p value) of Levene's Test is .000. In this observation .000 is smaller
than α, so we will assume that the variances are not equal and we will
use the bottom row of the output.
The column labeled "t" gives the observed or calculated t value.
In this example, assuming not equal variances, the t value is .458. (We
can ignore the sign of t for a two tailed t-test.) The column labeled "df"
gives the degrees of freedom associated with the t test and there are
761.627 degrees of freedom.
The column labeled "Sig. (2-tailed)" gives the two-tailed p value
associated with the test. In this example, the p value is .647.
Decide if we can reject H0: As the decision rule is given by: If sig
value or p > α, then accept H0 or sig value or p<α, then accept H1. Here
sig or p value .647 is greater than.05, so we will accept H0. That implies
that there is no significant difference between mean and sample values.
The daily mean return on FMCG Index during the period of the
recession (2008-09) was 0.02%, whereas the average daily returns for
the period during recovery (2010-11) were 0.06%. The results of the
independent sample test indicated that there was no significant difference,
at 5% level of significance, between the average daily returns generated
during the two periods. Whereas, Levene’s Test values for difference in
variance of daily stock returns were highly significant at 1% level of
significance, indicating that the volatility of daily index returns differed
considerably during bullish and bearish market conditions. Volatility In
daily index returns during recovery was 1.00%, which was significantly
lower than the volatility during the period during recession. These
122
results go with the general perception that the markets are more volatile
during recession.
Independent sample t test has been applied to test the equality of
daily mean returns on index and Levene’s Test for testing the difference
in volatility to test the following hypothesis:
1.
H0: µ2 = µ3
H1: µ2 ≠ µ3
H0: 0.02 % = 0.06 %
H1: 0.02 % ≠ 0.06 %
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value is > .05 it is (0.64) so our null hypothesis (H0)
accepted and (H1) rejected stating that there is no significant
difference between the mean sample values.
2.
Ho: V2 = V3
H1: V2 ≠ V3
H0: 1.8 % = 1.00%
H1: 1.8 % ≠ 1.00%
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (.000) is < (.05), hence our null hypothesis H0
rejected and H1 accepted. It depicts that there is significant
difference between variances and volatility does exist in markets
during the recession period as compared to recovery or boom.
123
4.5
For Finance Index
The CNX Finance Index is made to demonstrate the behavior and
performance of the Indian financial market which includes banks,
financial institutions, housing finance and other financial services
companies. The CNX Finance Index consisted of 15 stocks that are
listed on the National Stock Exchange (NSE). CNX Finance Index is
calculated using free float market capitalization method, wherein the
level of the index indicates the total free float market value of all the
stocks in the index relative to particular base market capitalization
value. CNX Finance Index can be utilized for several purposes such as
benchmarking fund portfolios, launching of index funds, ETF’s and
structured products.
4.5.1 Index Methodology
4.5.1.1: Eligibility Criteria for Selection of Constituent Stocks
•
To get included in the Finance index the companies must rank
within the top 500 companies ranked by average free-float market
capitalisation and aggregate turnover for the last six months.
•
Companies should constitute a part of the Finance sector.
•
In the last six months, the company’s trading frequency should be
at least 90%.
•
The company should have accounted a positive net worth.
•
The company should have reported an investable weight factor
(IWF) of at least 10%.
•
The company should have a listing history of 6 months. A company
which comes out with an IPO will be eligible for inclusion in the
index, if it fulfils the normal eligibility criteria for the index for a
3 month period instead of a 6 month period.
124
•
Final selection of 15 companies shall be made based on the freefloat market capitalization of the companies.
4.5.2 Index Re-Balancing:
Index is re-balanced on half yearly basis. The cut-off date is
January 31 and July 31 of each year, i.e. for semi-annual review of
indices, average data for six months ending the cut-off data is taken into
consideration. Six weeks prior notice is given to market from the date of
modification.
4.5.3 Index Governance:
A professional team at IISL deals with CNX Finance Index. The
three-tier governance structure comprises the Board of Directors of
IISL, the Index Policy Committee, and the Index Maintenance SubCommittee.
Graph 4.4: Index Performance CNX Finance Index
As on December 31, 2012
Source: www.nseindia.com
125
The above graph indicates that Finance sector was at peak in the
year 2008. In the year 2009 it showed extreme downfall which revealed
the fact that sector had been hit by recession. After 2009 the data
showed that sector was in recovery mode now.
Table 4.23: Portfolio Characteristics for Finance Index
Methodology:
Free Float Market Capitalization
No. of Constituents:
15
Launch Date:
September 07 , 2011
Base Date:
January 01,2004
Base Value:
1000
Calculation Frequency:
Real-time Daily
Index Rebalancing:
Semi-Annually
Index PE:
17.81
Source: www.nseindia.com
Table 4.24: Top 10 Constituents by Weightage for Finance Index
Company’s Name
Weight
(%)
ICICI Bank Ltd.
22.33
Housing Development Finance Corporation Ltd.
21.73
HDFC Bank Ltd.
21.04
State Bank of India
10.47
Axis Bank Ltd.
6.22
Kotak Mahindra Bank Ltd.
4.14
IDFC Ltd.
3.60
Punjab National Bank
1.97
Shriram Transport Finance Co. Ltd.
1.58
LIC Housing Finance Ltd.
Source: www.nseindia.com
1.49
126
The highest weightage has been given to the ICICI bank and
HDFC Ltd. in the finance index. SBI has also good weightage in the
above index.
4.5.4: Return Based Analysis of Finance Index
Table 4.25: Group Statistics for CNX Finance Index R1 v/s R2
Group Statistics
Daily Lognormal
Returns on
Finance Index
Factor
Values
N
Mean
Std.
Deviation
Std. Error
Mean
R1
498
.0018746
.01901717
.00085218
R2
489
.0003408
.03171192
.00143406
The above table shows that there are 498 observations in R1 (N)
and they have an average of .0018746 with a standard deviation of
.01901717. There are 489 observations in R2 (N) and they have on
average of - .0003408 with a standard deviation of 0.03171192.
The last column gives the standard error of the mean for each of
the two groups. Standard error mean of I column is .00085218
(.01901717/square root of 498). Standard error mean of II column is
.00143406 (.03171192/square root of 489)
The second part of the table gives the inferential statistics:
127
Table 4.26: Sample Test for CNX Finance Index R1 v/s R2
Independent Samples Test
t-test for Equality of Means
Daily
Lognormal
Returns on
Finance Index
Levene’s Test
for Equality of
Variances
F
Sig.
T
df
Equal variances
assumed
76.157
.000
1.334
985
Equal variances
not assumed
1.328 796.035
Sig.
Mean
(2-tailed) Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
.183
.00221534
.00166100
-.001044
.00547485
.185
.00221534
.00166816
-.001059
.00548985
In the above table the column labeled "Sig." under the heading
"Levene's Test for Equality of Variances” gives the significance (p
value) of Levene's Test is .000. In this observation .000 is smaller than
α, so we will assume that the variances are not equal and we will use the
bottom row of the output.
The column labeled "t" gives the observed or calculated t value.
In this example, assuming not equal variances, the t value is 1.328. (We
can ignore the sign of t for a two tailed t-test.) The column labeled "df"
gives the degrees of freedom associated with the t test and there are
796.035 degrees of freedom.
The column labeled "Sig. (2-tailed)" gives the two-tailed p value
associated with the test. In this example, the p value is .185.
Decide if we can reject H0: As the decision rule is given by: If sig
value or p>α, then accept H0 or sig value or p<α, then accept H1. Here
sig or p value .185 is greater than .05, so we will accept H0. That implies
that there is no significant difference between mean and sample values.
128
The daily mean return on Finance index during the period prior to
the recession (2006-07) was 0.18%, whereas the average daily returns
for the period under recession were (-) 0.03%, the results of the
independent sample test indicated that there was no significant
difference, at 5% level of significance, between the average daily returns
generated during the two periods. Whereas, Levene’s Test values for
difference in variance of daily stock returns were highly significant at
1% level of significance, indicating that the volatility of daily index
returns differed considerably during bullish and bearish market
conditions. Volatility in daily index returns during the recession was
3.17 %, which was significantly higher than the volatility during the
period prior to recession. These results go with the general perception
that the markets are more volatile during recession.
Independent sample t test has been applied to test the equality of
daily mean returns on Finance index and Levene’s Test for testing the
difference in volatility to test the following hypothesis:
1.
H0: µ1= µ2
H1: µ1≠µ2
H0: 0.18 % = (-) 0.03 %
H1: 0.18 % ≠ (-) 0.03%
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value is > .05 it is (0.18) so our null hypothesis (H0)
becomes true (H1) false stating that there is no significant
difference between the mean sample values.
129
2.
Ho: V1=V2
H1: V1≠V2
H0: 1.9 % = 3.1 %
H1: 1.9 % ≠ 3.1 %
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (.000) is < (.05), hence our null hypothesis H0
rejected and H1 accepted. It depicts that there is significant
difference between variances and markets are volatile in recession
period.
Table 4.27: Group Statistics for CNX Finance Index R1 v/s R3
Group Statistics
Daily Lognormal
Returns on Finance
Index
Factor
Values
N
Mean
Std.
Deviation
Std. Error
Mean
R1
498
.0018746
.01901717
.00085218
R3
499
.0001617
.01498252
.00067071
The above table shows that there are 498 observations in R1 (N)
and they have an average of .0018746 with a standard deviation of
.01901717. There are 499 observations in R3 (N) and they have an
average of - .0001617 with a standard deviation of 0.01498252.
The last column gives the standard error of the mean for each of
the two groups. Standard error mean of I column is .00085218
(.01901717/square root of 498). Standard error mean of II column is
.00067071 (.01498252/square root of 499). The second part of the table
gives the inferential statistics:
130
Table 4.28: Sample Test for CNX Finance Index R1 v/s R3
Independent Samples Test
Daily
Lognormal
Returns on
Finance Index
Equal variances
assumed
Equal variances
not assumed
Levene’s Test
for Equality of
Variances
F
10.834
Sig.
.001
t-test for Equality of Means
T
1.878
df
995
1.878 942.510
Sig.
Mean
(2-tailed) Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
.061
.00203628
.00108421
-.000091
.00416388
.061
.00203628
.00108446
-.000092
.00416452
In the above table the column labeled "Sig." under the heading
"Levene's Test for Equality of Variances” gives the significance (p
value) of Levene's Test is .001. In this observation .001 is smaller than
α, so we will assume that the variances are not equal and we will use the
bottom row of the output.
The column labeled "t" gives the observed or calculated t value.
In this example, assuming not equal variances, the t value is 1.878. (We
can ignore the sign of t for a two tailed t-test.) The column labeled "df"
gives the degrees of freedom associated with the t test and there are
942.510 degrees of freedom.
The column labeled "Sig. (2-tailed)" gives the two-tailed p value
associated with the test. In this example, the p value is .061.
Decide if we can reject H0: As the decision rule is given by: If sig
value or p>α, then accept H0 or sig value or p<α, then accept H1. Here
sig or p value .061 is greater than .05, so we will accept H0. That implies
that there is no significant difference between mean and sample values.
131
The daily mean return on Finance Index during the period prior to
the recession (2006-07) was 0.18 %, whereas the average daily returns
for the period under recovery (2010-11) were (-) 0.016 %. The results of
the independent sample test indicated that there was no significant
difference, at 5% level of significance, between the average daily returns
generated during the two periods. Whereas, Levene’s Test values for
difference in variance of daily stock returns were highly significant at
1% level of significance, indicating that the volatility of daily index
returns differed considerably during bullish and bearish market
conditions. Volatility in daily index returns during recovery was 1.4%,
which was significantly lower than the volatility during the period prior
to the recession. These results go with the general perception that the
markets are more volatile during recession and boom period as
compared to recovery period.
Independent sample t test has been applied to test the equality of
daily mean returns on index and Levene’s Test for testing the difference
in volatility to test the following hypothesis:
1.
H0: µ1= µ3
H1: µ1≠µ3
H0: 0.18 % = (-) 0.016 %
H1: 0.18 % ≠ (-) 0.016 %
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (0.061) is > .05, so our null hypothesis (H0)
accepted and (H1) rejected stating that there is no significant
difference between the mean sample values.
132
2.
Ho: V1=V3
H1: V1≠V3
H0: 1.9 % = 1.4 %
H1: 1.9 % ≠ 1.4 %
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (.001) is < (.05), hence our null hypothesis H0
rejected and H1 accepted. It depicts that there is significant
difference between variances and markets are volatile in boom &
recession period.
Table 4.29: Group s Statistics for CNX Finance Index R2 v/s R3
Group Statistics
Daily Lognormal
Returns on Finance
Index
Factor
Values
N
Mean
Std.
Deviation
Std. Error
Mean
R2
489
.0003408
.03171192
.00143406
R3
499
.0001617
.01498252
.00067071
The above table shows that there are 489 observations in R2 (N)
and they have an average of -.0003408 with a standard deviation of
.03171192. There are 499 observations in R3 (N) and they have an
average of - .0001617 with a standard deviation of 0.01498252.
The last column gives the standard error of the mean for each of
the two groups. Standard error mean of I column is .00143406
(.03171192/square root of 489). Standard error mean of II column is
.00067071 (.01498252/square root of 499). The second part of the table
gives the inferential statistics:
133
Table 4.30: Sample Test for CNX Finance Index R2 v/s R3
Independent Samples Test
Daily
Lognormal
Returns on
Finance Index
Levene’s Test
for Equality of
Variances
F
Equal variances 134.942
assumed
Equal variances
not assumed
Sig.
.000
t-test for Equality of Means
T
-.114
df
986
-.113 692.379
Sig.
Mean
(2-tailed) Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
.909
-.00017906
-00157300
-.003266
.00290776
.910
-.00017906
-00158316
-.003287
.00292930
In the above table the column labeled "Sig." under the heading
"Levene's Test for Equality of Variances” gives the significance
(p value) of Levene's Test is .000. In this observation .000 is smaller
than α, so we will assume that the variances are not equal and we will
use the bottom row of the output.
The column labeled "t" gives the observed or calculated t value.
In this example, assuming not equal variances, the t value is .113. (We
can ignore the sign of t for a two tailed t-test.) The column labeled "df"
gives the degrees of freedom associated with the t test and there are
692.379 degrees of freedom.
The column labeled "Sig. (2-tailed)" gives the two-tailed p value
associated with the test. In this example, the p value is .910.
Decide if we can reject H0: As the decision rule is given by: If sig
value or p > α, then accept H0 or sig value or p<α, then accept H1. Here
sig or p value .910 is more than .05, so we will accept H0. That implies
that there is no significant difference between mean and sample values.
134
The daily mean return on Finance Index during the period of the
recession (2008-09) was (-) 0.03%, whereas the average daily returns for
the period during recovery (2010-11) was (-) 0.016 %. The results of the
independent sample test indicated that there was no significant
difference, at 5% level of significance, between the average daily returns
generated during the two periods. Whereas, Levene’s Test values for
difference in variance of daily stock returns were highly significant at
1% level of significance, indicating that the volatility of daily index
returns differed considerably during bullish and bearish market
conditions. Volatility in daily index returns during recovery was 1.49%,
which was significantly lower than the volatility during the period
during the recession. These results go with the general perception that
the markets are more volatile during recession as compared to recovery
period.
Independent sample t test has been applied to test the equality of
daily mean returns on index and Levene’s Test for testing the difference
in volatility to test the following hypothesis:
1.
H0: µ2 = µ3
H1: µ2 ≠ µ3
H0: (-) 0.03 % = (-) 0.016 %
H1: (-) 0.03 % ≠ (-) 0.016 %
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (0.91) is > .05 it is so our null hypothesis (H0)
accepted and (H1) rejected stating that there is no significant
difference between the mean sample values.
135
2.
Ho: V2 = V3
H1: V2 ≠ V3
H0: 3.17 % = 1.49%
H1: 3.17 % ≠ 1.49%
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (.000) is < (.05), hence our null hypothesis H0
rejected and H1 accepted. It signifies that there is significant
difference between variances and volatility does exist in markets
during the recession period as compared to recovery or boom.
4.6
For Realty Index
CNX Realty Index is made to demonstrate the behavior and
performance of Real Estate companies. The Index comprises 10
companies listed on National Stock Exchange of India (NSE). CNX
Realty Index is calculated using free float market capitalization method,
wherein the level of the index indicates the total free float market value
of all the stocks in the index relative to particular base market
capitalization value. CNX Realty Index can be utilized for several
purposes such as benchmarking fund portfolios, launching of index
funds, ETF’s and structured products.
4.6.1 Index Methodology
4.6.1.1 Eligibility Criteria for Selection of Constituent Stocks
•
To get included in the realty index the companies must rank
within the top 500 companies ranked by average free-float market
capitalisation and aggregate turnover for the last six months.
•
Companies should constitute a part of the realty sector.
•
In the last six months, the company’s trading frequency should be
at least 90%.
136
•
The company should have accounted a positive net worth.
•
The company should have reported an intestable weight factor
(IWF) of at least 10%.
•
The company should have a listing history of 6 months. A
company which comes out with an IPO will be eligible for
inclusion in the index, if it fulfils the normal eligibility criteria for
the index for a 3 month period instead of a 6 month period.
•
Final selection of 20 companies shall be made based on the freefloat market capitalization of the companies.
4.6.2 Index Re-Balancing
Index is re-balanced on half yearly basis. The cut-off date is
January 31 and July 31 of each year, i.e. for semi-annual review of
indices, average data for six months ending the cut-off data is taken into
consideration. Six weeks prior notice is given to market from the date of
modification.
4.6.3 Index Governance
A professional team at IISL deals with CNX Realty Index. The
three-tier governance structure comprises the Board of Directors of
IISL, the Index Policy Committee, and the Index Maintenance SubCommittee.
137
Graph 4.5: Index Performance for CNX Realty Index
As on December 31, 2012
Source: www.nseindia.com
Realty index showed its highest performance in the year 2008.
Index value was more than 1500 in 2008. After 2008 sector showed
extreme downfall and still its level was below 500.
Table 4.31: Portfolio Characteristics for Realty Index
Methodology:
Free Float Market Capitalization
No. of Constituents:
10
Launch Date:
August 30 , 2007
Base Date:
December 29, 2006
Base Value:
1000
Calculation Frequency:
Real-time Daily
Index Rebalancing:
Semi-Annually
Index PE:
Source: www.nseindia.com
29.87
138
Table 4.32: Top 10 Constituents by Weightage for Realty Index
Company’s Name
Weight
(%)
DLF Ltd.
33.27
Unitech Ltd.
18.04
Housing Development and Infrastructure Ltd.
11.61
Oberoi Realty Ltd.
8.07
India Bulls Real Estate Ltd.
7.07
Sobha Developers Ltd.
5.82
D B Realty Ltd.
5.65
Godrej Properties Ltd.
4.60
Anant Raj Ltd.
3.98
Parsvnath Developer Ltd.
Source: www.nseindia.com
1.89
The above table shows that DLF Ltd. has 33.27% weightage
while Unitech ltd. and HDIL have given weightage of 18.04 & 11.61 %
respectively.
4.6.4: Return Based Analysis of CNX Realty Index
Table 4.33: Group Statistics for CNX Realty Index R1 v/s R2
Group Statistics
Daily Lognormal
Returns on Realty
Index
Factor
Values
N
Mean
Std.
Deviation
Std. Error
Mean
R1
498
.0022581
.04033607
.00180750
R2
489
.0002400
.03380604
.00152876
The above table shows that there are 498 observations in R1 (N)
and they have an average of -.0022581 with a standard deviation of
139
.04033607. There are 489 observations in R2 (N) and they have an
average of .0002400 with a standard deviation of 0.03380604.
The last column gives the standard error of the mean for each of
the two groups. Standard error mean of I column is .00180750
(.04033607/square root of 498). Standard error mean of II column is
.00152876 (.03380604/square root of 489). The second part of the table
gives the inferential statistics:
Table 4.34: Sample Test for CNX Realty Index R1 v/s R2
Independent Samples Test
Daily
Lognormal
Returns on
Realty Index
Equal variances
assumed
Equal variances
not assumed
Levene’s Test
for Equality of
Variance
F
10.367
Sig.
t-test for Equality of Means
t
.001 -1.054
df
985
-1.055 961.361
Sig.
Mean
(2-tailed) Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
.292
.00249816
.00237109
-.007151
.00215483
.292
.00249816
.00236731
-.007144
.00214755
In the above table the column labeled "Sig." under the heading
"Levene's Test for Equality of Variances” gives the significance (p
value) of Levene's Test is .001. In this observation .001 is smaller than
α, so we will assume that the variances are not equal and we will use the
bottom row of the output.
The column labeled "t" gives the observed or calculated t value.
In this example, assuming not equal variances, the t value is1 .055. (We
can ignore the sign of t for a two tailed t-test.) The column labeled "df"
gives the degrees of freedom associated with the t test and there are
961.361 degrees of freedom.
140
The column labeled "Sig. (2-tailed)" gives the two-tailed p value
associated with the test. In this example, the p value is .292.
Decide if we can reject H0: As the decision rule is given by: If sig
value or p > α, then accept H0 or sig value or p < α, then accept H1.
Here sig or p value .292 is greater than .05, so we will accept H0. That
implies that there is no significant difference between mean and sample
values.
The daily mean return on realty index during the period prior to
the recession (2006-07) was (-)0.22%, whereas the average daily returns
for the period under recession was 0.02% the results of the independent
sample test indicated that there was no significant difference, at 5%
level of significance, between the average daily returns generated during
the two periods. Whereas, Levene’s Test values for difference in
variance of daily stock returns were highly significant at 1% level of
significance, indicating that the volatility of daily index returns differed
considerably during bullish and bearish market conditions. Volatility in
daily index returns during recession was 3.3 %, which was significantly
lower than the volatility during the period prior to the recession. These
results go with the general perception that in realty sector markets are
more volatile during boom period as compared to recession.
Independent sample t test has been applied to test the equality of
daily mean returns on realty index and Levene’s Test for testing the
difference in volatility to test the following hypothesis:
1.
H0: µ1= µ2
H1: µ1≠µ2
H0: (-) 0.22 % = 0.02 %
141
H1: (-) 0.22 % ≠ 0.02%
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value is > .05 it is (0.29) so our null hypothesis (H0)
becomes true (H1) false stating that there is no significant
difference between the mean sample values.
2.
Ho: V1=V2
H1: V1≠V2
H0: 4.0 % = 3.3 %
H1: 4.0 % ≠ 3.3 %
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (.001) is < (.05), hence our null hypothesis H0
rejected and H1 accepted. It shows that there is significant
difference between variances and markets are volatile in boom &
recession period.
Table 4.35: Group Statistics for CNX Realty Index R1 v/s R3
Group Statistics
Daily
Lognormal
Returns on
Realty Index
Factor
Values
N
Mean
Std.
Deviation
Std. Error
Mean
R1
498
-.0022581
.04033607
.00180750
R3
250
-.0027382
.02286898
.00144636
The above table shows that there are 498 observations in R1 (N)
and they have an average of -.0022581 with a standard deviation of
.04033607. There are 250 observations in R3 (N) and they have on
average of - .0027382 with a standard deviation of 0.02286898.
142
The last column gives the standard error of the mean for each of
the two groups. Standard error mean of I column is .00180750
(.04033607/square root of 498). Standard error mean of II column is
.0014636 (.02286898/square root of 250). The second part of the table
gives the inferential statistics:
Table 4.36: Sample Test for CNX Realty Index R1 v/s R3
Independent Samples Test
Daily
Lognormal
Returns on
Realty Index
Equal variances
assumed
Equal variances
not assumed
Levene’s Test
for Equality of
Variances
F
32.767
Sig.
.000
t-test for Equality of Means
t
df
Sig.
Mean
(2-tailed) Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
.175
746
.861
.00048012
.00274975
-.004918
.00587828
.207
735.412
.836
.00048012
.00231496
-.004065
.00502483
In the above table the column labeled "Sig." under the heading
"Levene's Test for Equality of Variances” gives the significance
(p value) of Levene's Test is .000. In this observation .000 is smaller
than α, so we will assume that the variances are not equal and we will
use the bottom row of the output.
The column labeled "t" gives the observed or calculated t value.
In this example, assuming not equal variances, the t value is .207.
(We can ignore the sign of t for a two tailed t-test.) The column labeled
"df" gives the degrees of freedom associated with the t test and there are
735.412 degrees of freedom.
The column labeled "Sig. (2-tailed)" gives the two-tailed p value
associated with the test. In this example, the p value is .836.
143
Decide if we can reject H0: As the decision rule is given by: If sig
value or p > α, then accept H0 or sig value or p < α, then accept H1.
Here sig or p value .836 is greater than .05, so we will accept H0. That
implies that there is no significant difference between mean and sample
values.
The daily mean return on Realty Index during the period prior to
the recession (2006-07) was (-) 0.22 %, whereas the average daily
returns for the period under recovery (2010-11) was (-) 0.27 %. The
results of independent sample test indicated that there was no significant
difference, at 5% level of significance, between the average daily returns
generated during the two periods. Whereas, Levene’s Test values for
difference in variance of daily stock returns were highly significant at
1% level of significance, indicating that the volatility of daily index
returns differed considerably during bullish and bearish market
conditions. Volatility in daily index returns during recovery was 2.28%,
which was significantly lower than the volatility during the period prior
to the recession. These results go with the general perception that the
markets are more volatile during recession & boom period.
Independent sample t test has been applied to test the equality of
daily mean returns on index and Levene’s Test for testing the difference
in volatility to test the following hypothesis:
1.
H0: µ1= µ3
H1: µ1≠µ3
H0: (-) 0.22 % = (-) 0.27 %
H1: (-) 0.22 % ≠ (-) 0.27 %
Sig value < 0.05 → H1 True, H0 rejected
144
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (0.836) is > .05, so our null hypothesis (H0)
accepted and (H1) rejected stating that there is no significant
difference between the mean sample values.
2.
Ho: V1=V3
H1: V1≠V3
H0: 4.0 % = 2.2 %
H1: 4.0 % ≠ 2.2 %
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (.000) is < (.05), hence our null hypothesis H0
rejected and H1 accepted. It represents that there is significant
difference between variances and markets are volatile in recession
and boom period.
Table 4.37: Group Statistics for CNX Realty Index R2 v/s R3
Group Statistics
Daily Lognormal
Returns on Realty
Index
Factor
Values
N
Mean
Std.
Deviation
Std. Error
Mean
R1
489
.0002400
.03380604
.00152876
R3
250
-.0027382
.02286898
.00144636
The above table shows that there are 489 observations in R2 (N)
and they have an average of .0002400 with a standard deviation of
.033880604. There are 250 observations in R3 (N) and they have on
average of- .0027382 with a standard deviation of 0.02286898.
The last column gives the standard error of the mean for each of
the two groups. Standard error mean of I column is .00152876
145
(.03380604/square root of 489). Standard error mean of II column is
.0014636 (.02286898/square root of 250). The second part of the table
gives the inferential statistics:
Table 4.38: Sample Test for CNX Realty Index R2 v/s R3
Independent Samples Test
Daily
Lognormal
Returns on
Realty Index
Equal variances
assumed
Equal variances
not assumed
Levene’s Test
for Equality of
Variances
F
10.640
Sig.
.001
t-test for Equality of Means
t
1.254
df
737
1.415 681.885
Sig.
Mean
(2-tailed) Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
.210
.00297827
.00237540
-.001685
.00764163
.157
.00297827
.00210454
-.001154
.00711042
In the above table the column labeled "Sig." under the heading
"Levene's Test for Equality of Variances” gives the significance (p
value) of Levene's Test is .001. In this observation .001 is smaller than
α, so we will assume that the variances are not equal and we will use the
bottom row of the output.
The column labeled "t" gives the observed or calculated t value.
In this example, assuming not equal variances, the t value is 1.415. (We
can ignore the sign of t for a two tailed t-test.) The column labeled "df"
gives the degrees of freedom associated with the t test and there are
681.885 degrees of freedom.
The column labeled "Sig. (2-tailed)" gives the two-tailed p value
associated with the test. In this example, the p value is .157.
146
Decide if we can reject H0: As the decision rule is given by: If sig
value or p > α, then accept H0 or sig value or p < α, then accept H1.
Here sig or p value .157 is greater than .05, so we will accept H0. That
implies that there is no significant difference between mean and sample
values.
The daily mean return on Realty Index during the period of the
recession (2008-09) was 0.02%, whereas the average daily returns for
the period during recovery (2010-11) were (-) 0.27 %. The results of the
independent sample test indicated that there was no significant
difference, at 5% level of significance, between the average daily returns
generated during the two periods. Whereas, Levene’s Test values for
difference in variance of daily stock returns were highly significant at
1% level of significance, indicating that the volatility of daily index
returns differed considerably during bullish and bearish market
conditions. Volatility in daily index returns during recovery was 2.28%,
which was significantly lower than the volatility during the period
during the recession. These results go with the general perception that
the markets are more volatile during recession and boom period as
compared to recovery period.
Independent sample t test has been applied to test the equality of
daily mean returns on index and Levene’s Test for testing the difference
in volatility to test the following hypothesis:
1.
H0: µ2 = µ3
H1: µ2 ≠ µ3
H0: 0.02 % = (-) 0.27 %
H1: 0.02 % ≠ (-) 0.27 %
147
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value is > .05 it is (0.21) so our null hypothesis (H0)
accepted and (H1) rejected stating that there is no significant
difference between the mean sample values.
2.
Ho: V2 = V3
H1: V2 ≠ V3
H0: 3.38 % = 2.28%
H1: 3.38 % ≠ 2.28 %
Sig value < 0.05 → H1 True, H0 rejected
Sig value > 0.05 →H0 True, H1 rejected
Here sig value (.001) is < (.05), hence our null hypothesis H0
rejected and H1 accepted. It signifies that there is significant
difference between variances and volatility does exist in realty
markets during the boom and recession period as compared to the
recovery period.
148
REFERENCES:
1.
www.nseindia.com
2.
www.sebi.gov.in
3.
www.nseindia.com/products/content/equities/.../s_n_p_cnx_nifty.
htm
4.
http://en.wikipedia.org/wiki/Student's_t-test
149