INTRODUCTION:

In the financial market the return is based on appropriate investment strategies. In this competitive world financial markets exhibit dramatic movements as per the market analysis, and stock prices may appear too volatile to be justified by changes in fundamentals. Buyers and sellers cause prices to change as they decide how valuable each stock is. Basically, share prices change because of supply and demand. If more people want to buy a stock than sell it - the price moves up. Conversely, if more people want to sell a stock, there would be more supply (sellers) than demand (buyers)-the price would start to fall. Volatility in the stock return is an integral part of stock market with the alternating bull and bear phases.

In the bullish market, the share prices soar high and in the bearish market share prices fall down and these ups and downs determine the return and volatility of the stock market. Volatility is a symptom of a highly liquid stock market and pricing of securities depends on volatility of each asset. An increase in stock market volatility brings a large stock price change of advances or declines. Investors interpret a raise in stock market volatility as an increase in the risk of equity investment and consequently they shift their funds to less risky assets. It has an impact on business investment spending and economic growth through a number of channels. Changes in local or global economic and political environment influence the share price movements and show the state of stock market to the general public. The issues of return and volatility have become increasingly important in recent times to the Indian investors, regulators, brokers, policy makers, dealers and researchers with the increase in the FIIs investment. This research work is based on the major Index to provide a single value for the aggregate performance of a number of companies representing a group of related industries or within a sector of the economy. These markets Index are convenient gauges of the stock market that also indicate the direction of the market over a period of time. By using these markets Index, the investor can compare how well individual stocks have performed against market indicators for the same period, which will help them to take effective investment decisions.

LITERATURE REVIEW:

Several studies have been conducted to analyze the risk factors on the stock Index.

In India only after 1990’s researches have started to head towards this area. Chaudhury, SK (1991) measured the Seasonality in Share Returns which seems to be the Preliminary Evidence on Day of the Week Effect. Roy, MK and Karmakar (1995) focused on the measurement of average level of volatility as a sample standard deviation and examines whether volatility has increased in the early 1990’s.

Poshakwale Sunil (2002) examined the random walk hypothesis in the emerging Indian stock market by testing for the nonlinear dependence using a large disaggregated daily data from the Indian stock market. The sample used was 38 actively traded stocks in the BSE National Index. He found that the daily returns from the Indian stock market do not conform to a random walk. Daily returns from most individual stocks and the equally weighted portfolio exhibit significant non-linear dependence. This is largely consistent with previous research that has shown evidence of non-linear dependence in returns from the stock market Index and individual stocks in the US and UK. Harvinder Kaur (2004) studied whether the day of the week effect, calendar month effect and spillover from U.S effect is present in SENSEX an NIFTY or not using GARCH, EGARCH and TARCH models.

Yakob, Beal and Delpachitra (2005) examined seasonal effects of ten Asian Pacific stock markets, including the Indian stock market, for the period January 2000 to March 2005. They stated that this is a period of stability and therefore ideal for examining seasonality as it was not influenced by the Asian financial crisis of the late nineties. Yakob, et al., concluded that the Indian stock market exhibited a month-of-the-year effect in that statistically significant negative returns were found in March and April whereas statistically significant positive returns were found in May, November and December. Of these five statistically significant monthly returns,November generated the highest positive returns whereas April generated the lowest negative returns. In a similar study by Bodla and Jindal (2006) several seasonal anomalies in the Indian stock market utilizing the S&P CNX Nifty for the period January 1998 to August 2005. For the monthly effect, they did find some significant differences utilizing NOVA for their sub-period, January 2002 to August 2005. However, they were unable to find any significant differences among individual months.

Rakesh Kumar and Raj S Dhankar (2011) in their article titled, “Distribution of Risk and Return: A test of normality in Indian stock market”, examined the normality of return and risk of daily, weekly, monthly and annual returns in Indian stock market. Theyused parametric and non-parametric test to prove these objectives. They have selectedSensex, BSE 100 and BSE 500 Index from Bombay Stock Exchange (BSE) for the period1996 to 2006. The results show that, the returns are negatively skewed for all the Index overthe period. Asymmetry is found in risk and return in case of daily and weekly returns i.e., risk and return relationship seems inconsistent in case of daily and weekly returns. Monthly andannual return, however are found normally distributed for all three indices over the period oftime. The study shows the importance of time horizon in investment strategy for the Indianstock market.

Raja sethuDurai and Saumitra N Bhadurai (2011) in their article titled,“Correlation dynamics in Equity markets”, aimed to analyze the correlation structure of theIndian equity markets with that of world markets. The indices considered for the study areNASDAQ composite (USA), S & P 500 (USA), FTSE 100 (UK) and DAX 30 (Germany)classified as developed markets. KLSE composite (Malaysia), Jakarta composite (Indonesia), Straits times (Singapore), Seoul composite (South Korea), Nikkei (Japan), Taiwan weightedIndices (Taiwan) and the S & P CNX Nifty (India) are classified as Asian market, for theperiod 1997 to 2006. The logistic smooth transition regression (LSTR) model results for theconditional time varying correlation of S & P CNX Nifty with six Asian market and S & PCNX Nifty with four developed markets show that there is a significant regime shift in theyear 2000 and there is a considerable increase in integration in the second regime. Thisindicates that the S&P CNX Nifty Indices is moving towards a better integration with otherworld markets but not at a very noteworthy phase.

Dr.G.Shanmugasundram And D.John Benedict(2013) in their article “Volatility of The Indian Sectoral Indices-A Study With Reference To National Stock Exchange” examined the Major Indiceswas designed to provide a single value for the aggregateperformance of a number of companies representing a sector of the economy. His study was anattempt to provide an empirical support to identify the risk factors in sectoral indices and CNX Nifty Indices and also to see the risk relationship in different time intervals. The indicesselected for the study were CNX Nifty Indices, CNX Auto Indices, CNX Bank Indices, CNXFMCG Indices, CNX Infrastructure Indices and CNX Information Technology Indices for theperiod from 01/01/2004 to 30/04/2012. The results show that there is no difference in the Standard deviation among various sectoral indices and there is a significant difference in the mean scores of various time intervals. The results exhibit important implications to individual investors and portfolio managers in terms of reducing portfolio risk and enhancing their returns.

A research paper by Birau, Ramona, Simica, Marian and Trivedi (2014) examined the long-term volatility pattern of R.P.G.U (Romania, Poland, Greece and USA) stock markets using asymmetric GARCH class models. The empirical framework provides additional evidence regarding volatility patterns, similar reaction to external shocks, international contagion, and the impact of new information’s on the market and risk management optimal strategies, investor risk aversion and international portfolio diversification benefits. Further analysis suggests that volatility does not diverge to infinity and seems to react significantly different considering the case of high positive or high negative stock returns. Moreover, research paper attempts to provide a better understanding of the relationship between the R.P.G.U stock markets in order to facilitate global diversification investing perspective for international investors.

In research article Yadav, Sameer. (2017) analyzed that in India listed Stock Market are Bombay Stock Exchange (BSE), the National Stock Exchange (NSE) and the Calcutta Stock Exchange (CSE). These three are largest Indian Stock Market. Volatility is a statistical measure of the dispersion of returns for a given security or Market Index. Commonly, the higher the volatility greater the risk associated with the security. Volatility estimation is important for several reasons associated with different category of investor in the market. The developed markets continue to provide over long period of time with higher returns constituting low volatility as per the research work findings. Indian stock market has started becoming informational and more efficient as compared to developed countries.

IMPORTANCE OF THE STUDY:

First, the market indices provide an historical perspective of stock market performance, giving investors more insight into their investment decisions. Investors who don’t have much knowledge about individual stocks to invest they can use Index as amethod of choosing their stock investments. The second benefit of stock market is that they provide a yardstick with which investors can compare the performance of their individual stock portfolios. Individual investors with professionally managed portfolios can use the Index to determine how well their managers are doing in managing their money. The third major uses of stock market Index are as a forecasting tool. Studying the historical performance of the stock market Index, you can forecast trends in the market.

OBJECTIVES OF THE STUDY:

The broad objective of this study is to assess the Volatility Patterns of the Index of different economic sectors in Indian Stock Market. The aim is to help the investors (current and potential) understand the impact of important sectoral Index in Indian Stock exchange.

The specific objectives of the study are

· To measure the volatility of various Index in Bombay Stock Exchange.

· To assess the aggregate volatility of various Index in Bombay Stock Exchange.

RESEARCH METHODOLOGY:

The Prowess database provides information regarding the daily opening high, low and closing values of the SENSEX, NIFTY, and BSE 200 Index among other Index along with the BSE 30 companies. We will use this data related to a period of 12 years which is from 2006 to 2018.

The daily mean Index value based on all the four reported figures of the day opening, high, low and closing will be used for calculating the daily returns. The earlier studies had used the closing values for return generating procedure with an implied assumption of trading done at the closing value. There would not be any need for such a restrictive trading assumption in case average of the available opening high, low, and closing values is used. The continuously compounded annual rate of return is a well- accepted approach to measure the daily relative mean Index value to measure the daily return used for this study. Following formula will be used to calculate the return.

Rt = In [It/ It – 1]

Where

Rt – Return on day t.

It = Index mean value on day‘t’

It – 1 = Index mean value on day “t-1”

And In = Natural log.

ANANLYSIS AND INTERPRETATION:

We have applied different parametric tests like Mean, Stand deviation, Skewness and Kurtosis to study the distribution pattern of the daily returns. Apart from the different parametric test we have also applied regression and P test to the return series in order to measure volatility pattern of Indian stock market and we have also used the GARCH model.

Bombay Stock Exchange is one of the most widely used Index representing the price movement of the Indian stock market. The major Index of Bombay Stock Exchange BSE 30, BSE 100, BSE 200 and BSE 500, which are actively traded markets, represent the various industrial sectors of the Indian economy. So we have tested the volatility pattern of the above Index, by applying the Descriptive Statistics whose results are depicted in the Table:

DESCRIPTIVE ANALYSIS OF BOMBAY STOCK EXCHANGE

Particulars	BSE 30	BSE 100	BSE200	BSE500
Mean	0.000390	0.000400	0.000410	0.000420
Standard Deviation	0.015492	0.015471	0.015455	0.015446
Skewness	-0.197400	-0.378710	-0.478830	-0.548230
Kurtosis	7.023670	6.629420	6.999170	6.933550

Source: Results obtained from Eviews package for statistical analysis

It has been found from the above analysis table, that the entire Index have the positive mean returns and almost identical. BSE 500 found to be the highest mean return (0.000420) followed by BSE 200, whereas the BSE 30 has the lowest mean return (0.000390). The standard deviation as a measure of volatility is found to be the maximum (0.015492) of BSE 30 where as it is minimum (0.015446) in the case of BSE 500. All the Index return distributions are negatively skewed. The BSE 500 return distribution is utmost negative (-0.548230) while the BSE 30 is bottommost negative (-0.197400) skewed as compare to the other Index. The return distributions all the Index are observed to be leptokurtic by nature and it is uppermost peaked in the case of BSE 30 and lowermost in case of BSE 100.

In the above table BSE 500 return is comparatively higher than other BSE Index with a minimum risk i.e., 0.015446 and it is also more negatively skewed. On the other hand, BSE 50 (Sensex) has a lowest mean return with a maximum risk i.e., 0.015490 while with a minimum negatively skewed values -0.197400 and highest positive kurtosis value i.e.7.023670. Therefore, investment in BSE 500 Index has provided more returns to the investor with a minimum risk whereas BSE 30 (Sensex) has underachieved during the study period.

The advancement of econometrics has produced a new way of testing the risk and return volatility under the notion that risk premium is conditional upon time and the error term is non-normal and heteroscedastic. The Generalised Autoregressive Conditional Heteroscedasticity (GARCH) model holds the advantage of handling time series data that fail to satisfy the basic assumption of classical linear regression model (CLRM). Within the premise of the original GARCH model, the conditional mean and variance of stock returns are assumed to be influenced by the past returns and volatility based on the available information at a particularly point in time. The GARCH model, introduced by Engle, Lilien and Robins (1987), provides a new framework for studying the relationship between risk and return since the model explicitly links the conditional variance to the conditional mean of returns. Therefore, GARCH model has been applied here to determine the Omega, Alpha, Beta values.

GARCH ANALYSIS

Particulars	BSE 30	BSE 100	BSE200	BSE500
Omega	0.000110	0.006369	0.002926	0.005733
Alpha_1	0.093279	0.000139	0.643002	0.014963
beta_1	0.559751	0.273062	0.205360	0.145545
Jarque Bera	8099. 926000	63845048. 000000	733353. 700000	88767661. 000000
Ljung-Box	0.135934	0.004702	0.655350	0.017679
P value	0.000000	0.000000	0.000000	0.000000

Source: Results obtained from Eviews package for statistical analysis

The above table indicates the value of omega, alpha, beta, Jarque Bera, Ljung-box and p-value with the help of GARCH Model. It can be observed that the measure of active return alpha value of BSE 50 (Sensex) has the highest active return (0.093279) as compare to BSE 200 (0.064300), BSE500 (0.014963) and BSE 100 (0.000139). Nonetheless the measure of risk and volatility beta value of BSE 30 i.e. 0.559751 is greater than other Index while beta of BSE 500 is the lowest i.e. 0.145545. Here the sum of α1 and β1 is less than 1 for all Index which, shows the presence of mean reversion for all the Index. The Ljung-Box statistics provide evidence in favour of intertemporal dependencies, which shows the distribution is not normal. At this juncture the calculated p value is less than 0.05. So the variation in returns across different Index of the BSE is significant at the 5% level.

CONCLUSION:

As per the above descriptive and GARCH it can be observed that the volatility pattern of four major Index of Bombay stock market viz., the Sensex, the BSE 100, the BSE 200 and the BSE 500 witnessed that BSE 500 found to be the highest mean return and BSE 30 has the lowest mean return whereas the volatility is found to be the highest of BSE 30 and lowest of BSE 500. So, it can help the investor to take investment decision in Index instead of individual share .This study can be applied to other Stock Market Index also for better result and understanding.

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Received on 27.05.2019 Modified on 10.06.2019

Asian Journal of Management. 2019; 10(3): 236-240.

DOI: 10.5958/2321-5763.2019.00037.4