Stock Market Index Forecasting Model Using the GARCH Tool

8/6/2019 Stock Market Index Forecasting Model Using the GARCH Tool.

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[Type the document title] [Year]

CHRIST UNIVERSITY INSTITUTE OF MANAGEMENT-BENGALURU Page 1

A PROJECT REPORT ON

STOCK MARKET INDEX FORECASTING MODEL ON THE

BASIS OF MACROECONOMIC VARIABLES USING

MULTIVARIATE STATISTICAL AND ECONOMETRIC TOOLS

Submitted in partial fulfillment of the requirement for the award of degree in

Master of Business Administration

By,

HARISH HOSMANI

REGISTER NUMBER:0921212

Under the guidance of:

PROF T.S.RAMACHANDRAN

Senior professor-MBA-Finance

CUIM-Bengaluru

HOSUR ROAD, BENGALURU


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1. Introduction:

1.1: Genesis of the problem:

Due to liberalization privatization and globalization. Indian capital markets has witnessed farreaching changes in 1990s and 2010s .The corporate sectors were also churning out good results.

Stock market is highly volatile and is high risk and high return investment. The profitability of

investing and trading in the stock market to a large extent depends on the predictability. If any

system be developed which can consistently predict the trends of the dynamic stock market, would

make the owner of the system wealthy. More over the predicted trends of the market will help the

regulators of the market in making corrective measures.

Another motivation for research in this field is that it possesses many theoretical and experimental

challenges. The most important of these is the Efficient Market Hypothesis (EMH); Efficient

Capital Markets. The hypothesis says that in an efficient market, stock market prices fully reflect

available information about the market and its constituents and thus any opportunity of earning

excess profit ceases to exist. So it is ascertain that no system is expected to outperform the market

predictably and consistently. Hence, modeling any market under the assumption of EMH is only

possible on the speculative, stochastic component not on the changes on the changes in value or

other fundamental factors.

Moreover, many researchers claim that the stock market is a chaos system. Chaos is a non linear

deterministic system which only appears random because of its irregular fluctuations. These systems

are highly sensitive to the initial conditions of the systems. The Indian capital market performance is

function of various macro economic variables. The behavior of capital market is related to macro

economic variables.


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1.2 Major concepts involved:

The asset returns and macroeconomic events are connected as the marginal value of wealth that

derives the asset market is also important for macroeconomic analysis. In dynamic macroeconomicstheory the most important relationships are the equality of saving and investment, the equality of

marginal rate of substitution with marginal rate of transformation and the factors that determine the

allocation of consumption and investment across time and states of nature. The asset markets

provide mechanism that performs all these equilibrating processes. Asset returns underlie the price

line that draws together marginal rates of substitution and marginal rates of transformation. The asset

market gives the marginal value of wealth, and measurement of important variables depends on

modern and dynamic macroeconomics.

Many researchers find the evidence of time varying behavior of risks and risk premiums associated

with the economic variables. The conditional model provides the specification of information

environment that investors use to form their expectations. Therefore, the model is extended to

include conditional information set consist of business-cycle variables, which generate time-varying

risks and premiums associated with these risks.

The research on linking macroeconomic variables to asset returns are extensively done for developed

markets. It is relatively new area for developing markets. Although it is commonly believed that

macroeconomic factors affect stock returns, the nature and direction of influence on stock prices is

not so clear in case of Indian market. The linkage of asset prices and macro-economy is investigated

for Indian market in statistic and dynamic settings.

Multiple regression concepts were primitively used in major areas of finance to design the normal

forecasting model of any system which is dependent on various variables. In later days had

evolved to arbitrage pricing theory to predict the market behavior on various risks co-efficient.

Other various concepts are also used to study the market behavior.


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1.3 Need for the study:

The macroeconomic variables influence the asset returns in developed markets. There is a surge of

interest to uncover the relationship of macroeconomic variables with stock prices among financialeconomist in India. Since, economists have started taking interest in this issue only recently, many

areas on research are still not covered. In this perspective the present study aims to make a

contribution to the literature by investigating the firm level multifactor price behavior with reference

to NATIONAL STOCK EXCHANGE.

As in NSE the derivatives trading is done on the high volumes . In the derivative trading section the

index options has got LIONs share. The model designed for studying the stock market behavior

can help the various investors to take decisions on taking call on the various strike prices to have

better returns on the index options. The movement of stock market which is predicted on the basis of

the model design can be helpful for both regulators and investors to take the decision.

1.4. overview of the study:

The study is mainly involved to provide the blue print how the movement of stock market can be

observed for the given macro economic variables which are considered as important to decide the

movement of the stock market. As the finance is considered as HARD NUT TO CRACK, the

study can contribute to nullify the difficulty of understanding the concepts of finance. The

understanding of macroeconomic variables can provide the insight about the movement of economic

status in India. The macroeconomic variables have some significant effects on asset pricing. Overall,

the results suggest that time variation in economic risks and their rewards provide some explanation

of variation in expected returns across assets.

The plan of this study is as follows. Section 1 briefly reviews the previous empirical findings. The

macroeconomic risk factors which are expected to be priced in the stock market and their data

sources are discussed in section 3. In section 4, the empirical methodology is outlined. The analytical

framework of unconditional multifactor model is presented using observed economic variables. Then

the multifactor model is extended by including conditional moments and, finally, the behavior of

time varying risks and risk premiums associated with economic variables are incorporated into the

model. Section 5 discusses the results and last section concludes the study.


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CHAPTER 2

Literature review


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2.1-Mode of review done:

The methodology applied to review the literature is going through various articles available in

websites like JSTOR, EBSCHO, NSE, SSRN, IIM AHMEDABAD, MADRAS SCHOOL OF

ECONOMICS, ICFAI JOURNAL OF APLLIED ECONOMICSetc.. Both offline and online

research is done to find the preliminary study on the research done on the modeling of the stock

market index.

2.2 studies conducted abroad:

y Attiya Y. Javid and Eatzaz Ahmad.(2009)Testing multifactor capital asset pricingmodel in case of Pakistani market by This article provides how the macro economic

variables influence the capital market of Pakistan.

The analysis of this study explores a set of macroeconomic variables along with market return as the

systematic sources of risks explaining variations in expected stock returns for 49 stocks traded at

Karachi Stock Exchange for the period 1993-2004. Some of these economic variables are found to

be significant in explaining expected stock returns. The test of conditional multifactor CAPM is

carried out by specifying conditional variance as a GARCH (1,1)-M process. The results of the

conditional multifactor CAPM-with- GARCH-M model reveal that conditional model shows very

marginal improvement in explaining risk-return relationship in Pakistani Market during the sample

period. As regards the risk premium for variance risk, the results are not so supportive, only for a

few stocks significant compensation for variance risk to investors is observed. The model is then

extended to allow variability in economic risk variables and conditioning information is taken as

lagged macroeconomic variables that influence business conditions in Pakistan. The results show

evidence in support of conditional multifactor CAPM. The economic variables that are observed to

perform relatively well in explaining variations in assets returns include consumption growth,

inflation risk, call money rate, term structure. However, the market return, foreign exchange risk and

oil price risk, which explain a significant portion of the time series variability of stock returns, have


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limited influence on the asset pricing. Therefore we can conclude that expected returns variation

could be explained by macroeconomic variations and this variability has some business cycle

correlations.

The result of the model reveal that conditional CAPM performs relatively well in explaining risk-return relationship in Pakistan during 1993-2004. As regards the risk premium for variance risk, the

results are not so convincing, only for a few stocks significant compensation for this risk by

investors is observed. The model is then extended to allow variability in economic risk variables and

their rewards. The empirical results show evidence in support of conditional multifactor CAPM. The

conditioning information is taken as lagged macroeconomic variables that influence business

conditions in Pakistan.

The economic variables that are observed to perform relatively well in explaining variations in

assets returns include consumption growth, inflation risk, call money rate and term structure .

However, the market return, exchange risk and oil prices risk, which explain a significant portion of

the time series variability of stock returns, have limited influence on the asset pricing.

y Ahmad Eatzaz and Badar-u-Zaman (1999) Volatility and Stock Return at Karachi StockExchange.Pakistan Economic and Social Review 37:1, 2537.

Which provides study empirically investigates the Fama-French three-factor model and

consumption CAPM model in unconditional and conditional setting with individual stocks

traded at Karachi Stock Exchange (KSE), the main equity market in Pakistan for the period

1993-2004. This study empirically investigates the Fama-French three-factor model an

consumption CAPM model in unconditional and conditional setting with individual stocks

traded at Karachi Stock Exchange (KSE), the main equity market in Pakistan for the period1993-2004. These extensions are in response of the empirical findings that do not support

standard CAPM as a model to explain assets pricing in Pakistani equity market. The observation

is that the dynamic size and book-to-market value coefficients explain the cross-section of

expected returns in some sub-periods. In the second stage, the consumption risk is incorporated

in standard CAPM in static and dynamic context. The findings reveal that the market rewards


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systematic risk for higher return, but the relevant measure for systematic risk appears to be

conditional consumption beta rather than market beta. This evidence leads to investigate

macroeconomic risks that can describe the variation in expected return in a more complete and

meaningful way.The standard CAPM is extended with Fama-French (1992) variables, size and book-to-

market value, in unconditional and conditional setting. The observation is that the dynamic size

and style coefficient explain the cross-section of expected returns in some sub-periods . The

consumption risk is incorporated in standard CAPM in static and dynamic way. The findings

reveal that the market rewards systematic risk for higher returns, but the relevant measure for

systematic risk appears to be conditional consumption beta rather than market beta. This

evidence leads to investigate macroeconomic risks that can describe the variation in expected

return in a more complete and meaningful way.

y Antoniou, A., I. Garrett and Priestley, R. (1998) Macroeconomic Variables as CommonPervasive risk factors and the Empirical Content of Arbitrage Pricing Theory .Journal

of Empirical Finance 5, 221240. This paper models UK fixed income security returns of

various bond types and maturities with Ross's (1976) Arbitrage Pricing Theory.

In this paper authors investigated the performance of the APT for securities traded on the

London Stock Exchange. We analyze performance in terms of the presence of common

pervasive factors across two different samples allowing for the fact that returns exhibit an

approximate factor structure. Unlike most previous studies, we find that for two subsamples

of assets it is possible to arrive at a unique return generating process in the sense that three

factors relating to the money supply, inflation and excess returns on the stock market are

priced and carry the same prices of risk in both samples.


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The Arbitrage Pricing Theory (APT) of Ross [1976] is one of the most important building

blocks of modern asset pricing theory, and the prime alternative to the celebrated Capital

Asset Pricing Model (CAPM) of Sharpe [1964], Lintner [1965], and others. This paper briefly reviews the theoretical underpinnings underlying the APT and highlights the

econometric techniques used to test the APT with pre-specified macroeconomic factors .

Besides this, the prime objective of this study is to perform an empirical test of the APT

in the Pakistani stock market by using pre-specified macroeconomic factors and

employing Iterative Non-Linear Seemingly Unrelated Regressions (ITNLSUR). These

empirical results will be, hopefully, helpful for corporate managers undertaking cost of

capital calculations, for domestic and international fund managers making investment

decisions and, amongst others, for individual investors who wish to assess the

performance of managed funds.

In this paper, we have examined the risk-return relationship of the Pakistani stock market.

The purpose of the study was to examine whether the APT has any empirical validity for the

Pakistani stock market. Our results suggest that domestic macroeconomic factors -

unexpected inflation, exchange rate, trade balance, and oil prices - are a source of systematic

risk in the Pakistani stock market, and the APT pricing restrictions hold. These results can

help corporate managers undertaking cost of capital calculations, domestic and international

fund managers making investment decisions and, amongst others, individual investors who

wish to assess the performance of managed funds. These results, however, do not suggest

that the macroeconomic variables that are found to have significant risk premia in this paper

are the only factors that carry systematic risk, but these results could be used as a benchmark

to help the key market players in the Pakistani stock market upgrade their knowledge about

the phenomenon of risk and return.


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y Chen, Nai-Fu, Roll, Richard and Stephen A. Ross. Economic Forces and the StockMarket.

The Journal of Business 59, 3 (1986): pp.383-403. Chen, Roll and Ross (1986) were amongthe earliest researchers to identify and test economics factors that should affect stock returns

either through future cash flows or through the discount rate. By analyzing factors such as

inflation, the term structure of interest rates, industrial production etc. and discovered them to

be important in explaining stock returns. Simply stated, Chen et al. strove to discover, the

relation of stock price and macroeconomic variables.

This paper tests whether innovations in macroeconomic variables are risks that are rewarded

in the stock market. Financial theory suggests that the following macroeconomic variables

should systematically affect stock market returns: the spread between long and short interest

rates, expected and unexpected inflation, industrial production, and the spread between high-

and low- grade bonds. We find that these sources of risk are significantly

priced. Furthermore, neither the market portfolio nor aggregate consumption are priced

separately. We also find that oil price risk is not separately rewarded in the stock -market.

2.3 STUDIES CONDUCTED IN INDIA:

Manna Majumder, MD Anwar Hussian: FORECASTING OF INDIAN STOCK MARKET

INDEX USING ARTIFICIAL NEURAL NETWORK: (2009).

This paper presents a computational approach for predicting the S&P CNX Nifty 50 Index. A neural

network based model has been used in predicting the direction of the movement of the closing value

of the index. The model presented in the paper also confirms that it can be used to predict price

index value of the stock market.

The uniqueness of the research comes from the fact that this will help to develop neural network as

another forecasting tool for highly volatile Indian market . In this paper, we attempted to find an

optimal architecture of the neural network to predict the direction of the CNX S&P Nifty 5 0 Index

with a high level of accuracy. This paper has considered most of the issues and critical factors for

designing the neural network model and has tested the performance of each of the structures at


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various historic periods of the trading sessions of the Indices. A rigorous trial and error method is

employed in selecting each of the features of the network structure.

In a highly volatile market like Indian Stock Market, the performance levels of the neural network

models, reported in the paper will be very useful. Especially, the prediction of the direction of themarket with fairly high accuracy will guide the investors and the regulators. However, for prediction

at different time in future, the network may be trained periodically and need be there the network

may be revalidated with changes in the some of the features of the model. This is recommended as

with time the characteristic of the market changes and the network may miss out on the additional

information. We believe that neural network tool gives a promising direction to the study of

prediction of the markets and other economic time series.

Desai, V. S., & Bharati, R., (1998). A comparison of linear regression and neural network

methods for predicting excess returns on large stocks. Annals of Operations Research, 78, 127

163.

Recent studies have shown that there is predictable variation in returns of financial assets over time.

We investigate whether the predictive power of the economic and financial variables employed in

the above studies can be enhanced if the statistical method of linear regression is replaced by feed

forward neural networks with back propagation of error.

A shortcoming of backpropagation networks is that too many free parameters allow the neural

network to fit the training data arbitrarily closely resulting in an "overfitted" network. Overfitted

networks have poor generalization capabilities. We explore two methods that attempt to overcome

this shortcoming by reducing the complexity of the network. The results of our experiments confirm

that an "overfitted" network, while making better predictions for within-sample data, makes poor

predictions for out-of-sample data. The methods for reducing the complexity of the network,

explored in this paper, clearly help improve out-of-sample forecasts. We show that one cannot say

that the linear regression forecasts are conditionally efficient with respect to the neural networks

forecasts with any degree of confidence. However, one can say that the neural networks forecasts are

conditionally efficient with respect to the linear regression forecasts with some confidence.


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T Manjunatha and T Mallikarjunappa: Bivariate Analysis of Capital Asset Pricing Model in

Indian Capital Market(2009):

Explain the variations in security portfolio returns, the other combinations do not explain thevariation in the security/portfolio returns. Further analysis in this paper has shown that beta, with

some of the combinations of the independent variables, explains the variation in security/portfolio

returns.

Capital Asset Pricing Model (CAPM) establishes the relationship between risks and returns in the

efficient capital markets. A review of studies conducted for various markets

in the world reveals that researchers have used a number of methodologies to test the

validity of CAPM. While some studies have supported the validity of CAPM, some others have

revealed that beta alone is not a suitable determinant of asset pricing and that a

number of other factors could explain the cross-section of returns. This paper has attempted to test

the validity of the combination effect of the two parameter CAPM to

determine the security/portfolio returns. The results show that:

Intercept is not significantly different from zero.

In case of portfolios, the combination of p and Rm-Rf explains the variation of portfolio returns

when portfolios formed with market value weights under both percentage and log returns and p and

ln(BE/ME)p explain the portfolio percentage returns when market value weights are used . It is

observed that while combinations of some of the independent variables, as opposed to the univariate

variable considered in Manjunatha and Mallikarjunappas (2006) paper, explain the variations in

security/portfolio returns, the other combinations do not explain the variation in the

security/portfolio returns. Further analysis in this paper has shown that beta, with some of the

combinations of the independent variables, explains the variation in security/portfolio returns.

However, beta alone, when considered individually in the two parameter regressions, does not

explain the variation in security/portfolio returns. This casts doubt on the validity of the standard

form of CAPM.


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2.4 use fullness of review:

The review provided a perfect macro and micro picture of forecasting stock market index. Review

also helped in understanding the status of research work done in both in INDIA and ABROAD. The

review also showed that the kind of research work on the finance in INDIA is not too much

satisfactory compared to the quality work done in the abroad. This also gives an opportunity to

explore in the research work of forecasting the stock market index.


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CHAPTER 3

DESIGN

AND

METHOD OF STUDY


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3.1. Variables of the study:

Dependent Variable: SENSEX

INDEPENDENT VARIABLES:

1. Manufacturing Output Index (IIP) .2. FII.3. Call Money Rate (CR).4. GDP5. Whole Sale Price Index (WPI)6. Money Supply.(M3)7. Foreign Exchange rate (E).

SECONDARY DATA COLLECTION:

All the data is secondary data which is collected from www.rbi.org.

DATA HORIZON:1993-2010

FREQUENCY OF DATA: Monthly

Sample Number of observations of each variable:192(16(years) *12 (months))

SENSEX:

The 'BSE SENSEX' is a value-weighted index composed of 30 stocks and was started on January 1,

1986. The Sensex is regarded as the pulse of the domestic stock markets in India. It consists of the

30 largest and most actively traded stocks, representative of various sectors, on the Bombay Stock

Exchange. in INDIA These companies account for around fifty per cent of the market capitalization

of the BSE. The base value of the sensex is 100 on April 1, 1979, and the base year of BSE-

SENSEX is 1978-79.

SENSEX is one of the barometer which is used to measure the stock market efficiency of INDIA.


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Institutional investors will have a lot of influence in the management of corporations because they

will be entitled to exercise the voting rights in a company. They can actively engage incorporate

governance. Furthermore, because institutional investors have the freedom to buy and sell shares,

they can play a large part in which companies stay solvent, and which go under. Influencing theconduct of listed companies, and providing them with capital are all part of the job of investment

management.

Foreign institutional investment (FII) is expected to influence stock market development positively.

Call Money Rate (CR):

yThe money market is a market for short-term financial assets that are close substitutes ofmoney. The most important feature of a money market instrument is that it is liquid and can

be turned over quickly at low cost and provides an avenue for equilibrating the short-term

surplus funds of lenders and the requirements of borrowers. The call/notice money market

forms an important segment of the Indian money market. Under call money market, funds are

transacted on overnight basis and under notice money market; funds are transacted for the

period between 2 days and 14 days.

Banks borrow in this money market for the following propose.

To fill the gaps or temporary mismatches in funds

To meet the CRR & SLR Mandatory requirements as stipulated by the Central bank

To meet sudden demand for funds arising out of large outflows

The call money usually serves the role of equilibrating the short-term liquidity position of

banks.

The lower the interest rate in the fixed income segment, the higher the incentive for the investors to

flock to the stock market to get better returns and thus stock market should get a boost. Thus interest

rate is expected to have a negative relationship on stock market development.


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Whole Sale Price Index (WPI):

The Wholesale Price Index (WPI) is the price of a representative basket of wholesale goods . Some

countries use WPI changes as a central measure of inflation. The Wholesale Price Index or WPI is

the price of a representative basket of wholesale goods. Some countries use the changes in this index

to measure inflation in their economies, in particular India The Indian WPI figure is released

weekly on every thursday and influences stock and fixed price markets . The Wholesale Price Index

focuses on the price of goods traded between corporations, rather than goods bought by consumers,

which is measured by the Consumer Price Index. The purpose of the WPI is to monitor price

movements that reflect supply and demand in industry, manufacturing and construction. This helps

in analyzing both macroeconomic and microeconomic conditions.

Inflation rate can be used to proxy macroeconomic instability. It is expected that higher the

volatility of the underlying economic situation, the less incentive firms and savers would have to

participate in the market. At times of high macroeconomic instability, prices became signals with

large standard deviations which make it very difficult to assert whether price changes were

temporary or permanent and stock markets become more uncertain. Hence inflation is expected to

have a negative relationship with stock market development.

Money Supply.(M3):

In economics, the money supply ormoney stock is the total amount of money available in

an economy at a particular point in time. There are several ways to define "money," but standard

measures usually include currency in circulation and demand deposits (depositors' easily-accessed

assets on the books of financial institutions).

Money supply data are recorded and published, usually by the government or the central bank of the

country. Public and private sector analysts have long monitored changes in money supply because of

its possible effects on the price level, inflation and the business cycle.

That relation between money and prices is historically associated with the quantity theory of money .

There is strong empirical evidence of a direct relation between long-term price inflation and money-


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supply growth, at least for rapid increases in the amount of money in the economy. This is one

reason for the reliance on monetary policy as a means of controlling inflation.

EXCHANGE RATE:

In finance, the exchange rates (also known as the foreign-exchange rate, forex rate orFX rate)

between two currencies specify how much one currency is worth in terms of the other. It is the value

of a foreign nations currency in terms of the home nations currency.

A fall in the exchange rate should lead to more exports and more foreign exchange into the

economy, which will increase the money supply and inflation in the economy. Hence the impact of

exchange rate on stock market development is ambiguous.

3.2: objectives of study:

The objective of the study is to have deep insight into the determinants of stock marketindex in INDIAN corporate sector.

To find the importance of the macro economic variables in deciding the return of stockmarket in INDIA.

3.3: Hypothesis of the study:

H0: 1=2=3=n=0(no linear relationship between market index and the explanatory

variables)

H1: at least i0 ( linear relationship between market index and at least one of the variable)


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3.4: Design of study:

Multiple linear regression and GARCH model can used.

In linking macroeconomic variables with expected returns, we start our analysis with the

unconditional multifactor linear regression The multifactor linear regression model implies that the

expected returns of assets are related to their sensitivity to change in the state of the economy. A set

of economic variables is specified as proxies for economic risks and it is investigated whether or not

these risk factors are rewarded in the stock market. For the analysis a modified version two-step

estimation procedure is used. The set of macroeconomic variables is included in the test of CAPM

with the perspective to see whether these factors have pricing significance as against the market

index. First, the changes in asset returns are linked to the changes in economic variables, therefore,

the step one is time series regression of the excess returns of each asset on the economic variables

and market return.

The slope coefficients in these time-series regressions give estimates of assets

Sensitivity to economic state variables, called betas. The estimated sensitivity or betas are used as

independent variables in cross-sectional regressions with average assets excess returns of a

particular month being the dependent variable. The step two is cross-sectional regression estimation

done year by year

Each set of coefficients of cross section for any particular month gives estimate of risk premiums

associated with the economic variables for that month. Then these two steps are repeated for each

year and as a result time series of these estimated risk premiums are obtained. Then time series

means of these estimates are tested for statistical significance under the null hypotheses that the

means of risk premiums are equal to zero. The t-ratio for testing the hypothesis that the average

premium is zero is calculated using the standard deviation of the time series of estimated risk

premiums. Since estimated betas are used in second stage regressions, the regression involves error-

in-variables problem.


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Methodology applied:

Raw data ofSENSEX, FOREX, IIP, WPI, CALL RATE, MONEYSUPPLY, FII, GDPis collected from RBI website from 1994 to 2010 with frequency of monthly.

The same excel file uploaded to SPSS software interface to find the complete descriptivestatistics of all the variables.

Multiple regression tools is used in the SPSS to find the co-efficient of all the variablesconsidered for predicted the movement the stock market index.

Individual regression plots are drawn between the SENSEX and all other variables, so thatone can easily understand the co relation of variable with the SENSEX.

Complete correlation matrix is drawn among the variables which are used to understand thecorrelation among the variables.

Individual beta coefficients are found that to find the generalized linear multiple regressionequation with sensex as output variable and all other variables which are considered to be as

independent variables.

Later the same excel file is used as input to software EVIEWS to find the GARCHCo-efficient, so that generalized multivariate GARCH model is used to find forecasting the

index.

GARCH CO-EFFICENTS can be used understand the volatatilty of each variables. Corellogram is drawn for each variable which is considered for the analysis. In the corellogram one can find the autocorelation and partial auto correlation. When the auto correlation diminishes from value 1 to 0 as time tends infinity it indicates that

the variable is perfectly co related with its past variables.

In the GARCH analysis FII is not considered as one of the input variable for analysis as FIIhas got negative values which means that FII involved only selling the shares in that

particular month where positive value indicates bulk buys of shares in the Indian equity

market.

In the end of GARCH analysis one can get the generalized model of return on sensex withthe GARCH coefficients of each variable.


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3.5: TOOLS USED IN THE STUDY:

MULTIPLE REGRESSION:

The general purpose of multiple regression (the term was first used by Pearson, 1908) is to learn

more about the relationship between several independent or predictor variables and a dependent orcriterion variable. For example, a real estate agent might record for each listing the size of the house

(in square feet), the number of bedrooms, the average income in the respective neighborhood

according to census data, and a subjective rating of appeal of the house . Once this information has

been compiled for various houses it would be interesting to see whether and how these measures

relate to the price for which a house is sold. For example, you might learn that the number of

bedrooms is a better predictor of the price for which a house sells in a particular neighborhood than

how "pretty" the house is (subjective rating). You may also detect "outliers," that is, houses that

should really sell for more, given their location and characteristics.

Personnel professionals customarily use multiple regression procedures to determine equitable

compensation. You can determine a number of factors or dimensions such as "amount of

responsibility" (Resp) or "number of people to supervise" (No_Super) that you believe to contribute

to the value of a job. The personnel analyst then usually conducts a salary survey among comparable

companies in the market, recording the salaries and respective characteristics (i.e., values on

dimensions) for different positions. This information can be used in a multiple regression analysis tobuild a regression equation of the form:

Salary = .5*Resp + .8*No_Super.

Once this so-called regression line has been determined, the analyst can now easily construct a graph

of the expected (predicted) salaries and the actual salaries of job incumbents in his or her company.

Thus, the analyst is able to determine which position is underpaid (below the regression line) or

overpaid (above the regression line), or paid equitably.


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GARCH : ( Genaralised Autoregressive Conditional Heteroscedasticity)

An econometric term developed in 1982 by Robert F. Engle, an economist and 2003 winner of the

Nobel Prize for Economics to describe an approach to estimate volatility in financial markets. There

are several forms of GARCH modeling. The GARCH process is often preferred by financialmodeling professionals because it provides a more real-world context than other forms when trying

to predict the prices and rates of financial instruments.

The general process for a GARCH model involves three steps. The first is to estimate a best-fitting

autoregressive model; secondly, compute autocorrelations of the error term and lastly, test for

significance.

GARCH models are used by financial professionals in several arenas including trading, investing,

hedging and dealing. Two other widely-used approaches to estimating and predicting financial

volatility are the classic historical volatility (VolSD) method and the exponentially weighted moving

average volatility (VolEWMA) method.

ARCH/GARCH Processes

The simplest ARCH model can be written as follows. Suppose that X is the random variable to be

modeled,Zis a sequence of independent standard normal variables, and is a hidden variable. The

ARCH(1) model is written as

This basic model was extended by Bollerslev17 who proposed the GARCH(p,q) model written as


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Its generalization, the GARCH family of models, applies to processes such as financial time series

that exhibit volatility clustering. The GARCH(m,q) model can be further generalized to multivariate

processes by modeling not only the processs volatility but the entire variance-covariance matrix. In

this form the model is known as multi variate GARCH. Because multivariate GARCH becomes

rapidly unmanageable with the number of assets, simplified forms have been proposed. GARCH

models are not necessarily stationary insofar as their stationary depends on the coefficients of the

ARMA process. If the ARMA process is not stationary, then the process is called IGARCH. While

ARCH and GARCH models model volatility, asset pricing models require that returns depend on

volatility as higher volatility commands a higher return. Engle, Lilien, and Robins24 suggested

adding an expected return term to the GARCH equations. Equations then become

While ARCH and GARCH models are based on empirical findings of volatility clustering, Markov-

switching models are based on a generalization of the idea that a models parameters cannot be

considered stable for long periods of time. If our objective is to retain linear models as the basic

DGP, then we have to accept that parameters will change in time. Markov switching models use a

Markov chain to drive the parameters of a basic linear model. The Hamilton model, for example,

uses a Markov chain to drive the parameters of a random walk. In a more general Markov-switching

VAR, a Markov chain drives the parameters of a VAR model.


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CHAPTER 4:

ANALYSIS

OF

DATA


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Descriptive statistics.

RETURN

EXCHANG

E IIP WPI MONEY CALL GDP

Mean 0.797325 3.740169 5.196449 5.259042 14.23861 8.035440 14.66596

Median 1.579049 3.776318 5.148657 5.075174 14.23431 6.750000 14.63150

Maximum 25.33067 3.936300 5.853638 7.355588 15.54472 34.83000 15.58508

Minimum -27.88713 3.445693 4.604170 4.605170 13.00994 0.730000 13.73781

Std. Dev. 7.270688 0.133011 0.306449 0.612863 0.726557 5.098787 0.501088

Skewness -0.288658 -0.950429 0.163141 1.865643 0.062950 2.797910 0.045450

Kurtosis 4.149947 2.783047 2.058276 5.571073 1.893234 13.13434 2.045982

Jarque-Bera 13.24538 29.43517 7.987817 165.1188 9.926249 1077.729 7.385579

Probability 0.001330 0.000000 0.018428 0.000000 0.006991 0.000000 0.024902

Sum 153.0864 721.8527 1002.915 1014.995 2733.814 1550.840 2830.530

Sum Sq.

Dev. 10096.81 3.396831 18.03088 72.11548 100.8259 4991.544 48.20919

Observations 192 193 193 193 192 193 193

TABLE 1: Descriptive statistics Output of EVIEWS SOFTWARE


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INTREPRETATION:

Only FII variable is missing in the output as the software does not accept negative values of FII.

After return of sensex the variable call rate has got the maximum standard deviation whichindicates that both call rate and sensex returns are more volatile in nature as a part

fundamental statistical analysis.

Call rate and WPI have higher kurtosis which means that more of the variance is the result ofinfrequent extreme deviations, as opposed to frequent modestly sized deviations.

TABLE 2: SPSS OUTPUT OF CO-EFFICIENTS OF REGRESSION

Generalized Multiple regression model;

SENSEX=10018.277-342.274*(EXCHG)+0.002*FII+34.451*IIP-

5.407*WPI+0.003*M3+0*GDP


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RESULT OF HYPOTHESIS:

NULL HYPOTHESEIS is rejected as various coefficients are having NON zero values.

Residuals Statistics

Minimum Maximum Mean

Std.

Deviation N

Predicted Value 2305.8772 17396.7168 6905.0691 4539.56986 192

Residual -4064.09863 3833.47607 .00000 1328.33863 192

Std. Predicted

Value

-1.013 2.311 .000 1.000 192

Std. Residual -3.003 2.833 .000 .982 192

a. Dependent Variable: SENSEXTABLE 3: SPSS OUTPUT OF RESIDUALS STATISTICS.

INTREPRETATION: GDP value has less got lesser value coefficient where as IIP has got the

higher positive co-efficient when compared to high negative coefficient for EXCHANGE RATE,

which indicates that the variables has got both negative and positive influence on the movement of

stock market index. From residual statistics one can easily find out that there more deviation among

forecasting of sensex based on the variables.


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TABLE 4: SPSS OUTPUT OF CORRELATION COEFFICIENTS AMONG VARIABLES.

INTREPREATION:

Sensex has got the more correlation with GDP, M3, and IIP, when compared to lowercorrelation with call rate.

Exchange rate has got more correlation with GDP, IIP numbers which indicates thatexchange rates are more decided on the movement on GDP and IIP.

M3 has negative correlation with call rate but high correlation with IIP. FII move with IIP and GDP which means that growth in the economy and production in

INDIA makes more investment from overseas investors.

Call rate has got negative co-relation with all the variables which indicates that rise in the callrates always has negative impact on the economy.

WPI has got more correlation with M3 when compared to other variables which always saysthat more the money supply more the impact on WPI.


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GRAPH 1: Partial regression plot between sensex and ex-rate

INTREPRETATION:

Sensex is negatively correlated with the exchange rate, which indicates that sensex will move

opposite direction of exchange rate. The exchange rate increase will make a negative impact on the

equity market index.A fall in the exchange rate should lead to more exports and more foreign

exchange into the economy, which will increase the money supply and inflation in the economy.

Hence the impact of exchange rate on stock market development is negative.


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GRAPH 2: Partial regression plot between SENSEX and FII

INTREPRETATION:

The regression plot shows that sensex movement with FII flows is quiet ambiguous , not able to

predict the movement of sensex on the basis of direction of FII. The FII has very less importance

on the prediction of sensex in the future. It also indicates that FII and sensex had clustered on one

particular time horizon, which also means that FII has invested in the equity market for lesser

number of years.


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GRAPH 3: Partial regression plot between SENSEX and IIP

INTREPRETATION:

The regression plot shows that sensex movement with IIP flows is predictable, i.e able to predict the

movement of sensex on the basis of direction of IIP. The IIP data has very high importance on the prediction of sensex in the future. The plot also shows that sensex is moving with IIP for more

extent. The sensex has got the better correlation with the IIP data, which indicates that

manufacturing activity has got more positive impact on the equity market index.


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GRAPH 4: Partial regression plot between SENSEX and GDP

The regression plot shows that sensex movement with GDP flows is less predictable, i.e not able to

predict the movement of sensex on the basis of direction of GDP. The data has very high

importance on the prediction of sensex in the future. The plot also shows that sensex is moving with

GDP for more extent. The sensex has got the better correlation with the GDP data, which indicates

that income level has got more positive impact on the equity market index.


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GRAPH 5 : Partial regression plot between SENSEX and WPI

INTREPRETATION:

The regression plot shows that sensex movement with WPI flows is predictable, i.e able to predict

the movement of sensex on the basis of direction of WPI. The WPI data has very high importance on

the prediction of sensex in the future. The plot also shows that sensex is moving opposite with WPI

for more extent. The sensex has got the better correlation with the WPI data, which indicates that

inflationary activity has got more negative impact on the equity market index.


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GRAPH 6: Partial regression plot between sensex andM3

The regression plot shows that sensex movement with M3 flows is un predictable, i.e not able to

predict the movement of sensex on the basis of direction of M3. The M3 data has very high

importance on the prediction of sensex in the future. The plot also shows that sensex is moving with

M3 for more extent. The sensex has got the lesser correlation with the M3 data, which indicates that

manufacturing activity has got more diversified impact on the equity market index.


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GRAPH 7: Partial regression plot between SENSEX and CALL RATE

INTREPRETATION:

The regression plot shows that sensex movement with CALL RATE flows is un predictable, i.e not

able to predict the movement of sensex on the basis of direction of CALL RATE. The CALL RATE

data has very high importance on the prediction of sensex in the future . The plot also shows that

sensex is moving with CALL RATE for more extent. The sensex has got the better correlation with

the CALL RATE data, which indicates that manufacturing activity has got more positive impact on

the equity market index.


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CALL RATE:

GRAPH 8:CORRELOGRAM for CALL RATE:

INTREPRETATION:

The auto correlation and partial auto correlation graph shows call rate is completely alternating

series which does have both positive and negative correlation with various lags. This means that the

predictability of call rate in the future values based on the past values is more difficult.

-0.4

-0.2

0

0.2

0.4

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Auto correlation of call rate

AC

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Partial Auto correlation of call rate

PAC


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EXCHANGE RATE:

GRAPH 9:CORRELOGRAM for EXCHANGE RATE


series which does have both positive correlation with some set of lags and negative correlation with

some set of This means that the predictability of exchange rate in the future values based on thepast values is lesser difficult as it has got fixed correlation with for some set of lags.

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Auto correlation of Exchange rate

-0.2

-0.1

0

0.1

0.2

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Partial auto correlation of Exchange

Rate


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GDP:

GRAPH 10:CORRELOGRAM for GDP

The auto correlation and partial auto correlation graph shows GDP is not alternating series which

have only positive correlation with almost all lags. This means that the predictability of GDP in the

future values based on the past values is quiet easy. The graphs show that GDP data is stationary

series.

It is more stationery series without cyclicity.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Partial Auto correlation of GDP

PAC

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Auto correlation of GDP


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IIP: ( INDEX OF INDUSTRIAL PRODUCTION)

GRAPH 11 :CORRELOGRAM for IIP

The auto correlation and partial auto correlation graph shows IIP is completely alternating series

which does have both positive and negative correlation with various lags. This means that thepredictability of call rate in the future values based on the past values is more difficult.

The extent of cyclicity in the IIP is less.

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Auto correlation of IIP

-1

-0.5

0

0.5

1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Partial Auto correlation of IIP

Series1


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MONEY SUPPLY:

GRAPH 12:CORRELOGRAM for MONEY SUPPLY


series which does have both positive and negative correlation with various lags. The M3 data has gotthe alternating variation which means that money supply is completely depend on the economic

cycle. It has got the cyclic variation on the whole time horizon which is considered.

There is cyclicity in the money supply over the period.

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Partial Auto correlation of Money

supply

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Auto correlation of Money supply

Series1


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WPI ( WHOLE SALE PRICE INDEX)

GRAPH 13:CORRELOGRAM for WPI

The auto correlation and partial auto correlation graph shows WPI is not alternating series which

have only positive correlation with almost all lags. This means that the predictability of WPI in thefuture values based on the past values is quiet easy. The graphs show that WPI data is stationary

series. No cyclicity in the WPI data.

0

0.2

0.4

0.6

0.8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Auto correlation of WPI

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Partial correlation of WPI


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SENSEX:

GRAPH 14:CORRELOGRAM for RETURN ON SENSEX

The auto correlation and partial auto correlation graph shows RETURN ON SENSEX is not

alternating series which have only positive correlation and negative correlation with various lags.

This means that the predictability of RETURN ON SENSEX in the future values based on the past

values is not easy. The graphs show that RETURN data is NOT stationary series.

That means sensex is not correlated with its past data so always there are some drivers to move the

sensex in particular.

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Auto correlation of Return of Sensex

Series1

-0.6

-0.4

-0.2

0

0.2

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Partial Auto correlation of Return of

sensex


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GARCH: (TABLE 5)

Dependent Variable: RETURN

Method: ML - ARCH (Marquardt) - Normal distribution

Date: 01/31/11 Time: 00:09

Sample (adjusted): 2 192

Included observations: 191 after adjustments

Convergence achieved after 45 iterations

Variance backcast: ON

GARCH = C(3) + C(4)*RESID(-1)^2 + C(5)*GARCH(-1) + C(6)*CALL +

C(7)*EXCHANGE + C(8)*GDP + C(9)*IIP + C(10)*MONEY +

C(11)*WPI

Coefficient Std. Error z-Statistic Prob.

C 1.247380 0.090115 13.84215 0.0000

RETURN(-1) 0.163979 0.079080 2.073578 0.0381

Variance Equation

C 177.0766 524.5293 0.337591 0.7357

RESID(-1)^2 0.077809 0.021220 3.666698 0.0002

GARCH(-1) -1.026436 0.005231 -196.2327 0.0000

CALL -0.468240 0.030027 -15.59400 0.0000

EXCHANGE 242.0789 91.76407 2.638058 0.0083

GDP -53.33163 138.4341 -0.385249 0.7001

IIP 64.38223 24.09387 2.672141 0.0075

MONEY -76.76519 120.6444 -0.636293 0.5246

WPI 107.4097 47.23356 2.274011 0.0230

R-squared 0.012493 Mean dependent var 0.810982

Adjusted R-squared -0.042369 S.D. dependent var 7.287326

S.E. of regression 7.440102 Akaike info criterion 6.765878

Sum squared resid 9963.922 Schwarz criterion 6.953182

Log likelihood -635.1414 F-statistic 0.227715

Durbin-Watson stat 2.067009 Prob(F-statistic) 0.993332


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RETURN = 177.0766 + 0.077809*RESID (-1) ^2 + 1.026436*

GARCH (-1) -0.468240*CALL+242.0789*EXCHANGE --

53.33163*GDP + 64.38223*IIP -76.76519*MONEY +

107.4097*WPI.

A MULTI VARIATE GARCH MODEL FOR ONE MONTH RETURN OF SENSEX

INTREPRETATION:

Exchange rate, IIP, WPI has got positive coefficients which indicate that these variables areboosting variables to move forward the equity market index.

Call rate, Money supply, GDP has got negative coefficients which indicate these variablesare demotivating factors for the forward movement of sensex.

.R-SQUARED value is 0.0124 which indicates that the prediction factor has got lesssignificance.

Durbin-Watson stat value is 2.06707 which indicate that there is no autocorrelation in thereturn of sensex.

Akaike info criterion has to be between 1 and 2 which indicates that goodness of fitting ofdata with statistics, but its value 6.765 which indicates that it is difficult to make inferences

on the results got statistically.

S.E of regression is low which indicates low error in estimation.


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CHAPTER -5

SUMMARY

AND

CONCLUSIONS


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5.1 Major findings

There is always more volatility in the return of sensex. Exchange rate, IIP, WPI are more motivating factors for the forward movement of stock

market index.

WPI is motivating for the movement of sensex in forward direction though it soundsparadoxical but it is irony to understand insight into it.

The GDP factor unfortunately considered as negative factor for the equity market index, butit is quiet questionable and the arguable.

The variables selected are having mixed response for the movement of the equity marketindex.

5.2 Conclusions.

The generalized linear model of multiple regression has shown that GDP has zerocontribution for the movement of sensex.

As per GARCH based model application one came to know that GDP has negativecontribution for the movement of the sensex.

It indicates that GARCH based model application has got more efficiency in terms ofestimation of the return of index.

The movement of equity market index has got the more drivers for its movement in bothforward and backward direction.


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5.3 Educational implications.

Got to know that there are many generalized linear time series models like GARCH, ARIMA..etc. Volatility can only analyzed by using econometrical models like ARCH, ARIMA. Econometrical models are necessary to understand the time series models.

5.4 LIMITATIONS OF THE STUDY:

The research on the study of implications of macroeconomic variables on stock market index has gotless significance in INDIA when compared to study done on abroad.

The multiple regressions has got limitation on forecasting the complex variable like SENSEX return. Lot of data transformation needed to give as inputs for the GARCH model. Perfection in the forecasting the index is questionable on the basis of multiple regression model . Non availability of free software like EVIEWS on internet. Lot of calculations needed to arrive at the output of GARCH MODEL. GARCH MODEL output has got the both residuals and LAG Factors which makes quiet difficult to

compare the predicted value and actual value.

FII variable is not considered in GARCH as it does not accept the negative values .

5.5. Suggestions for further study.

The further more variables can be taken to understand the movement of sensexlike...Corporate earnings of companies which are components of sensex, market

capitalization ratio which means amount of new capitalization raised through stock

offerings. as percentage of GDP.

The same study can be studied to forecast the sensex on ARIMA (AUTO REGRESSIVEINTEGRATED MOVING AVERAGE) basis.

The same kind of study can be further studied by using software like MATLAB,

FINANCIAL TOOL BOX by (MATHWORKS), and R.


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14-BIBLIOGRAPHY

WEBSITES:

WWW.NSE-INDIA.COM

WWW.JSTOR.ORG WWW.EBSCHO.ORG WWW.EBSCOHOST.COM WWW.MSE.AC.IN ( Madras school of economics) WWW.IIMAHD.ERNET.IN WWW.EUROJOURNALS.COM WWW.EMERALDINSIGHT.COM/JOURNALS.HTML WWW.MENTORMYPROJECT.COM. WWW.MUIC.MAHIDOL.AC.TH


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REFERENCES:

Serialno

Author Title Edition Pages

1) Attiya Y. Javid and

Eatzaz Ahmad

Testing multifactor capital asset

pricing model in case of Pakistani

market

4th 1-25

2) Ahmad Eatzaz and

Badar-u-Zaman (1999)

Volatility and Stock Return at

Karachi Stock Exchange.

2ND

25-37

3) Antoniou, A., I.

Garrett and Priestley,

R.

Macroeconomic Variables as

Common Pervasive risk factors

and the Empirical Content of

Arbitrage Pricing Theory.

- 221-

240

4) Chen, Nai-Fu, Roll,

Richard and Stephen

A. Ross

Economic Forces and the Stock

Market.

59.3 383-

403

5) Desai, V. S., &

Bharati, R.,

A comparison of linear regression

and neural network methods for

predicting excess returns on large

stocks.

- 57-62

6) T Manjunatha and T

Mallikarjunappa

Bivariate Analysis of Capital Asset

Pricing Model in Indian Capital

Market

- 10-20


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Documents

Stock Market Index Forecasting Model Using the GARCH Tool