A Study on Designing Profitable Trading Rule - Indian Stock Market

krunal_dhabhi · Sep 30, 2014

Description
The Indian stock market, along with its sectors, around the financial crisis. To understand the market structure, the study makes use of exploratory factor analysis.

Chapter 2
Trends in Indian Stock Market: Scope
for Designing Pro?table Trading Rule?
Abstract This chapter explores the latent structure in the Indian stock market,
along with its sectors, around the ?nancial crisis. To understand the market
structure, the study makes use of exploratory factor analysis. It also tracks the
factor scores along with the cycles in the respective indexes to scrutinize the
underlying market behavior. Apart from looking for the latent structure, the
chapter seeks to explore the following issues: How the market has behaved over
the period of study? What are the trends at sectoral level? Are they similar, or
otherwise to the market trends? Are the trends independent of the selection of the
stock market exchanges and whether, and how ?nancial crisis could affect such
trends? The rationale behind such analyses is to see whether there has been any
discernible change in the market structure before and after the shock. A clear
behavioral pattern would hint toward an inef?cient market and possible scope for
designing pro?table portfolio mix.
Keywords Indian stock market
Á
Bombay stock exchange
Á
National stock
exchange
Á
Stock market cycle
Á
Structural break
Á
Exploratory factor analysis
In the business world, the rearview mirror is always clearer
than the windshield.
Warren Buffett
2.1 Introduction
The presence of momentum trading and the resultant trial put on the ef?cient
market hypothesis have attracted the attention of ?nancial analysts and researchers.
Momentum trading is a result of irrational investor behavior or ‘‘psychological
biases’’ or ‘‘biased self-attribution’’, and may lead to, in extreme cases, herd
behavior, formation of bubble, and subsequent panic and crashes in ?nancial
market. The speculative bubble generated by momentum trading in?ate, becomes
G. Chakrabarti and C. Sen, Momentum Trading on the Indian Stock Market,
SpringerBriefs in Economics, DOI: 10.1007/978-81-322-1127-3_2,
Ó The Author(s) 2013
5
‘self-ful?lling’ until they eventually burst with their far-reaching, ruinous impact
on real economy. The crash is usually followed by an irrational, negative bubble.
Momentum trading thus leads to irrational movement in prices in both directions
and its presence is a serious attack on the myth that a capitalist system is self-
regulating heading toward a stable equilibrium. Rather, as noted by Shiller and
others, it is an unstable system susceptible to ‘‘irrational exuberance’’ and ‘‘irra-
tional pessimism’’.
Ours is a study that explores the possible presence of momentum trading in the
Indian stock market in recent years, particularly in light of the recent global ?nancial
melt-down of 2007–2008. Given the close connection between ?nancial melt-down
and speculative trading, the relevance of the study is obvious. The study starts with
an exploration of the trend and latent structure in the Indian stock market around the
crisis and eventually tries to relate the instability to the speculative trading.
2.2 Trends and Latent Structure in Indian Stock Market
While analyzing the trends in the Indian stock market around the ?nancial crisis of
2007–2008, the study uses some benchmark stock market indexes along with
different sectoral indexes. The Bombay stock exchange (BSE) and the National
stock exchange (NSE) are the two oldest and largest stock market exchanges in
India and hence, could be taken as representatives of the Indian stock market. The
study analyzes the trends, their similarities and dissimilarities, in the two
exchanges to get a complete description of Indian stock market movements. While
analyzing the market trends the study concentrates on the following:
How the market has behaved over the period of study. Has there been any latent
structure in the market?
What are the trends at sectoral level? Are they similar, or otherwise, to the market
trends?
Are the trends independent of the selection of the stock market exchanges?
Whether and how ?nancial crisis could affect the market trends?
Before we go into the detailed analysis let us brie?y report on the market index and
the sectoral indexes that the study picks up from the two exchanges.The study uses
daily price data for all the market and sectoral indexes for the period ranging from
January 2005 to September 2012. The price data are then used to calculate daily
return series using the formula R
t
= ln(P
t
/P
t-1
), where P
t
is the price on the t’th day.
2.2.1 The Market and the Sectors: Bombay Stock Exchange
The study considers BSE SENSEX or BSE Sensitive Index or BSE 30 as the
market index from BSE. BSE SENSEX, which started in January 1986 is a value-
6 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
weighted index composed of 30 largest and most actively traded stocks in BSE.
The SENSEX is regarded as the pulse of the domestic stock markets in India.
These companies account for around 50 % of the market capitalization of the BSE.
The base value of the SENSEX is 100 on April 1, 1979, and the base year of BSE-
SENSEX is 1978–1979. Initially, the index was calculated on the ‘full market
capitalization’ method. However, it has switched to the free ?oat method since
September 2003. The stocks represent different sectors such as, housing related,
capital goods, telecom, diversi?ed, ?nance, transport equipment, metal, metal
products and mining, FMCG, information technology, power, oil and gas, and
healthcare.
As far as the sectoral indexes are concerned, we select 11 market capitalization
weighted sectoral indexes introduced by BSE in 1999. These are BSE AUTO, BSE
BANKEX, BSE CD, BSE CG, BSE FMCG, BSE IT, BSE HC, BSE PSU, BSE
METAL, BSE ONG, and BSE POWER. Of these indexes, only BANKEX has its
base year in 2000. All the others have base year in 1999 with base value of 100 in
February 1999. The indexes represent different sectors in the Indian economy
namely, automobile, banking, consumer durables, capital goods, fast moving
consumer goods, information technology, healthcare, public sector unit, metal, oil
and gas, and power, respectively.
2.2.2 The Market and the Sectors: National Stock Exchange
The NSE is the stock exchange located at Mumbai, India. In terms of market
capitalization, it is the 11th largest index in the world. By daily turnover and
number of trades, for both equities and derivative trading it is the largest index in
India. NSE has a market capitalization of around US$1 trillion and over 1,652
listings as of July 2012. NSE is mutually owned by a set of leading ?nancial
institutions, banks, insurance companies, and other ?nancial intermediaries in
India but its ownership and management operate as separate entities. In 2011, NSE
was the third largest stock exchange in the world in terms of the number of
contracts traded in equity derivatives. It is the second fastest growing stock
exchange in the world with a recorded growth of 16.6 %. As far as the sectoral
indexes are concerned, we select some market capitalization weighted sectoral
indexes introduced by NSE. These are CNX BANK, CNX COMMO, CNX
ENERGY, CNX FINANCE, CNX FMCG, CNX IT, CNX METALS, CNX MNC,
CNX PHARMA, CNX PSU BANK, CNX PSE, CNX INFRA, and CNX SER-
VICES. The indexes represent different sectors in the Indian economy namely
Bank, Consumptions sector, Energy, Finance, FMCG, IT, Metal, MNC, Pharma-
ceutical, Public Sector Unit, Infrastructure, and Services.
The study is conducted and market trends are analyzed over three phases in the
Indian stock market:
2.2 Trends and Latent Structure in Indian Stock Market 7
1. The entire period: 2005 January to 2012 September. The trends obtained for
this entire period could be taken as the ‘average’ market trend.
2. The prologue of crisis: 2005 January to 2008 January.
3. The aftermath of crisis: 2008 February to 2012 September.
The phases are constructed using the methods of detecting a structural break in
a ?nancial time series. Any ?nancial crisis could well be thought of as a switch in
regime that is often re?ected in a structural break in the market volatility. In that
way, a ?nancial crisis could possibly be associated with a volatility break or
regime switches that might lead to ?nancial crises. While identifying volatility
breaks, we use the same methodology, introduced originally by Inclan and Tiao
(1994), and used in our earlier studies (2011, 2012). We recapitulate the meth-
odology brie?y in the following sections.
2.3 Detection of Structural Break in Volatility
The parameters of a typical time series do not remain constant over time. It makes
paradigm shifts in regular intervals. The time of this shift is the structural break
and the period between two breakpoints is known as a regime. There have been
several studies aimed at measuring the breakpoints. As usual, a majority of them
are in the stock market. As only the algorithm used to detect the breakpoints is
important rather than the underlying time series, the following section discusses
those studies with important breakthroughs in the algorithm.
The ?rst group of studies was able to detect only one unknown structural
breakpoint. Perron (1990, 1997a), Hansen (1990, 1992), Banerjee et al. (1992),
Perron and Vogelsang (1992), Chu and White (1992), Andrews (1993), Andrews
and Ploberger (1994), Gregory and Hansen (1996), did some major works in this
area. Studies by Nelson and Plosser (1982), Perron (1989), Zivot and Andrews
(1992) tested unit root in presence of structural break. Bai (1994, 1997) considered
the distributional properties of the break dates.
The second group of studies was an improvement over the ?rst as it was able to
detect multiple structural breaks in a ?nancial time series, most importantly
endogenous breakpoints. Signi?cant contributions were made by Zivot and Andrews
(1992). Perron (1989, 1997b), Bai and Perron (2003), Lumsdaine and Papell (1997)
tests for unit root allowing for two breaks in the trend function. Hansen (2001)
considers multiple breaks, although he considers the breaks to be exogenously given.
The major breakthrough was the study by Inclan and Tiao (1994), who pro-
posed a test to detect shifts in unconditional variance, that is, the volatility. This
test is used extensively in ?nancial time series to identify breaks in volatility
(Wilson et al. 1996; Aggarwal et al. 1999; Huang and Yang 2001). This test was
later modi?ed by (Sansó et al. 2004) to account for conditional variance as well.
Hsu et al. (1974) proposed in their study a model with non-stationary variance
which is subjected to changes. This is probably the ?rst work involving structural
8 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
breaks in variance. Hsu’s later works in 1977, 1979, and 1982 were aimed at
detecting a single break in variance in a time series. Abraham and Wei (1984)
discussed methods of identifying a single structural shift in variance. An
improvement came in the study of Baufays and Rasson (1985) who addressed the
issue with multiple breakpoints in their paper. Tsay (1988) also discussed ARMA
models allowing for outliers and variance changes and proposed a method for
detecting the breakpoint in variance. More recently, Cheng (2009) provided an
algorithm to detect multiple structural breakpoints for a change in mean as well as
a change in variance.
This study does not explicitly incorporate any regime switching model but
considers the period between two breaks as a regime. Schaller and Norden (1997)
used Markov Switching model to ?nd very strong evidence of regime switch in
CRSP value-weighted monthly stock market returns from 1929 to 1989. Marcucci
(2005) used a regime switching GARCH model to forecast volatility in S&P500
which is characterized by several regime switches. Structural breaks and regime
switch is addressed by Ismail and Isa (2006) who used a SETAR-type model to test
structural breaks in Malaysian Ringgit, Singapore Dollar, and Thai Baht.
Theoretically, volatility break dates are structural breaks in variance of a given
time series. Structural breaks are often de?ned as persistent and pronounced
macroeconomic shifts in the data generating process. Usually, the probability of
observing any structural break increases as we expand the period of study. The
methodology used in this chapter is the line of analysis followed by Inclan and
Tiao (1994). In the following section, we brie?y recapitulate the methodology.
We may start from a simple AR(1) process as that described in (2.1)
y
t
¼ a þ qy
tÀ1
þ e
t
Ee
2
t
¼ r
2
ð2:1Þ
Here e
t
is a time series of serially uncorrelated shocks. If the series is stationary,
the parameters a; q and r
2
are constant over time. By de?nition, a structural break
occurs if at least one of the parameters changes permanently at some point in time
(Hansen 2001). The time point where the parameter changes value is often termed
as a ‘‘break date’’. According to Brooks (2002), structural breaks are irreversible in
nature. The reasons behind occurrence of structural breaks, however, are not very
speci?ed. Economic and non-economic (or even unidenti?able) reasons are
equally likely to bring about structural break in volatility. (Valentinyi-Endrész
2004).
2.3.1 Detection of Multiple Structural Breaks in Variance:
The ICSS Test
The Iterative Cumulative Sum of Squares (or the ICSS) algorithm by Inclan and
Tiao (1994) can very well detect sudden changes in unconditional variance for a
2.3 Detection of Structural Break in Volatility 9
stochastic process. Hence, the test is often used to detect multiple shifts in vola-
tility. The algorithm starts from the premise that over an initial period, the time
series under consideration displays a stationary variance. The variance changes
following a shock to the system and continues to be stationary till it experiences
another shock in the future. This process is repeated over time till we identify all
the breaks. Structural breaks can effectively capture regime switches (Altissimo
and Corradi 2003; Gonzalo and Pitarakis 2002; Valentinyi-Endrész 2004). The
different tests for identifying volatility breaks isolate dates where conditional
volatility moves from one stationary level to another. The idea is similar to those
lying behind the Markov regime switching models, where a system jumps from
one volatility regime to another.
2.3.1.1 The Original Model: Breaks in Unconditional Variance
The original model of Inclan and Tiao (1994) are reproduced as follows:
Let C
k
¼
P
k
t¼1
a
2
t
; k ¼ 1; . . .; T is the cumulative sum of squares for a series of
independent observations a
t
f g, where a
t
iidN 0; r
2
ð Þ and t = 1, 2, …, T, r
2
is the
unconditional variance.
r
2
¼
s
0
; 1\t\j
1
s
1
; j
1
\t\j
2
. . .
s
N
T
; j
N
T
\t\T
8
>
>
<
>
>
:
ð2:2Þ
where 1\j
1
\j
2
\Á Á Á j
N
T
\T are the breakpoints, that is, where the breaks in
variances occur. N
T
is the total number of such changes for T observations. Within
each interval, the variance is s
2
j
; j ¼ 0; 1; . . .; N
T
The centralized or normalized cumulative sum of squares is denoted by D
k
where
D
k
¼
C
k
C
T
À
k
T
! D
0
¼ D
T
¼ 0 ð2:3Þ
C
T
is the sum of squared residuals for the whole sample period.
If there is no volatility shift D
k
will oscillate around zero. With a change in
variance, it will drift upward or downward and will exhibit a pattern going out of
some speci?ed boundaries (provided by a critical value based on the distribution of
D
k
) with high probability. If at some k, say k*, the maximum absolute value of D
k
,
given by max
k
??????????????
T=2D
k
p

exceeds the critical value, the null hypothesis of constant
variance is rejected and k* will be regarded as an estimate of the change point.
Under variance homogeneity,
??????????????
T=2D
k
p
behaves like a Brownian bridge
asymptotically.
For multiple breakpoints, however, the usefulness of the D
k
function is ques-
tionable due to ‘‘masking effect’’. To avoid this, Inclan and Tiao designed an
10 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
iterative algorithm that uses successive application of the D
k
function at different
points in the time series to look for possible shift in volatility.
2.3.1.2 Modi?ed ICSS Test: Breaks in Conditional Variance
The modi?ed ICSS test is reproduced and used in this study. Sansó et al. (1994)
found signi?cant size distortions for the ICSS test in presence of excessive kurtosis
and conditional heteroscedasticity. This makes original ICSS test invalid in the
context of ?nancial time series that are often characterized by fat tails and con-
ditional heteroscedasticity. As a remedial measure, they introduced two tests to
explicitly consider the fourth moment properties of the disturbances and the
conditional heteroscedasticity.
The ?rst test, or the k
1
test, makes the asymptotic distribution free of nuisance
parameters for iid zero mean random variables.
j
1
¼ sup
k
T
À1=2
B
k

; k ¼ 1;. . .; T
B
k
¼
C
k
À
k
T
C
T
???????????????
^n
4
À ^ r
4
p ; ^g
4
¼ T
À1
X
T
t¼1
e
4
t
and ^ r
4
¼ T
À1
C
T
ð2:4Þ
This statistic is free of any nuisance parameter. The second test, the j
2
test
solves the problems of fat tails and persistent volatility.
j
2
¼ sup
k
T
À1=2
G
k

ð2:5Þ
where G
k
¼ ^ x
À
1
2
4
ðC
k
À
k
T
C
T
Þ
^ x
4
is a consistent estimator of x
4
. A nonparametric estimator of x
4
can be
expressed as
^ x
4
¼
1
T
X
T
i¼1
ðe
2
t
À ^ r
2
Þ
2
þ
2
T
X
m
l¼1
xðl; mÞ
X
T
t¼1
ðe
2
t
À ^ r
2
Þðe
2
tÀ1
À ^ r
2
Þ ð2:6Þ
xðl; mÞ is a lag window, such as Bartlett and de?ned as xðl; mÞ ¼ 1 À l= m þ 1 ð Þ ½ ?:
The bandwidth m is chosen by Newey-West (1994) technique. The j
2
test is more
powerful than the original Inclan-Tiao test or even the j
1
test and is best ?t for our
purpose.
The use of the above-mentioned tests on our data set identi?es the sub-phases
mentioned earlier. One point, however, is to be noted while considering these sub-
phases. The period of aftermath might be found to be characterized by further
?uctuations in the Indian stock market, some of which might even be capable of
generating further ?nancial market crisis. However, analysts often consider it too
early to call this period another era of ?nancial crisis. This period of ?nancial
turmoil and vulnerability should be better treated as aftershocks of the crisis of
2007–2008 than altogether a new eon of crisis. Moreover, the ?uctuations in recent
years are yet to be comparable to the older ones in terms of their overall
2.3 Detection of Structural Break in Volatility 11
devastating impact on the real economy. Our study hence is built particularly
around the ?nancial crisis of 2007–2008. And hence, the crisis period and its
aftermath are exclusively in terms of this ?nancial crisis.
2.4 Identifying Trends in Indian Stock Market:
The Methodology
The latent structure in the market could be best analyzed by using an exploratory
factor analysis (EFA). EFA is a simple, nonparametric method for extracting
relevant information from large correlated data sets (Hair et al. 2010). It could
reduce a complex data set to a lower dimension to reveal the sometimes hidden,
simpli?ed structures that often underlie it. In EFA, each variable (X
i
) is expressed
as a linear combination of underlying factors (F
i
). The amount of variance each
variable shares with others is called communality. The covariance among variables
is described by common factors and a unique factor (U
i
) for each variable. Hence,
X
i
¼ A
i1
F
1
þ Á Á Á þ A
im
F
m
þ V
i
U
i
ð2:7Þ
and F
i
¼ W
i1
X
1
þ Á Á Á þ W
ik
X
k
ð2:8Þ
where, A
i1
is the standardized multiple regression coef?cient of variable i on factor
j; V
i
is the standardized regression coef?cient of variable i on unique factor i; m is
the number of common factors; W
i
’s are the factor scores, and k is the number of
variables. The unique factors are uncorrelated with each other and with common
factors.
The appropriateness of using EFA on a data set could be judged by Bartlett’s
test of sphericity and the Kaiser-Meyar-Olkin (KMO) measure. The Bartlett’s test
of sphericity tests the null of population correlation matrix to be an identity matrix.
A statistically signi?cant Bartlett statistic indicates the extent of correlation among
variables to be suf?cient to use EFA. Moreover, KMO measure of sampling
adequacy should exceed 0.50 for appropriateness of EFA.
In factor analysis, the variables are grouped according to their correlation so
that variables under a particular factor are strongly correlated with each other.
When variables are correlated they will share variances among them. A variable’s
communality is the estimate of its shared variance among the variables represented
by a speci?c factor.
Through appropriate methods, factor scores could be selected so that the ?rst
factor explains the largest portion of the total variance. Then a second set,
uncorrelated to the ?rst, could be found so that the second factor accounts for most
of the residual variance and so on. This chapter uses the Principal Component
method where the total variance in data is considered. The method helps when we
isolate minimum number of factors accounting for maximum variance in data.
12 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
Factors with eigenvalues greater than 1.0 are retained. An eigenvalue represents
the amount of variance associated with the factor. Factors with eigenvalues less
than one are not better than a single variable, because after standardization, each
variable has a variance of 1.0.
Interpretation of factors will require an examination of the factor loadings. A
factor loading is the correlation of the variable and the factor. Hence, the squared
loading is the variable’s total variance accounted by the factor. Thus, a 0.50
loading implies that 25 % of the variance of the variable is explained by the factor.
Usually, factor loadings in the range of ±0.30 to ±0.40 are minimally required for
interpretation of a structure. Loadings greater than or equal to ±0.50 are practi-
cally signi?cant while loadings greater than or equal to ±0.70 imply presence of
well-de?ned structures.
The initial or unrotated factor matrix, however, shows the relationship between
the factors and the variables where factor solutions extract factors in the order of
their variance extracted. The ?rst factor accounting for the largest amount of
variance in the data is a general factor where almost every variable has signi?cant
loading. The subsequent factors are based on the residual amount of variance. Such
factors are dif?cult to interpret as a single factor could be related to many vari-
ables. Factor rotation provides simpler factor structures that are easier to interpret.
With rotation, the reference axes of the factors are rotated about the origin, until
some other positions are reached. With factor rotation, variance is re-distributed
from the earlier factor to the latter. Effectively, one factor will be signi?cantly
correlated with only a few variables and a single variable will have high and
signi?cant loading with only one factor. In an orthogonal factor rotation, as the
axes are maintained at angles of 90°, the resultant factors will be uncorrelated to
each other. Within the orthogonal factor rotation methods, VARIMAX is the most
popular method where the sum of variances of the required loading of the factor
matrix is maximized. There are, however, oblique factor rotations where the ref-
erence axes are not maintained at 90° angles. The resulting factors will not be
totally uncorrelated to each other. This chapter will use that method of factor
rotation which will ?t the data best.
The study then employs Cronbach’s alpha as a measure of internal consistency.
In theory a high value of alpha is often used as evidence that the items measure an
underlying (or latent) construct. Cronbach’s alpha, however, is not a statistical test.
It is a coef?cient of reliability or consistency.
The standardized Cronbach’s alpha could be written as: a ¼
N:c
vþ NÀ1 ð Þ:c
Here N is the number of items (here markets); c is the average inter-item
covariance among the items and v is the average variance. From the formula, it is
clear that an increase in the number of items increases Cronbach’s alpha. Addi-
tionally, if the average inter-item correlation increases, Cronbach’s alpha increases
as well (holding the number of items constant). This study uses Cronbach’s alpha
to check how closely related a set of markets are as a group and whether they
indeed form a ‘group’ among themselves.
2.4 Identifying Trends in Indian Stock Market: The Methodology 13
2.5 Trends and Latent Structure in Indian Stock Market:
Bombay Stock Exchange
1. Trends over the entire period: 2005 January to 2012 September
The study starts from an analysis of correlation among the different indexes.
Table 2.1 suggests presence of statistically signi?cant correlation among market as
well as sectoral returns over the entire study period.
To justify the use of EFA over the chosen data set we consider the KMO and
Bartlett’s tests for data adequacy. The KMO measure of sampling adequacy takes
a value of 0.873 and Bartlett’s test statistic of sphericity is signi?cant at one
percent level of signi?cance implying validity of using EFA on our data set.
Based on eigenvalue a single factor (eigenvalue 8.784) is extracted that
explains 73.2 % of total variability. The single factor contains all the indexes that
are highly loaded in that factor. The Cronbach’s alpha stands at 0.9631 and
declines with exclusion of each index. This makes the extracted structure a valid
one (Table 2.2).
The presence of a single structure implies the presence of a single dominant
trend in the market. All the sectors and the market move in similar fashion and
direction (as re?ected in their positive loadings on the factor). The indexes are
highly correlated and together they re?ect a distinct and broad market trend. The
detailed analysis of such broad, dominant trend could be of further interest.
Analysis of market trend: use of factor score
In EFA, factors represent latent constructs. From a practical standpoint,
researchers often estimate scores on a latent construct (i.e., factor scores) and use
them instead of the set of items that load on that factor. While constructing a factor
score, researchers could use the sum or average of the scores on items loading on
that factor. However, the procedure could be re?ned and made statistically
acceptable by using the information contained in the factor solution. The problem
with such elementary construction of factor score is that simple average uses only
the information that the set of items load on a given factor. The process fails if
items have different loadings on the factor. In such cases, some items, with rela-
tively high loadings, are better measures of the underlying factor (i.e., more highly
correlated with the factor) than others. Therefore, construction of ‘good’ factor
scores requires attaching higher weights to items with high loadings and vice
versa. The weights that are used to combine scores on observed items to form
factor scores could be obtained through some form of least squares regression.
Thus, the factor scores obtained serve as estimates of their corresponding unob-
served counterparts.
The use of EFA on our data set extracts a single factor that could be thought of
as representing the broad trend in the stock market. However, the stock market
trend could not be properly or effectively analyzed until and unless we could get
some proxy for this trend. Individual items in the factors (the market index and all
the sectoral indexes) could be analyzed separately but the process will provide us
14 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
T
a
b
l
e
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r
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n
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x
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e
t
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r
n
s
(
2
0
0
5
–
2
0
1
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)
A
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T
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0
.
6
6
0
0
.
6
1
1
0
.
0
6
8
1
B
S
E
C
G
0
.
7
4
7
0
.
7
8
0
0
.
8
6
6
0
.
6
6
4
B
S
E
F
M
C
G
0
.
6
0
7
0
.
5
5
7
0
.
6
9
0
0
.
5
2
7
0
.
5
6
4
B
S
E
H
C
0
.
6
8
7
0
.
6
3
9
0
.
7
4
4
0
.
6
3
1
0
.
6
6
8
0
.
6
1
3
B
S
E
I
T
0
.
5
7
5
0
.
5
8
5
0
.
7
5
8
0
.
5
0
1
0
.
5
7
7
0
.
4
8
8
0
.
5
5
7
B
S
E
P
S
U
0
.
7
7
0
0
.
8
2
4
0
.
8
8
1
0
.
7
0
1
0
.
8
2
1
0
.
6
2
2
0
.
7
3
4
0
.
5
6
9
B
S
E
M
E
T
A
L
0
.
7
4
9
0
.
7
3
1
0
.
8
4
7
0
.
6
7
2
0
.
7
5
7
0
.
5
8
5
0
.
6
8
0
0
.
5
8
9
0
.
8
1
8
B
S
E
O
N
G
0
.
7
0
1
0
.
7
2
6
0
.
8
8
3
0
.
6
1
0
0
.
7
3
6
0
.
5
7
2
0
.
6
6
7
0
.
5
9
0
0
.
8
3
3
0
.
7
6
6
B
S
E
P
O
W
E
R
0
.
7
6
3
0
.
7
9
2
0
.
8
8
5
0
.
6
9
1
0
.
8
8
7
0
.
6
1
0
0
.
7
1
3
0
.
5
8
7
0
.
8
9
9
0
.
8
0
3
0
.
7
9
6
A
l
l
c
o
r
r
e
l
a
t
i
o
n
s
a
r
e
s
t
a
t
i
s
t
i
c
a
l
l
y
s
i
g
n
i
?
c
a
n
t
a
t
1
%
l
e
v
e
l
o
f
s
i
g
n
i
?
c
a
n
c
e
2.5 Trends and Latent Structure in Indian Stock Market: Bombay Stock Exchange 15
with hardly any insight regarding the broad trend. We could instead construct the
factor score for our single extracted factor. These factor scores then could serve as
a proxy for the latent structure of the market. That is where the study moves next.
The movement or behavior of market trends (given by the factor scores),
henceforth described as the stock market is depicted in Fig. 2.1. As is evident from
the diagram, the stock market movement is highly volatile, characterized by the
presence of volatility clustering where periods of high (low) volatility are followed
by periods of high (low) volatility. However, from the simple plot it is dif?cult to
form any idea regarding the trends and nature of movements properly.
The trend could be better analyzed if it is possible to bring out the nature of the
cycle inherent in the series. For this purpose, the study uses the method of band
pass (frequency) ?lter. The band pass (frequency) ?lters are used to isolate the
cyclical component of a time series by specifying a range for its duration. The
band pass ?lter is a linear ?lter that takes a two-sided weighted moving average of
the data where cycles in a ‘‘band’’, given by a speci?ed lower and upper bound, are
‘‘passed’’ through, or extracted, and the remaining cycles are ‘‘?ltered’’ out. To use
a band pass ?lter, we have to ?rst specify the ‘periods’ to ‘pass through. The
periods are de?ned in terms of two numbers (P
L
and P
U
) based on the units of the
frequency of the series used. There are different band pass ?lters that differ in their
treatment of the moving average. The study uses the full sample asymmetric ?lter,
where the weights on the leads and lags are allowed to differ. The asymmetric ?lter
is time-varying with the weights both depending on the data and changing for each
observation. The study uses the Christiano–Fitzgerald (CF) form of this ?lter. As a
rule of thumb, P
L
and P
U
are set as 1.5 and 8 years for yearly data. The ranges for
daily data should be adjusted accordingly. The series is found to be level stationary
using Augmented Dickey Fuller test statistic (null hypothesis of unit root is
Table 2.2 Factor loadings in
the single factor extracted:
entire period
BSE AUTO 0.862 BSE HC 0.812
BSE BANK 0.871 BSE IT 0.714
BSE SENSEX 0.974 BSE PSU 0.930
BSE CD 0.773 BSE METAL 0.882
BSE CG 0.891 BSE ONG 0.871
BSE FMCG 0.719 BSE POWER 0.926
-10
-5
0
5
10
0
4
-
J
a
n
-
0
5
0
4
-
J
a
n
-
0
6
0
4
-
J
a
n
-
0
7
0
4
-
J
a
n
-
0
8
0
4
-
J
a
n
-
0
9
0
4
-
J
a
n
-
1
0
0
4
-
J
a
n
-
1
1
0
4
-
J
a
n
-
1
2
Fig. 2.1 Movements in
factor scores, BSE
(2005–2012)
16 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
rejected at one percent level of signi?cance). We chose to de-trend the data before
?ltering. The cycle is depicted in Fig. 2.2.
The return-cycle for the stock market enables us to identify the ups and downs
in BSE. The stock market as a whole experiences a boom during the phases
namely, 2006–2007, 2009–2010, and since early 2012. The market as a whole
slides down from its peak over the periods namely, 2007–2008 and 2010–2011.
Our analysis is concentrated around the ?rst cycle.
The trend is further analyzed through an examination of the risk-return rela-
tionship in the market as a whole. The variance of a series could serve as a good
proxy for the risk of the series. As is suggested by the simple plot of the stock market
return, the series is characterized by volatility clustering or volatility pooling.
Moreover the series is negatively skew (skewness -0.23), highly peaked (kurtosis
6.65), and non-normal. Such a series is best analyzed by an appropriate GARCH
family model and risk for such a series is proxied best by its conditional variance.
The stock market is modeled best by Exponential GARCH (EGARCH) model,
an asymmetric GARCH model of order (1, 1). The study uses the version of the
model ?rst proposed by Nelson in 1991. The EGARCH (1, 1) model can be
speci?ed as:
log r
2
t
À Á
¼ x þ a z
tÀ1
j j À E z
tÀ1
j j ð Þ ð Þ þ cz
tÀ1
þ blogðr
2
tÀ1
Þ; where e
tÀ1
¼ r
tÀ1
z
tÀ1
ð2:9Þ
The dependent variable is not the conditional variance, but rather the log of
conditional variance. Hence the leverage effect is exponential rather than quadratic
in the EGARCH model. The EGARCH model overcomes the most important
limitation of the GARCH model by incorporating the leverage effect. If a [0 and
c ¼ 0; the innovation in log r
2
t
À Á
is positive (negative) when z
tÀ1
is larger (smaller)
than its expected value. And if a ¼ 0 and c\0, the innovation in log r
2
t
À Á
is
positive (negative) when z
tÀ1
is negative (positive). Another signi?cant
improvement of the EGARCH process is that it contains no inequality constraint,
and by parameterizing the log r
2
t
À Á
can take negative value so there are fewer
restrictions on the model. Lastly, the EGARCH process can capture volatility
persistence quite effectively. log r
2
t
À Á
can easily be checked for volatility
-0.5
0
0.5
D
a
t
e
6
-
J
u
n
-
0
5
1
0
-
N
o
v
-
0
5
1
9
-
A
p
r
-
0
6
1
5
-
S
e
p
-
0
6
2
2
-
F
e
b
-
0
7
2
7
-
J
u
l
-
0
7
3
1
-
D
e
c
-
0
7
6
-
J
u
n
-
0
8
1
1
-
N
o
v
-
0
8
2
8
-
A
p
r
-
0
9
3
0
-
S
e
p
-
0
9
1
0
-
M
a
r
-
1
0
1
1
-
A
u
g
-
1
0
1
2
-
J
a
n
-
1
1
1
7
-
J
u
n
-
1
1
2
4
-
N
o
v
-
1
1
2
7
-
A
p
r
-
1
2
Fig. 2.2 Cycle in the BSE
return (2005–2012)
2.5 Trends and Latent Structure in Indian Stock Market: Bombay Stock Exchange 17
persistence by looking at the stationarity and ergodicity conditions. However, the
EGARCH model is also not free from its drawbacks. This model is dif?cult to use
for there is no analytic form for the volatility term structure.
As is suggested by Table 2.3, the stock market is characterized by asymmetric
response of volatility toward positive and negative announcements in the market.
The market reacts more toward the negative news than toward the good news.
The conditional volatility for the series is saved and depicted in Fig. 2.3.
The conditional variance, after de-trending, exhibits signi?cant cyclical pattern
(Fig. 2.4).
Table 2.3 Application of EGARCH model on factor score for BSE (2005–2012)
Dependent variable: factor score for BSE (2005–2012)
Method: ML—ARCH (Marquardt)—student’s t distribution
Included observations: 1909
Convergence achieved after 23 iterations
Presample variance: backcast (parameter = 0.7)
LOG(GARCH) = C(1) ? C(2)*ABS(RESID(-1)/@SQRT(GARCH(-1))) ? C(3) *RESID(-
1)/@SQRT(GARCH(-1)) ? C(4)*LOG(GARCH(-1))
Variance equation
Coef?cient Std. Error z-Statistic Prob.
C(1) -0.18787 0.023173 -8.10761 5.16E-16
C(2) 0.226826 0.028853 7.861378 3.80E-15
C(3) -0.11943 0.017101 -6.98381 2.87E-12
C(4) 0.961732 0.007329 131.2155 0
T-DIST. DOF 7.678726 0.986114 7.786851 6.87E-15
R-squared 1.11E-15 Mean dependent var -4.71E-08
Adjusted R-squared -0.0021 S.D. dependent var 1
S.E. of regression 1.00105 Akaike info criterion 2.433343
Sum squared resid 1908 Schwarz criterion 2.447891
Log likelihood -2,317.63 Hannan-Quinn criter. 2.438697
Durbin–Watson stat 1.804131
0
2
4
6
8
10
12
14
0
4
-
J
a
n
-
0
5
0
4
-
J
u
l
-
0
5
0
4
-
J
a
n
-
0
6
0
4
-
J
u
l
-
0
6
0
4
-
J
a
n
-
0
7
0
4
-
J
u
l
-
0
7
0
4
-
J
a
n
-
0
8
0
4
-
J
u
l
-
0
8
0
4
-
J
a
n
-
0
9
0
4
-
J
u
l
-
0
9
0
4
-
J
a
n
-
1
0
0
4
-
J
u
l
-
1
0
0
4
-
J
a
n
-
1
1
0
4
-
J
u
l
-
1
1
0
4
-
J
a
n
-
1
2
0
4
-
J
u
l
-
1
2
Fig. 2.3 BSE conditional variance (2005–2012)
18 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
The conditional volatility has been signi?cantly higher during the period of
?nancial crisis of 2007–2008. The two other peaks are not at all signi?cant
compared to this peak. Thus, although the return cyclebrings out two signi?cant
peaks in BSE return, conditional variance cycle rules out one and suggests pres-
ence of a single high-volatile period in the market. The peak of 2010–2011 is not
associated with a very high volatility. This justi?es our choice of ?nancial crisis of
2007–2008 as the most signi?cant ?nancial crisis of recent years. The cycle of
2010–2012 is yet to be designated as a true ?nancial crisis. Interestingly, the nature
of cycle of conditional variance is completely opposite to the cyclical nature of the
return series. Return peaks are always associated with low conditional variance or
conditional variance slumps. This is further analyzed and depicted in Fig. 2.4. The
nature of time-varying conditional correlation between stock market return and
conditional variance brings out the negative relationship between risk and return in
the market.
The conditional correlation has been computed using a multivariate GARCH
technique that models the variance–covariance matrix of a ?nancial time series.
This section makes use of Diagonal Vector GARCH (VECH) model of Bollerslev
et al. (1988). In a Diagonal VECH model the variance–covariance matrix of stock
market returns is allowed to vary over time. This model is particularly useful,
unlike the BEKK model of Baba et al. (1990), with more than two variables in the
conditional correlation matrix (Scherrer and Ribarits 2007). However, it is often
dif?cult to guarantee a positive semi-de?nite conditional variance–covariance
matrix in a VECH model (Engel and Kroner 1993; Brooks and Henry 2000).
Following the methodology of Karunanayake et al. (2008) this study avoids this
problem by using the unconditional residual variance as the pre-sample conditional
variance. This is likely to ensure positive semi-de?nite variance–covariance matrix
in a diagonal VECH model. Since, we are more interested in volatility co-
movement and spill over, the mean equation of the estimated diagonal VECH
model contains only the constant term. In the n dimension variance–covariance
matrix, H, the diagonal terms will represent the variance and the non-diagonal
terms will represent the covariances. In other words, in
H
t
¼
h
11t
Á Á Á h
1nt
Á Á Á Á Á Á Á Á Á
h
n1t
Á Á Á h
nnt
-1
-0.5
0
0.5
1
1.5
6
-
J
u
n
-
0
5
1
0
-
N
o
v
-
0
5
1
9
-
A
p
r
-
0
6
1
5
-
S
e
p
-
0
6
2
2
-
F
e
b
-
0
7
2
7
-
J
u
l
-
0
7
3
1
-
D
e
c
-
0
7
6
-
J
u
n
-
0
8
1
1
-
N
o
v
-
0
8
2
8
-
A
p
r
-
0
9
3
0
-
S
e
p
-
0
9
1
0
-
M
a
r
-
1
0
1
1
-
A
u
g
-
1
0
1
2
-
J
a
n
-
1
1
1
7
-
J
u
n
-
1
1
2
4
-
N
o
v
-
1
1
2
7
-
A
p
r
-
1
2
Fig. 2.4 Cycle in the factor
score BSE conditional
variance (2005–2012)
2.5 Trends and Latent Structure in Indian Stock Market: Bombay Stock Exchange 19
h
iit
is the conditional variance of ‘ith market in time t; h
ijt
is the conditional
covariance between the ith and jth market in period t (i = j). The conditional
variance depends on the squared lagged residuals and conditional covariance
depends on the cross lagged residuals and lagged covariances of the other series
(Karunanayake et al. 2008). The model could be represented as:
VECH H
t
ð Þ ¼ C þ A:VECHðe
tÀ1
e
0
tÀ1
Þ þ B:VECH H
tÀ1
ð Þ ð2:10Þ
A and B are
N Nþ1 ð Þ
2
Â
N Nþ1 ð Þ
2
parameter matrices. C is
N Nþ1 ð Þ
2
vector of constant.
a
ii
in matrix A, that is the diagonal elements show the own spillover effect. This is
the impact of own past innovations on present volatility. The cross diagonal terms
(a
ij
; i 6¼ j) show the impact of pat innovation in one market on the present vola-
tility of other markets. Similarly, b
ii
in matrix B shows the impact of own past
volatility on present volatility. Likewise, b
ij
represents cross volatility spill over or
the impact of past volatility of the ith market on the present volatility of jth market.
For our purpose, a
ij
’s and b
ij
’s are more important.
As pointed out by Karunanayake et al. (2008) an important issue in estimating a
diagonal VECH model is the number of parameters to be estimated. To solve the
problem, Bollerslev et al. (1988) suggested use of a diagonal form of A and B. A
related issue is to ensure the positive semi-de?niteness of the variance–covariance
matrix. The condition is easily satis?ed if all of the parameters in A, B, and C are
positive with a positive initial conditional variance–covariance matrix. Bollerslev
et al. (1988) suggested some restrictions to impose that have been followed by
Karunanayake et al. (2008). They used maximum likelihood function to generate
these parameter estimates by imposing some restriction on the initial value. If h be
the parameter for a sample of T observations, the log likelihood function will be:
T h ð Þ ¼
X
T
t¼1
l
r
h ð Þ; where l
t
h ð Þ ¼
N
2
ln 2p ð Þ À
1
2
ln H
t
j j À
1
2

0
t
H
À1
t

t
ð2:11Þ
The presample values of h can be set to be equal to their expected value of zero
(Bollerslev et al. 1988). The Ljung Box test statistic could further be used to test
for remaining ARCH effects. For a stationary time series of T observations and a
multivariate process of order (p, q) the Ljung Box test statistic is given as:
Q ¼ T
2
X
s
j¼1
ðT À jÞ
À1
tj C
À1
Y
t
ð0ÞC
Y
t
ðjÞC
À1
Y
t
ð0ÞC
0
Y
t
ðjÞ
n
ð2:12Þ
Y
t
is VECH (y
t
, y
0
t
), C
Y
t
ðjÞ is the sample autocovariance matrix of order j, s is
the number of lags used, T is the number of observations. For large sample, the test
statistic is distributed as a v
2
under the null hypothesis of no remaining ARCH
effect.
A multivariate GARCH of appropriate order has been estimated for the data on
factor scores for BSE return and BSE conditional variance and the conditional
correlation values have been saved. The movement in this conditional correlation
20 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
re?ects the risk-return relationship in the context of BSE. During most of the time
period, particularly during the ?nancial crisis of 2007–2008, risk and return had
been perfectly negatively correlated (correlation coef?cient = -1). For only a
short period of time, risk and return was perfectly positively correlated (correlation
coef?cient = +1). This suggests the presence of dominantly negative (perfect)
risk-return relationship in BSE. More interestingly, correlation coef?cient was
either +1 or -1. Only for a short period of time (during August 2010 to January
2012) correlation coef?cient remained positive and ?uctuated. The characteristics
in conditional correlation could further be traced in the cycle in conditional cor-
relation (Fig. 2.5).
The analysis of overall market trend would now be supplemented by analyses
of market trend before and after the crisis.
2. The trends in the pre-crisis period: 2005 January to 2008 January
The analysis of trends in the market in the pre-crisis period starts from iden-
ti?cation of latent structure in the market.
Table 2.4 suggests presence of statistically signi?cant correlation among mar-
ket as well as sectoral returns during the pre-crisis.The correlation coef?cients are
more or less the same in magnitude compared to those for the entire period.
The use of EFA over the pre-crisis data set is further justi?ed by the favorable
values of the KMO measure of sampling adequacy and Bartlett’s tests for data
adequacy. The KMO measure of sampling adequacy takes a value of 0.885 and
Bartlett’s test statistic of sphericity is signi?cant at one percent level of signi?-
cance implying validity of using EFA on the pre-crisis data set.
On the basis of eigenvalue a single factor (eigenvalue 8.908) is extracted that
explains 74.2 % of total variability. Both the eigenvalue and the total variability
explained by the single factor extracted are higher than those obtained for the
entire period. Once again, the single factor contains all the indexes that are highly
loaded in that factor. The Cronbach’s alpha stands at 0.9650 (which is higher than
the entire period) and declines with exclusion of each index. This makes the
extracted structure, once again a valid one (Table 2.5).
-1
-0.5
0
0.5
1
1.5
D
a
t
e
2
-
A
u
g
-
0
5
7
-
M
a
r
-
0
6
5
-
O
c
t
-
0
6
1
4
-
M
a
y
-
0
7
7
-
D
e
c
-
0
7
1
4
-
J
u
l
-
0
8
1
9
-
F
e
b
-
0
9
2
9
-
S
e
p
-
0
9
7
-
M
a
y
-
1
0
2
-
D
e
c
-
1
0
5
-
J
u
l
-
1
1
7
-
F
e
b
-
1
2
CYCLE_MARKET
CYCLE_CON_VAR
CYCLE_COND_COR
Fig. 2.5 Return-risk relationship BSE (2005–2012)
2.5 Trends and Latent Structure in Indian Stock Market: Bombay Stock Exchange 21
T
a
b
l
e
2
.
4
C
o
r
r
e
l
a
t
i
o
n
m
a
t
r
i
x
a
m
o
n
g
B
S
E
i
n
d
e
x
r
e
t
u
r
n
s
(
2
0
0
5
–
2
0
0
8
)
A
U
T
O
B
A
N
K
S
E
N
S
E
X
C
D
C
G
F
M
C
G
H
C
I
T
P
S
U
M
E
T
A
L
O
N
G
B
S
E
A
U
T
O
B
S
E
B
A
N
K
0
.
6
9
3
B
S
E
S
E
N
S
E
X
0
.
8
5
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22 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
The presence of a single structure implies the presence of a single dominant
trend in the market even in the pre-crisis period. All the sectors and the market
move in similar fashion and direction (as re?ected in their positive loadings on the
factor). The indexes are highly correlated and together they re?ect a distinct and
broad market trend. The detailed analysis of such broad, dominant trend in the pre-
crisis period would be our further area of analysis.
Analysis of market trend in pre-crisis period: use of factor score
The use of EFA on our pre-crisis data set extracts a single factor that could be
thought of as representing the broad trend in the stock market in the pre-crisis
period. However, this stock market trend cannot be properly or effectively ana-
lyzed until and unless we could get some proxy for this trend. Just like the previous
case, we have constructed the factor score for our single extracted factor for the
pre-crisis period. These factor scores then serve as a proxy for the latent structure
of the pre-crisis market.
The movement or behavior of market trends (given by the factor scores),
henceforth described as the stock market in pre-crisis period, is depicted in
Fig. 2.6. As is evident from the diagram, the stock market movement is highly
volatile, characterized by the presence of volatility clustering where periods of
high (low) volatility are followed by periods of high (low) volatility. However,
from the simple plot it is dif?cult to form any idea regarding the trends and nature
of movements properly. The trend in the pre-crisis period resembles that for the
entire Period.
The trend could be better analyzed if it is possible to bring out the nature of the
cycle inherent in the series. The cycle is generated once again using the method of
band pass (frequency) ?lter in its CF form. The pre-crisis series is found to be
level stationary using Augmented Dickey Fuller test statistic (null hypothesis of
unit root is rejected at one percent level of signi?cance). We chose to de-trend the
data before ?ltering. The cycle is depicted in Fig. 2.7.
Table 2.5 Factor loadings in
the single factor extracted:
pre-crisis period
BSE AUTO 0.894 BSE HC 0.861
BSE BANK 0.818 BSE IT 0.733
BSE SENSEX 0.971 BSE PSU 0.943
BSE CD 0.760 BSE METAL 0.879
BSE CG 0.882 BSE ONG 0.879
BSE FMCG 0.776 BSE POWER 0.909
-8
-6
-4
-2
0
2
4
6
04-Jan-05 04-Jan-06 04-Jan-07 04-Jan-08
Fig. 2.6 Movements in
factor scores, BSE
(2005–2008)
2.5 Trends and Latent Structure in Indian Stock Market: Bombay Stock Exchange 23
The cycle for the stock market enables us to identify the ups and downs in
returns in the BSE in the pre-crisis period. As suggested by our earlier analysis, the
stockmarket as a whole experienced a boom during the phases namely, 2006–2007,
2009–2010, and since early 2012. The market as a whole slides down from its peak
over the periods namely, 2007–2008 and 2010–2011. An analysis of the pre-crisis
period return shows distinct cycle that is different from the cycle that we obtained
from our earlier analysis of the entire period. If we could take the pre-crisis period
separately, and not as a part of the entire period, a small peak could be traced
during the period of 2005–2006. This peak was not very prominent in the cycle for
the entire period. There has been another signi?cant peak in the pre-crisis period
that could be traced during the period of 2007–2008. The market in the pre-crisis
period started declining just toward the end of the period namely in January 2008.
The trend is further analyzed through examination of the risk-return relation-
ship in the market as a whole. The variance of a series could serve as a good proxy
for the risk of the series. As is suggested by the simple plot of the stock market
return, the series is characterized by volatility clustering or volatility pooling.
Moreover, the series is negatively skew (skewness -0.25), highly peaked (kurtosis
8.65), and non-normal. Such a series is best analyzed by an appropriate GARCH
family model and risk for such a series is proxied best by its conditional variance.
The stock market is modeled best by EGARCH, an asymmetric GARCH model
of order (1, 1, 1). As is suggested by Table 2.6, the stock market in the pre-crisis
period is characterized by asymmetric response of volatility toward positive and
negative announcements in the market. The market reacts more toward the neg-
ative news than toward the good news.
The conditional volatility for the pre-crisis series is saved and depicted in
Fig. 2.8.
The conditional variance, after de-trending, exhibits signi?cant cyclical pattern.
The conditional volatility has been signi?cantly higher during the period of
2005–2006. The conditional volatility was signi?cantly lower during mid-2007.
However, just before the crisis was to set in, conditional volatility started
mounting. Thus risk in a market (given by the conditional variance) starts esca-
lating as the market approaches a crisis. The risk-return relationship in the market
is further analyzed and depicted in Fig. 2.9. The nature of time-varying conditional
-0.15
-0.1
-0.05
0
0.05
0.1
04-Jan-05 04-Jan-06 04-Jan-07 04-Jan-08
Fig. 2.7 Cycle in the BSE
return (2005–2008)
24 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
correlation brings out the presence of a positive relationship between risk and
return in the market. While the correlation ?uctuates, it started declining since
mid-2007 and approached zero toward the beginning of the crisis.
Hence, the analysis of pre-crisis period reveals few notable characteristics of
Indian stock market:
• Indian stock market is dominated by a ‘‘single’’ trend where all the sectors and
the market move together. The trend in the pre-crisis period is stronger than the
‘average’ (the trend for the entire period) market trend.
• The entire stock market is characterized by signi?cant volatility with volatility
clustering.
Table 2.6 Application of EGARCH model on factor score for BSE (2005–2008)
Dependent Variable: Return in the pre-crisis period
Method: ML—ARCH (Marquardt)—Student’s t distribution
Included observations: 771 after adjustments
Convergence achieved after 20 iterations
Presample variance: backcast (parameter = 0.7)
LOG(GARCH) = C(1) ? C(2)*ABS(RESID(-1)/@SQRT(GARCH(-1))) ? C(3) *RESID(-1)/
@SQRT(GARCH(-1)) ? C(4)*LOG(GARCH(-1))
Variance equation
Coef?cient Std. error z-statistic Prob.
C(1) -0.230081 0.051685 -4.451629 0
C(2) 0.252992 0.062029 4.078632 0
C(3) -0.235055 0.039617 -5.933215 0
C(4) 0.882705 0.024141 36.56491 0
T-DIST. DOF 6.19328 1.366128 4.533454 0
R-squared 0 Mean dependent var 0.000391
Adjusted R-squared -0.005222 S.D. dependent var 1.00059
S.E. of regression 1.003199 Akaike info criterion 2.424167
Sum squared resid 770.9089 Schwarz criterion 2.454307
Log likelihood -929.5162 Hannan-Quinn criter. 2.435765
Durbin–Watson stat 1.780743
-0.15
-0.1
-0.05
0
0.05
0.1
04-Jan-05 04-Jan-06 04-Jan-07 04-Jan-08
Fig. 2.8 Cycle in the factor
score BSE conditional
variance (2005–2008)
2.5 Trends and Latent Structure in Indian Stock Market: Bombay Stock Exchange 25
• Asymmetric response of volatility toward good and bad news where volatility
responds more toward bad news. The leverage effect is more pronounced in the
pre-crisis period (coef?cient = -0.23) compared to the entire period (-0.11)
• Returns start falling and risks start mounting as the market approaches a crisis.
• Market is mostly characterized by a positive risk-return relationship. However,
the correlation coef?cient between risk and return starts declining as the market
approaches crisis. Just before the crisis sets in, the correlation coef?cient
becomes zero.
3. The trends in the post-crisis period: 2008 February to 2012 September
The analysis of market trend in the post-crisis period starts from identi?cation
of latent structure in the market. Table 2.7 suggests presence of statistically sig-
ni?cant correlation among market as well sectoral returns during the post-crisis
period. The correlation coef?cients are more or less the same in magnitude
compared to those for the entire and pre-crisis period.
The use of EFA over the post-crisis period data set is once again justi?ed by the
favorable values of the KMO measure of sampling adequacy and Bartlett’s tests
for data adequacy. The KMO measure of sampling adequacy takes a value of 0.866
and Bartlett’s test statistic of sphericity is signi?cant at one percent level of sig-
ni?cance implying validity of using EFA on the post-crisis data set.
On the basis of eigenvalue a single factor (eigenvalue 8.740) is extracted that
could explains 72.83 % of total variability. Both the eigenvalue and the total
variability explained by the single factor extracted are lower than those obtained
for the entire period as well as for the pre-crisis period. Once again, the single
factor contains all the indexes that are highly loaded in that factor. The Cronbach’s
alpha stands at 0.9625 (which is lower than those obtained for the entire period as
well as for the pre-crisis period) and declines with exclusion of each index. This
makes the extracted structure, once again a valid one (Table 2.8).
-0.4
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CYCLE_BEFORE_cv
CYCLE_BEFORE
CON_CORR
Fig. 2.9 Return-risk relationship BSE (2005–2008)
26 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
T
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2.5 Trends and Latent Structure in Indian Stock Market: Bombay Stock Exchange 27
The presence of a single structure implies the presence of a single dominant
trend in the market even in the post-crisis period. All the sectors and the market
move in similar fashion and direction (as re?ected in their positive loadings on the
factor). The indexes are highly correlated and together they re?ect a distinct and
broad market trend. The detailed analysis of such broad, dominant trend in the
post-crisis period would be our further area of analysis.
Analysis of market trend in post-crisis period: use of factor score
The use of EFA on our post-crisis data set extracts a single factor that could be
thought of as representing the broad trend in the stock market in the post-crisis
period. However, to analyze this stock market trend properly and effectively, we
need to get some proxy for this trend. Just like the previous two cases, we have
constructed the factor score for our single extracted factor for the post-crisis
period. These factor scores then serve as a proxy for the latent structure of the post-
crisis market.
The movement or behavior of market trends (given by the factor scores),
henceforth described as the stock market in post-crisis period, is depicted in
Fig. 2.10. As it is evident from the diagram, the stock market movement is highly
volatile, characterized by the presence of volatility clustering where periods of
high (low) volatility are followed by periods of high (low) volatility. However,
from the simple plot it is dif?cult to form any idea regarding the trends and nature
of movements properly. The trend in the post-crisis period resembles those for the
entire as well as the pre-crisis periods. The volatility is signi?cantly higher during
the period of February 2008 to March 2009: the period when stock market was
sliding.
Table 2.8 Factor loadings in
the single factor extracted:
post-crisis period
BSE AUTO 0.844 BSE HC 0.787
BSE BANK 0.900 BSE IT 0.705
BSE SENSEX 0.977 BSE PSU 0.924
BSE CD 0.781 BSE METAL 0.883
BSE CG 0.897 BSE ONG 0.867
BSE FMCG 0.686 BSE POWER 0.936
-10
-5
0
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10
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b
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1
2
0
1
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u
n
-
1
2
Fig. 2.10 Movements in
factor scores, BSE
(2008–2012)
28 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
The trend could be better analyzed if it is possible to bring out the nature of the
cycle inherent in the series. The cycle in the post-crisis market return movement is
depicted in Fig. 2.11. The cycle is generated once again using the same method of
band pass (frequency) ?lter in its CF form. The post-crisis series is found to be
level stationary using Augmented Dickey Fuller test statistic (null hypothesis of
unit root is rejected at one percent level of signi?cance). We chose to de-trend the
data before ?ltering. The cycle is depicted in Fig. 2.11.
The cycle for the stock market enables us to identify the ups and downs in
returns in the BSE in the post-crisis period. The return was lower during the period
of 2008–2009, the period of crisis. Return increased gradually over the year of
2009 and reached a peak in November 2009. Return dipped since then and made a
gradual, but not very signi?cant improvement since mid-2011. The trend is further
analyzed through examination of the risk-return relationship in the market as a
whole in the post-crisis period. The variance of a series could serve as a good
proxy for the risk of the series. As is suggested by the simple plot of the stock
market return, the series is characterized by volatility clustering or volatility
pooling. Moreover, the series is negatively skew (skewness -0.26), highly peaked
(kurtosis 7.65), and non-normal. Such a series is best analyzed by an appropriate
GARCH family model and risk for such a series is proxied best by its conditional
variance.
The stock market is modeled best by EGARCH, an asymmetric GARCH model
of order (1, 1). As is suggested by Table 2.9 the stock market in the post-crisis
period is characterized by asymmetric response of volatility toward positive and
negative announcements in the market. The market reacts more toward the neg-
ative news than toward the good news.
The conditional volatility for the post-crisis series is saved and depicted in
Fig. 2.12.
The conditional variance, after de-trending, exhibits signi?cant cyclical pattern.
The conditional volatility has been signi?cantly higher during the period of
2008–2009. The conditional volatility was signi?cantly lower during late
2009–2011. Thus, volatility and hence risk, remained signi?cantly higher during
the period of crisis. The risk-return relationship in the market is further analyzed
and depicted in Fig. 2.13. The nature of time-varying conditional correlation
-0.15
-0.1
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0
0.05
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Fig. 2.11 Cycle in the BSE (2008–2012)
2.5 Trends and Latent Structure in Indian Stock Market: Bombay Stock Exchange 29
brings out the presence of a positive relationship between risk and return in the
market. During the period of 2008, the correlation coef?cient was negative,
implying a negative risk-return relationship in the market. Since then the risk-
return relationship has been mostly positive, with some exceptions during
2010–2011 and during late 2012. The conditional correlation cycle in the post-
crisis period is, however, smoother compared to that in the pre-crisis period.
Hence, the analysis of post-crisis period reveals few notable characteristics of
Indian stock market:
Table 2.9 Application of EGARCH model on factor score for BSE (2008–2012)
Dependent variable: return in the post-crisis period
Method: ML—ARCH (Marquardt)—Student’s t distribution
Included observations: 1137
Convergence achieved after 28 iterations
Presample variance: backcast (parameter = 0.7)
LOG(GARCH) = C(1) ? C(2)*ABS(RESID(-1)/@SQRT(GARCH(-1))) ? C(3) *RESID(-
1)/@SQRT(GARCH(-1)) ? C(4)*LOG(GARCH(-1))
Variance equation
Coef?cient Std. error z-statistic Prob.
C(1) -0.14429 0.025556 -5.64629 0
C(2) 0.17386 0.03189 5.451858 0
C(3) -0.08342 0.017128 -4.87047 0
C(4) 0.983369 0.005623 174.8838 0
T-DIST. DOF 11.02265 1.913501 5.760461 0
R-squared 0 Mean dependent var -1.76E-08
Adjusted R-squared -0.00353 S.D. dependent var 1
S.E. of regression 1.001765 Akaike info criterion 2.422552
Sum squared resid 1136 Schwarz criterion 2.444699
Log likelihood -1372.22 Hannan–Quinn criter. 2.430917
Durbin–Watson stat 1.814822
-1
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2
Fig. 2.12 Cycle in the factor
score BSE conditional
variance (2008–2012)
30 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
• Indian stock market is dominated by a ‘‘single’’ trend where all the sectors and
the market move together. The trend in the post-crisis period is weaker than the
‘average’ (the trend for the entire period) market trend as well as the trend in the
pre-crisis period.
• The market is characterized by signi?cant volatility with volatility clustering.
• Asymmetric response of volatility toward good and bad news where volatility
responds more toward bad news. The leverage effect is less pronounced in the
post-crisis period (coef?cient = -0.08) compared to that in the entire period (-
0.11) and in the pre-crisis period (-0.23).
• Returns start falling and risks start mounting as the market plunges into a crisis.
• Market is mostly characterized by a positive risk-return relationship. However,
the correlation coef?cient between risk and return starts declining and becomes
negative as the market dips into crisis.
The trends in BSE: Any ‘Signal’ to frame pro?table trading strategy?
Over the past 8 years, the Indian stock market, as represented by the BSE, is
dominated by a ‘‘single’’ trend where all the sectors and the market move together.
The latent structure of the market is constructed of all the sectors and the market
Index. The structure has remained unchanged over the past 8 years and has been
independent of the cycles in the economy. Moreover, the trend in the post-crisis
period is weaker than the ‘average’ (the trend for the entire period) market trend,
whereas the trend in the pre-crisis period is stronger than the ‘average’. This is
revealed by the EFA where the single factor extracted could account for more
variability (as given by the values of the Eigenvectors) in the pre-crisis period than
for the post-crisis period. Further analysis of eigenvalue and eigenvector compo-
sition might provide us with signi?cant signals that might be useful as an indicator
of future events. For example, if a unique eigenvector composition is consistently
observed before a market crash or period of market growth, then this unique
eigenvector provides a signal that can be responded to in the future. As the
economy passes through different stages, and market forces change, the eigen-
vectors might be expected to change to describe the new situation. Thus, an
analysis of trends in Eigenvector might help us identify pattern and trend in market
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
RETURN_cycle
COND_VAR_CYCLE_cv
COND_CORR_cycle
0
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2
Fig. 2.13 Return-risk relationship BSE (2008–2012)
2.5 Trends and Latent Structure in Indian Stock Market: Bombay Stock Exchange 31
movements. This in turn might help investors design strategies that would reduce
risk and increase gains.
As suggested by our earlier analysis, the market is dominated by a single trend.
The single eigenvalue, however, is changing from month to month (Fig. 2.14). The
fraction of market variation captured by the ?rst eigenvector thus changes over
time. The movements are sometime marked by sharp changes.
Starting from January 2005, eigenvalue increases sharply over the ?rst 15
months. It then falls gradually and reaches a slump during the 25th month. The
following months (25th to 40th) witnessed a moderate rise in eigenvalue. The 45th
to 65th months witnessed a fall in eigenvalue. The movement in the eigenvalue
might indicate the fact that the periods between 0th and 10th month and between
25th and 40th month might be associated with some signi?cant market event so
that a larger portion of market variability is being captured by the ?rst (in this
context, the single) eigenvector. Thus, when the market experiences or passes
through some ‘extra-ordinary’ events, some ‘unique’ or ‘special’ trend persists in
the market. As the economy reverts back to its ‘normal’ state this ‘special’ trend
weakens in the sense that the variability captured by the ?rst factor declines
steadily. For investors this information might be extremely useful in designing
pro?table trading strategy. To be more speci?c, if it is possible to identify when
this special trend would set in or how long it would last, investors might be able to
design strategies to make pro?t out of market movements. The movements in the
?rst factor eigenvalue reveal few more observations. The eigenvalue increases
during the periods of recovery and reaches maximum just before the peak. During
a stable period, however, the eigenvalue falls or reaches a plateau. Therefore, the
‘special’ trend persists during the phases of recovery and weakens during the
periods of recession or stability. The market crash could be predicted from a high
eigenvalue of the ?rst factor and high eigenvalue could be associated with market
crash. In Indian context, hence, there is immense scope for the investors to use this
piece of information to design pro?table trading strategyin BSE.
Apart from the presence of a special trend in the market, BSE is characterized by
the presence of signi?cant volatility in stock return. The volatility responds asym-
metrically toward good and bad news with sharper reaction toward bad news. The
asymmetric responses (the ‘leverage’ effect) tend to be sharper during the pre-crisis
period rather than in the post-crisis period. The ‘normal’ positive relationship between
risk and return seems to exist in the market. However, the correlation coef?cient
7
7.2
7.4
7.6
7.8
8
8.2
8.4
8.6
8.8
9
5
1
0
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5
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6
5
E
i
g
e
n
V
a
l
u
e
Month
Fig. 2.14 Nature of
eigenvalue for BSE
(2005–2012)
32 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
between risk and return starts declining and becomes negative (or even zero) as the
market dips into crisis. Distinct and persistent trends thus are perceptible in the Indian
stock market leaving the ef?cient market hypothesis on trial. Such trends could
skillfully be used by investors to design pro?t making strategies to beat the market.
Let us now consider the other stock exchange, namely the NSE and explore
whether the movements and other characteristics in the NSE resemble the trends in
BSE. While exploring the issues, we shall be following the same methodologies
that were followed in the previous sections. Hence, we are not repeating the
methodology, but reporting the results only focusing on the analytical discussion.
2.6 Trends and Latent Structure in Indian Stock Market:
National Stock Exchange
1. Trends over the entire period: 2005 January to 2012 September
The analysis of market movement in NSE starts from the analysis of correlation
among the different indexes. Table 2.10 reveals signi?cant correlation pattern in
the NSE.
While statistically signi?cant correlation exists among the sectoral returns,
correlation between the market and the sectoral returns has been almost negligible.
This is in sharp contrast with the trends in BSE. While in BSE all the sectors and
the market were intertwined, NSE market is likely to be segregated from the
sectors as a whole. Such a simple correlation analysis, however, hardly suf?ces to
establish such segregation. EFA might help us better analyze the trends.
The KMO measure of sampling adequacy takes a value of 0.89 and Bartlett’s
test statistic of sphericity is signi?cant at one percent level of signi?cance
implying validity of using EFA on our data set.
On the basis of eigenvalue, two factors are extracted. The ?rst factor with an
eigenvalue of 9.129, explains 70 % of total variability. The second factor has an
eigenvalue of 1.006 and explains 8 %of total variability. The ?rst factor contains all
the sectoral indexes that are highly loaded in that factor. The Cronbach’s alpha stands
at 0.95 and declines with exclusion of each index. This makes the extracted structure
a valid one. The second factor contains the market index only (Table 2.11).
Identi?cation of two factors reveals presence of two structures, and hence two
dominant trends in the NSE. All the sectors move in similar fashion and direction
(as re?ected in their positive loadings on the factor) and together they constitute
the broad, dominant trend in NSE. The sectoral returns however are completely
dissociated from the market trend. The sectoral trend happens to be more dominant
than the market itself. The detailed analysis of such broad, dominant trend could
be of further interest.
Analysis of market trend in NSE: use of factor score
The use of EFA on our data set for NSE extracts two factors that could be
thought of as representing the broad trends in the stock market. Now we construct
2.5 Trends and Latent Structure in Indian Stock Market: Bombay Stock Exchange 33
T
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34 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
factor scores for the two uncorrelated factors. These factor scores, just like our
earlier analysis, would serve as a proxy for the latent structure of the market and
help us analyze the stock market trend in proper or effective way.
The factor scores for the ?rst factor would depict the movement or behavior at
the sectoral level. Such trends will henceforth be described as the sectoral trend.
The sectoral trend is depicted in Fig. 2.15. As is evident from the diagram, the
sectoral return movement is highly volatile, characterized by the presence of
volatility clustering where periods of high (low) volatility are followed by periods
of high (low) volatility. The period of ?nancial crisis that is the period of
2007–2009 is characterized by high volatility.
The factor scores for the second factor re?ects the movement in NSE market
index and would be henceforth described as re?ecting the market trend. The
market trend is depicted in Fig. 2.16. Just like the trends at the sectoral level, the
market movements volatile are characterized by the presence of volatility clus-
tering where periods of high (low) volatility are followed by periods of high (low)
volatility. The period of ?nancial crisis that is the period of 2007–2009 is char-
acterized by high volatility.
However, from the simple plot it is dif?cult to form any proper or conclusive
idea regarding the trends and nature of movements.
Table 2.11 Factor loadings
in the factors extracted: entire
period
Sectors 1 2
Commodity 0.958 –
Energy 0.916 –
Finance 0.893 –
FMCG 0.772 –
Infrastructure 0.939 –
IT 0.756 –
Market – 0.986
Metal 0.855 –
MNC 0.913 –
Pharmaceutical 0.779 –
PSE 0.922 –
PSUBank 0.741 –
Service 0.954 –
-10
-5
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S
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p
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1
1
Fig. 2.15 Movements in
factor scores for factor 1(NSE
sector) (2005–2012)
2.6 Trends and Latent Structure in Indian Stock Market: National Stock Exchange 35
Just like our earlier analysis, trends at market and sectoral levels would now be
analyzed by bringing out the nature of the cycle inherent in the series. Toward the
purpose, the study uses once again the method of band pass (frequency) ?lter. Both
the series are found to be level stationary using Augmented Dickey Fuller test
statistic (null hypothesis of unit root is rejected at one percent level of signi?-
cance). We chose to de-trend the data before ?ltering. The cycle for the sectoral
return is depicted in Fig. 2.17.
The cycle for the sectoral return enables us to identify the ups and downs in
NSE sectoral indexes. The sectors as a whole experience a boom during the phases
namely, 2006–2007, 2009–2010, and since early 2012. The trends are similar to
those experienced in the context of BSE. The sectors as a whole slide down from
its peak over the periods namely, 2007–2008 and 2010–2011. Our analysis is
concentrated around the ?rst cycle. This cycle, however, is in terms of return in the
sectors.
The market return cycle is depicted in Fig. 2.18. The nature of the cycle is
exactly similar to those experienced at the sectoral level.
-10.0000
-5.0000
0.0000
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p
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1
Fig. 2.16 Movements in
factor scores for factor 2
(NSE market) (2005–2012)
-0.00300
-0.00200
-0.00100
0.00000
0.00100
0.00200
0.00300 Fig. 2.17 Cycle in the
sectoral return (NSE)
(2005–2012)
-0.0030000
-0.0020000
-0.0010000
0.0000000
0.0010000
0.0020000
0.0030000
0
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Fig. 2.18 Cycle in the
market return (NSE)
(2005–2012)
36 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
Although the two latent structures in the market are uncorrelated, the cycles are
similar at the sectoral as well as at the market level. States of economy (recovery
or recession) are having similar impacts on sectoral and market level.
The trend is further analyzed through an examination of the risk-return rela-
tionship in the market as a whole. The variance of a series could serve as a good
proxy for the risk of the series. As is suggested by the simple plot of the market
and sectoral return, the two series are characterized by volatility clustering or
volatility pooling. Moreover, the two series are negatively skew, highly peaked,
and non-normal. Such series are best analyzed by an appropriate GARCH family
model and risk for such a series is proxied best by its conditional variance.
The two series are modeled best by simple GARCH model of order (1, 1). The
two series are hence not characterized by asymmetric response of volatility toward
positive and negative announcements in the market. There is no evidence that the
market or the sectors reacts more toward the negative news than toward the good
news. The sectoral return as a whole is characterized by signi?cant presence of
ARCH (or, the news) effect and GARCH (the own past volatility) impacts. The
ARCH effect (0.12), however, is weaker than the GARCH effect (0.87). Hence, past
volatility, rather than past news at the sectoral level has relatively stronger impact
on present volatility of the sectoral return. The market return is also characterized
by signi?cant presence of ARCH (0.11) and GARCH (0.88) effects with GARCH
effects stronger than the ARCH effects. The results are similar to those obtained for
the sectoral level. The ARCH effect at the sectoral level is marginally higher and
GARCH effect is marginally lower compared to the market level.
The conditional volatility for the sectoral return is saved and depicted in
Fig. 2.19.
The conditional variance, after de-trending, exhibits signi?cant cyclical pattern
(Fig. 2.20).
The conditional volatility has been signi?cantly higher during the period of
?nancial crisis of 2007–2008. The two other peaks are not at all signi?cant compared
to this peak. The trend reminds us about the trend in BSE over the same period. Once
again, the nature of cycle of conditional variance is completely opposite to the
cyclical nature of the return series. Return peaks are always associated with low
conditional variance or conditional variance slumps. This is further analyzed and
0
2
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6
8
10
12
14
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2
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4
-
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-
1
2
Fig. 2.19 NSE sectoral conditional variance (2005–2012)
2.6 Trends and Latent Structure in Indian Stock Market: National Stock Exchange 37
depicted in Fig. 2.21. The nature of time-varying conditional correlation between
sectoral return in NSE and conditional variance is used to bring out the relationship
between risk and return at the sectoral level in NSE. Like the previous section, the
conditional correlation has been computed using a multivariate GARCH technique
that models the variance–covariance matrix of a ?nancial time series. Amultivariate
GARCHof appropriate order has been estimated for the data on two factor scores for
NSE return and NSE conditional variance and the conditional correlation values
have been saved. The movement in this conditional correlation re?ects the risk-
return relationship in the context of NSE.
The risk-return relationship has been negative and falling until mid-2006. During
the period that immediately preceded the crisis, risk-return relationship started
rising. However, it remained negative until mid 2007. As crisis set in, the risk-return
relationship became positive and continued to rise. As crisis continued, risk-return
relationship at the NSE sectoral level remained constant and positive. However, as
the economy was recovering, the conditional correlation between risk and return
started dwindling. Eventually, the risk-return relationship became negative.
Let us now consider the conditional variance at the market level. The market is
highly volatile and the volatility has been signi?cantly higher during the period of
?nancial crisis. The trend could be better analyzed if we could consider the cycle
in volatility at the market level (Fig. 2.22).
The cycle in market return volatility in NSE is depicted in Fig. 2.23. The nature
of the cycle is similar, however not identical, to that in the sectoral return. Vol-
atility remained constant at a very high level during the period of ?nancial crisis.
Volatility has been much lower during the pre-crisis and the post-crisis periods.
-1
-0.5
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1
2
Fig. 2.20 Cycle in the NSE
sectoral conditional variance
(2005–2012)
-0.00000150
-0.00000100
-0.00000050
0.00000000
0.00000050
0.00000100
0
3
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-
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1
Fig. 2.21 Cycle of risk-
return relationship at NSE
sectoral level (2005–2012)
38 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
However, volatility started mounting as the market was approaching the crisis. As
the market was recovering volatility dwindled to reach the ?oor.
The risk-return relationship at the market level, however, has been different at
the market level rather than at the sectoral level in NSE. Risk-return relationship
has been negative during the period of January 2005 to January 2007. However, as
the economy was approaching the crisis since mid-2006, the correlation between
risk and return started rising. As the economy was plunging into crisis, the cor-
relation ?uctuated but remained negative. The correlation became positive only in
the post-crisis period and eventually started dwindling since mid-2010 (Fig. 2.24).
The analysis of overall market trend would now be supplemented by analyses
of market trend before and after the crisis.
2. The trends in NSE in the pre-crisis period: 2005 January to 2008 January
The analysis of trends in the market in the pre-crisis period starts from iden-
ti?cation of latent structure in the market.
Table 2.12 suggests presence of statistically signi?cant correlation among
different sectoral returns. The market returns however are not strongly correlated
0.000000
2.000000
4.000000
6.000000
8.000000
10.000000
12.000000
0
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1
1
Fig. 2.22 NSE market
conditional variance
(2005–2012)
-0.0000015000
-0.0000010000
-0.0000005000
0.0000000000
0.0000005000
0.0000010000 Fig. 2.23 Cycle in the NSE
market conditional variance
(2005–2012)
-0.3000
-0.2000
-0.1000
0.0000
0.1000
0.2000 Fig. 2.24 Cycle of risk-
return relationship at NSE
market level (2005–2012)
2.6 Trends and Latent Structure in Indian Stock Market: National Stock Exchange 39
T
a
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1
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(
2
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40 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
with the sectoral returns. The results are same as those obtained for the entire
period.
The use of EFA over the pre-crisis data set is further justi?ed by the favorable
values of the KMO measure of sampling adequacy and Bartlett’s tests for data
adequacy. The KMO measure of sampling adequacy takes a value of 0.897 and
Bartlett’s test statistic of sphericity is signi?cant at one percent level of signi?-
cance implying validity of using EFA on the pre-crisis data set.
On the basis of eigenvalue two factors are retained that are uncorrelated with
one another. This signi?es the presence of two dominant but distinct trends in the
NSE during the pre-crisis period. The ?rst factor with an eigenvalue of 9.373 could
explain 72 % of total variability. All the sectoral indexes have strong and positive
loading in the ?rst factor. The Cronbach’s alpha stands at 0.9750 (which is higher
than the entire period) and declines with exclusion of each index. This makes the
extracted structure a valid one. Thus the sectors are strongly connected, move in
similar fashion and direction and together they constitute the dominant trend in the
market in the pre-crisis period.The second factor has the market index with strong
loading in it. The market thus is completely decoupled from the sectors that are
closely connected among themselves. The second factor with an eigenvalue of
1.01 could explain only 7.76 % of total variability in the NSE (Table 2.13).
The detailed analysis of such broad, dominant trend in the pre-crisis period
would be our further area of analysis.
Analysis of market trend in NSE in pre-crisis period: use of factor score
Factor scores are constructed for the two factors extracted for the NSE. The
factor scores for the ?rst factor represent the sectoral behavior in the market. The
market movement will be proxied by the second factor score. The movement or
behavior of sectoral returns as a whole (given by the factor scores), henceforth
described as the sectors in pre-crisis period, is depicted in Fig. 2.25. As is evident
from the diagrams, the market as well as sectoral movements are highly volatile,
characterized by the presence of volatility clustering where periods of high (low)
Table 2.13 Factor loadings
in the factors extracted: pre-
crisis period (NSE)
Factor 1 Factor 2
Commodity 0.958 –
Energy 0.915 –
Finance 0.853 –
FMCG 0.819 –
Infrastructure 0.933 –
IT 0.747 –
Market – 0.966
Metal 0.833 –
MNC 0.919 –
Pharmaceutical 0.83 –
PSE 0.929 –
PSUBANK 0.797 –
Service 0.933 –
2.6 Trends and Latent Structure in Indian Stock Market: National Stock Exchange 41
volatility are followed by periods of high (low) volatility. However, from the
simple plots it is dif?cult to form any idea regarding the trends and nature of
movements properly. The trend in the pre-crisis period resembles that for the
entire Period.
The trend could be better analyzed if it is possible to bring out the nature of the
cycle inherent in the series. The cycle in the pre-crisis sectoral and market
movements are depicted in Fig. 2.26. The cycles are generated once again using
the method of band pass (frequency) ?lter in its CF form. Both the pre-crisis series
-8
-6
-4
-2
0
2
4
6
03-Jan-05 03-Jan-06 03-Jan-07 03-Jan-08
Movement in Market
-10
-5
0
5
10
03-Jan-05 03-Jan-06 03-Jan-07 03-Jan-08
Movement in Sector
Fig. 2.25 Movements in factor scores, NSE (2005–2008)
-0.01
-0.005
0
0.005
0.01
0.015
0.02
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3
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MARKET_CYCLE
SECTOR_CYCLE
Fig. 2.26 Cycles in the NSE return (2005–2008)
42 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
are found to be level stationary using Augmented Dickey Fuller test statistic (null
hypothesis of unit root is rejected at one percent level of signi?cance). We chose to
de-trend the data before ?ltering. The sectoral return reached top during January
2006 and falls then after. The market, however, reached peak in January 2007 and
then plummeted. As the market was riding high, the sectors were offering higher
returns than the market (‘‘beating the market’’, perhaps). During the recession,
sectoral returns remained considerably lower than the market return. The sectoral
peak, however, has been lower than the market peak.
The trend is further analyzed through examination of the risk-return relation-
ship in the market as a whole. The variance of a series could serve as a good proxy
for the risk of the series. As is suggested by the simple plots of the market and
sectoral returns, the series are characterized by volatility clustering or volatility
pooling. Moreover, the series are negatively skew, highly peaked, and non-normal.
Such series are best analyzed by an appropriate GARCH family model and risk for
such a series are proxied best by their conditional variance.
The NSE return is modeled best by simple GARCH model of order (1, 1). The
market, as well as sectors as a whole is characterized by signi?cant ARCH and
GARCH effects. The ARCH coef?cients are 0.21 and 0.26 respectively for the
market and the sector. The GARCH coef?cients for the market and sectors as a
whole are 0.71 and 0.67 respectively. Thus past volatility impacts on present
volatility are stronger than the news impact for the market as well as sectors. Past
volatility impacts however are relatively stronger and news impacts are relatively
weaker for the market rather than the sectors. This is in line with the results
obtained for the entire period. The conditional volatilities for the pre-crisis series
are saved and depicted in Fig. 2.27.
The conditional variance, after de-trending, exhibits signi?cant cyclical pattern.
Both the cycles in the conditional variance have been of inverted u shape. Vola-
tility increased, reached a top and then fell for both the sector and the market.
When market volatility was rising, sectoral volatility was higher than the market
volatility up to a certain point. The sectoral volatility reached its peak much before
the crisis had set in and much before the market volatility did so. The conditional
volatility in market increased signi?cantly and remained high as the economy was
approaching the crisis. The diagram shows a comparative study of risks (given by
-0.000100
-0.000050
0.000000
0.000050
0.000100
SECTOR_CV
market_CV
Fig. 2.27 Cycle in the factor
score conditional variance
(NSE: 2005–2008)
2.6 Trends and Latent Structure in Indian Stock Market: National Stock Exchange 43
the conditional variance) at the sectoral and the market level. The risk-return
relationship in the NSE is further analyzed and depicted in Fig. 2.28.
The nature of time-varying conditional correlation brings out the presence of a
positive relationship between risk and return in the NSE as a whole. While the
correlation ?uctuates, it started declining sharply since early-2007 for the market
and plummeted to a very low level in mid-2007. The risk-return correlation in the
market was increasing sharply during the recession. The sectoral correlation has
mostly been higher than the correlation at the market level. The sectoral corre-
lation dropped to a low level only during mid-2005. The ?nancial crisis of
2007–2008 did not have much impact on the risk-return correlation at the sectoral
level. For most of the times, the value of correlation coef?cient remained higher
than 0.8.
3. The trends in the post-crisis period: 2008 February to 2012 September
The analysis of market trend in the post-crisis period starts from identi?cation
of latent structure in the market.
Table 2.14 suggests presence of statistically signi?cant correlation among
sectoral returns during the post-crisis period. The correlation between the market
and the sector, however, has been quite low and in signi?cant. The results are
similar to those obtained for the previous phases. The correlation coef?cients are
more or less the same in magnitude compared to those for the entire and pre-crisis
period.
The use of EFA over the post-crisis period data set is once again justi?ed by the
favorable values of the KMO measure of sampling adequacy and Bartlett’s tests
for data adequacy. The KMO measure of sampling adequacy takes a value of 0.875
and Bartlett’s test statistic of sphericity is signi?cant at one percent level of sig-
ni?cance implying validity of using EFA on the post-crisis data set.
On the basis of eigenvalue, once again, two factors are extracted that are
uncorrelated to each other. The ?rst factor with an eigenvalue 9.007 explains
69.29 % of total variability. The second factor with eigenvalue of 1.009 explains
7.76 % of total variability. Both the eigenvalue and the total variability explained
by the single factor extracted are lower than those obtained for the entire period as
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0
3
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7
0
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-
J
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-
0
8
SECTOR
MARKET
Fig. 2.28 Return-risk
relationship NSE
(2005–2008)
44 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
T
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1
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2.6 Trends and Latent Structure in Indian Stock Market: National Stock Exchange 45
well as for the pre-crisis period. Once again, the ?rst factor contains all the
sectoral indexes that are highly and positively loaded in that factor. The Cron-
bach’s alpha stands at 0.9525 (which is lower than those obtained for the entire
period as well as for the pre-crisis period) and declines with exclusion of each
index. This makes the extracted structure, once again a valid one. The second
factor has the market index with strong loading in it (Table 2.15).
The NSE is characterized by two distinct trends in the post-crisis period. The
sectors constitute the broad, dominant trend and they, among themselves are
strongly correlated and move in similar fashion and similar direction even in the
post-crisis period. All the sectors and the market move in similar fashion and
direction (as re?ected in their positive loadings on the factor). The detailed
analysis of the dominant trends in the post-crisis period would be our further area
of analysis.
Analysis of market trend in post-crisis period: use of factor score
Just like the previous cases, we have constructed the factor scores for the two
extracted factors for the post-crisis period. These factor scores would serve as a
proxy for the latent structure of the post-crisis market.
The movement or behavior of market and sectoral trends (given by the factor
scores), are depicted in Fig. 2.29. As is evident from the diagram, the market and
sectoral movements are highly volatile, characterized by the presence of volatility
clustering where periods of high (low) volatility are followed by periods of high
(low) volatility. However, from the simple plot it is dif?cult to form any idea
regarding the trends and nature of movements properly. The trend in the post-crisis
period resembles those for the entire as well as the pre-crisis periods. The vola-
tility is signi?cantly higher during the period of February 2008 to March 2009: the
period when stock market was sliding.
The trend could be better analyzed if it is possible to bring out the nature of the
cycle inherent in the series. The cycles are generated once again using the same
method of band pass (frequency) ?lter in its CF form. The post-crisis series are
Table 2.15 Factor loadings
in the factors extracted
(NSE): post-crisis period
Factor 1 Factor 2
Commodity 0.957 –
Energy 0.916 –
Finance 0.919 –
FMCG 0.734 –
Infrastructure 0.942 –
IT 0.767 –
Market – 0.992
Metal 0.876 –
MNC 0.909 –
Pharmaceutical 0.744 –
PSE 0.916 –
PSUBANK 0.690 –
Service 0.964 –
46 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
found to be level stationary using Augmented Dickey Fuller test statistic (null
hypothesis of unit root is rejected at one percent level of signi?cance). We chose to
de-trend the data before ?ltering. The cycles are depicted in Fig. 2.30.
The cycle for the stock market enables us to identify the ups and downs in
returns in the NSE in the post-crisis period. The sectoral and market cycles are
almost similar in nature. Both the cycles are inverted u-shaped. When the economy
was recovering after the crisis, sectoral returns were marginally lower than the
market return. Similar behavior was observed when economy is sliding down in
recent years. The sectoral peak, however, is higher than the market peak. This
relationship is completely different from that obtained for the pre-crisis period.
The trend in NSE is further analyzed through examination of the risk-return
relationship at the market as well as sectoral level in the post-crisis period. As is
suggested by the simple plot of the stock market returns, both the series are
characterized by volatility clustering or volatility pooling. Moreover the series are
-10
-5
0
5
10
11-Feb-08 11-Feb-09 11-Feb-10 11-Feb-11
Movement in sector
-10
-5
0
5
10
11-Feb-08
11-Feb-09 11-Feb-10 11-Feb-11
Movement in market
Fig. 2.29 Movements in
factor scores, NSE
(2008–2012)
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
11-Feb-08 11-Feb-09 11-Feb-10 11-Feb-11
SECTOR_cycle
MARKET_cycle
Fig. 2.30 Cycles in the
sectoral and market return
(NSE) (2008–2012)
2.6 Trends and Latent Structure in Indian Stock Market: National Stock Exchange 47
negatively skew, highly peaked, and non-normal. Such series could be best ana-
lyzed by an appropriate GARCH family model and risks for such series are
proxied best by the conditional variance.
The market is modeled best by EGARCH, an asymmetric GARCH model of
order (1, 1). As is suggested by Table 2.16, the sectoral return in the post-crisis
period is characterized by asymmetric response of volatility toward positive and
negative announcements in the market. The sectoral return reacts more toward the
negative news than toward the good news.
The market in the post-crisis period is also characterized by asymmetric
response of volatility toward positive and negative announcements in the market.
The market reacts more toward the negative news than toward the good news
(Table 2.17).
This result is in sharp contrast to what we obtained for the pre-crisis period.The
conditional volatility cycles for the post-crisis series are depicted in Fig. 2.31.
The conditional variance, after de-trending, exhibits signi?cant cyclical pattern.
The conditional volatility has been signi?cantly higher during the period of
2008–2009. The conditional volatility was signi?cantly lower during late
2009–2011. Thus, volatility and hence risk, remained signi?cantly higher during
the period of crisis. The risk cycles have been almost similar in nature for the
market and the sectors as a whole. As risks were falling sectoral risks were
Table 2.16 Application of EGARCH model on ?rst factor score for NSE (2008-2012)
Dependent Variable: SECTOR
Method: ML—ARCH (Marquardt)—Normal distribution
Included observations: 959 after adjustments
Convergence achieved after 33 iterations
Presample variance: backcast (parameter = 0.7)
LOG(GARCH) = C(2) ? C(3)*ABS(RESID(-1)/@SQRT(GARCH(-1))) ? C(4) *RESID(-1)/
@SQRT(GARCH(-1)) ? C(5)*LOG(GARCH(-1))
Variance equation
Coef?cient Std. error z-statistic Prob.
C(1) 0.006771 0.021494 0.315034 0.7527
C(2) -0.154017 0.021982 -7.006553 0.0000
C(3) 0.189606 0.026871 7.056247 0.0000
C(4) -0.072713 0.015861 -4.584505 0.0000
C(5) 0.986357 0.004444 221.9540 0.0000
R-squared -0.000046 Mean dependent var -3.13E-08
Adjusted R-squared -0.004239 S.D. dependent var 1.000000
S.E. of regression 1.002117 Akaike info criterion 2.432335
Sum squared resid 958.0441 Schwarz criterion 2.457704
Log likelihood -1161.304 Hannan-Quinn criter. 2.441996
Durbin–Watson stat 1.922791
48 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
marginally higher than the market risk. However, during any downfall in the
market when risks were mounting sectoral risks almost coincide with the market
risk.
The risk-return relationship in the NSE in the post-crisis period is further
analyzed and depicted in Fig. 2.32. The nature of time-varying conditional cor-
relation brings out the nature of risk-return relationship in the market. The cor-
relation between risk and return in the market level fell just after the crisis and
remained marginally positive over the entire post-crisis period. Risk-return rela-
tionship has been ?uctuating and mostly negative at the sectoral level. The cor-
relation became close to zero during the period of 2008–2009 when the economy
was plummeted in crisis.
Table 2.17 Application of EGARCH model on second factor score for NSE (2008–2012)
Dependent Variable: MARKET
Method: ML—ARCH (Marquardt)—Normal distribution
Included observations: 959 after adjustments
Convergence achieved after 43 iterations
Presample variance: backcast (parameter = 0.7)
LOG(GARCH) = C(2) ? C(3)*ABS(RESID(-1)/@SQRT(GARCH(-1))) ? C(4) *RESID(-1)/
@SQRT(GARCH(-1)) ? C(5)*LOG(GARCH(-1))
Variance equation
Coef?cient Std. Error z-Statistic Prob.
C(1) 0.004767 0.022068 0.216029 0.8290
C(2) -0.144538 0.023330 -6.195442 0.0000
C(3) 0.179236 0.028700 6.245237 0.0000
C(4) -0.059043 0.013842 -4.265462 0.0000
C(5) 0.990431 0.004079 242.7968 0.0000
R-squared -0.000023 Mean dependent var -6.26E-08
Adjusted R-squared -0.004216 S.D. dependent var 1.000000
S.E. of regression 1.002106 Akaike info criterion 2.461329
Sum squared resid 958.0219 Schwarz criterion 2.486699
Log likelihood -1175.207 Hannan-Quinn criter. 2.470991
Durbin–Watson stat 1.922218
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
11-Feb-08 11-Feb-09 11-Feb-10 11-Feb-11
market_cv_cycle
SECTOR_CV_CYCLE
Fig. 2.31 Cycle in the NSE
conditional variance
(2008–2012)
2.6 Trends and Latent Structure in Indian Stock Market: National Stock Exchange 49
The trends in National Stock Exchange: Any ‘Signal’ to frame pro?table
trading strategy?
NSE has been dominated by two dominant trends in the market. The most
dominant or ‘market’ trend is formed by all the sectors in the NSE. The sectors as
a whole are completely decoupled from the market. The trend has lasted for the
past 8 years. The sectors among themselves however are closely connected among
themselves and move in similar fashion and in similar direction. Such dissociation
between sectoral indexes and market index, that is independent of the states of the
economy, might offer investors pro?table business opportunities. Moreover, the
trend in the post-crisis period is weaker than the ‘average’ (the trend for the entire
period) market trend where as the trend in the pre-crisis period is stronger than the
‘average’. This is revealed by the EFA where the single factor extracted could
account for more variability (as given by the values of the eigenvectors) in the pre-
-0.6
-0.4
-0.2
0
0.2
0.4
SECTOR_COR
MARKET_COR
Fig. 2.32 Return-risk relationship BSE (2008–2012)
7
7.2
7.4
7.6
7.8
8
8.2
8.4
8.6
8.8
9
5
1
0
1
5
2
0
2
5
3
0
3
5
4
0
4
5
5
0
5
5
6
0
6
5
E
i
g
e
n
V
a
l
u
e
Month
Fig. 2.33 Nature of eigenvalue for ?rst factor in NSE (2005–2012)
50 2 Trends in Indian Stock Market: Scope for Designing Pro?table Trading Rule?
crisis period than for the post-crisis period. In our earlier analysis of eigenvalue
and eigenvector composition for BSE has revealed how that might provide us with
signi?cant signals that might be useful as an indicator of future events. The
changing nature of eigenvalue for the ?rst factor in NSE has been shown in
Fig. 2.33. The eigenvalue has changed from month to month. The fraction of
market variation captured by the ?rst eigenvector thus changes over time. The
movements are sometime marked by sharp changes.
Thus, just like BSE, when the market experiences or passes through some
‘extra-ordinary’ events, some ‘unique’ or ‘special’ trend persists in the market. As
the economy reverts back to its ‘normal’ state this ‘special’ trend weakens in the
sense that the variability captured by the ?rst factor declines steadily. For investors
this information might be extremely useful in designing pro?table trading strategy.
To be more speci?c, if it is possible to identify when this special trend would set in
or how long it would last, investors might be able to design strategies to make
pro?t out of market movements. The movements in the ?rst factor eigenvalue
reveal few more observations. The eigenvalue increases during the periods of
recovery and reaches maximum just before the peak. During a stable period,
however, the eigenvalue falls or reaches a plateau. Therefore, the ‘special’ trend
persists during the phases of recovery and weakens during the periods of recession
or stability. The market crash could be predicted from a high eigenvalue of the ?rst
factor and high eigenvalue could be associated with market crash. In the Indian
context, hence, there is immense scope for investors to use this piece of infor-
mation to design a pro?table trading strategy in the National Stock Exchange.
While it is evident that some trading or fruitful investment strategies could be
derived for the Indian stock market, it would be of interest to explore how such
strategies could be framed. That is where we move to next.
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A Study on Designing Profitable Trading Rule - Indian Stock Market

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