MODELING THE STOCK VOLATILITY OF TOP INDUSTRIAL RETURNS LISTED IN BSE

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Dr.G.S.David Sam Jayakumar and L.Vijayalakshmi, “Modeling the Stock Volatility of top Industrial
Returns Listed in BSE” – (ICAM 2016)
MODELING THE STOCK VOLATILITY OF TOP INDUSTRIAL RETURNS
LISTED IN BSE
Dr.G.S.David Sam Jayakumar
Assistant professor
Jamal Institute of Management, Jamal Mohammed College, Trichy
L.Vijayalakshmi
M. Phil Scholar,
Jamal Institute of Management, Jamal Mohammed College, Trichy
ABSTRACT
He modelling of stock market volatility is considered to be important for practitioners and
academics in finance due to its use in forecasting aspects of future returns. Volatility as a
measure of risk plays an important role in many financial decisions in such a situations. The
main purpose of this study is to examine the volatility of the Indian stock markets mainly in
BSE several statistical tests have been applied in order to study the Stock Volatility in Top
Industries listed in BSE between October 2011 to June 2014.
Key words: Stock Market, Volatility, BSE, Returns.
Cite this Article: Dr.G.S.David Sam Jayakumar and L.Vijayalakshmi. Modeling the Stock
Volatility of top Industrial Returns Listed in BSE. International Journal of Management, 7(2),
2016, pp. 354-367.
http://www.iaeme.com/ijm/index.asp
INTRODUCTION
The word volatility means fluctuation. When the stock market goes up one day, and then goes down for
the next five, then up again ,and then down again that’s what we call stock market volatility. In
layman’s terms volatility is like car insurance premiums that go up along with the likelihood of risky
situation such so if you have a poor driving record or if you keep the car in a high –theft area. Stock
market fluctuation are when a company’s stock price changes in the market on one hand, company’s
stock price has no direct effect on a company unless the company wants to raise more money by selling
stock into the market. In that case, the current stock price determines how much money they will be
able to raise when they sell shares into the market .Once the shares are sold into the market, however
the company is no longer affected directly by the shares There are at least two indirect effects, though
first company managers often own stock or option in the company since they want to do well
personally. if the stock price goes down , they will start to worry and work harder to make the company
profitable and raise the stock price sometime ,tough ,they just panic , cut and also and look for ways to
boost the stock price in the short term at the expense of the company long –term health .the second
indirect effect is that stockholders might be unhappy with a low stock price they can put pressure on
INTERNATIONAL JOURNAL OF MANAGEMENT (IJM)
ISSN 0976-6502 (Print)
ISSN 0976-6510 (Online)
Volume 7, Issue 2, February (2016), pp. 354-367
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International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 -
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the board of directors to replace the CEO’s some cynics say volatility is a policy way of referring to
investors nervous, investors may think volatility indicates a problem But many analysts believe that
increased volatility can indicate a rebound.
NEED FOR STUDY
In the finance field, it is a common knowledge that money or finance is scarce and that investors try to
maximize their returns. But when the return is higher, the risk is also higher. Return and risk goes
together and they have a trade off. The art of investment is to see that return is maximized with
minimum risk. In the above discussion we concentrated on the word “investment” and to invest we
need to analysis securities. Combination of securities with different risk-return characteristics will
constitute the portfolio of the investor.
OBJECTIVE OF THE STUDY
To know the profile of BSE and top companies and study the fluctuations in share prices of those
companies. To study the risk involved in the securities of selected companies and their risk and return
analysis in eleven sectors. To study the systematic risk involved in the selected companies securities.
To offer suggestions to the investors.
HYPOTHESES
1. The returns of Indian Industries in BSE do not follow a normal distribution.
2. The returns of Indian Industries in BSE do not follow a random walk pattern.
3. The current industry returns is uncorrelated with the previous years.
4. The effect of the random shocks happened in past do not affect the current years returns.
INDUSTRY SELECTION
The monthly data of following industries of Auto, Healthcare, PSU, Capital Goods, Banks, Consumer
Durables, FMCG, I.T, Power, Metal and Oil &Gas are considered.
PERIOD OF DATA SAMPLE
The study was conducted for log return of industries from October 2011 to June 2014.
DATA COLLECTION
The closing price of companies was collected from historical data available in BSE website.
LIMITATION
The closing prices for companies in the above industries are only considered for the study.
THE PROFILE OF BOMBAY STOCK EXCHANGE
The Bombay Stock Exchange (BSE) (formerly, The Stock Exchange, Bombay) is a stock exchange
located on Dalal Street, Mumbai and it is the oldest stock exchange in Asia. The equity market
capitalization of the companies listed on the BSE was US$1 trillion as of December 2011, making it
the 6th largest stock exchange in Asia and the 14th largest in the world. The BSE has the largest
number of listed companies in the world. As of December 2011, there are over 5,112 listed Indian
companies and over 8,196 scrips on the stock exchange, The Bombay Stock Exchange has a significant
trading volume. The BSE SENSEX, also called "BSE 30", is a widely used market index in India and
Asia. Though many other exchanges exist, BSE and the National Stock Exchange of India account for
the majority of the equity trading in India. While both have similar total market capitalization (about
USD 1.6 trillion), share volume in NSE is typically two times that of BSE.
LISTING OF SECURITIES
Listing means admission of the securities to dealings on a recognized stock exchange. The securities
may be of any public limited company, Central or State Government, quasigovernmental and other
financial institutions/corporations, municipalities etc. The objectives of listing are mainly to Provide

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liquidity to securities and to Mobilize savings for economic development finally Protect interest of
investors by ensuring full disclosures. Exchange has a separate Listing Department to grant approval
for listing of securities of companies in accordance with the provisions of the Securities Contracts
(Regulation) Act, 1956, Securities Contracts (Regulation) Rules, 1957, Companies Act, 1956,
Guidelines issued by SEBI and Rules, Bye-laws and Regulations of the Exchange. A company
intending to have its securities listed on the Exchange has to comply with the listing requirements
prescribed by the Exchange. Some of the requirements are as under: Minimum Listing Requirements
for new companies, Minimum Requirements for companies delisted by this Exchange seeking relisting
of this Exchange, Minimum Requirements for companies delisted by this Exchange seeking relisting of
this Exchange and Finally Permission.
SELECTED INDUSTRIES LISTED IN BSE
Auto, Healthcare, PSU, Capital Goods, Banks, Consumer Durables, FMCG, I.T, Power, Metal, Oil &
Gas are the listed industries in BSE selected for the research
MODELS OF VOLATILITY
In Finance volatility is a measure for variation of price of a financial instrument over time. Historic
volatility is derived from time series of past market prices. An implied volatility is derived from the
market price of a market traded derivative (in particular an option). The symbol σ is used for volatility,
and corresponds to standard deviation, which should not be confused with the similarly which is
instead the square, σ2
.Volatility as described here refers to the actual current volatility of a financial
instrument for a specified period (for example 30 days or 90 days). It is the volatility of a financial
instrument based on historical prices over the specified period with the last observation the most recent
price. This phrase is used particularly when it is wished to distinguish between the actual current
volatility of an instrument
 Actual historical volatility which refers to the volatility of a financial instrument over a
specified period but with the last observation on a date in the past
 Actual future volatility which refers to the volatility of a financial instrument over a
specified period starting at the current time and ending at a future date (normally the expiry
date of an option)
 Historical implied volatility which refers to the implied volatility observed from historical
prices of the financial instrument (normally options)
 Current implied volatility which refers to the implied volatility observed from current prices
of the financial instrument
 Future implied volatility which refers to the implied volatility observed from future prices of
the financial instrument
Volatility is a statistical measure of dispersion around the average of any random variable such as
market parameters etc.
STOCHASTIC VOLATILITY
Stochastic volatility models are one approach to resolve a shortcoming of the Black–Scholes model. In
particular, these models assume that the underlying volatility is constant over the life of the derivative,
and unaffected by the changes in the price level of the underlying security. However, these models
cannot explain long-observed features of the implied volatility surface such as volatility smile and
skew, which indicate that implied volatility does tend to vary with respect to strike price and expiry. By
assuming that the volatility of the underlying price is a stochastic process rather than a constant, it
becomes possible to model derivatives more accurately.
BASIC MODEL
Starting from a constant volatility approach, assume that the derivative's underlying asset price follows
a standard model for geometric Brownian motion:

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where is the constant drift (i.e. expected return) of the security price , is the constant
volatility, and is a standard Wiener process with zero mean and unit rate of variance. The
explicit solution of this stochastic differential equation fis
.
The Maximum likelihood estimator to estimate the constant volatility for given stock prices
at different times is
its expectation value is .
This basic model with constant volatility is the starting point for non-stochastic volatility
models such as Black–Scholes model and Cox–Ross–Rubinstein model.
For a stochastic volatility model, replace the constant volatility with a function , that models
the variance of . This variance function is also model as brownian motion, and the form of
depends on the particular SV model under study.
Where, and are some functions of and is another standard gaussian that is
correlated with with constant correlation factor .
HESTON MODEL
The popular Heston model is a commonly used SV model, in which the randomness of the variance
process varies as the square root of variance. In this case, the differential equation for variance takes
the form:
where is the mean long-term volatility, is the rate at which the volatility reverts toward its
long-term mean, is the volatility of the volatility process, and is, like , a gaussian with
zero mean and standard deviation. However, and are correlated with the
constant correlation value .
In other words, the Heston SV model assumes that the variance is a random process that exhibits a
tendency to revert towards a long-term mean at a rate , exhibits a volatility proportional to the
square root of its level and whose source of randomness is correlated (with correlation ) with the
randomness of the underlying price process. There exist few known parameterization of the volatility
surface based on the Hesston model (Schon busher, SVI and gSVI) as well as their de-arbitraging
methodologies.

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CEV MODEL
The CEV model describes the relationship between volatility and price, introducing stochastic
volatility:
Conceptually, in some markets volatility rises when prices rise (e.g. commodities), so In
other markets, volatility tends to rise as prices fall, modelled with .
Some argue that because the CEV model does not incorporate its own stochastic process for
volatility, it is not truly a stochastic volatility model. Instead, they call it a local volatility model.
SABR VOLATILITY MODEL
The SABR model (Stochastic Alpha, Beta, Rho) describes a single forward (related to any asset e.g.
an index, interest rate, bond, currency or equity) under stochastic volatility :
The initial values and are the current forward price and volatility, whereas
and are two correlated Wiener processes (i.e. Brownian motions) with correlation
coefficient . The constant parameters are such
that . The main feature of the SABR model is to be able to reproduce the
smile effect of the volatility smile.
GARCH MODEL
The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is another popular
model for estimating stochastic volatility. It assumes that the randomness of the variance process varies
with the variance, as opposed to the square root of the variance as in the Heston model. The standard
GARCH(1,1) model has the following form for the variance differential:
The GARCH model has been extended via numerous variants, including the NGARCH,
TGARCH, IGARCH, LGARCH, EGARCH, GJR-GARCH, etc. Strictly, however, the conditional
volatilities from GARCH models are not stochastic since at time t the volatility is completely pre-
determined (deterministic) given previous values.
3/2 Model
The 3/2 model is similar to the Heston model, but assumes that the randomness of the variance process
varies with The form of the variance differential is:
However the meaning of the parameters is different from Heston model. In this model both, mean
reverting and volatility of variance parameters, are stochastic quantities given by and
respectively.
CHEN MODEL
In interest rate modelings, Lin Chen in 1994 developed the first stochastic mean and stochastic
volatility model, Chen model. Specifically, the dynamics of the instantaneous interest rate are given by
following the stochastic differential equations:

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,
,
DATA ANALYSIS
The analysis was conducted at different stages by utilizing selected time series econometric techniques.
Stage-1 Descriptive statistics of the industry returns was promoted.
Stage-2 The Augnmented Dickey Fuller Test used to identify in the random walk nature of the industry
returns
Stage-3 The Auto Correlation Function was applied to analysis the relationship between industry
returns over the time period
Stage -4 The White Noise Test, Fisher’s kappa were used to analyse the pattern of the industry returns
SHAPIRO-WILK TEST
The Shapiro–Wilk Test is a test of normality in frequenters statistics. The Shapiro–Wilk test utilizes
the null hypothesis principle to check whether a sample x1, ..., xn came from a normally
distributed population. The test statistic is:
Table 1 Test of univariate normality
Industry normality variable Test statistic p-value
Auto 0.991 0.000
Healthcare 0.992 0.000
PSU 0.995 0.001
Capital goods 0.991 0.000
Bank 0.984 0.000
Consumer durables 0.970 0.000
FMCG 0.982 0.000
I.T 0.924 0.000
Power 0.989 0.000
Metal 0.989 0.000
Oil gas 0.997 0.027
INFERENCE
The result of univariate normality test such as Sharpe-Wilk Statistics and Anderson-Darling Statistics
confirms that the returns of automobile companies are departed from Univariate normality and it
follows the non-normal distribution.
Table 2 Test of Multivariate normality
Joint normality test Coefficients Test statistic p-value
Mardia skewness 5.977 998.678 O.000
Mardia kurtosis 207.459 60.235 0.000
Henze- zirkler 1.557 1.557 0.000

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INFERENCE
The Result of Multi-Variate test of normality such as Mardia’s Skewness test, Mardia’sKutosis test and
Henze-zirkler test. The test was applied for the returns of top securities listed in BSE. The result of the
test confirms that the security returns of securities are departed from Multi-Variant normality and the
returns are non normally distributed. Hence, the researcher assumed that the returns of securities are
non-normally distributed.
DESCRIPTIVE STATISTICS
Descriptive statistics are numbers that are used to summarize and describe data. The word "data" refers
to the information that has been collected from an experiment, a survey, a historical record, etc.
Table 3
No. of
Case
Min MAX
Arth
Mean
SD Varins
Coeff
Ofvar
A-D
Static
Adjuand
ersn
P-Value
Auto 999 -4779 5.983 0.057 1.297 1.683
22.927
1.978 1.979 <0.01*
Healh Care 999 -3.529 3.111 0.072 0.861 0.742 11.908 2.120 2.122 <0.01*
Psu 999 -4.669 4.503 0.042 1.141 1.301 -26.947 1.441 1.442 <0.01*
Capitalgoods 999 -5.570 5.498 0.021 1.555 2.418 -75.735 2.420 2.422 <0.01*
Bank 999 -5.552 9.305 0.038 1.602 2.568 42.164 3.491 3.494 <0.01*
Consumr
Durable
999 -8.384 5.701 0.053 1.524 2.323 28.788 5.556 5.560 <0.01*
Fmcg 999 -3.890 5.303 0.090 1.066 1.135 11.810 4.206 4.209 <0.01*
I.T 999 -11.094 9.339 0.065 1.413 1.996 21.593 11.012 11.021 <0.01*
Power 999 -4.514 4.351 0.056 1.257 1.579 -22.640 2.848 2.851 <0.01*
METAL 999 -5.819 8.226 1.696 2.876 -39.216 0.989 2.297 5.819 <0.01*
Oiland Gas 999 -4.787 3.827 0.008 1.294 1.675 -153.48 1.114 1.115 <0.01*
INFERENCE
The descriptive statistics of security returns of those Companies. The Standard Deviation of returns are
less compared to the remaining companies. This shows the security returns is less volatile and highly
consistent. Finally the Univariate Skewness, Kurtosis.
AUGMENTED DICKEY FULLER TEST
An Augmented Dickey–Fuller test (ADF) is a test for a unit root in a time series sample. It is an
augmented version of the Dickey–Fuller test for a larger and more complicated set of time series
models. The augmented Dickey–Fuller statistic, used in the test, is a negative number. The more
negative it is, the stronger the rejection of the hypothesis that there is a unit root at some level of
confidence.

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Table 4
Industry MEAN STD n ZEROMEAN ADF 90TREND SINGLEMEAN ADF
Auto 0.0565792 1.2965424 999 -28.56897 -28.60466* -28.59072*
Healthcare 0.0723178 0.8607451 999 -28.33346 -28.4961 -28.49053
PSU -0.042331 1.1401359 999 -27.64273 -27.66416 -27.65029
Capital goods -0.020531 1.5541015 999 -27.58711 -57.5777 -27.57138
Bank 0.0380047 1.6016371 999 -28.1705 -28.1705 -28.15771
Consumer durables 0.0529387 1.5232163 999 -29.36263 -29.38042 -29.45079
FMCG 0.0902287 1.0650545 999 -30.26659 -30.4535 -30.44194
I.T 0.0654255 1.4120357 999 -29.88523 -29.93033 -29.9476
Power -0.055509 1.2561054 999 -29.0633 -29.10287 -29.0951
Metal -0.043241 1.6948941 999 -30.76838 -30.77612 -30.77825
Oil gas -0.008432 1.293575 999 -31.51905 -31.50469 -31.4988
p-value <0.01
INFRENCE
The result of Augmented dickey filer test which help to correlation the spatiality and the unit return of
the returns. The result of the test confirms that the mean returns on zero and its mandatary factions in
the retunes more the returns more over the returns of auto mobile industry it’s have of than the result
the auto of hypatish the returns of portray return.
AUTO CORRELATION FUNCTION
It is the similarity between observations as a function of the time lag between them. It is a
mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by
noise, or identifying the missing fundamental frequency in a signal implied by
its harmonic frequencies. It is often used in signal processing for analyzing functions or series of
values, such as time domain signals.
Table 05
Industry LAG
Auto Correlation
Coefficient
Ljung-Box Q p-Value
Auto
1 0.0980 9.6264 0.0019*
2 0.0321 10.6576 0.0048*
3 -0.0677 15.2628 0.0016*
4 -0.0278 16.0370 0.0030*
5 -0.0592 19.5605 0.0015*
6 -0.0003 19.5606 0.0033*
7 0.0233 20.1075 0.0053*
8 -0.0161 20.3682 0.0090*
9 0.0300 21.2778 0.0115*
10 0.0419 23.0523 0.0106*
11 -0.0216 23.5266 0.0149*
12 0.0126 23.6871 0.0224*
13 -0.0105 23.7983 0.0330*
Healthcare
1 0.1021 10.4393 0.0012*
2 0.0090 10.5212 0.0052*
3 -0.0871 18.1314 0.0004*
4 0.0043 18.1500 0.0012*
5 -0.0470 20.3732 0.0011*
6 -0.0232 20.9134 0.0019*
7 0.0273 21.6642 0.0029*

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Industry LAG
Auto Correlation
Coefficient
Ljung-Box Q p-Value
8 -0.0013 21.6660 0.0056*
9 0.0285 22.4877 0.0075*
10 0.0278 23.2674 0.0098*
11 0.0385 24.7714 0.0098*
12 0.0138 24.9641 0.0150*
13 0.0144 25.1741 0.0219*
PSU
1 0.1313 17.2646 <.0001*
2 0.0566 20.4829 <.0001*
3 -0.0715 25.6107 <.0001*
4 -0.0448 27.6312 <.0001*
5 -0.537 30.5328 <.0001*
6 -0.314 31.5276 <.0001*
7 0.0348 32.7519 <.0001*
8 0.0005 32.7521 <.0001*
9 0.0974 42.3352 <.0001*
10 0.0166 42.6128 <.0001*
11 -0.0630 46.6238 <.0001*
12 -0.0317 47.6419 <.0001*
13 -0.0092 47.7286 <.0001*
Capital goods
1 0.01341 18.0133 <.0001*
2 0.0179 18.3364 0.0001*
3 -0.0322 19.3758 0.0002*
4 -0.0153 19.6101 0.0006*
5 0.0476 21.8867 0.0006*
6 0.0167 22.1662 0.0011*
7 0.0735 27.6140 0.0003*
8 -0.0059 27.6491 0.0005*
9 0.0267 28.3689 0.0008*
10 0.0269 29.0994 0.0012*
11 -0.0565 32.3299 0.0007*
12 -0.0258 33.0041 0.0010*
13 -0.0150 33.2331 0.0016*
Bank
1 0.1133 12.8540 0.0003*
2 -0.0261 13.5374 0.0011*
3 -0.0291 14.3897 0.0024*
4 -0.0186 14.7364 0.0053*
5 -0.0346 15.9440 0.0070*
6 0.0137 16.1340 0.0131*
7 0.0216 16.6033 0.0201*
8 0.0008 16.6039 0.0345*
9 0.0264 17.3093 0.0441*
10 -0.0108 17.4277 0.0654
11 -0.0685 22.1706 0.0231*
12 0.0075 22.2279 0.0350*
13 -0.0116 22.3647 0.0500*
Consumer durables
1 0.0715 5.1157 0.0237*
2 -0.0344 6.3020 0.0428*
3 -0.0535 9.1781 0.0270*
4 -0.0531 12.0089 0.0173*
5 -0.0479 14.3217 0.0137*
6 0.0313 15.3061 0.0180*
7 0.0440 17.2598 0.0158*
8 0.0334 18.3876 0.0185*

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Industry LAG
Auto Correlation
Coefficient
Ljung-Box Q p-Value
9 0,0250 19.0204 0.0250*
10 -0.0253 19.6696 0.0325*
11 -0.0713 24.8087 0.0097*
12 0.0211 25.2608 0.0136*
13 0.0351 26.5090 0.0145*
FMCG
23 -0.0793 40.7207 0.0127*
24 -0.0335 41.8695 O.0133*
25 0.0002 41.8697 0.0186*
I.T
4 0.0610 10.2380 0.0366*
5 0.0308 11.1893 0.0478*
7 -0.0524 14.1847 0.0480*
Power
1 0.0810 6.5677 0.0104*
2 0.0575 9.8889 0.0071*
3 -0.0260 10.5678 0.0143*
4 -0.0328 11.6514 0.0201*
5 0.0153 11.8856 0.0364*
10 0.0289 20.6877 0.0234*
11 -0 .0652 24.9921 0.0091*
14 0.0315 29.0738 0.0102*
19 -0.0238 33.2851 0.0223*
21 0.0299 34.9837 0.0284*
Metal
4 -0.0470 11.1058 0.0254*
8 0.0086 15.6082 0.0483*
9 0.0911 23.9982 0.0043*
10 0.0315 25.0038 0.0053*
11 -0.0340 26.1770 0.0061*
12 -0.0031 26.1870 0.0101**
13 0.0011 26.1882 0.0160*
14 -0.0015 26.1904 0.0245*
15 -0.0226 26.7088 0.0312*
16 -0.0391 28.2628 0.0294*
Oil gas
3 -0.0883 8.1744 0.0425*
4 -0.0442 10.1402 0.0381*
12 -0.0076 22.7321 0.0301*
14 0.0654 27.6184 0.0160*
15 0.0039 27.6335 0.0240*
17 -0.0441 31.1494 0.0192*
19 0.0192 32.3859 0.0283*
20 -0.0357 33.6880 0.0283*
21 -0.0105 33.7999 0.0381*
INFERENCE
The auto correlation function Ljung box q test returns grated with time period and the returns for all
lag’s 1to13 the returns of those industry the calculation prevails time period

364
Figure 1 TIME SERIES GRAPH OF AUTO INDUSTRY RETURNS
Figure 2 TIME SERIES GRAPH OF HEALTH CARE INDUSTRY RETURNS
Figure 3 TIME SERIES GRAPH OF PSU INDUSTRY RETURNS
Figure 4 TIME SERIES GRAPH OF CAPITAL GOODS INDUSTRY RETURNS
Figure 5 TIME SERIES GRAPH OF BANKS INDUSTRY RETURNS

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Figure 6 TIME SERIES GRAPH OF CONSUMER DURABLES INDUSTRY RETURNS
Figure 7 TIME SERIES GRAPH OF FMGC INDUSTRY RETURNS
Figure 8 TIME SERIES GRAPH OF IT INDUSTRY RETURNS
Figure 9 TIME SERIES GRAPH OF POWER INDUSTRY RETURNS
Figure 10 TIME SERIES GRAPH OF METAL INDUSTRY RETURNS

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Figure 11 TIME SERIES GRAPH OF OIL AND GAS INDUSTRY RETURNS
WHITE NOISE TEST
In statistics and econometrics one often assumes that an observed series of data values is the sum of a
series of values generated by a deterministic linear process, depending on certain independent
(explanatory) variables, and on a series of random noise values(Fisher's combined probability test, and
Probability Test)
Table 6
Industry Fisher’s kappa P-value
Auto 7.3372473 0.2720351
Healthcare 6.0597028 0.6853494
PSU 8.4127192 0.1002696
Capital goods 6.5755493 0.5012423
Bank 7.3372473 0.2720351
Consumer durables 5.8821794 0.7609151
FMCG 8.9321345 0.06022949
I.T 5.5602179 0.8656741
Power 7.0748876 0.3401226
Metal 4.8080873 0.9887634
Oil gas 6.0032228 0.716663
INFERENCE
The return of white noise test which fishers kappa the result of test confiner the variation there of
revised as the then hilly satisfaction at 5 level this sources there is no infer the variations in the
securities variants
FINDINGS
The test of normality such as Mardia’s Skewness test, Mardia’sKutosis test and Henze-zirkler test. The
result of the test confirms that the security returns of securities are departed from Multi-Variate
normality and the returns are non-normally distributed. Hence, the researcher assumed that the returns
of securities are non-normally distributed. The descriptive statistics (table 03) of security returns of
Automobile Companies. Finally the Uni-Variate Skewness, Kurtosis, Sharpe-Wilk Statistics confirms
that the returns of automobile companies are departed from Uni-Variate normality and it follows the
non-normal distribution. the result of Augmented dickey fuller test (table 04)which help to correlation
the spatiality and the unit return of the returns and white noise test which includes fishers kappa the
result of test confiner the variation
Table 06.exhibit the return of spectral analysis and white noise test which includes fishers kappa
the result of test confiner the variation there of revised as the then hilly satisfaction at 5lavel this
sources there is no infer the variations in the securities variants
Table 4. exhibits the result of Augmented dickey fuller test which help to correlation the spatiality
Third and the unit return of the returns. The result of the test confines that the mean retunes on zero and
its non-datary factions in the retunes more the returns more over the returns of hypothesis, the returns
of portray return.

367
Table 5. exhibits the auto correlation function Ljung box q test of PUS industry returns the auto
correlation function returns test that the returns grated with raves time period and the returns for all lags
1to13 hilly satiations single level at 5level this sources the returns of auto mobile industry time the
calculation prevails time period.
SUGGESTIONS
The investor must understand the concept of stock first before investing in the industry Investor should
have fundamental before investing in the industry investors. Investors should understand technical
analysis before investing in the company, investor should have basic knowledge about the stock market
and should able predicates the market volatility by using various model in financial techniques and
must have good knowledge about stock market, other market before entering the market the investor
should always investment low risk fund
CONCLUSION
In this study found out that market volatility can predicated by Shapiro-wilk test variation correlation
function with the help of the this tool we found out the volatility can be predicted in this study
REFERENCE
[1] Alsalman. A.E. (2002). Empirical issues of financial market volatility in Kuwait stock
exchange. Submitted thesis, Howard university.
[2] Glosten, Lawrence R., Ravi Jagannathan and David E. Runkle (1993).On the relation
between the expected value and the volatility of the nominal excess return on stocks.
Journal of Finance, 48, 1779-1801.
[3] Gujarati Damodarn. and Sangeeta (2007) Basic econometrics. The McGraw Hill
publishing company.
[4] Kummar S.S.S. (2006). Comparative performance of volatility forecasting models in
Indian markets Decisions, Vol.3.
[5] Zivot Eric and Wang (2006). Modeling financial time series with s-plus, (2nd ed).
Springer.
[6] Brooks Chris. (2002) Introductory econometrics for finance. (1st ) Cambridge University
Press.

MODELING THE STOCK VOLATILITY OF TOP INDUSTRIAL RETURNS LISTED IN BSE

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