To
The Joint Editor,
Pacific Business Review International,
Pacific Hill, Airport Road,
Udaipur – 313001
Sub: Publication of Research article in journal “Pacific Business Review International”
Dear Sir/Madam,
I am enclosing herewith as an attachment of the article titled “Comparative Study on Dynamics Of CBOE VIX^{®} And India VIX ” with request for its publication in the ensuing issue of Pacific Business Review International. I assure you that this article has
neither been published in any other journal and nor is its consideration for publication elsewhere.
A line of confirmation as above will highly be appreciated.
Thanking you and looking forward to here from your good office.
With regards,
Yours Sincerely,
Priyanka Sharma
ExConsultant, PWC
EMail: priyanka.academics@gmail.com
Contact: +91 8444833213/7654614984
Mailing Address:
H/o Kashinath Gupta,
C/o Gopal Prasad Sharma
Bakerganj Bajaja, Nataraj Gali, Bakipore,
Patna800004, Bihar, India.
Comparative Study on Dynamics of CBOE VIX^{®} and India VIX
Abstract
The present study endeavors to compare the dynamics of CBOE and India VIX using a simple plausible framework. The study by way of showing graphical
analysis for visual inspection, comparison of descriptive statistics and check of normality assumptions shows that the volatility indices of both CBOE
and NIFTY shows similar features. It is more sensitive towards the negative shock in stock prices as compared to positive jolts. The instances of
asymmetry between stock index and VIX as reflected by the previous studies also found to be present over the period of study.
Keywords:
Stock Markets, Volatility Index, Efficient Market Hypothesis (EMH)
Comparative Study on Dynamics of CBOE VIX^{®} and India VIX
Introduction
In the recent times, burgeoning scholarly work on analysis of stock market volatility in the domain of finance and economics literature is fairly evident.
It has been one of the extensively researched areas by both academicians and practitioners across the globe for its impending implications on the financial
system of an economy. To understand the probable volatility sentience in the stock markets an indicative measure/standard was ought to be set which is
known as the Volatility Index (VIX).
The Chicago Board of Exchange (CBOE) introduced CBOE VIX^{® }in the year 1993, which was intended to act as an assessment measure of expectation of
the market of a shortterm (30 days) volatility implied by atthemoney Standard & Poor’s (S&P) 100^{®} Index (OEX^{®} Index)
option prices. In 2003, CBOE in association with Goldman Sachs upgraded the VIX to come up with a new measure of expected volatility, that is broadly used
by financial theorists, risk managers and volatility traders in a similar way. The modified VIX is based on the S&P 500® Index (SPX^{SM}), the
core index for U.S. equities, and the expected volatility is estimated by averaging the weighed price of SPX puts and calls over a wide range of strike
prices. This measure of volatility (VIX^{®}) has been referred as the fear estimate of investors, because of the very fact that high level of VIX
corresponded to higher scale of market instability (Whaley, 2000).
In the context of India, India VIX (IVIX) is used which is computed by National Stock Exchange (NSE) based on the order book of NIFTY options. For the
purpose the best bidask quotes of near and nextmonth NIFTY option contracts which are traded on the Futures and Options (F&O) segment of NSE is used.
Traditionally one of the underlying reasons of volatility as put forth by noted academicians is arrival of a new piece of information in the market which
takes us back to the axioms of Efficient Market Hypothesis (EMH). Fama (1970) discernibly ratified EMH. Fama (1970) states that market in which the stock
prices always “fully reflect” available information is called “efficient”. In such a form of market, when a new piece of information enter, the asset
prices accurately respond to that information and integrate all information at any point of time and reach a new level of equilibrium. The theory of
rational expectation is grounded upon the rational expectation theory. This theory assumes that investors attain at a rational expectation estimate about
future security return. According to Fama (1970), expected returns represent the conditions of market equilibrium and such ‘expected returns equilibrium is
function of its risk’. Following Fama (1970) has represented return on asset as:
SR_{t }= ψ_{t1} (y^{m}_{t}) + π_{t }
(1.1)_{}
Where, SR_{t }is stock returns, ψ_{t1} (y^{m}_{t}) represents equilibrium return expected at_{t1} period, π_{t }is the abnormal component. To attain at the equilibrium level market captures information. Assume I_{t1 }to represent information set. Then the equation stands:
ψ_{t1} (y^{m}_{t}) = ψ(y^{m}_{t}ǀI_{ t1}) _{ }
(1.2)_{}
The equation (1.2) implies that the stock market would stand efficient when it uses all relevant information accurately and timely in determining the
market price.
The prominent works of other researchers negate the fact that the prime cause of volatility is new information arrival (French and Roll, 1986). The
subsequent studies have introduced various other causal factors such as investor behavior, financial performance of organizations, dynamics of
macroeconomic variables and dissemination of other public information [refer Ross (1989), Andersen et al. (2006), Sen, Das and Goyal (2015)].
The previous literature also provides evidences on a significant negative correlation between stock returns and VIX with due cogency. Further the traces of
asymmetric relationship between stock returns and implied volatility (i.e. higher magnitude of implied volatility on negative return shocks as compared to
the positive return jolt) is also laid down (Shaikh and Padhi, 2014, Chandra and Thenmozhi, 2015). The present study endeavors to examine this phenomenon
of asymmetric relationship and compare descriptive statistics of IVIX with the CBOE VIX^{®} as benchmark to appraise the performance of IVIX as a
measure of market volatility.
The next segment of the study briefly revisits the intellectual efforts of previous researchers, followed by the comparison of statistical properties of
CBOE and IVIX and finally the results are discussed in the end segment.
Brief Overview of Previous Literature
In the vast literature of financial economics and allied domains considerable empirical works are reported, a snapshot of which presented as below:
Whaley (2009) in his study says that volatility index is affected by increased demand to buy index, and hence, change in volatility index rises at a higher
absolute rate in a situation where stock market falls than when it tends to rise. The empirical findings of the study support the view that the volatility
index is to be assumed as investor’s fear index rather greed index. Followed by evidences on large negative contemporaneous correlation between volatility
index and market return index Dash and Moran (2005) in their study finds a negative correlation between volatility index (VXO) and hedge fund returns,
further this correlation was found asymmetric in nature. On the other hand Guo and whitelaw (2006) confirms that market returns are positively related to
volatility index. In the literature base there exists some contradiction to the literature as well. Dowling and Muthuswamy (2005) in their study on
Australian markets found no asymmetry between volatility and market index returns. Recent studies in Indian context, Kumar (2010) observed negative
relationship between market returns and volatility only during market declines, Shaikh and Padhi (2014) concludes asymmetry prevails among IVIX and the
NIFTY index; at the same time the magnitude of asymmetry is not identical. The result show that the change in IVIX occurs bigger for the negative return
shocks than that of positive return shocks. Chandra and Thenmozhi (2015) examines the asymmetric relationship between IVIX and stock market returns and
demonstrates that NIFTY returns are negatively related to changes in IVIX levels, but in the case of high upward movements in the market, the returns on
the two indices tend to move independently.
Examining the Statistical Properties
Graphical Analysis
This section of the study deals with the statistical property check for both IVIX and CBOE VIX for the purpose of intercomparison. The study is conducted
for a period of 6 years i.e. from 28/08/2009 to 25/08/2015 for India and for U.S. the study period is 31/07/2009 to 31/07/2015. The Indian data is obtained
from the NSE website and the U.S. data is extracted from the CBOE website. It is intended to study the behavior of VIX and market index returns for both
NIFTY and SPX^{SM}.
Figure 1. Intertemporal Relationship between India VIX and NIFTY Index
The figure 1 above is the timeseries plot of IVIX and NIFTY index for the period of study. The figure by a simple visual inspection reveals that IVIX is
more sensitive to decline in index as compared to the rise. Hence, the connotation of fear index as proposed by Whaley found to be evident in this case.
Figure 2. Intertemporal Relationship between CBOE VIX^{®} and SPX^{SM} Index
The figure 2 reflects the similar phenomena as reflected by figure 1. Thus it can be seen that asymmetry prevails in both the cases. A simple graphical
analysis confirms that volatility index is hypersensitive to negative return shocks to positive return trends, which is consistent to the previous
literature.
Descriptive Statistics and Test of Normality
Table 1. Descriptive Statistics of NIFTY, IVIX and Market Index Return
NIFTY


IVIX


Market Index Return








Mean

6110.674262

Mean

20.3631057

Mean

0.000343

Standard Error

30.66501872

Standard Error

0.133727701

Standard Error

0.000278

Median

5724.225

Median

19.38875

Median

0.00046

Mode

5274.85

Mode

16.82

Mode

#N/A

Standard Deviation

1183.685611

Standard Deviation

5.161958539

Standard Deviation

0.010734

Sample Variance

1401111.626

Sample Variance

26.64581596

Sample Variance

0.000115

Kurtosis

0.213121967

Kurtosis

0.167031402

Kurtosis

1.407901

Skewness

1.052187874

Skewness

0.70100997

Skewness

0.15996

Range

4452.05

Range

26.14

Range

0.098352

Minimum

4544.2

Minimum

11.565

Minimum

0.06097

Maximum

8996.25

Maximum

37.705

Maximum

0.03738

Sum

9104904.65

Sum

30341.0275

Sum

0.509995

Count

1490

Count

1490

Count

1489

Confidence Level(95.0%)

60.15122528

Confidence Level(95.0%)

0.262314696

Confidence Level(95.0%)

0.000546

The above output in table 1 show the average volatility is approximately 20% with a standard deviation of 5.16% (approx.). The modal value i.e. most
occurring volatility rate is 16.82%. The minimum and maximum volatility stood to be 11.565% and 37.705% respectively.
The table 2 below shows the descriptive statistics for the U.S. data which shows the mean volatility is around 18.68% with a standard deviation of 6.09%.
The value of mode is approximately 12.66%. However the minimum and the maximum values varies significantly, it is 10.32 and 48 respectively.
Table 2. Descriptive Statistics of SPX, VIX and Market Index Return
SPX


VIX


Market Index Return








Mean

1494.41751

Mean

18.6847651

Mean

0.00032

Standard Error

8.792871372

Standard Error

0.15785699

Standard Error

0.001847

Median

1391.01

Median

17.07

Median

0.006

Mode

1178.1

Mode

12.66

Mode

0

Standard Deviation

339.4093908

Standard Deviation

6.0933616

Standard Deviation

0.071268

Sample Variance

115198.7346

Sample Variance

37.12905559

Sample Variance

0.005079

Kurtosis

1.156798979

Kurtosis

2.494984524

Kurtosis

3.275791

Skewness

0.442926915

Skewness

1.506471998

Skewness

0.711877

Range

1151.09

Range

37.68

Range

0.756054

Minimum

979.73

Minimum

10.32

Minimum

0.35059

Maximum

2130.82

Maximum

48

Maximum

0.405465

Sum

2226682.09

Sum

27840.3

Sum

0.47682

Count

1490

Count

1490

Count

1489

Confidence Level(95.0%)

17.24773077

Confidence Level(95.0%)

0.309645706

Confidence Level(95.0%)

0.003623
0.003623

Table 3. Tests of Normality for NIFTY, IVIX and Market Index Returnpacing="0" cellpadding="0" align="left" width="106%">
