Study of Association between Volatility Index and Nifty using VECM

International Journal of Engineering and Management Research e-ISSN: 2250-0758 | p-ISSN: 2394-6962
Volume-11, Issue-1 (February 2021)
www.ijemr.net https://doi.org/10.31033/ijemr.11.1.27
200 This Work is under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Study of Association between Volatility Index and Nifty using VECM
Dr. Avijit Sikdar
Assistant Professor, Department of Commerce, Kidderpore College, INDIA
Corresponding Author: sikdar.avijit2014@gmail.com
ABSTRACT
Volatility in capital markets is the measure degree
of variability of stock return from their expected return.
The volatility in the capital market is the basis for price
discovery in the financial asset. The volatility index (VIX) is
the measurement index of the volatility of the capital
market. It is the fear index of the capital market. The
concept is first coined in 1993 in Chicago Board Options
Exchange (CBOE). In India, such an index was introduced
in 2008 by NSE. India VIX calculates the expected market
volatility over the coming thirty days on Nifty Options. It
Market index is the performance metric of the Indian
capital market. This index is designed to reflect the overall
market sentiments. An index is an important parameter to
measure the performance of the economy as a whole.
While the market index measures the direction of the
market and is calculated by the price movements of the
underlying stocks, the Volatility Index measures the
volatility of the market and is calculated using the order
book of the underlying index's options. In this study, we
examine the association between India VIX and Nifty Index
returns by using Johanson's co-integration, Vector Error
Correction Model (VECM), and Granger causality Tools.
The data for this study covers closing data of VIX value
and Nifty closing value from January 2014 to December
2019 and has a total of 1474 daily observations. The result
confirms that there are co-integrating relationships (long-
run association) between VIX and Nifty. The Granger
causality indicates Nifty does Granger Cause VIX but VIX
does not granger Cause Nifty.
Keywords-- VIX, Data Stationarity, Johansen
Cointegration Test, VECM
I. INTRODUCTION
Volatility is the measure of uncertainty about
the variation in the return of the stock market, bond
market, commodity market, and foreign exchange
market. A higher volatility means a large variation in the
return, whereas low volatility indicates fluctuation in the
value of a security is not dramatically. Estimation of the
volatility of a financial time series has gained large
popularity among researchers and academicians and
market players. Volatility can be of two types.
Unconditional volatility-which is the single measure of
the volatility of asset return over time and other, is
conditional volatility which is varying over time and
depends on own past volatility (Autoregressive) and
upon past asset returns (conditional). The volatility in the
capital market is the basis for the determination of price
in the financial asset, like option pricing. In this context
Volatility index (VIX) is the measurement index of the
volatility of a capital market. It is the fear index of the
capital market. The concept is first coined in 1993 in
Chicago Board Options Exchange (CBOE). In India,
such an index was introduced in 2008 by the National
Stock Exchange. India VIX captures the expected market
volatility over the next thirty days based on the implied
volatility in the used in Nifty Options. The market index,
Nifty is the performance metric of the Indian capital
market. This index is designed to reflect the overall
market sentiments. An index is an important parameter
to measure the performance of the economy as a whole.
While the market index measures the direction of the
market and is calculated by the price movements of the
underlying stocks, the Volatility Index measures the
volatility of the market and is calculated using the
underlying Index’s options. Volatility is the indicator of
expected risk in the capital market. Market return
decreases when the volatility increases as investors are
reluctant to invest in the risky market, leads to a fall in
the demand of share as well as price (as demand in the
stock market is less). However, return increases when
volatility decreases as investors are willing to invest in
the capital market, which leads to an increase in demand
as well as price. Thus the correlation between the capital
market return and volatility is negative. Most of the
researches on volatility modelling are based on the past
fluctuation in market return. Hence it has less future
prediction capability. In this context, VIX is based on the
future Nifty option price of the next 30 days. It is the
Index of the market expectation of volatility over a
short-term period and indicates the implied volatility as
well as an implied risk of the stock market. Since the
volatility index looks into the future and is derived from
the option prices, it may offer important clues to the
investors by observing the sentiments of the options
investors to buy and sell in the market. This paper will
investigate the association between VIX and Nifty and
their short-term causality and dynamics using VAR
Framework.
II. LITERATURE STUDY
Floros (2008) modelled the volatility applying
daily data from two Middle East stock indices viz., the
Egyptian CMA index and the Israeli TASE-100 index,
and used GARCH, EGARCH, and TGARCH. The study
found that the coefficient of the EGARCH model
showed a negative and significant value for both the
indices, indicating the existence of the leverage effect.

Ahmed and Aal (2011) studied Egyptian stock
market return volatility and his study showed that
EGARCH is the best fit model among the other models
for measuring volatility.
Karmakar (2005) estimated the volatility model
to study the feature of Indian stock market volatility..
The study also capture the presence of leverage effect in
the Indian stock market volatility and the study showed
that the GARCH (1,1) model provided reasonably good
forecasts of market volatility. Whereas, in another study,
he (Karmakar2007) found that the conditional variance
was asymmetric during the study period and the
EGARCH-M was found to be an adequate model that
reveals a positive relationship between risk and return.
Goudarzi and Ramanarayanan (2010) examined
the volatility of the Indian stock market using the BSE
500 stock index as the proxy for ten years. ARCH and
GARCH models were estimated and the best model was
selected using the model selection criterion viz., Akaike
information criterion (AIC) and Schwarz Information
Criterion (SIC). The study found that GARCH (1,1) was
the most appropriate model for explaining volatility
clustering.
Goudarzi and Ramanarayanan (2011) in their
study, investigated the volatility of the BSE 500 stock
index and modelled two non-linear asymmetric models
viz., EGARCH (1,1) and TGARCH (1,1) and found that
TGARCH(1,1) model was found to be the best-preferred
model as per Akaike Information Criterion (AIC) and
Schwarz Information Criterion (SIC).
Mittal, Arora, and Goyal (2012) examined the
behaviour of Indian stock price and investigated to test
whether volatility is asymmetric using daily returns from
2000 to 2010. The study reported that GARCH and
PGARCH models were found to be best-fitted models to
capture symmetric and asymmetric effects respectively.
Mall, S.Mishra P.K Mishra B.B Pradhan
(2014) in their study they examine the relationship by
implementing Johanson's co-integration and Granger
causality methods between India VIX and Nifty index
returns. This study confirms cointegration between VIX
and Nifty as well as in the long run VIX will cause Nifty
movement whereas in the short run reverse is true.
Based on the above literature review we can
conclude that in India very little work has been
conducted to study the co-integration between VIX and
Stock return under the VECM framework.
III. OBJECTIVES OF THE STUDY
1. To study the existence of unit root (Stationarity)
in the Nifty data and VIX data using ADF
(Augmented Dickey-Fuller) and PP (Phillips-
Perron) Test.
2. To study the long-term association between
Nifty and VIX using Johansen Co-integration
Test.
3. To study the cause-effect relationship between
the two variables using Granger Causality Test.
4. To study the long-term and short-term causality
and dynamics among these variables Using
VAR Framework.
IV. RESEARCH METHODOLOGY
Sample: The data for this study covers the closing value
of the Volatility Index (VIX) and Market Index (Nifty).
Sample Period: The sample covers daily data from
January 2014 to December 2019 and has a total of 1474
daily observations.
Data Source: The entire data has been collected from
the NSE (National Stock Exchange) Website.
Research Tools: Various statistical tools ADF
(Augmented Dickey-Fuller) and PP (Phillips-Perron)
Test and Jarque-Bera statistic were utilised to study the
stationarity. For the long-term relationship between the
indices, we can use Engle-Garner Cointegration Test or
Johansen Co-integration Test. However, we use here the
Johansen Co-integration Test. Now to study the
interrelationship in the variation among the variable we
can use Vector Auto-Regressive (VAR) model or Vector
Error Correction Model (VECM). If the variables are
non-stationary at the level form and cointegrated we can
use restricted VAR but if data are not cointegrated then
we should use unrestricted VAR. The entire null
hypothesizes are tested using appropriate test statistics at
a 5% level of significance.
Research Software: The entire econometrics analysis
has been done using E-views 8 Econometrics package.
V. RESEARCH FINDINGS
We have used the Augmented Dickey-Fuller
Test to check whether the time series data are stationary
at the level form and stationary at the first difference.
For that purpose, we can form the following
hypothesizes.
Null Hypothesis: VIX return (growth) and Nifty return
(growth) data are not stationary.
Alternative Hypothesis: The above time series is
stationary.
If the p-value is less than 5%, we will reject the
hypothesis, and if the p-value more than 5% we accept
the null hypothesis.

Table 1: Augmented Dickey-Fuller test statistic and Phillips-Perron test statistic
Return Nifty Return VIX
t-Statistic Prob.* t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -35.631904 0.00 -30.60226 0.00
Test critical values: 1% level -3.4345728 -3.434579
5% level -2.8632921 -2.863295
10% level -2.5677513 -2.567753
Adj. t-Stat Prob.* Adj. t-Stat Prob.*
Phillips-Perron test statistic -35.534196 0.00 -38.42132 0.00
Test critical values: 1% level -3.4345728 -3.434576
5% level -2.8632921 -2.863293
-2.567752
The results of the test are given in table 1. The
result indicates that all the daily index data are not
stationary at the level form but stationary at first
difference i.e. I (1). This result indicates that we can
move on with the two tests of cointegration. The
stationarity is further confirmed by the Phillips-Perron
test. The tabulated values of these series are much higher
than critical values at 1%, 5%, and 10% levels of
significance. Hence we reject the null hypothesis that
these series have no unit root and conclude that data of
the time series for the entire study period is non-
stationary at the level form but stationary at the 1st
level
difference.
The next step is to examine whether there exists
a long-run equilibrium relationship among variables.
This is called Co-integration analysis which is very
significant to avoid the risk of spurious regression. The
co-integration analysis is important because if the Co-
integration relationship is identified, the model should
include residuals from the vectors (lagged one period) in
the dynamic VECM system. In this stage, Johansen's Co-
integration test is used to identify a co-integrating
relationship between the variables. The Johansen method
applies the maximum likelihood procedure to determine
the presence of co-integrated vectors in non-stationary
time series.
Null Hypothesis: No cointegration among the time
series data.
Alternative hypothesis: there is cointegration among
the variables.
The test statistics used for this purpose are Trace
Statistic and Max-Eigen Statistic and they are tested at a
5% level of significance. The decision rule is the same as
above. If the p-value is less than 0.05 we will reject the
hypothesis and if the p-value more than 0.05 we accept
the null hypothesis.
Table 2: Johansen’s Co-integration test
Trend assumption: Linear deterministic trend
Series: NIFTY VIX
Lags interval (in first differences): 1 to 3
Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.015450155 24.26460306 15.49471288 0.00186611
At most 1 0.000901755 1.328884964 3.841465501 0.249002854
Trace test indicates 1 cointegrating equation(s) at the 0.05 level
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized Max-Eigen 0.05

No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.015450155 22.93571809 14.26460015 0.001690988
At most 1 0.000901755 1.328884964 3.841465501 0.249002854
Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
The result of the Johansen Cointegration Test
indicates that VIX and Nifty have a long-term
association at level form as both the Trace and the Max-
Eigen statistics is significant at 5%. If the variables are
cointegrated or have long-run relationships or
associations then we can use restricted VAR i.e. VECM
(vector error correction model) to study short-term
dynamics and causality. The existence of Co-integration
implies the existence of Granger causality at least in one
direction. To study the short-run causality between the
VIX and the Nifty a standard Granger causality test has
been performed based on F statistics. The result is given
in table 3.
Table 3: Granger Causality
Pair-wise Granger Causality Tests
Null Hypothesis: F-Statistic Prob. Decision
NIFTY does not Granger Cause RVIX 5.2039 0.0055 Reject
RVIX does not Granger Cause NIFTY 1.492 0.2252 Accept
The result in Table 3 indicates VIX does not
Granger cause of Nifty. However, Nifty Granger causes
the VIX index in the short run. Here variables (VIX and
Nifty) are non-stationary (at level form) and stationary at
1st
level difference. Hence, we can use the vector error
correction model (VECM). The VECM is the restricted
VAR designed for use with non-stationary series that are
co-integrated. The VECM has co-integrating relations
built into specification so that it restricts the long-run
behaviour of endogenous variables to converge to their
co-integrating relationship while allowing for short-run
adjustment dynamics. The co-integrating term is known
as the error correction term since the deviation from
long-run equilibrium is corrected gradually through a
series of short-run dynamic adjustments. In VECM, the
value of variables is expressed as a linear function of
past or lagged values of that variable and all other
variables included in the model. Here the result is
presented in table -4 below:
Test 4: Vector Error Correction Estimates
Error Correction: D(RVIX) Prob. Decision D(NIFTY) Prob. Decision
CointEq1 –C1 -0.03214 0.00 Sig. 0.87005 0.140681 No Sig.
D(VIX(-1))-C2 0.062 0.04 Sig -2.45815 0.317402 No Sig.
D(VIX(-2)) –C3 -0.11694 0.00 Sig. 0.272667 0.911058 No Sig.
D(NIFTY(-1))-C4 0.001059 0.00 Sig 0.061943 0.037836 Sig
D(NIFTY(-2))-C5 -0.00041 0.05 Sig. -0.00579 0.846153 No Sig.
C -0.00621 0.80 No Sig. 3.817607 0.059778 No Sig.
R-squared 0.034661 0.00737
Akaike AIC -2.703894 11.54415
The coefficient of the co-integrated equation of
D(VIX) is negative and significant at a 5% level. Hence,
there is long-term causality running from Nifty and VIX.
However, The coefficient of the co-integrated equation
of D (NIFTY) is positive and not significant. Hence,
there is no long-term causality running from VIX to
Nifty. We also state that there is short-term casualty
running from Nifty and VIX and Short-run dynamics in

the variable D(VIX) as the coefficient C2, C3, C4, and
C5 are significant statistically in the case of the first
equation. However, there is no short-term causality
running from VIX to Nifty and short-run dynamics in
variable D(Nifty) as most of the variables are statistically
insignificant. The negative value of the Akaike
Information Criterion indicates the appropriateness of
the VAR system in the first equation. To examine the
possible presence of autocorrelation in our model, we
have conducted the Autocorrelation LM test which
shows the absence of serial correlation in the VAR
model that we have estimated.
VI. CONCLUSION
Augmented Dickey-Fuller Test indicated that
VIX and Nifty are non-stationary at the level form but
stationary at first difference. Co-integrating relationships
between the variables are confirmed through the
Johansen test of cointegration. The Trace statistic and
Max-eigenvalue statistic suggest the presence of a
cointegrating vector. The Granger causality test also
indicates that Nifty does granger causes VIX. The
VECM shows that the long-run and short-run casualty
running from Nifty to VIX but no such causality running
from VIX to Nifty. This study is useful for
understanding the behaviour of India VIX and helps for
hedging and risk management for the financial
institution and the investors. Further, this study will help
policymakers in the design of appropriate derivative
instruments based on India VIX for hedging and risk
management. The paper is, however, not devoid of
limitations. First, the data used in the study is restricted
to the last six years which can be extended from 2008;
second, we are using the closing value of Nifty and VIX,
however, we can use the average value of opening,
closing, a high and low value of these variables of
particular trading days; third we have used here Johansen
Co-integration Test to study the Long-run relationship.
However, we can use Engle-Garner Co-integration Test.
Subject to these limitations the study reveals that long
term association between VIX and Nifty and there exist
long and short-term casualty running from Nifty to VIX.
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