Lead Lag effect between Nifty 50 and Midcap 50 of Indian Stock Market

 

Haritika Arora

Assistant Professor, C K D Institute of Management and Technology, Opp. Model Town, Near Railway Station, G.T. Road, Amritsar

 

ABSTRACT:

This study has made a attempt to establish the lead lag relationship between the Nifty 50 and Midcap 50 for period 1st January 2011 to 31^st December 2015. For this purpose, this study have used Johansen Co-integration Test, Vector Autoregressive (VAR) Model, Variance decomposition and Impulse response function. Results revealed that there is no long term co-integrating relationship between the Nifty 50 and the Midcap 50. Further, Vector Autoregressive (VAR) Model, Variance decomposition and Impulse response function clearly provide evidence of Nifty to be influenced by its own lagged returns. On the other hand, Midcap is highly influenced by the Nifty lagged returns and then by its own returns. Hence, Nifty leads the Midcap.

 

 

 

INTRODUCTION:

Many studies have recognized the temporal relationship between small or middle capitalization and large capitalization stocks. (Mech, 1993; Richardson, and Whitelaw, 1994; Badrinath, Kale, and Noe, 1995; McQueen, Pinegar, and Thorley, 1996; Campbell, Lo, and MacKinlay, 1997; Hou, K. 2007 etc.). These researchers established that returns between large and small stocks are cross-correlated. Furthermore, various studies have also revealed that these cross-correlations are asymmetric i.e. the returns of small stock portfolios tend to be interdependent with the lagged returns of large stock portfolios, whereas the returns of large capitalization share portfolios tend to be uncorrelated with the lagged returns of small capitalization share portfolios.

 

Lo and MacKinlay (1990) observed a significant lead–lag relation using weekly data between small and large size firms portfolio returns for the NYSE. Their study revealed that large size firms stocks lead and small size firms stock follows. The inference of such relationship relate to the aptitude of investors or traders to predict the returns of small-firm portfolio according to the returns of large-firm portfolios. Extensive literature discuss these findings in order to recognize the complex mechanism of information transmission between large size and small size firm portfolio returns.

 

Most of the literature on the lead–lag relationship among small and large capitalization stocks in US and UK financial market. However, some studies have put consideration to other mature and emerging markets. Chang et al. (1999) made available evidence of lead–lag effects in various Asian markets, whereas Chui and Kwok (1988), Li et al. (2000), Kang et al. (2002) have recognized such a lead–lag effect for diverse stocks of Chinese stock market. Altay (2004) found evidence of a lead–lag relationship for the German and Turkish equity markets.  In addition, Marshall and Walker (2002) and Poshakwale and Theobald (2004) tried to explore short-run lead–lag relationship between large and small capitalization portfolios using cross-autocorrelations for the Chilean stock market and the Indian stock market respectively.

 

For Indian stock markets, Karmakar (2010) examined both casual and dynamic relationship between the large stocks and small stocks in the National stock exchange using daily index data. This study used SandP CNX Nifty, CNX Nifty Junior and CNX Midcap and employed VAR model with the variance decomposition and the impulse response function approach. Results have shown significant return spillovers from the stock portfolio of large firms to the portfolio of small firm stocks. The purpose of this paper is to re-investigate this lead–lag effect in Indian Stock Market using Nifty 50 and Midcap 50 for period of 1st January 2011 to 31st December 2015.

 

DATABASE AND METHODOLOGY:

Daily data for Nifty 50 and Midcap 50 for period of 1st January 2011 to 31st December 2015 is obtained from historical database available from website of National stock exchange. In order to investigate the lead lag relationship between Nifty 50 and Midcap 50, Johansen Co-integration test and VAR model has been used.  However, before testing for co-integration, the order of integration of price series must be determined. To identify whether our price series are I(1), Augmented Dickey–Fuller (ADF) test  has been used. ADF test is also a test for a unit root in a time series sample.

 

Johansen Co-integration Test:

Variables are said to be co-integrated, if two or more variables are integrated at same order d where d>0, and there is presence of a stationary linear pattern of these variables. Deceptive inference is perceived by regressing non-stationary variables concerning degree of association. As a result, prior to test for co-integration, the order of integration of price series should be determined.  The Johansen test moves toward the test of co-integration by exploring the number of independent linear combinations (k) meant for time series variables (r) that capitulate stationary course of action. Johansen suggests following two Maximum Likelihood based tests to determine the number of non-zero Eigen-values: The Lamda Max or Max- Eigen () Test and The Trace Test.

 

Order of integration of the Midcap 50 and Nifty 50:

All variables need to have the similar order of integration. Based on following cases, relationship between two variables is explored:

1)     The Nifty and Midcap are co-integrated:  The error correction term has to be incorporated in the VAR model named as "Vector error correction model (VECM)" which can be observed as a restricted VAR.

2)     The Nifty and Midcap are not co-integrated: The variables have first to be differenced "d" times and estimated as Vector Autoregressive (VAR) Model.

 

Variance Decomposition and Impulse Response Function:

Once the VAR system is estimated, short-run dynamic analysis is done with the help of variance decomposition (VDC) and impulse response function (IRF). The Variance decomposition forms an estimate of some portion of the movement of time series up to the few steps forward and forecast for error variance of a variable in the VAR system that is due to its own shock and the shock from the another variable. Similarly, the IRF shows plotting of dynamic relationship between two variables and capturing the response of the variable to its shock and shock due to another variable.

 

EMPIRICAL FINDINGS:

As the backdrop of the research work, Figure 1 represents the two graphs: one of the price series of Nifty and Midcap and another is return series of the Nifty and Midcap. From this graphical representation, it is observed that the price levels are non-stationary, returns series are stationary. 

 

Figure 1 : Graphical representation of price and return series of Nifty 50 and Midcap 50.

 

Johansen co-integration test:

To explore the lead lag relationship between Nifty 50 and Midcap 50, first step is to consider the possibility of co integration between the two series of each disjoint set. First pre-condition of Johansen co-integration test is that Nifty 50 and Midcap 50 should integrated at same level of differentiation. Therefore, the Augmented Dickey Fuller test statistics is conducted as presented in Table 1. ADF test statistics reveal that the price series are non-stationary. However, both the series become stationary at first difference. Hence, Nifty 50 and Midcap 50 is integrated [I(1)] or stationary [I(0)].

 

The results of the Johansen co-integration test are presented in Table 2. The null hypothesis that the Nifty and Midcap are not co-integrated (r = 0) against the alternative of one co-integrating vectors (r > 0). From the trace test statistics and Max-Eigen test statistics are not significant at a 5% level of each disjoint set. Thus, according to the Johansen’s (1991) test, there is no evidence of co-integration relationship between the Nifty 50 and the Midcap 50. This means there is no definite long-term connection between two indices, hence, Nifty and Midcap do not converge in long term and react differently to information. The results are consistent with Karmakar (2010), who tried to explore the long run equilibrium between Nifty and Midcap as well as Nifty and Nifty Junior, but did not find any co-integrated relationship.

 

As there is no co-integrating relationship between the Nifty 50 and the Midcap 50, this study tried to explore the further dynamics with a VAR (Vector Auto-regressive Model) analysis, which covers Granger causality, decomposition of variance and the impulse response function.

 

Table 1: Augmented Dickey Fuller test statistics

	At Level		1st Difference series
	t-statistics	p-value	t-statistics	p-value
Nifty 50	-0.682626	0.8490	-32.11760	0.0000
Midcap 50	-0.977716	0.7629	-31.55841	0.0000

 

Table 2: Johansen co-integration test

Unrestricted Cointegration Rank Test (Trace)
Hypothesized			Trace	0.05
No. of CE(s)	Eigenvalue		Statistic	Critical Value	Prob.**
None	0.005399		7.988913	15.49471	0.4666
At most 1	0.001054		1.302967	3.841466	0.2537
Trace test indicates no cointegration at the 0.05 level  * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized			Max-Eigen	0.05
No. of CE(s)		Eigenvalue	Statistic	Critical Value	Prob.**
None		0.005399	6.685946	14.26460	0.5269
At most 1		0.001054	1.302967	3.841466	0.2537
Max-eigenvalue test indicates no cointegration at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values

 

Vector Autoregressive (VAR) Model:

The outcome of the estimated coefficients of VAR is revealed in Table 3. The optimal lag length in the VAR model is selected by the AIC (Akaike information criterion). Once the VAR structure is estimated, the volatility dynamic between Nifty 50 and Midcap 50 is analyzed by variance decomposition (VDC) and impulse response function (IRF).

 

The VAR estimate between Nifty 50 and Midcap 50 shows that the significant lag returns at 5% level on each other. Results depicts that returns of Nifty 50 is not dependent on the lagged returns of Midcap 50. Contrary, Midcap 50 is highly influence by the lagged return of Nifty 50. Thus results indicate that past information about the Nifty has ability to predict the return of the Midcap and vice-versa is untrue. Therefore, Nifty leads the Midcap. These results corroborated the earlier studies outcome which depicts that small or middle capitalization stocks follows the large capitalization stocks (Richardson, and Whitelaw, 1994; Badrinath, Kale, and Noe, 1995; McQueen, Pinegar, and Thorley, 1996).

 

Table 3:Vector Autoregressive (VAR) Model

Vector Auto regression Estimates
Standard errors in ( ) and t-statistics in [ ]
	NIFTYRETURN	MIDCAPRETURN
NIFTYRETURN(-1)	0.155047	0.160844
	(0.04955)	(0.06683)
	[ 3.12888]*	[ 2.40674]*
NIFTYRETURN(-2)	-0.063478	-0.024780
	(0.04950)	(0.06676)
	[-1.28240]	[-0.37120]
MIDCAPRETURN(-1)	-0.061343	0.012184
	(0.03676)	(0.04958)
	[-1.66867]	[ 0.24574]
MIDCAPRETURN(-2)	0.045408	0.033840
	(0.03661)	(0.04937)
	[ 1.24041]	[ 0.68543]
C	0.000200	9.60E-05
	(0.00030)	(0.00041)
	[ 0.66247]	[ 0.23599]
R-squared	0.010664	0.017134
Adj. R-squared	0.007452	0.013943
Sum sq. resids	0.138615	0.252124
S.E. equation	0.010607	0.014305
F-statistic	3.319831	5.369241

* 5% level of significance

 

Further dynamics of information transfer between Nifty and Midcap is explored by Variance decomposition and Impulse response function. Variance decomposition and the impulse response function try to capture the contemporaneous impact of any shock to two time series and the ability of series to decay the effect of shock. The result of the Variance Decomposition analysis provides further evidence of the influence of the Nifty on the Midcap and vice-versa from table 4. The movement in Nifty is explained by their own shock up to level of 99% and rest explained by shock in Midcap up to level of 0.30%. In other words, volatility of Nifty is only influenced by its own shocks..

 

Contrary, movement in Midcap is explained by their own shock up to level of 32.4% and rest explained by shock in Nifty up to level of 67.5% In other words, Volatility of Midcap is influenced by majority shocks in Nifty returns and minority by its own shocks. The results of this study corroborate the result of Karmakar (2010), which observed that Nifty returns react only to their own shocks. The shocks to the return of the Nifty Junior and the Midcap do not have a significant effect on the dynamics of the Nifty.

 

Table 4: Variance Decomposition

Variance Decomposition of NIFTY:
Period	S.E.	NIFTYRETURN	MIDCAPRETURN
1	0.010607	100.0000	0.000000
2	0.010659	99.77654	0.223460
3	0.010664	99.70342	0.296577
4	0.010664	99.69923	0.300768
5	0.010664	99.69923	0.300773
6	0.010664	99.69922	0.300779
7	0.010664	99.69922	0.300779
8	0.010664	99.69922	0.300779
9	0.010664	99.69922	0.300779
10	0.010664	99.69922	0.300779
Variance Decomposition of MIDCAP:
Period	S.E.	NIFTYRETURN	MIDCAPRETURN
1	0.014305	67.02899	32.97101
2	0.014425	67.56738	32.43262
3	0.014429	67.56913	32.43087
4	0.014430	67.56787	32.43213
5	0.014430	67.56785	32.43215
6	0.014430	67.56785	32.43215
7	0.014430	67.56785	32.43215
8	0.014430	67.56785	32.43215
9	0.014430	67.56785	32.43215
10	0.014430	67.56785	32.43215
Cholesky Ordering: NIFTY MIDCAP

 

Figure 2: Impulse response function

Further, from figure 2, the outcome of the Impulse response function analysis is corroborative evidence for Variance decomposition analysis. Graphical representation of Impulse response function clearly provide evidence of Nifty to be influenced by its own lagged returns. However, Midcap is highly influenced by the Nifty lagged returns and then by its own returns.

 

CONCLUSION:

Understanding the relationship between the temporal movement of small or middle capitalization and large capitalization stocks is important researchers, traders, investors and market regulators in their respective fields. This study re-attempt to establish this relationship by exploring the lead lag nexus between the Nifty 50 and Midcap 50. For this purpose, this study have used Johansen Co-integration Test, Vector Autoregressive (VAR) Model, Variance decomposition and Impulse response function. Results revealed that there is no long term co-integrating relationship between the Nifty 50 and the Midcap 50. Further, Vector Autoregressive (VAR) Model, Variance decomposition and Impulse response function clearly provide evidence of Nifty to influenced by its own lagged returns. However, Midcap is highly influenced by the Nifty lagged returns and then by its own returns. In other words, Nifty leads the Midcap. For this reason, this study provide an evidential support of small or middle capitalization following the large capitalization stocks.

 

REFERENCES:

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Accepted on 21.06.2017          © A&V Publications all right reserved