Measurement of Sectoral Indices Volatilty with Reference to Bombay Stock Market

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Measurement of Sectoral Indices Volatilty with Reference to Bombay Stock Market

1Goutam Tanty, ²Pramod Kumar Patjoshi

1Rourkela Institute of Management Studies

2Centurion University

Abstract : The Measurement 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. In this study, the sector-based index is designed 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. The index is based on a statistical compilation of the share prices of a number of representative stocks. It also creates the basis for portfolio trading by both active and passive investors.The Sector-based index is designed to provide a single value for the aggregate performance of a number of companies representing a sector of the economy. This study is an attempt to provide an empirical support to identify the risk factors in sectoral indices and BSE SENSEX index and also to see the risk relationship in different time intervals. This provided the data that is better refined than an individual selecting few organisations representing the industry. for the period from 01/01/2004 to 31/03/2015. The data has been taken from the official website of Bombay stock exchange. The results show that 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.

Key Words: ARCH,GARCH, ARMA, BSE & sectoral indices.

I. INTRODUCTION

Indian Financial markets exhibit dramatic movements in a stock prices may appear too volatile to be justified by changes in fundamentals factors. As Volatility is termed to be the fluctuation in price of any instrument over a period of time. The prices may be high during some periods of time and it may be low during some other periods. This variation in the price of commodities is measurable and in our study we have tried to measure the volatility in different sectors in India. There are different types of volatility such as the actual volatility and implied volatility. If volatility is calculated for the actual stocks themselves then they may be termed as actual volatility and if it is calculated for some underlying instrument then they may be termed as

implied volatility and both the actual and implied volatility may be calculated for different time periods say past, present and future termed respectively as historical, current and future volatility.The 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 higher 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.

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 are interpreting 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 the 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.

In this study, the sector-based index is designed 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. The index is based on a statistical compilation of the share prices of a number of representative stocks. It also creates the basis for portfolio trading by both active and passive investors. These market indices are convenient gauges on the stock market that also indicate the direction of the market over a period of time. By using these market

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indices, you can compare how well individual stocks and mutual funds have performed against market indicators for the same period.

II. LITERATURE REVIEW

In past volatility is measured using a constant one period variance. A new class of stochastic process called autoregressive conditional heteroskedasticity (ARCH) was introduced by Robert. F. Engle in 1982 after which many extensions of that model were developed in this process. A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process is proposed by Bollerslev in 1986. Engle himself along with Ng (1993) published the paper “Measuring and Testing the Impact of News on Volatility”, he defines the news impact curve. Phillip A. Braun, Daniel B.

Nelson, Alain M. Sunier (1995) investigated the conditional covariance of stock returns using bivariate exponential ARCH (EGARCH) models. Lawrence R.

Glosten, Ravi jagannathan, David E. Runkle ( 1993) published the paper On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. “Threshold heteroskedastic models” by Jean-Michel Zakoian (1994) is the paper wherein TARCH model was specified. Enrique Sentana(1995) published the Quadratic ARCH Models.In India only after 1990‟s researches have started to head towards this area. Chaudhury, S K (1991) measured the Seasonality in Share Returns which seems to be the Preliminary Evidence on Day of the Week Effect. Roy, M K and Karmakar (1995)focused on the measurement of an average level of volatility as a sample standard deviation and examines whether volatility has increased in the early 1990‟s. then after 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 to be 38 actively traded stocks in the BSENational 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 nonlinear dependence in returns from the stock market indices 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 seasonally 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 index for the period January 1998 to August 2005. For the monthly effect, they did find some significant differences utilizing ANOVA 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. They used parametric and non-parametric test to prove these objectives. They have selectedSensex, BSE 100 and BSE 500 indices from Bombay Stock Exchange (BSE) for the period1996 to 2006. The results show that, the returns are negatively skewed for all the indices over the 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 and annual 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 Indian stock market. Raja sethuDurai and Saumitra N Bhadurai (2011) in their article titled,“Correlation dynamics in Equity markets”, aimed to analyze the correlation structure of the Indian equity markets with that of world markets. The indices considered for the study are NASDAQ 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 weighted index (Taiwan) and the S & P CNX Nifty (India) are classified as Asian market, for the period 1997 to 2006. The logistic smooth transition regression (LSTR) model results of the conditional time varying correlation of S & P CNX Nifty with six Asian markets and S & PCNX Nifty with four developed markets show that there is a significant regime shift in the year 2000 and there is a considerable increase in integration in the second regime. This indicates that the S & P CNX Nifty index is moving towards a better integration with other world markets but not at a very noteworthy phase and

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 Sector-based index was designed to provide a single value for the aggregate performance of a number of companies representing a sector of the economy. His study was an attempt to provide an empirical support to identify the risk factors in sectoral indices and CNX Nifty index and

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also to see the risk relationship in different time intervals. The indices selected for the study were CNX Nifty index, CNX Auto index, CNX Bank index, CNX FMCG index, CNX Infrastructure index and CNX Information Technology index for the period 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 resulting exhibit important implications for individual investors and portfolio managers in terms of reducing portfolio risk and enhancing their returns and Swarna Lakshmi P in her research article “Volatility Patterns in Various Sectoral Indices in Indian Stock Market” used the ARCH model to measure the volatility in NIFTY and various sectoral indices in India. Global meltdown started all over the world around the year 2007. But in India the year 2008 seems to be highly volatile. Hence we have taken our period of study from 2008 to study the crucial impact and the period was till 2013. As NSE witness higher turnover, the 11 sectoral indices of NSE were taken for study and the volatility of the sectors such as NSE CNX Auto, NSE CNX Bank, NSE CNX Energy, NSE CNX Finance, NSE CNX FMCG, NSE CNX IT, NSE CNX Media, NSE CNX Metal, NSE CNX Pharma, NSE CNX PSU Bank , NSE CNX Realty was measured and it had been found out that the realty sector has witnessed higher volatility than any other sector.

III. 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 do not have much knowledge about individual stocks to invest they can use indexing as a method of choosing their stock investments.The second benefit of stock market indices are 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 indices to determine how well their managers are doing in managing their money.The third major use of stock market indices is as a forecasting tool. Studying the historical performance of

the stock market indices, you can forecast trends in the market and the broad objective of this study is to assess the Volatility Patterns of the Indices of different economic sectors in Indian Stock Market. The aim is to help the investors (current and potential) understand the impact of important sectoral indices in Indian Stock exchange.

IV. RESEARCH METHODOLOGY:

The database provides information regarding the daily opening high, low and closing values of the SENSEX.We have used this data related to a period of 11 years which is from 2004 to 2015.In this study I have considered 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.

The returns data will put in various models to find out a rational decision. Various statistical methods like regression analysis, time series analysis, correlation and other technologies to be used. The following models like a random walk model, a historical mean model moving average model, weighted moving average model exponentially weighted moving average model, an exponential smoothing model, a regression model, a GARCH model, an ARCH model will be applied to get the concrete results .

V. ANALYSIS

Table 1: ARMA (1, 1) Model Diagnosis:

Sl.

No

Sector Log

likelihood

AIC SIC HQC DWS

1 BSE_REALITY 4837.875 -4.226586 -4.204001 -4.218349 2.001972

2 BSE_AUTOMOBILE 10998.38 -5.458615 -5.455487 -5.457507 1.996390

3 BSE_BANK 8290.828 -5.025070 -5.012118 -5.020434 1.998577

4 BSE_BASIC_MATERIAL 6030.007 -5.123142 -5.078960 -5.107050 1.998788

5 BSE_CAPITAL_GOODS 10245.26 -5.090903 -5.075237 -5.085351 2.000966

6 BSE_CONSUMER_DISCRESTIONARY 6562.173 -5.585795 -5.526761 -5.564291 1.998830

7 BSE_CONSUMER_DURABLE 10054.79 -4.994675 -4.982147 -4.990235 2.000473

8 BSE_ENERGY 6038.392 -5.136970 -5.080416 -5.116370 2.001093

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9 BSE_FINANCE 5965.802 -5.051527 -5.039311 -5.047079 2.001779

10 BSE_FMCG 6837.851 -5.819685 -5.763130 -5.799085 2.003112

11 BSE_HEALTHCARE 7153.548 -6.080569 -6.036387 -6.064478 1.996279

12 BSE_INDUSTRIAL 6115.931 -5.196362 -5.152180 -5.180270 1.996979

13 BSE_IT 6248.301 -5.289539 -5.279769 -5.285982 1.999618

14 BSE_METAL 9557.354 -4.748746 -4.733080 -4.743194 2.000208

15 BSE_OIL___GAS 10273.55 -5.113491 -5.080517 -5.101804 1.999605

16 BSE_POWER 6589.154 -5.200755 -5.159194 -5.185675 2.000463

17 BSE_TECH 8741.782 -5.312691 -5.273694 -5.298728 2.000169

18 BSE_TELECOME 5804.713 -4.913777 4.904006 -4.910219 2.001895

19 BSE_UTILITY 6094.131 -5.179140 -5.132487 -5.162148 2.001498

Table 2: GARCH (1, 1) Model Diagnosis:

SECTORIAL INDEX OF BSE

obsered data

Test Coefficient Std. Error z-Statistic Prob.

BSE_REALITY 2203

omega 0.00016118 1.797E-05 8.9671332 0

alpha_1 0.50838383 0.0353255 14.391401 0

beta_1 0.37475222 0.0377376 9.9304753 0

Log Likelihood 5037.41183

Jarque Bera 4110.65869 0

Ljung-Box 3.97372435 0.0462154

BSE_AUTOMOBILE 4030

omega 2.2008E-05 2.446E-06 8.9979683 0

alpha_1 0.76063176 0.0132651 57.340799 0

beta_1 0.17295764 0.0121731 14.20821 0

Ljung-Box 0.5836051 0.4449027

BSE_BANK 3303

omega 5.0241E-05 4.227E-06 11.884627 0

alpha_1 0.62352135 0.020545 30.349034 0

beta_1 0.24652386 0.0175284 14.064222 0

Ljung-Box 3.9811673 0.0460117

BSE_BASIC MATERIAL 2364

omega 7.7647E-06 1.459E-06 5.3225915 1.023E-07

alpha_1 0.86214954 0.0109502 78.733943 0

beta_1 0.11949703 0.0105665 11.309003 0

Ljung-Box 0.00832351 0.9273073

BSE_CAPITAL GOODS 4030

omega 2.5965E-05 2.125E-06 12.218518 0

alpha_1 0.63974915 0.0151287 42.287004 0

beta_1 0.3608103 0.0180431 19.997155 0

Ljung-Box 65535 65535

BSE_CONSUMER DISCRE 2364

omega 6.1788E-06 8.181E-07 7.5527612 4.263E-14

alpha_1 0.84248284 0.0089084 94.571536 0

beta_1 0.13481474 0.0111295 12.11324 0

Ljung-Box 1.7074839 0.1913121

BSE_CONSUMER

DURABLE 4030

omega 5.8949E-05 5.116E-06 11.521844 0

alpha_1 0.59457227 0.0212566 27.971146 0

beta_1 0.29936501 0.0199974 14.970191 0

Ljung-Box 3.84527186 0.0498864

BSE_ENERGY 2364

omega 1.6553E-05 1.909E-06 8.6714126 0

alpha_1 0.68398548 0.0185657 36.841368 0

beta_1 0.28171089 0.0214474 13.134962 0

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Ljung-Box 3.85524349 0.0495907

BSE_FINANCE 2364

omega 7.4798E-05 6.88E-06 10.871416 0

alpha_1 0.44654153 0.0289576 15.420525 0

beta_1 0.51941349 0.0364673 14.243277 0

Ljung-Box 13.1784867 0.0002832

BSE_FMCG 2364

omega 6.8026E-06 1.054E-06 6.4555661 1.078E-10

alpha_1 0.8399814 0.0144074 58.302031 0

beta_1 0.12196387 0.012564 9.7074079 0

Jarque Bera 1281.03044 Prob 0

Ljung-Box 0.00266152 Prob 0.9588555

BSE_HEALTH 2364

omega 3.2733E-05 2.722E-06 12.02739 0

alpha_1 0.41196015 0.0243411 16.924477 0

beta_1 0.49661306 0.0322047 15.420524 0

Ljung-Box 5.84825551 0.0155925

BSE_INDUSTRIAL 2364

omega 6.2428E-05 4.303E-06 14.507329 0

alpha_1 0.31337962 0.0182293 17.191003 0

beta_1 0.78651839 0.0375407 20.951102 0

Ljung-Box 65535 0.65535

BSE_INFORMATION

TECH 2364

omega 7.7481E-05 7.474E-06 10.366777 0

alpha_1 0.48123094 0.0180348 26.683399 0

beta_1 0.59860897 0.0415784 14.397124 0

Ljung-Box 65535 65535

BSE_METAL 4030

omega 3.1486E-05 2.53E-06 12.445436 0

alpha_1 0.73122838 0.0115776 63.158763 0

beta_1 0.19012233 0.0115334 16.484446 0

Ljung-Box 2.94933064 0.0859131

BSE_OIL AND GAS 4030

omega 1.7685E-05 1.842E-06 9.6017425 0

alpha_1 0.74936649 0.0137607 54.457033 0

beta_1 0.19909216 0.0122729 16.222082 0

Ljung-Box 1.65610377 0.1981302

BSE_POWER 2544

omega 1.7466E-05 1.817E-06 9.6113696 0

alpha_1 0.78387051 0.014087 55.64479 0

beta_1 0.16562291 0.0136098 12.16936 0

Ljung-Box 0.2939283 0.5877141

BSE_TECH 3303

omega 1.6759E-05 1.411E-06 11.877724 0

alpha_1 0.70980435 0.0162003 43.814265 0

beta_1 0.27949789 0.0186775 14.96445 0

Ljung-Box 4.15374645 0.0415425

BSE_TELECOME 2364

omega 5.9091E-05 5.914E-06 9.9918621 0

alpha_1 0.63530929 0.025667 24.751995 0

beta_1 0.17106589 0.013206 12.953632 0

Ljung-Box 0.11660392 Prob 0.7327474

BSE_UTILITY 2364 omega 0.00010505 4.388E-06 23.939546 0

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alpha_1 0.2061813 0.0196419 10.497014 0

beta_1 0.68662044 0.0462094 14.858879 0

Ljung-Box 3.44227826 Prob 0.063548

VI. CONCLUSION

The peculiar observations reveal that health and consumer durable indexes are earning against the market index returns, whereas Technology, oil, Capital goods and banking remained the main contributors to the overall market index returns. GARCH models illustrate that lower volatility clustering involved with the presence of the realty and power sectoral indices. The liquidity measured on the basis of Market efficiency coefficients (MEC) have provided that the sectors like health care, consumer durables and the auto sectoral indices have high long term variance in the returns where as oil and gas sector have lower value. It is found that all sectoral indices of BSE have more than one as MEC, indicating the higher long term variance than short term variance of sectoral indices. The return of the BSE sectoral indices exhibit the characteristics of normality, stationarity and heteroskedasticity. Also the ACF and PACF indicate that ARMA(1,1) is the suitable one for modeling the average return. The residuals of the ARMA(1,1) of the sectoral index returns except for IT and TECH are heteroskedastic. Hence, a non-linear model is to found to model the volatility of the return series. An attempt is made to model the volatility of the return series and found that GARCH(1,1) model is the best one.

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