CALENDAR ANOMALY IN BSE/NSE INDICES ON ...This paper examines the possible existence and stability of the calendar anomaly for BSE Sensex and NSE Nifty 50 indices on both the mean
Post on 26-Apr-2020
3 Views
Preview:
Transcript
CALENDAR ANOMALY IN BSE/NSE INDICES ON MARKET
EFFICIENCY
Mrs.A.Shanthi Assistant Professor
School of Management Studies
Sathyabama Institute of Science and Technology, Chennai – 600 119 Email: vshanthi.shashank@gmail.com
Tel: +91-9710306468
Dr. R. Thamilselvan
Associate Professor School of Management Studies
Sathyabama Institute of Science and Technology, Chennai – 600 119
Email: drrts2007@gmail.com
Tel: +91-94427-14150
Abstract
This paper primarily aims to investigate the stability of calendar anomaly for two stock
market index BSE Sensitivity Index of Bombay Stock Exchange and NSE Nifty 50 of
National Stock Exchange in India to check the degree of market efficiency. The dataset
attempted for the study consist of daily market index returns for the period ranging from
1stJanuary 1995 to 31stDecember 2015. The whole dataset for Nifty 50 and BSE Sensex were
divided with pre period starting from 1stJanuary 1995 till 31stDecember 2005 and post period,
respectively. The unit root test is performed to ensure that the index return series have no unit
root. The asymmetric Threshold GARCH regression model was employed by using dummy
variables starting from January to December. The findings of the study observed that the
return is abnormally high during pre period for both the market in the conditional mean
International Journal of Pure and Applied MathematicsVolume 119 No. 15 2018, 355-376ISSN: 1314-3395 (on-line version)url: http://www.acadpubl.eu/hub/Special Issue http://www.acadpubl.eu/hub/
355
equation, which can be addressed to be the turn of the year end effect. On the other hand in
the conditional variance equation, the result shows that the Bombay Sensitivity Index 30 and
Nifty 50 was highly volatility during thefull period. But, the results of the pre and post
indicate that the BSE Sensitivity Index was more volatility in the post period and NSE Nifty
50 indicated with less volatile in the post period. Overall, the conclusion is that monthly
seasonal might simply be in the eye of the beholder.
Keywords: Calendar Anomaly, Volatility, TGARCH Model, Non-Linearity, Market
Efficiency
1. Introduction
In the era of behavioural finance, moral hazard and asymmetry of information,
financial market seems to be affected by different subjective and non-subjective factors. In
case of this work, we try to assess the impact of such elements on the financial market
with striking anomalies like calendar, fundamental and technical anomalies have been
observed by stock market return series across different countries over the period of time. The
research work into calendar anomalies is one of the oldest strands in finance literature that
challenges the foundation of modern finance theory. The presence of calendar anomalies in
stock returns has engrossed the attention of academia and researchers to challenge the
appropriateness of the efficient market efficiency theory by Fama (1970) over the few
decades. Consequently, the calendar anomalies in stock prices have created a need to identify
the causal nexus between the volatility price movements and stock returns. For investors, it is
important to know the total variation in asset returns but also the variances in returns. In
case of calendar anomalies in organized stock market, the market inefficiency is present and
investors should be able to earn abnormal rates of return by predicting the stock market
movement on given days. Hence, the calendar anomalies seem to contradict the weak from of
Efficient Market Hypothesis (EMH). In case of EMH, the stocks are priced in an efficient
manner to reflect all available information about the intrinsic value of the security. The
arbitrage transactions eliminate all the unexploited profit opportunities in an efficient market.
International Journal of Pure and Applied Mathematics Special Issue
356
This paper examines the possible existence and stability of the calendar anomaly for
BSE Sensex and NSE Nifty 50 indices on both the mean and conditional volatility for
attempting degree of market efficiency. In case of market efficiency, the weak form
hypothesis required that there is no consistent patterns in the index returns and have a major
consequence on the returns. The volatility is mainly due to the fact that the efficient market,
the information is price out in such a way that no arbitrage possibilities in any volatility
structure of prices would be possible. Apart from that, the high inflation with challenging
expectations on the future inflation makes it even more complicated to analyses what
determines the requires rate of return by the investors in the stock market. Since, most of the
emerging countries have been witnessing unstable financial environment with high inflation
and deflation, risk free rate of returns have to be considered in the analysis. Since, most of the
emerging markets have a structural predisposed to market inefficiency and leads to further
investigation of return and volatility patterns on market returns. As more empirical research
evidences are obtained through global stock markets around the world, the puzzle still
remains a mystery
Numerous researchers have noticed that the typical propensity of researchers to
concentrate on any unordinary example and findings could prompt the over-disclosure of
anomalies. One such sort of anomaly gives acceptable clarification to the end of the week
impact, a plenty of late papers Levi (1982) and Connolly (1989, 1991), Lakanishok and, Jaffe
and Westerfield (1985), Smirlock and Starks (1986), Agrawal and Tandon (1994) and
Abraham and Ikenberry (1994). Past examinations have announced that regular stock returns,
all thingsconsidered, are strangely low on Mondays and anomalous high on Fridays. The
above-cited references, except Jaffe and Westerfield (1985), Agrawal and Tandon (1994),
provide empirical evidence from the USA. Jaffe and Westerfield (1985) find similar results in
Japanese, Canadian and Australian stock markets as well as in the USA. Agrawal and Tandon
(1994) provide international evidence from stock markets in 18 countries in support of the
day of the week effects. Berument (2003) also considered the influence of public and
provide information as well as unanticipated returns among the reasons for day-of-the week
effects on market volatility. Apolinario, Santana, Sales, and Caro (2006) used the
GARCH and T-GARCH models to examine 13 European stock markets and revealed a
normal behavior of returns is present in these markets. Baker, Rahman, and Saadi (2008)
International Journal of Pure and Applied Mathematics Special Issue
357
study the conditional volatility on the S&P/TSX Canadian returns index and found that the
day-of-the-week effect is sensitive to both the mean and the conditional volatility.
Seasonal anomalies in stock market returns has been widely studied and documented
in finance literature by the academia, researcher and policy makers during the period starting
from late 1970’s. Seasonality in stock market has covered equity, foreign exchange and the T
– Bill markets. The day of the week end effect attempted by Cross (1973) studied the returns
on the S&P 500 Index over the period of 1953 to 1970 and suggested that the mean return on
Friday is higher than the mean return on Monday. The January effect explains the structural
changes in stock returns in January as an average higher than for the other months. In the US
stock market, the January effect was first documented by Rozeffand Kinney (1976). Later,
Keim (1983) noticed that the January effect is mainly confined to stocks of small firms and to
the first few trading days in the month of January. The study examined by Gultekin and
Gultekin (1983) analyzed for 17 major industrialized economy and observed unusual pattern
in the month of January returns in most of the economy. Wong and Ho (1986) portrayed that
the mean daily return in January is significantly higher than the returns in other months over
the period 1975 -1984. Jaffe and Westterfield (1989) explored an weak monthly effect in
stock returns on many countries.
Brooks (2004) identifies with calendar anomalies at first look may infer inefficiency
of the market; this won't be valid for two reasons. Bildik (2004) uncovers the calendar
anomalies demonstrate either market insufficiencies in the hidden resource valuing model
and reminds thatrecorded anomalies to have a tendency to vanish over some undefined
time frame as demonstrated by Schwert (2001).Some of the studies provided by Ng
and Wang (2004) evidenced the support above the hypothesis that institutional investors
would sell the loser stocks extremely in the last quarter and buy many stocks in the following
quarter, which creates the turn-of-year effect or January effect. Borges (2009) revised the
previous methodologies using the most appropriate application of the bootstrapping and
GARCH model to determine the calendar effects. Sahar Nawaz and NawazishMirza (2012)
inspected the share trading system anomalies by ordering into calendar, key and specialized
anomalies in nature Shanthi, Thamilselvan and Srinivasan (2015) proposed the experts
market watchers who know about the everyday return example ought to change the planning
of their purchasing and pitch to exploit the impact. To our knowledge, there has been no
International Journal of Pure and Applied Mathematics Special Issue
358
studies have investigated to explore the calendar anomaly by introducing the dummy variable
in mean equation and the conditional variance equation with the application of Asymmetric
Threshold GARCH model by considering pre and post studies in the national level. This is
unfortunate given the importance of to our economies. Despite, the obvious importance of
exploring the calendar anomaly is a paucity of research on this topic in emerging markets.
The remainder of the paper is presented in the following way. Section - 2 reviews the
material and methods employed in this study by using Asymmetric model. Section –
3 discusses the empirical evidence and section - 4 concludes the research work.
2. Material and Methods
Our dataset consists of the daily index returns of two major indexes of Bombay
StockExchange, Sensex and National Stock Exchange, Nifty 50 of India over the period
spanning from1stJanuary 1995 to 31stDecember 2015. The dataset for Nifty 50 and BSE
Sensex were equally divided with pre period starting from 1stJanuary 1995 till 31stDecember
2005 and post period. The Nifty 50 capitalization weighted index consists of most 50 top
liquid stocks traded in NSE. The Sensex 30 is also a capitalized weighted index based on free
float methodology and itsconstituents are the 30 most important stocks listed in the BSE. The
time period of the study were taken evenly due to country specification and depending on the
availability of the data. The data was analysed by using TGARCH regression model based on
dummy variables starting from January to December. The variables considered too measure
of dummy on monthly effects and is set equal to one if the day is in month i and zero
otherwise. The study also reveals from theextensive literature review through prior studies
that most of the work attempted to identify the price behaviour have used last trading price
for return generating procedure with an implied assumption of trading done at the closing or
last trading price. The continuous compounded return is well accepted approach to measure
the daily returns of the time series. Therefore, in this study the equation is used to determine
the continuous daily return of indices for each working day is calculated based on Rt = l n
(Pt/Pt-1), where Pt refers to the price of the index on day t. Pt-1 is the price of the respective
index on day t-1 and l n is the logarithm return of the respective index represents the value of
index at time t. The reason for considering logarithm return is mainly analytically more
traceable when linked together with sub period over longer interval horizon. Moreover, the
logarithmic returns are more likely to be normally distributed and smoothens data series,
which is highly applicable as standard statistical techniques.
International Journal of Pure and Applied Mathematics Special Issue
359
Unit Root Test
In statistics and econometrics the use of single equation or multi equation regression
models are used frequently to test the time series for modeling economic variables and their
interrelations. The unit root test models employed are based on the Box and Jenkins (1970)
models and their underlying assumptions and their use of time series stationarity is quite
equal to multi model specification with asymptotic distribution. The time series models are
also denoted as integration of order d when they are after the d differentiations stationary.
The determination, order of verifications and integration is quite wide area that includes an
extensive list of test known as Dickey and Fuller test, Augmented Dickey Fuller (1979) test
and Phillips-Perron (1988) test to check the stationarity of the series.
Augmented Dickey Fuller (ADF) test
A basic test for the order of integration is the Dickey Fuller test. The Dickey Fuller
test is simulated on the assumptions pertaining to the alternative is a random walk, with or
without drift terms, and that the residual process is white noise. The Dickey Fuller test is
quite sensitive to the presence of negative MA(1) process (-1). But, in Augmented Dickey
Fuller (ADF) test is considered to be one of the best known and most widely used unit root
test methods. ADF test is based on the model of the first order AR(1) process with white
noise errors. Many financial time series have more complicated and dynamic structure that
have easily captured by a simple AR(1)model. Said and Dickey (1984) suggested the basic
AR(1) unit root test can accommodate general ARMA(p,q) models with unknown orders and
their test is referred to Augmented Dickey Fuller test statistics. In ADF test the null
hypothesis of a time series yt is I(1) against the alternative hypothesis that is also said to be
I(0), assuming that the dynamic in the data series have an Autoregressive Moving Average
structure. The ADF test is based on estimating the testregression
p
t t t 1 j t j t
j 1
Y D y y
Where, Dt is a vector of deterministic terms, which indicate constant or trend. The p
lagged difference terms ∆yt-j, are used to approximate the ARMA structure of the white noise,
and the value of p is set so that the error εtis serially uncorrelated in nature. Due to this, the
error term is also assumed to be homoscedastic. The model stipulation of the verifying terms
International Journal of Pure and Applied Mathematics Special Issue
360
depends chiefly on the assumed behaviour of the ytunder the alternative hypothesis of trend
stationarity. In the null hypothesis, ytis I (1) which mean φ = 1.
Phillips-Peron (PP) test
The Phillips and Perrson (1988) developed a number of unit roots test, which have
been successful and popular in analysing the financial time series of the data. The Phillips
Perron unit root tests differ from the Augmented Dickey Fuller test and shows how the work
will deal with serial correlation and heteroscedasticity in the errors. Especially, the
Augmented Dickey Fuller test use a parametric autoregression to approximate the ARMA
structure of the errors in the rest regression, the Phillips Perron test discount any issues
related to serial correlation in the rest regression. The PP regression equations are as follows;
Yt 1 0 yt 1 t
Where, the εt is I(0) and may be heteroscedasticity in nature. The Phillips Perron test
correct for any serial correlation and heteroscedasticity in the errors ε tof the test regression by
directly modifying the test statistics. The statistics are all used to test hypothesis γ = 0, i.e.,
there exists a unit root. So, the PP statistics are just modifications of the ADF t statistics that
take into account the less restrictive nature of the error process.
Threshold Generalized Autoregressive Conditional Heteroscedasticity Model
The Autoregressive Conditional Heteroscedasticity (ARCH) model was developed by
Engle (1982), which is widely and extensively used models in the finance literature. The
ARCH model portrays the variance of residuals at time tdepends on the squared error terms
from past time periods. Here, the error term εit is conditional and normally distributed with
serially uncorrelated effect. The major strength of ARCH technique is to establish well
specified models for economic forecasting of various variables; the conditional mean and
conditional variance are the only two specifications employed over here. A useful
generalization of this model is the GARCH parameterization. Bollerslev (1986) extended
Engle’s ARCH model to the GARCH model and it is based on the assumption that forecasts
of time varying variance depend on the lagged variance of the asset. The GARCH model
specification is found to be one of the more appropriate statistical models than the standard
models. Due to the consistent with return distribution the leptokurtic effect will allow the
long-run memory in the conditional variance return distributions. Consequently, the
International Journal of Pure and Applied Mathematics Special Issue
361
unexpected increase or decrease in returns at time t will generate an increase or decrease in
the expected variability during the next period.
The Threshold Generalized Autoregressive Conditional Heteroscedasticity
(TGARCH) model has been developed to observe the positive and negative shocks of equal
magnitude. Due to market shocks, the impact on stock market volatility have been attributed
to a “leverage effect” Black (1976). The Threshold GARCH model was introduced by
Zakoian (1994) and Glosten, Jaganathan and Runkle (1993). The objective of this model is to
capture the asymmetric impact in terms of positive and negative shocks and adds independent
dummy variable to capture the statistical significance of the model. The conditional mean
and variance for the simpleTGARCH model is provided below
12
t 0 lt 1 it 2t r
i 1
R C R D
t t 1 t| I N(0,h )
p q2 2
t 0 i t 1 j t j t t 1
i 1 j 1
h C h u du
Where, Rt is the index return for BSE Sensitivity Index and S&P CNX Nifty Index at time t.
Here, the Dit are dummy variable such that D2t = 1 if month t is January and zero otherwise
and so forth, α1 to α12 denotes the mean return for January through December and R1t-1indicate
the coefficients of the lag values. In conditional variance, the ht refers the conditional
volatility of the series, which is proxies by β, α and ψ are the coefficients to be estimated. The
scaling parameter βi now depends both on past values of the information, which is captured
by the lagged squared residual terms, and on past values of itself, which are captured by
lagged ht-1 terms. The αj parameter refers to the last periods forecast variance, the larger
coefficients value was characterized by the informational effects to conditional variance that
take a long time to die out. Finally, the ψt takes the value of 1 if εtis negative, and 0 otherwise,
identifying “good news” and “bad news” have a different impact.
3. Results and Discussion
The below Table 1 reveals the Ljung-Box Q statistics for BSE Sensitivity Index and
NSE Nifty 50 to test the statistical measure used to check whether any group of
International Journal of Pure and Applied Mathematics Special Issue
362
autocorrelations of a time series for both at the normalized residual at lag 5, 10, 15 and 20
and their results are presented below. Rather than testing randomness at each distinct
lag, it tests the general anomalies in view of various lags. The aftereffect of Ljung-Box
measurement demonstrates serial relationship in the standardized residuals has no serial
connection in the squared standardized residuals. Aside from this, the outcome additionally
watched that the lagged values are noteworthy at various levels and show the dismissal of
null hypothesis of no autocorrelation up to order 20 lags. Overall, the study suggests that the
GARCH class of family model is an adequate description of the volatility process of both the
indices and no higher lags are needed to capture the autocorrelation.
Table: 1 Ljung Box Q - Statistics for BSE & NSE Returns
Index Lag Level Pre Period Post Period Full Period
Nifty 50
LB (5) 50.717 397.03 272.40
LB (10) 61.597 413.38 291.60
LB (15) 67.599 431.89 305.11
LB (20) 77.848 451.06 318.38
Sensex
LB (5) 188.46 205.99 382.14
LB (10) 208.81 222.21 415.83
LB (15) 218.08 237.45 432.55
LB (20) 251.41 246.90 464.18
Note: Ljung Box (5), (10), (15) and (20) refers to 5 lag, 10 lag, 15 lag and 20 lags, respectively.
To set the stage for the distributional properties of finance research, the explosion for
testing the stationarity of the series has gained important and major focus has given by the
researchers to check the existence of unit root test. Otherwise, the regression analysis used to
identify the unit root test is said to be spurious in nature, which leads to misleading
interpretation and conclusion. In Table: 2, the results of Augmented Dickey Fuller (ADF) test
and Phillips Perron (PP) test has been examined for BSE Sensitivity Index and NSE Nifty 50
indices for pre period, post period and full period by measure the z-statistic and it will be
compared to the critical value given by MacKinnon (1991). The ADF and PP test were
examined by investigating constant and linear with trend for I(0) and I(1) of the series by
International Journal of Pure and Applied Mathematics Special Issue
363
considering the optimal lag length Akaike’s Final Prediction Error (FPE) Criteria before
proceeding to identify the probable order of integrity. Finally, the unit root test results
identifies that the return series are found to be stationary at first-order difference and
integrated at the order of I(1).
Table: 2 Unit Root Test for BSE & NSE Returns
Note: ADF is the Augmented Dickey Fuller test and PP refers to Phillips -Perron test. *MacKinnon (1996) one-
sided p-values.
In Table 3 explains the Threshold Generalized Autoregressive Conditional
Heteroscedasticity (TGARCH) Model was examined to assess the conditional mean with
dummy variable and conditional variance for Bombay Stock Exchange (BSE) Sensitivity
Index for pre period, post period and full period and their results were presented over there.
In the conditional mean equation, the Rt-1 reveals the lagged coefficient value was statistically
significant at 1 percent level for all the period. Out of all the three period, the pre period
effect were highly significant for the January, March, April, July, October and November,
which indicate the turn of the ear end effect, January effect and tax effect on each quarter
plays an vital role in the pre period. In case of post period and full period, the month of
Index Augmented Dickey Fuller Test Phillip Perron Test
Period Constant Linear &
Trend
Constant Linear & Trends
Pre Period
Post Period
0.8313
-1.1907
-0.4335
-2.3611
1.0443
-1.2092
-0.2736
-2.3505
Full Period 0.0104 -2.4203 0.0309 -2.4116
Δ Pre Period
Δ Post Period
-21.269
-22.322
-21.287
-22.321
-43.912
-31.478
-43.917
-31.472
Δ Full Period -30.935 -30.932 -55.165 -55.159
Sensex
Pre Period
Post Period
1.0066
-1.2702
-0.0912
-2.3190
1.1659
-1.2829
0.0207
-2.3033
Full Period
Δ Pre Period
-0.0292
-21.098
-2.3642
-21.122
-0.0046
-37.327
-2.3496
-37.332
Δ Post Period
Δ Full Period
-22.791
-30.985
-22.791
-30.982
-36.570
-52.294
-36.564
-52.288
International Journal of Pure and Applied Mathematics Special Issue
364
September and January were having positive and negative impact on the market with 1 per
cent and 5 per cent level of significant with a coefficient value 0.002034 and -0.001350,
respectively. Therefore, in post period and full period, the investor’s behavior is quite
illogical and they behave randomly in the market to reap the benefit of it. In variance
equation, the ARCH and GARCH coefficient value were significant for all the study period.
Henceforth, the positive shock has a greater impact on α while the negative shocks have a
lower impact of ARCH (β) + λ and observed close to 1 with 0.922 in pre period and post
period with 0.920, respectively. In case of ψ is concerned, throughout the period the
Sensitivity index shows positive effect and revealed that the investors are not concerned
about the positive and negative shocks in the markets. Therefore, the information reached to
the investors will take a short time to die in the market. In addition, the goodness of fit
measure like Log Likelihood, DW test, AIC Criterion and SIC Criterion were also considered
to add extra value to the analysis. The Log Likelihood test and Durban Watson test suggest
with positive value and approximately to 2, which suggest the work have minimal
issues on the autocorrelation issues. The AIC criterion and SIC criterion also have a value
with minimal deviation and indicate the model is best fitted in nature.
Figure 1, 2 and 3 also reveals the graphical representing of the calendar
anomalies for Bombay Stock Exchange, Sensex for all the period. In Figure 1 and 2
explains about the major stock market movements from 1stJanuary 1996 till 31stDecember
2005 and 1st January2006 till 31stDecember 2015. From the Figure 1, the Sensex was highly
volatile during the pre-period, which may due to Asian Stock Market Crisis, Y2K Issue and
entertained niggling worries about the possible effect of rising official interest rates on
consumer spending in countries towards housing boom, such as the U.K., Spain, and Ireland.
Due to this issue, the major stock markets weakened and the equity investors turned more
risk-averse and concerned about the real strength of the global economic recovery. Hence, the
pre period was considered to be highly volatility period in the international market and had a
major impact on the emerging markets.
International Journal of Pure and Applied Mathematics Special Issue
365
Table: 3 TGARCH Model for Calendar Anomaly for BSE Sensex Return
Particulars Pre Period Post Period Full Period
Mean Equation
C 0.001948* -0.000173 0.000709
Rt-1 αDJanuary αDFebruary (3.06141)
0.320217*
(15.7735)
-0.003211*
(-3.84044)
-8.31E-05
(-0.34422)
0.348199*
(17.9589)
-0.000222
(-0.35384)
0.000311
(1.77634)
0.337021*
(25.0190)
-0.001350**
(-2.60044)
0.000126
(-0.09884) (0.42867) (0.23220)
αDMarch -0.002611* 0.000835 -0.000358
(-2.67777) (1.14830) (-0.61967)
αDApril -0.002675* 0.000521 -0.000733
(-2.73890) (0.72409) (-1.21641)
αDMay -0.000945 0.000243 -0.000326
(-0.97857) (0.36023) (-0.58507)
αDJune -0.000503 0.000156 0.000010
(-0.51374) (0.22190) (0.01721)
αDJuly -0.001836** 0.00000 -0.000700
(-2.03272) (0.05621) (-1.24988)
αDAugust -0.001521 0.000380 -0.000404
αDSeptember
(-1.63106)
-0.001644
(0.52668)
0.002034*
(-0.69933)
0.000568
(-1.76635) (3.11591) (1.04043)
αDOctober -0.002046** 0.000517 -0.000572
(-2.13870) (0.77277) (-0.99613)
αDNovember -0.000534 0.000177 -0.000056
(-0.50414) (0.24812) (-0.09404)
International Journal of Pure and Applied Mathematics Special Issue
366
Variance Equation
C 0.000000*
(6.01764)
0.000002*
(5.56290)
0.000000*
(7.81805)
α 0.084340* 0.052655* 0.075808*
β
(6.54001)
0.838043*
(5.91429)
0.832472*
(10.8572)
0.844659*
Ψ
(73.1421)
0.114061*
(71.2290)
0.221905*
(116.269)
0.145608*
(6.79816) (9.65156) (12.0016)
Goodness of Fit
Log Likelihood 7478.592 7969.403 15428.91
Durban Watson test 2.033599 2.054496 2.045184
Akaike Info Criterion -6.012564 -6.418404 -6.211974
Schwarz Criterion -5.972722 -6.378510 -6.189672
Note: Ljung Box statistics upto 15 lag. a
&b
indicate statistically significant at 1 per cent and 5 per cent,
respectively.
International Journal of Pure and Applied Mathematics Special Issue
367
.
The below Table 4, exhibit the Threshold Generalized Autoregressive Conditional
Heteroscedasticity (TGARCH) Model for NSE Nifty 50 index. The dataset for Nifty 50 was
divided into pre period; post period and full period were portrayed by using conditional mean
and conditional variance equation by applying TGARCH model by applying dummy variable
the mean specification. Apart from that, the results of goodness of fit measures were provided
International Journal of Pure and Applied Mathematics Special Issue
368
to assess the best fit of the model. The conditional mean equation for pre period indicate that
the return of past days were influential about the future information. During the month of
January, March and April were significant with -0.003049, -0.001667 and 0.005619 with 1
per cent and 5 per cent level of significant. But, the remaining month, does not have any
impact with the future index return of the series. Likewise in the post period and full period,
the impact of monthly effect were totally insignificant over the period, which suggest
the information is not disseminated to a higher level in the Nifty 50. In the variance
equation, the ARCH and GARCH specification were highly significant and indicate the
volatility impact on information is very high and suggest that Nifty 50 index movement is in
line with the international market. The post period the ß value observed with insignificant
with 0.600000. Moreover, the Ψ revealed positive impact is high during all the period. Hence,
the investors can base their investment decision based on long term period. The fluctuation in
market index is temporary in nature. In addition, the goodness of fit measure like Log
Likelihood, DW test, AIC Criterion and SIC Criterion were also considered to add extra
value to the analysis. The Log Likelihood function also observed with positive effect. The
Durban Watson test for post period and full period indicate with1.846252 and 2.278377. Only
in case of pre period, the Durban Watson test shows high value at2.439071 and suggests there
may be slight autocorrelation issues in the model fit. AIC criterion and SIC criterion also
have a value with minimal deviation and considered to be the best fitted model.
Table: 4 TGARCH Model for Calendar Anomaly for NSE Nifty 50
PrePeriod PostPeriod FullPeriod
MeanEquation
C 0.001166* 0.000263 0.000414
(2.14968) (0.13437) (1.14830)
Rt-1 0.422387*
(20.2314)
0.391033*
(10.1756)
0.427426*
(30.7037)
αDJanuary -0.003049*
(-3.89092)
-0.00085
(-0.3197)
-0.00134*
(-2.7087)
αDFebruary -0.000259 -0.00053 0.000136
(-0.34851) (-0.1990) (0.26636)
αDMarch -0.001667** 0.000574 -0.00026
(-2.32748) (0.22211) (-0.5111)
αDApril -0.002166* 0.001180 -0.00073
International Journal of Pure and Applied Mathematics Special Issue
369
(-2.64552) (0.42841) (-1.2869)
αDMay -0.000936
(-1.07430)
-0.00051
(-0.2024)
-0.00050
(-0.9495)
αDJune -0.000797
(-0.91829)
-0.00024
(-0.0934)
-0.00030
(-0.5491)
αDJuly -0.001548 0.000190 -0.00080
(-1.95537) (0.07166) (-1.5160)
αDAugust -0.001381
(-1.59492)
-0.00039
(-0.1547)
-0.00052
(-0.9492)
αDSeptember -0.001399 0.000775 0.00060
(-1.62837) (0.30962) (1.2020)
αDOctober 0.005619*
(7.17886)
0.000071
(-0.0283)
0.00246*
(5.4504)
αDNovember -0.000294 -0.00014 0.00004
Variance Equation
Goodness of Fit
Log Likelihood 7571.021 7489.424 15573.12
Durban Watson test 2.439071 1.846252 2.278377
Akaike Info Criterion -6.033563 -6.02857 -6.24242
Schwarz Criterion -5.994012 -5.98869 -6.22020
Note: Ljung Box statistics upto 15 lag. a
&b
indicate statistically significant at 1 per cent and 5 per cent,
respectively.
C 0.00001*
(7.11462)
0.000081*
(3.38431)
0.000051*
(9.34271)
α 0.174756*
(7.12889)
0.150000**
(1.99401)
0.106510*
(9.42874)
β 0.632095* 0.600000 0.764057*
(26.0294) (0.60563) (72.3812)
Ψ 0.439506*
(8.98260)
0.050000*
(5.37032)
0.284096*
(12.5480)
International Journal of Pure and Applied Mathematics Special Issue
370
In Figure 4, 5 and 6 also reveals the graphical representing of the calendar anomalies
for National Stock Exchange, Nifty 50 index for all the period. In Figure 4 and 5 explains
about the major stock market movements from 1stJanuary 1996 till 31stDecember 2005 and
1stJanuary2006 till 31stDecember 2015. From the Figure 1, the Nifty 50 script, the volatility
was very low, which indicate reversal pattern when compared to BSE Sensex index. The
market is highly volatility in NSE Nifty 50 index due to recession impact, Oil price crisis,
Chinese Crisis, Russian Crisis all plays a vital role for the major movements in the emerging
stock market.
International Journal of Pure and Applied Mathematics Special Issue
371
Conclusion
This chapter study about the calendar anomaly for two famous stock market indices in
India like BSE Sensex and NSE Nifty 50. The study also used to check the volatility pattern
in stock market returns might enable investors to take advantage of both the market by
designing various trading strategies in predicting the pattern of the market movements. The
results of conditional mean and conditional volatility in TGARCH model explains the degree
of efficiency for different period by using dummy variables starting from January to
December. The results suggest that both the market are quite contrary and does not have any
link with Nifty 50 and Sensex index. Even, the lagged return has only minimal influence on
conditional mean of the series. The Threshold value indicate positive impact are very higher
in both the market due to sentimental factors, internal issues of the companies plays dominant
movement to the local market Finally, the seasonality in emerging market creates arbitrage
opportunities to the stock market participants by using different yield spreads, due to the
effect of different period account settlement, investor sentiment and unsystematic risk in the
market.
The findings of the study observed that the return is abnormally high during pre
period for both the market in the conditional mean equation, which can be addressed to be the
turn of the year end effect. The return during the turn of month period, which could be
observed due to the last trading day and the first four trading days of the following months, is
also abnormally high. Due to this, the turn of the year end effect can create an opportunity to
make above average profit to investors exploiting these calendar anomalies. In case of the
International Journal of Pure and Applied Mathematics Special Issue
372
conditional variance, theresult shows that the Bombay Sensitivity Index 30 and Nifty 50 was
highly volatility during the full period. But, the results of the pre and post indicate that the
BSE Sensitivity Index was more volatility in the post period and NSE Nifty 50 indicated with
less volatile in the post period. Therefore, the calendar anomalies may be difficult to be
exploited in practice because of transaction costs and ability to replicate the stock index
return, the existing evidence of calendar anomalies can help investors as the clue for the
timing of investment. Overall, the conclusion is that monthly seasonal might simply be in the
eye of the beholder. As a matter of concern, the research work can be attempted by using
other anomalies in stock market such as turn-of-the- month, Halloween and holiday effect,
could be included to the analysis. In some other cases, the securities could also be analysed
independently or they could be divided into groups based on the impact on various sectors
towards the global economy.
References:
1. Abraham, A. &Ikenberry, D. L. (1994), The Individual Investor and the Weekend Effect,Journal of Financial and Quantitative Analysis, Vol: 29, Pp: 263–77.
2. Agrawal. A.&Tandon, K. (1994), Anomalies or Illusions? Evidence from Stock
Markets inEighteen Countries, Journal of International Money & Finance, Vol: 13, Pp: 83-106.
3. Apollinario, R., Santana, O., Sales, L. and Caro, A. (2006), “Day of the Week Effect onEuropean stock markets, International Research Journal of Finance and Economics, Vol. 2, pp.53–70.
4. Baker. H. Kent, Abdul Rahman and Samir Saadi (2008), “The Day-of-the-Week Effect and Conditional Volatility: Sensitivity of Error Distributional Assumptions”,
Review of Financial Economics, Vol. 17(4), pp. 280-295.
5. Berument, H. and Kiymaz, H. (2003), “The Day-of-the-Week Effect on Stock Market Volatility,Journal of Economics and Finance, Vol. 25, pp. 181–93.
6. Bildik. R (2004), “Are Calendar Anomalies Still Alive? Evidence from Istanbul StockExchange”, Istanbul Stock Exchange.
7. Black. F. (1976), Studies of Stock Market Volatility Changes, Proceedings of the AmericanStatistical Association, Business and Economic Statistics Section, Pp: 177-181.
8. Bollerslev, T. (1986), Generalized Autoregressive Conditional Heteroskedasticity, Journal ofEconometrics, Vol: 31, Pp: 307-327.
International Journal of Pure and Applied Mathematics Special Issue
373
9. Box, G. E. P. and Jenkins, G. M. (1970), “Time Series Analysis: Forecasting and
Control”, 2nd
Edition. Holden-Day, San Francisco.
10. Brooks, C. (2004), “Introductory Econometrics for Finance”. (6thEdition). The United
Kingdom: Cambridge University Press.
11. Connolly. R. (1989), An Examination of the Robustness of the Weekend Effect,
Journal ofFinancial and Quantitative Analysis, Vol: 24, Pp: 133-69.
12. Connolly. R.A. (1991), A Posterior Odds Analysis of the Weekend Effect ,
Journal ofEconometrics, Vol: 49, Pp: 51-104.
13. Cross, Frank (1973), “The Behavior of Stock Prices on Mondays and Fridays”,
FinancialAnalysts Journal, Vol. 29, pp. 67-69.
14. Dickey. D. A and Fuller. W. A (1979), “Distribution of the Estimators for
Autoregressive TimeSeries with a Unit Root”, Journal of American Statistical Association, Vol. 74, pp. 427 – 431.
15. Engle, R. F. (1982), “Autoregressive Conditional Heteroskedasticity with
estimates of the variance of United Kingdom Inflation”, Econometrica, Vol: 50, Pp: 987-1008.
16. D.Sasikala, R.Roshiniya, Sarishnaratnakaran, Tapati Deb, “Texture Analysis of Plaque in Carotid Artery”, International Journal of Innovations in Scientific and Engineering Research(IJISER), Vol.4, No.2, pp.66-70, 2014.
17. Fama, E. (1970), Efficient Capital Markets: A Review of Theory and Empirical Work Journal ofFinance, Pp. 383-417.
18. Glosten, L. R; Jagannathan, R., &Runkle, D. E, (1993), On the Relation between the
Expected Value and the Volatility of the Nominal Excess Returns on Stocks. Journal of Finance, Vol: 48, No: 5, Pp: 1779-1791.
19. Gultekin, M.N. and Gultekin, N.B (1983), “Stock Market Seasonality: International
Evidence”,Journal of Financial Economics, Vol. 12, pp. 469-481.
20. Jaffe. J. and Westerfield, R. (1985), The Week-End Effect in Common Stock Returns: TheInternational Evidence, Journal of Finance, Vol: 40, Pp: 433–54.
21. Jaffe. J.F. and Westerfield, R. (1989), Is There a Monthly Effect in Stock Market
Returns?,Journal of Banking and Finance, Vol: 13, Pp: 237-44.
22. Keim, D.B (1983), “Size-Related Anomalies and Stock Returns Seasonality: Further EmpiricalEvidence”, Journal of Financial Economics, Vol. 12, pp. 13-32.
23. Lakanishok, J. and Levi, M. (1982), Weekend Effects in Stock Returns: A Note,
Journal ofFinance, Vol: 37, Pp: 883–89.
24. BorgesMaria Ross (2009), “Calendar Effects in Stock Markets: Critique of PreviousMethodologies and Recent Evidence in European Countries” Working Paper
37/2009/DE/UECE
25. Ng Lilian and Qinghai Wang (2004), “Institutional Trading and the Turn-of-the-Year
Effect”,The Journal of Business, Vol. 77(3), pp. 493-509.
International Journal of Pure and Applied Mathematics Special Issue
374
26. Phillips. R. C. B andPerron. P (1988), Testing for Unit Root in Time Series RegressionBiometrika, Pp: 335 -346.
27. Rozeff, M.S. and Kinney, Jr. W.R., (1976), “Capital Market Seasonality: The Case of StockReturns”, Journal of Financial Economics, Vol. 3, pp. 379-402.
28. Sahar Nawz1andNawazishMirza (2012), “Calendar Anomalies and Stock Returns: A Literature Survey” Journal of Basic. Applied Science Research, Vol.2 (12), pp.12321-12329.
29. Said E. Said and David A. Dickey (1984),”Testing for Unit Roots in Autoregressive MovingAverage Models of Unknown Order” Biometrika, Vol 71(3), pp. 599 – 607.
30. Schwert William G (2001), “Stock Volatility in the New Millenium: How Wacky is NASDAQ?”National Bureau of Economic Research Working Paper 8436.
31. Shanthi, Thamilselvan and Srinivasan (2015), “The Day of the Week Effect and
Conditional Volatility in Indian Stock Market: Evidence from BSE & NSE” International Journal of Applied Engineering Research, Vol 10(3), pp. 7495-7508.
32. Smirlock. M. and Starks, L. (1986), Day-of-the-Week and Intraday Effects in Stock Returns,Journal of Financial Economics, Vol: 17, Pp: 197–210.
33. Wong, K.A. and Ho, H.D. (1986), “The Weekend Effect on Stock Returns in
Singapore”, HongKong Journal of Business Management, Vol. 4, pp. 31-50.
34. Zakoian, J.M. (1994), “Threshold Heteroscedasticity Models”, Journal of Economic
Dynamics and Control, Vol. 18, pp. 931-944.
International Journal of Pure and Applied Mathematics Special Issue
375
top related