An empirical study of macroeconomic factors and stock market an indian perspective

EDHEC Business School 1


An Empirical Study ofMacroeconomic Factors and StockMarket: An Indian Perspective

Saurabh YadavEDHEC Business School

Master’s in Risk and Investment [email protected]

June 26, 2012

EDHEC Business School

Abstract

This thesis is an empirical study of relationship between Indian stockmarkets and macro economy. There is a huge literature about such kind ofempirical studies but mostly on US/UK stock markets and macroeconomicindicators. This study is similar to many of the earlier studies in someaspects, so it uses econometric tools used in earlier studies but at the sametime this study differentiates itself from other studies in the sense it usesIndian markets and macroeconomic data for analysing the relationshipand it also tries to analyse the impact of global economy on the Indianmarkets. The period that will be used for the study will be from 1990to 2011. We have chosen this period as it represents big regulatory andstructural changes in Indian economy. So, an analysis of this period canprovide us with insights to how some regulatory and structural changesimpact the economy and asset prices in that country. In this study we willuse Unit root tests, cointegration, Ljung-Box Q test and multivariate VARanalysis for analysing each macro economic and asset prices time seriesindividually and to build a model that can analyse the impact of one overthe other. Also, we will conduct Granger’s Causality test and Impulseresponse analysis between Stock market and macro economic indicatorsto analyze the impact of macro economic news/shocks on India Stockindex (BSE).


Acknowledgment

I am thankful to Professor Robert Kimmel for his comments and guidanceon the subject. He has been a constant source of inspiration and a good men-tor, from whom I learned a lot. I am also grateful to Stoyan Stoyanov, MarcRakotomalala, Aishwarya Iyer, Wen lei, Lixia Loh for some great insights intothe subject. Their timely comments and suggestions on empirical tests helpedme improve the statistical significance of my tests. I thank EDHEC Risk In-stitute for allowing me to use their resources to get the data from various dataproviders. In the end i’ll like to thank my parents and my sister for constantsupport and motivation without which it would have been impossible to climbthis arduous path.

Regards,Saurabh YADAV


CONTENTS

Contents

1 Introduction 7

2 Literature Review 9

3 Data 133.1 Description of Macroeconomic Indicators . . . . . . . . . . . . . 133.2 Description of Stock Market Indices . . . . . . . . . . . . . . . . 14

4 Methodology 154.1 Construction of Time Series . . . . . . . . . . . . . . . . . . . . 154.2 Unit Root Test and Stationarity . . . . . . . . . . . . . . . . . . . 15

4.2.1 Mathematical representation of Stationary series and unitroot test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2.2 Augmented Dickey Fuller Unit Root Test . . . . . . . . . 174.3 Testing Long Term Relationships . . . . . . . . . . . . . . . . . . 18

4.3.1 Johansen test for Cointegration . . . . . . . . . . . . . . . 184.4 Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5 Results 21

6 Conclusions 24

7 Graphs and Tables 257.1 Graphs of Time series . . . . . . . . . . . . . . . . . . . . . . . . 257.2 Graphs of Time Series - Differenced . . . . . . . . . . . . . . . . 297.3 Correlograms of Time series . . . . . . . . . . . . . . . . . . . . . 337.4 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

7.4.1 Table for Unit root test of Time series . . . . . . . . . . . 407.4.2 Tables for Unit root test of Differenced time series . . . . 407.4.3 Tables for Residual based test of cointegration . . . . . . . 407.4.4 Johansen cointegration test . . . . . . . . . . . . . . . . . 437.4.5 Impulse response tests . . . . . . . . . . . . . . . . . . . . 467.4.6 Granger causality test between IP and BSE . . . . . . . . 49

8 Bibliography 50


1 INTRODUCTION

1 Introduction

In the past few decades there has been a growing interest among academiciansand practitioners about the relationship between macroeconomic variables andasset prices, mainly stocks and house prices. In a good and expanding economy,prices of stocks are supposed to increase as there is an increase in expectationof large future cash flows/ profits for the companies and various role playersin the economy. Similarly, during a bad or downward spiralling economy theexpectation of large future cash flows and profits decrease and consequently theprice of stocks decrease.Stock markets are representative of economy of a country and investors belief.They are able to capture macro economic movements in the economy as well asidiosyncratic factors related to each company or industry. As Stock prices arereal time and are more frequent than macroeconomic releases they are betterreflector of changes in domestic and global economy and can predict the move-ment of macroeconomic indicators. In other words stock markets are a leadingindicator of the economy.Markets respond to different macroeconomic indicators in different ways. Theresponse of Stock markets to any macroeconomic news is dependent on how thenews will effect the profits and interest rates. The price of the stock accordingto the Discounted Cash Flow formula is:

Pt =Div1

(1 + r1)1+

Div2(1 + r2)2

+ . . .+Divt

(1 + rt)t(1)

As both dividends and interest rates enter into the formula for value of astock the reaction of stock price to a macro news will depend on how the newseffect the discounting factor ( Interest rates ) and future profits of the com-panies. Macro economic factors that project brighter times and more profitsfor the companies like, increasing Industrial production, Increasing M1 moneysupply, good consumer confidence levels will have a positive effect on the stockprices. Whereas, macro news that point to economic recession or slow growthlike, decreasing Industrial production coupled with Rising interest rates, Risein inflation, rise in unemployment, etc. will have a downward effect on stockprices.First people to do an empirical study on this subject were Eugene Fama andKenneth French. In their 1981 paper ”Stock returns, Real activity, Inflationand money” they analysed the relationship between stock returns, real activityinflation and money supply using macro economic data. After that study therehas been a barrage of studies on relationship between stock returns and macroeconomic factors based on US and UK data. Another important paper pub-lished on this research was by Chen,Roll and Ross (1986) who analysed whetherinnovations in the macroeconomic variables are risks that are awarded in thestock markets. They found that macroeconomic variables like, spread betweenlong and short interest rates, expected and unexpected inflation, Industrial pro-duction are some of the factors that are awarded by the markets. Further, theArbitrage pricing theory (APT) of Ross (1976) posits relation between stockprices and certain macro-economic variables. In the last decade or so the focusfor these kind of studies have started to shift from developed world economies todeveloping world economies. As developing world economies have shown signs


1 INTRODUCTION

of huge growth potential and leading the economies globally out of recessions,this motivates us to research on developing markets, like India. Such a studywill help us to find the relation between stock market and macroeconomic indi-cators and give a new insight to foreign investors, academicians,policy makers,traders and domestic investors.This study is important in a sense it provides an insight to how are Indian stockmarkets are related to its macroeconomic variables and global macro/micro eco-nomic factors. This study will also help us in analysing whether the Indian stockmarkets have become coupled to global factors or are they still dominated bydomestic economic factors.The focus of this study is on relation between Indian stock market, representedby BSE Sensex, and domestic macroeconomic factors and global factors repre-sented by Standard and Poor’s 500 Index. This study builds on earlier studiesdone in this area but also open some new doors for further research. It is sim-ilar to some earlier studies in a respect that it uses data, macro and microfactors and econometrics tools used in previous studies but at the same time itdifferentiates itself from earlier studies in a sense that it is done on a marketthat is still developing. Also, the time period used in the analysis is a periodwhere Indian market has undergone lot of regulatory changes that has createda structural change in the market. Further, in this study I’ll analyse whetherthe Indian markets are driven mainly by Domestic factors or do global factorshave more influence on Indian markets. To analyse the impact of internationalfactors I’ll use Standard and Poor’s 500 Index and USDINR exchange rate as asubstitute of global factors and to model domestic demand I’ll use macro factorslike Industrial production, M1 money supply, Consumer Price Index and Pro-ducer price Index. The outline of the thesis is as followings: Section 2 providesa literature review of the studies done earlier in this area, Section 3 provides adetailed description of the data used in the study Section 4 provides a detaileddescription of the methodology and various econometric tools that will be usedin the study, Section 5 provides the results of the study and Section 6 providesthe conclusion of the study.


2 LITERATURE REVIEW

2 Literature Review

Many studies and researchers have tried to find factors that can explain stockreturns. The most famous and earliest model is the Capital Asset Pricing Model(CAPM), developed by Sharpe (1964), Lintner (1965), Mossin (1967) and Black(1972). The concept of this single factor model is developed from diversifi-cation introduced by Markowitz (1952). In CAPM model the expected stockreturns can be explained with the help of Risk free rate and one risk factor,Market. CAPM says that the systematic risk can be captured by sensitivenessof each stock to change in overall market, which is measured by Beta. Accordingto CAPM, the market factor is the only factor determining the stock returns.CAPM was a revolutionary model. It changed the way people looked at thestock returns as something that is vary arbitrary. As it is very easy to under-stand and use, CAPM is very popular as the model used to determine the stockreturn in most of finance textbooks and used by many practitioners in stockmarket.However, the numerous set of assumptions made in deriving CAPM made itinconsistent with the real world and led to criticism of CAPM. To overcomethe limitations and assumptions made in CAPM many scholars came up withmulti- factor models like Fama-French three factor model, APT model, etc. InFama-French model they try to explain stock returns with help of three factors,market,small minus big and value minus growth. the model was able to explainthe returns based on these risk factors for some time before it failed. Therehave been many studies on failure of Fama-French model and markets where itis not applicable.The macroeconomic models of explaining stock returns started with APT (Ar-bitrage Pricing Theory) by Ross (1976), which was later refined by Roll andRoss (1980). APT is a multi-factor model and claims that the stock return canbe explained by unexpected changes or shocks in multiple factors. Chen,Rolland Ross (1986) perform the empirical study for APT model and identify thatsurprise or shock in macroeconomic variables can explain the stock return sig-nificantly. The variables used in their study are Industrial production index,default risk premium that can measure the confidence of investors, and changein yield curve that can be measured by term premium.The study of macroeconomic factors in explaining stock returns have been pop-ular since then. Stock price is present value of all discounted future cash flows.If a firm is performing well then the expectation of large future cash flows risesand consequently the stock price rises. On the other hand if a firm is performingbad for couple of years then the expectation of big future cash flows decreaseand in turn the stock price fall. This is a micro and idiosyncratic explanation ofstock prices and returns. But, the future cash flows of a stock does not dependsolely on the company’s performance or profits/loss. The systematic factor canhave a huge impact on the cash flows of not only one but many companies. Thesystematic factor here refers to macro economic variables. The state of Macroeconomic conditions lead to changes in Monetary and regulatory policies by thegovernment and which in turn affects the stock prices. For example a countrywith good economic conditions, represented by its Industrial production index,GDP, CPI, Interest rates will create an environment that is conducive for thegrowth of companies by lowering borrowing rates and other open market opera-tions. So, all macroeconomic factors that can influence future cash flows or the


2 LITERATURE REVIEW

discount rate by which the cash flows are discounted should have an influenceon the stock price.Many researcher have studies the relationship between stock prices and macroeconomic variables and tried to explain the affect of one over the other. Fama(1981) tries to establish a relationship between stock returns, real activity, infla-tion and money. In his paper he finds that Stock returns have positive relationwith real output and money supply but a negative relation with inflation. Heexplains that negative relation between stock returns and inflation is induced bynegative relation between real output, approximated by Industrial production,and inflation. This negative relationship between inflation and real activityis explained by money demand theory and quantity theory of money. Fama(1990) explains that measuring the total return variation explained by shocksto expected cash flows, time-varying expected returns, and shocks to expectedreturns is one way to judge the rationality of stock prices. In his paper hefinds that growth rates of production, used to proxy for shocks to expected cashflows, explain 45% of return variance. Chen,Roll and Ross (1986) explored therelationship between a set of economic variables and their systematic influenceon stock market returns. They found that Industrial production, changes inrisk premium, twists in yield curve had strong relationship and impact on stockreturns. A somewhat weaker effect was found for measures of unanticipatedinflation and changes in expected inflation during periods when these variableswere highly volatile. They concluded that stock returns were exposed to sys-tematic economic news, that they are priced in accordance to their exposures,and that the news can be measured as innovation in state variables. Chen(1991) found that state variables that are priced are those that can forecastchanges in the investment and consumption opportunity set. According to hisresearch, default spread, the term spread, the one-month T-Bill rate, the laggedindustrial production growth rate, and the dividend-price ration are importantdeterminants of future stock market returns. Bulmash and Trivoli (1991) showthe effect of business cycle movements on the relationship between stock returnsand money growth.An interesting paper in this field of research is by Fama (1990) and Schwert(1990). In the paper they claim that there are three explanations for the stronglink between stock prices and real economic activity:

“First, information about the future real activity may be reflected in stockprices well before it occurs — this is essentially the notion that stock pricesare a leading indicator for the well-being of the economy. Second, changesin discount rates may affect stock prices and real investment similarly, butthe output from real investment doesn’t appear for some time after it ismade. Third, changes in stock prices are changes in wealth, and thiscan affect the demand for consumption and investment goods” [Schwert(1990),p.1237]

Campbell and Ammer (1993) use a VAR approach to model the simulta-neous interactions between the stock and bond markets, since most previousworks do not address the channels through which the macroeconomic activityinfluences the stock prices. One example could be that industrial productioncould be linked to changing expectations of future cash flows (Balvers at al.1990). On the other hand, interest rate innovations could be the driving factor


2 LITERATURE REVIEW

in determining both industrial production (due to change in investment) andstock prices (due to change in the discounted present value of future cash flows).A VAR analysis can distinguish these possibilities. Mukherjee and Naka (1995)show a long-term relationship between the Japanese stock price and real macroe-conomic variables. Dr. Nishat (2004) studies the long term association amongmacroeconomic variables like money supply, CPI,IPI, and foreign exchange rateand stock markets in Pakistan. The results show that there are causal relation-ship among the stock price and macroeconomic variables. He uses data from1974 to 2004 in his study. As most of the financial time series are non station-ary in levels he uses unit root technique to make data stationary. Fazal Hussianand Tariq Massod (2001) used variables like investment, GDP and consumptionemploying Granger’s causality test to find relationship between macro factorsand stock markets. They show that at two lags all macroeconomic variableshave highly significant effect on stock prices. James et al. (1985) use a VARMAanalysis for investigating relationship between macro economy and stock mar-ket. Using VARMA analysis for finding causal relationship between factors isa better technique as the procedure does not preclude any causal structure apriori since it allows feedback among variables. Thus, the VARMA approachallow whatever causal relationship exist to emerge from the data. They findlinkages between real activity and stock returns and real activity and inflation.Also, they find that stock returns signal changes in the monetary base. Sincestock returns also signal changes in expected real activity, this suggests a linkbetween the money supply and expected real activity that is consistent with themoney supply explanation offered by Geske and Roll.In recent years the focus of these kind of studies have shifted from developedeconomies to developing economies. As developing economies are the economiesthat see a lot of structural and monetary policy changes an analysis of relation-ship between macro and micro can provide new insights. Also, one can analysethe effects of monetary policies on the asset prices especially on stock prices.Tangjitprom (2012) study of macroeconomic factors like unemployment rate,interest rate, inflation rate and exchange rate and stock market of Thailand con-cludes that macroeconomic factors significantly explain stock returns. He alsofinds that for Thailand unemployment rate and inflation rate are insignificant todetermine the stock returns. The reason he provides is that the unemploymentrate and inflation rate are not timely and there could be some lags before thedata becomes available. Also, Granger’s test to examine lead-lag relationshipamong the factors reveal that only few macroeconomic variables could predictthe future stock returns whereas the stock returns can predict most of futuremacro economic variables. This implies that performance of stock markets canbe a leading indicator for future macroeconomic conditions. Ali (2011) study ofimpact of macro and micro factors on stock returns reveals that inflation andforeign remittance have negative influence and industrial production index havepositive impact on stock markets. Also he didn’t found any Granger’s Causal-ity between stock markets and any of the explanatory variables. This lack ofGranger’s causality reveals the evidence of informationally inefficient markets.Ali uses a multivariate regression analysis on standard OLD formula for estimat-ing the relationship. Hosseini et al. (2011) tested the relationship between stockmarkets and four macro economic variables namely crude oil prices, Money sup-ply, Industrial production and inflation rate in China and India. They used aperiod of 1999 to 2009 for analysis. As most of the economic time series have unit


2 LITERATURE REVIEW

root, they first used the Augmented Dickey Fuller unit root test and found theunderlying series to be non-stationary at levels but stationary after in difference.Also, the use of Jhonson-Juselius (1990) Multivariate cointegration and VectorError Correction model technique, indicate that there are both long and shortrun linkages between macroeconomic variable and stock market index in each ofthe two countries. Their analysis shows that in long run the impact of increasein prices of crude oil for China is positive but for India is negative. In termsof money supply, the impact on Indian stock market is negative, but for China,there is a positive impact. The effect of Industrial production is negative onlyin China. In addition the effect of increases in inflation on these stock marketsis positive in both countries. Wickremasinghe (2006) analysed the relationshipbetween stock prices and macroeconomic variables in Sri Lanka. He used theUnit root tests, Jhonson’s test, Error-correction model, variance decomposi-tion and impulse response to analyse the relationships. His findings indicatethat there is both long term and short term causal relationship between stockprices and macroeconomic variables in Sri Lanka. The result indicate that thestock prices can be predicted from certain macroeconomic variables and henceviolate the validity of the semi-strong version of efficient market hypothesis.Ahmed (2008) investigates the causal relationship between Indian macroeco-nomic factors like Industrial Production, Exports, Foreign direct investment,Money supply, exchange rate, interest rate and stock market indices NSE NiftyIndex and BSE Sensex. For finding the long term relationship he applies Jo-hansen’s cointegration and Toda and Yamamoto Granger Causality tests. Foranalysing the Impulse response and variance decomposition he uses bivariateVAR. His findings reveal that stock prices in India lead macroeconomic activityexcept movement in interest rate. Interest rate seem to lead the stock price.The study also reveals that movement of stock prices is not only the outcomeof behaviour of key macro economic variables but it is also one of the causesof movement in other macro dimensions in the economy. An important paperby Bilson et al. (2001) argues that emerging markets local factors are moreimportant than global factors. They find that for emerging markets are at leastpartially segmented from global capital markets. The global factors are proxiedby world market returns and local factors by set of macro economic variableslike money supply, prices, real activity and exchange rate. Some evidence isfound that local factors are significant in their association with emerging equitymarket returns above than that explained by the world factor. When they usea larger set of variables the explanatory power of the model improves substan-tially such that they are able to explain a large amount of return variation formost emerging markets.


3 DATA

3 Data

3.1 Description of Macroeconomic Indicators

One of the biggest problems when conducting a research with macroeconomicdata is the frequency of the data. Most of the macroeconomic indicator timeseries are yearly,quarterly or monthly time series. This low frequency of themacroeconomic indicators results in very few data points for conducting a anal-ysis that is robust. A possible cure for the problem is to use longer time periodsto incorporate more data points for macroeconomic variables. But, anotherproblem that we face when we look at the macroeconomic indicators for Asiancountries is reporting of the data. For most of the Asian countries the macroe-conomic data doesn’t have a long history and same can be said about historyof Indian macroeconomic variables. So, in this research we have used a timeperiod for which we can find data for most of the macroeconomic indicators. Inthis paper we use a time period of 20 years starting from 1990 to 2011. Thistime period in Indian economy is representative of many structural and mone-tary policy changes like liberalization of India markets. Also as the time periodis long it gives us enough data point for each macroeconomic factors to do arobust empirical analysis.When one starts to build a model of interaction between macro and micro eco-nomic factors one dominant and important question one faces is, among themyriad of macro indicators available for an economy which factors to chooseto incorporate in the model. If one chooses macroeconomic factors that arehighly correlated among themselves then the power of test results decrease asit may result in a model where the macro indicators are able to explain mostof the movement of micro factors but the macro factors may not be relevant.To circumvent this problem we use variables that have been tested in earlierresearches and that have been proven to have effect on stock markets. I alsotest a few macro factors that have some financial theory behind them that con-nect them to stock markets. Ali (2011), Wickremasinghe (2006), Bilson et.al(2001) and Bailey (1996) find that Industrial production, CPI, exchange rate,M1 money supply, GDP are few of the macro economic factors that can signifi-cantly explain stock returns. Sahu(2011), Ahmed(2008), Tripathy(2011) studyon Indian markets specifically show that Industrial Production, Exchange rate,Inflation index are macro economic indicators that have a strong positive ornegative relationship with the stock markets. So, in our study we test 5 macroeconomic variables namely M1 money supply, Consumer and Producer price In-dex, Industrial production, Exchange rate. The time period for these indicatorsis from 1990-2011. The data for Inflation indices, Industrial production andexchange rate has been pulled from Bloomberg c©and Datastream c©. The datahas been processed for errors and missing values. Data for M1 money supplyhas been pulled from RBI website. For most of the indices like inflation andIndustrial production index, the base year has been changed to 1990. Also, assome of the indices are in levels and some in actual figures (M1 money supply),we convert all of the indicators to level form (starting at 100 in 1990).


3 DATA

3.2 Description of Stock Market Indices

Compared to Macro Indicators, stock market data is relatively easy to find andhas considerably long history. Also, the stock market data is a real time data soit has a very high frequency of seconds. Here, in our analysis we will make use ofBSE (Bombay Stock Exchange) as representation of Indian markets and SP500(Standard and Poor’s 500 Index) as representation of global factors. BSE is amarket cap-weighted of 30 stocks. It is the oldest Index in the Asian markets(established in 1875) and have had a long history. We choose this index as it isthe Index that represent the most liquid and traded stocks of the Indian stockmarket. Also, the index is most traded index in India and a good representationof trade prices of the stocks. Even in terms of an orderly growth, much beforethe actual legislations were enacted, BSE Limited had formulated a compre-hensive set of Rules and Regulations for the securities market. It had also laiddown best practices which were adopted subsequently by 23 stock exchangeswhich were set up after India gained its independence. Our choice of SP500 isbased on the fact that it has a long history and many researchers have usedthis index as a good proxy representation of global markets and economic con-ditions. We will take the monthly returns of each of the indices from 1990-2011in accordance with data frequency of macro economic variables. Also, as theindices have different levels at beginning of 1990 we rebase both the indices tobase year of 1990 starting at a level of 100.


4 METHODOLOGY

4 Methodology

4.1 Construction of Time Series

The first step in constructing an econometric model is constructing time seriesall of which are in same units. Most of the time series used in our analysis are indifferent formats. For example CPI, PPI, BSE Index, SP500 are in levels. M1money supply, USDINR exchange rate is in absolute current format. Industrialproduction is in absolute production levels. So, first we convert all of the giventime series to level. The way we construct time series in levels is firstly takingthe initial data point of each time series as 100. We then find the percentagechange from one period to the next one for each time series using a continuouscompounding assumption (taking a natural log of change in values). In math-ematical terms it can be stated as: Assume the original Index value at time tto be It and at time t+1 to be It + 1. Then we can compute the new rebasedindex by formula:

RIt+1 = RIt ∗ (1 + ln(It+1/It))

where,RIt= Rebased Index at time tRIt+1=Rebased Index at time t+1We can use these rebased indices in building and testing our econometric model.

4.2 Unit Root Test and Stationarity

Unit root test is to find whether the series is stationary or non-stationary. Astrictly stationary process is one where, for any t1, t2,...., tt ∈Z, any k ∈Z andT=1,2,...

Fyt1,yt2

,yt3,....,ytT

(y1, ...., yT ) = Fyt1+k,yt2+k

,yt3+k,....,ytT+k

(y1, ...., yT )

where F represents joint distribution function of the set of random variables.It can also be stated that the probability measure of sequence of yt is same asyt+k for all k. In other words a series is stationary if the distribution of its valueremain the same as time progresses. Similar to the concept of strict stationaryis weakly stationary process. A weakly stationary process is one which has aconstant mean, variance and autocovariance structure. Stationary is a necessarycondition for a time series to be tested in regression. A non-stationary seriescan have several problems like:

1. The shocks given to the series would not die of gradually, resulting inincrease of variance as time passes.

2. If the series is non stationary then it can lead to spurious regressions. If twoseries are generated independent of each other then if one is regressed onother it will result in very low R2 values. But if two series are trending overtime then a regression of one over the other will give high R2 even thoughthe series may be unrelated to each other. So, if normal regressions tools


4 METHODOLOGY

are used on non stationary data then it may result in good but valuelessresults.

3. If the variables employed in a regression model are not stationary, thenit can be proved that the standard assumptions for asymptotic analysiswill not be valid. In other words, the usual ’t-ratios’ will not follow at-distribution, and the F-statistic will not follow an F-distribution, and soon.

Stationarity is a desirable condition for any time series so that it can be usedin regressions and give meaningful result that have some value. to test for sta-tionarity a quick and dirty way is looking at the autocorrelation and partialcorrelation function of the series. If the series is stationary then the autocorre-lation function should die off gradually after few lags and the partial correlationfunction will me non zero for some lags and zero thereafter. Also we can usethe Ljung-Box test for testing that all m of σk autocorrelation coefficients arezero using Q-statistic given by formula:

Q = T (T + 2)Σmk=1

σk2

T − k∼ χ2

where, T = Sample size and m = Maximum lag lengthThe lag length selection can be based on different Information Criteria likeAkaike’s Information criteria (AIC), Schwarz’s Bayesian information criteria(SBIC), Hannan-Quinn criterion (HQIC). Mathematically different criteria arerepresented as:

AIC = ln(σ2) + 2kT

SBIC = ln(σ2) + kT lnT

HQIC = ln(σ2) + 2kT ln(ln(T ))

For a better test for stationarity we use augmented Dickey fuller Unit roottest on each time series separately. Augmented Dickey Fuller test is test ofnull hypothesis that the time series contains a unit roots against a alternativehypothesis that the series is stationary.

4.2.1 Mathematical representation of Stationary series and unit roottest

Assume a variable Y whose structure can be given by AR process with no driftequation:

yt = φ1yt−1 + φ2yt−2 + φ3yt−3 + ...+ φnyt−n + ut (2)

where, ut is the residual at time t. Using a Lag operator L we can write eq.(1)as:

yt = φ1L1yt + φ2L

2yt + φ3L3yt + ...+ φnL

nyt + ut (3)


4 METHODOLOGY

Rearranging eqn. (2) we get,

yt − φ1L1yt − φ2L2yt − φ3L3yt + ...− φnLnyt = ut (4)

yt(1− φ1L1 − φ2L2 − φ3L3 + ...− φnLn) = ut (5)

or,φ(L)yt = ut (6)

The time series is stationary if we can write eqn.(5) in form,

yt = φ(L)−1ut (7)

with φ(L)−1 converging to zero. It means the autocorrelation function woulddecline as lag length is increased. If eqn. (6) is expanded to a MA(∞) processthe coefficients of residuals should decrease such that the the residuals that theeffect of residuals decrease with increase in lags. SO, if the process is stationarythe coefficients of residuals will converge to zero and for non-stationary seriesthey will and converge to zero and will have long term effect. The condition fortesting of unit root for an AR process is that the roots of eqn.(6) or ’Charac-teristic equation’ should lie outside unit circle.

4.2.2 Augmented Dickey Fuller Unit Root Test

Consider an AR(1) process of variable Y

yt = φyt−1 + ut (8)

Subtracting yt−1 from both sides of eqn.(7) we get,

∆y = (φ− 1)yt−1 + ut (9)

Eqn.(8) is the test equation for Dickey Fuller test. For Dickey-Fuller Unit roottest,Null Hypothesis: The value of φ is equal to 1 or value of φ− 1 is equal to 0 v/s,Alternate Hypothesis: The value of φ is less than one or value of φ − 1 is lessthan zero Augmented Dickey-Fuller test is similar to normal Dickey-Fuller testsexcept, it takes the lag structure of more than one into account.

∆y = ψyt−1 +

p∑i=1

αi∆yt−i + ut (10)

If the series has one or more unit root it is said to be integrated of order n,where n is the number of unit roots of the characteristic equation. To makethese time series stationary they needs to be differenced. Mathematically, if

yt ∼ I (n) (11)

then

∆ (d) yt ∼ I (0) (12)

To make our time-series stationary we will use the natural log returns of theseseries in the analysis.


4 METHODOLOGY

4.3 Testing Long Term Relationships

Engle and Granger (1987) in their seminal paper described cointegration whichforms the basis for testing for long term relationship between variables. Accord-ing to Engle and Granger two variables are cointegrated if they are integratedprocess in their natural form (of the same order), but a weighted combinationof the variables can be found such that the combined new variable is integratedof order less than the order of individual time series. Mathematically, assumeyt to be a k X 1 vector of variables, then the components are cointegrated orintegrated of order (d,b) if:

1. All components of yt are I(d)

2. There is at least one vector of coefficients α such that

α′yt ∼ I (d− b) (13)

As most of the financial time series are integrated of order one we will restrictourselves to case d=b=1. Two or more variables are said to be cointegrated ifthere exist a linear combination of these variables that is stationary. Many ofthe series are non-stationary but ’move together’ over time which implies twoseries are bound by some common force or factor in long run. We will test forcointegration by a residual-based approach and Johansen’s VAR method.Residual Based approach Consider a model,

yt = β1 + β2x2t + β3x3t + ...+ ut (14)

where yt, x2t, x3t, ... are all integrated of order N. Now if the residual of this re-gression, ut is stationary then we can say that the variables are cointegrated elsethere exist no long term relationship between the variables. To test the resid-ual for stationarity we will run Augmented Dickey-Fuller tests on the residuals.Under the Null hypothesis the residual are integrated of order one or more andunder alternate hypothesis the residuals are I(0).

4.3.1 Johansen test for Cointegration

Johansen test for cointegration presents a better model for testing multiplecointegration among multiple variables. The Residual based approach can onlyfind atmost one cointegration and can be tested for a model with two variables.Even if more than two variables are present in the equation that are cointegrated,the Residual based approach will give only one cointegration. SO we will useJhoansen VAR based cointegration for testing more than one cointegration.Suppose that a set of g variables are under consideration that are I(1) andwhich are thought to be cointegrated. A VAR with k lags containing thesevariables could be set up.

yt = β1yt−1 + β2yt−2 + · · ·+ βkyt−k + ut (15)

g × 1 g × g g × 1 g × g g × 1 g × g g × 1 g × 1


4 METHODOLOGY

In order to use the Johansen test, the VAR above should be turned into avector error correction model of form,

∆yt = Πyt−k + ℘1∆yt−1 + ℘2∆yt−2 + · · ·+ ℘k−1∆yt−(k−1) + ut (16)

where, Π = (Σki=1βi)− Ig and ℘i = (Σi

j=1βj)− Ig

The Johansen’s test centers around testing the Π matrix which is the matrixthat represents the long term cointegration between the variables. The test fornumber of cointegration is calculated by looking at the rank of the Π matrixthrough its eigenvalues. The rank of the matrix is equal to number of roots(eigenvalues) λi of the matrix that are different from zero. The roots should beless than 1 in absolute value and positive. If the variables are not cointegratedthe rank of the matrix will not be significantly different from zero i.e. λi ≈ 0.There are two test statistics for Johansen test λtracer and λmax

λtrace (r) = −T∑g

i=r+1 ln(1− λ̌i)and,λmax(r, r + 1) = −T ln(1− ˇλr+1)

λtrace is a test statistic for joint test where the null hypothesis is that thenumber of cointegration vector is less than or equal to r against an alternativethat there are more than r.λmax conducts another separate test on eigenvalues and has null hypothesis thatthe number of cointegrating vector is r against r+1.

4.4 Impulse Response

Once we have determined whether the variables have long term relationship ornot we can form a multivariate VAR model for the variables. A multivariateVAR model between g variables is a model where the current value of a variabledepend on differnt combinations of the previous k values of all the variables anderror terms. A general representation of the model can be:

yBSEt = α+ βBSEyBSE + φIP yIP + γCPIyCPI + δM1yM1 + κSP500ySP500 + u1t(17)

where all the coefficients except α are g × k matrices and all variables y are k× 1 matrices.Once we have formed a model like this we can use the model for Impulse re-sponse. A VAR(p) model can be written as a linear fuction of the past innova-tions, that is,

rt = µ+ at + ψ1at−1 + ψ2at−2 + . . . (18)

where µ = [φ(1)]−1φ0 provided that the inverse exists, and the coefficient ma-trices ψi can be obtained by equating the coefficients of Bi in the equation

(I − φ1B − . . .− φPBP )(I + ψ1B + ψ2B2 + . . .) = I (19)


4 METHODOLOGY

where I is the Identity martix. This is a moving average representation of rtwith the coefficient matrix ψi being the impact of the past innovation at−i onrt. Equivalently, ψi is the effect of at on the future observation rt+i. Therefore,ψi is often referred to as the Impulse Response Function of rt. For our impulseresponse we will use equation of variables in first differnce form like,

∆BSEt = αt +

k∑i=0

α11(i)∆BSEt−i +

k∑j=1

α12(j)∆MIt−j + εBSEt(20)

∆MIt = αt +

k∑i=0

α21(i)∆MIt−i +

k∑j=1

α22(j)∆BSEt−j + εMIt (21)

Granger’s causality and Block’s F test of a VAR model will suggest which ofthe variables have statistically significant impacts on the future values of othervariables in the system. But F-test results cannot explain the sign of the re-lationship nor how long these effects require to take place. Such informationwill, however, be given by an examination of the VAR’s impulse responses andvariance decompositions. Impulse response is a technique that trace out theresponsiveness of the dependent variable in the VAR to shocks of each of theother variables. So for each variable from each equation separately we will applya unit shock to the error and trace the effects upon the VAR system over time.By using the impulse response technique we can determine how responsive isthe BSE stock index to Indian macro indicators and SP500. This will help usdetermine whether the BSE index is more reactive to domestic news or globalnews.


5 RESULTS

5 Results

Before we use the time series for VAR analysis or cointegration tests we need todetermine whether the series are Stationary or not. If the series are stationaryin levels, we can use them directly else we need to use the differenced time series.One way to look for autocorrelation or integrated process is to see the graphsof the various time series used. Section 7.1 shows the graphs of variables weuse for our analysis. As we can see from the graphs all of the time series havea trend in long run which points to an integrated process. As a second stepwe plot the graphs of differenced time series in Section 5.2. We can see thatthe differenced graphs in Section 7.2 don’t show a long term trend and crossthe X-axis frequently. This is usually a property of I(1) processes. So we checkthe series for autocorrelations at different lag lengths. Section 7.3 shows cor-relograms graph, autocorrelation coefficient, partial autocorrelation coefficient,Q-Stat and p-value for various time series up to 36 lags. As can be seen in thetables the Q-stat for all lags is zero and we can reject the joint null hypothesisthat all the autocorrelations up to 36 lags are zero. Table 7.4.1 shows that ifwe conduct a Unit root test on levels of the series we find that all the 7 seriesare integrated as we cannot reject the t-stat for unit root at 1% level. But ifwe conduct the same test on differenced values of the series we find that we canreject the null hypothesis of unit root at 1% significance level for all the seriesexcept CPI. This tells us that all the series are I(1) as there first difference seriesare I(0).As our series are I(1) we will work with index levels of time series to determineif there exist one or more cointegrating relationships between the series. Tablesin subsection 7.4.3 are based on residual approach where we run a regression ofBSE and various macroeconomic indicators and test the residuals for unit rootusing Augmented Dickey-Fuller test. As we assume the two series are cointe-grated we conduct the test with no trend and intercept. If the two series arecointegrated then the errors should not have any trend or intercept. We see thatwe can reject the null hypothesis of unit root at 1% significance for CPI,IP, M1.We can reject the null of unit root for PPI at 5 % and for SP500 and USDINRwe can’t reject the null hypothesis of unit root at even 5% level. This pointsto the fact that BSE has a strong long term relationship with IP, M1 moneysupply, CPI at 1% level with IP, M1, CPI, PPI at 5% significance level. Also,BSE has no long term relationship with SP500 and USD INR exchange rate.To test for multiple cointegrating relationship we now employ a Johansen VARbased cointegration test. The results of the test are displayed in subsection7.4.4. The first panel of the test results displays the value of λtrace andλmaxof Johansen test with different assumptions about intercept and trend. We cansee from this panel that when we consider a functional form of intercept and noTrend we have atleast and atmost three cointegrating relationships. The secondpanel of the results display the value of information criteria for lag lengths. Formost of the models we see that Akalike criteria points to a lag of three andSchwarz criteria points to a lag of one. To estimate the cointegrating model wechoose the model with intercept and no trend and run a cointegration test.Testresults are shown in Table 2 of subsection 7.4.4. At 5% significance level wecan reject the null of atmost two cointegrating factors for λtrace and same forλmax. Now to test which all variables have a long tern relationship we perform aRestricted cointegration with vector error correction model. As we had already


5 RESULTS

seen in our residual based test of cointegration that BSE has no cointegratingrelationship with SP500 and USDINR we create a restricted cointegration modelwhere we set coefficients of SP500 and USDINR as zero. The test results aredisplayed in Table 3 of subsection 7.4.4. In this case as there are two restrictions,the test statistic follow χ2 with two degrees of freedom. We can see that thep-value for the test is 13.33 % which tells us that the restrictions are supportedby data at 10% level of significance. So we can conclude that the BSE has along term relationship with CPI,IP,PPI,M1 money supply but has no long termrelationship with SP500 and USDINR exchange rate. One interpretation of thisresult can be that the Indian stock market, represented here by BSE Sensex,moves more in accordance with domestic factors like Industrial production, M1money supply, Consumer price index and Producer Price index than with globalfactors or in other words, as BSE is representation of largest market cap Indiancompanies we can say that the biggest companies in India are ones that aremore dependent on domestic demand rather than exports. This result presentsan opportunity for international investors to diversify their portfolio by invest-ing in BSE Sensex as it is decoupled with global markets and macroeconomicfactors.We use A bivariate Vector Autoregression (BVAR) technique to analyze thedynamic interaction between real asset prices and macro economy. VAR ispreferred method to study Macroeconomy and asset prices where variables en-dogenously effect each other.We begin with a bivariate VAR with no restriction. Asset prices and instru-ments are allowed to respond to each other freely. For paired variables withcointegration relationship, VAR is performed at levels whilst for those that arenot cointegrated VAR is performed at first difference. Constant term is ignoredwith loss of generality. We use the Bivariate Autoregression analysis for bothimpulse response and Granger’s causality tests.Impulse response results are displayed in subsection 7.4.5. From first graph ofimpulse response of BSE to USDINR we can see that USDINR has a negativeimpact on BSE. As impulse response is response of BSE to shocks given to US-DINR we can see that a positive shock or unexpected appreciation INR valuew.r.t USD, will have a negative effect on BSE for few lags and will disappearafter few lags. If we look at the constituents of BSE Index over time we seethat most of the time, some of its constituent are companies that thrive on ex-ports. Some of the biggest Market-Cap in India are companies in service sectorlike Infosys, TCS, etc that are hugely dependent on services provided to clientsfrom Europe and U.S.. So, an appreciation of INR compared to USD makesthese firms costlier for the global clients and in turn reduces the income of thesecompanies. As the firm’s revenue/ profit decreases the value of the stock alsodecreases that in turn affects the returns of BSE Sensex.Second graph (betwen BSE and SP500) shows that increase in SP500 has a pos-itive effect on BSE as higher returns of SP500 indicate strong global economywhich in turn results in higher trade between countries. The positive responseof BSE to one unit shock to SP500 indicates a spillover effect of global factorson Indian economy but the response is weak as can be seen from the graph.Moving forward, response of BSE to shocks in M1 money supply, CPI, PPImake economic sense. As for M1 money supply one unit shock means increasein M1 money supply. This increase in money supply allows companies to bor-row more money from banks at lower rates, which they can use for investing


5 RESULTS

in profitable projects and generating larger cash flows. For Inflation indicatorsone unit shock means increase in inflation. This increase in inflation results inhigher costs for the companies that in turn reduces their profit margins and asa result value of stocks.By looking at the graphs we can also see that shocks to Indian macroeconomicindicators creates stronger response by BSE as compared to global factors likeSP500 or USDINR. This indicates that BSE Index is driven by companies thatdepend hugely on domestic demand rather than exports. Response of BSE toshocks to Industrial Production are contradictory to theory. In theory an in-crease in industrial production should result in positive response from BSE butour analysis shows the other way. A possible reason for this response could bethat industrial production time series is seasonal as can be seen from the graph.So, there is a possibility of a lead/lag relationship between the two variables.To test for possibility of lead/lag relationship we run a Granger’s causality testbetween BSE and IP. The result in section 6.4.6 shows that at a lag lengthof 4 we can reject the Null hypothesis of BSE does not Granger cause IP at1% significance level. This proves that BSE is a leading indicator of industrialproduction and there exist a lead/lag relationship between the two indicators.


6 CONCLUSIONS

6 Conclusions

In this paper I tested the relations between Indian stock market, represented byBSE, and domestic and global macro economic factors. The research concludesthat the India stock markets are mainly driven by domestic demand and theinfluence of global macro factors on the stock market is weak. I also tested forGranger causality between BSE and IP and found that BSE is a leading indicatorof Industrial production and can help in predicting the industrial climate inIndia.The research is insightful for investors and professionals who are looking forinvestment opportunities to diversify their risks. As Indian stock markets aremore dependent on domestic factors one can invest in Indian indices and stocksto diversify their risks gained through investing in U.S. and European stocks.The paper opens new doors for research in this field. One can use variancedecomposition technique to see how much variance of BSE can be explained myvarious domestic and global macro factors. Also one can use different globalfactors like sovereign CDS spreads, T-Bill rates, a composite indicator of globaleconomy for further research on interaction between Indian stock market andglobal economy.One can also research on how various global macroeconomicnews affects India stock markets and for how long the effects persists.


7 GRAPHS AND TABLES

7 Graphs and Tables

7.1 Graphs of Time series


7 GRAPHS AND TABLES


7 GRAPHS AND TABLES


7 GRAPHS AND TABLES


7 GRAPHS AND TABLES

7.2 Graphs of Time Series - Differenced


7 GRAPHS AND TABLES


7 GRAPHS AND TABLES


7 GRAPHS AND TABLES


7 GRAPHS AND TABLES

7.3 Correlograms of Time series

BSE


7 GRAPHS AND TABLES

IP


7 GRAPHS AND TABLES

SP500


7 GRAPHS AND TABLES

USDINR


7 GRAPHS AND TABLES

CPI


7 GRAPHS AND TABLES

PPI


7 GRAPHS AND TABLES

M1


7 GRAPHS AND TABLES

7.4 Tables

7.4.1 Table for Unit root test of Time series

Variables T-Stat p-valueBSE -2.671 24.95 %

SP500 -1.315 88.18 %CPI -1.909 64.66 %IP -1.669 8.99 %M1 -2.420 36.79 %PPI -3.353 6.01 %

USDINR -2.955 14.69 %

7.4.2 Tables for Unit root test of Differenced time series

Variables T-Stat p-valueBSE -13.848 0.00 %

SP500 -14.832 0.00 %CPI -3.344 1.40 %IP -3.865 0.27 %M1 -3.867 0.26 %PPI -9.656 0.00 %

USDINR -13.701 0.00 %

7.4.3 Tables for Residual based test of cointegration

Table 1:BSE - CPI

t-Statistic Prob.*ADF test statistic -2.622676 0.87%Test critical values: 1% level -2.573818

5% level -1.9420410% level -1.615891

Table 2:BSE - IP


5% level -1.94213610% level -1.615828


7 GRAPHS AND TABLES

Table 3:BSE - M1


5% level -1.94203510% level -1.615894

Table 4:BSE - PPI


5% level -1.94203510% level -1.615894

Table 5:BSE - SP500


5% level -1.94203510% level -1.615894


7 GRAPHS AND TABLES

Table 6:BSE - USDINR


5% level -1.9420410% level -1.615891


7 GRAPHS AND TABLES

7.4.4 Johansen cointegration test


7 GRAPHS AND TABLES

Table 2


7 GRAPHS AND TABLES

Table 3


7 GRAPHS AND TABLES

7.4.5 Impulse response tests


7 GRAPHS AND TABLES


7 GRAPHS AND TABLES


7 GRAPHS AND TABLES

7.4.6 Granger causality test between IP and BSE


8 BIBLIOGRAPHY

8 Bibliography

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