1. EDHEC Business School 1

2. EDHEC Business School 2

3. An Empirical Study of
Macroeconomic Factors and Stock
Market: An Indian Perspective
Saurabh Yadav
EDHEC Business School
Master’s in Risk and Investment Management
saurabh.yadav@edhec.com
June 26, 2012
EDHEC Business School

4. Abstract
This thesis is an empirical study of relationship between Indian stock
markets and macro economy. There is a huge literature about such kind of
empirical studies but mostly on US/UK stock markets and macroeconomic
indicators. This study is similar to many of the earlier studies in some
aspects, so it uses econometric tools used in earlier studies but at the same
time this study differentiates itself from other studies in the sense it uses
Indian markets and macroeconomic data for analysing the relationship
and it also tries to analyse the impact of global economy on the Indian
markets. The period that will be used for the study will be from 1990
to 2011. We have chosen this period as it represents big regulatory and
structural changes in Indian economy. So, an analysis of this period can
provide us with insights to how some regulatory and structural changes
impact the economy and asset prices in that country. In this study we will
use Unit root tests, cointegration, Ljung-Box Q test and multivariate VAR
analysis for analysing each macro economic and asset prices time series
individually and to build a model that can analyse the impact of one over
the other. Also, we will conduct Granger’s Causality test and Impulse
response analysis between Stock market and macro economic indicators
to analyze the impact of macro economic news/shocks on India Stock
index (BSE).
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5. Acknowledgment
I am thankful to Professor Robert Kimmel for his comments and guidance
on 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, Marc
Rakotomalala, Aishwarya Iyer, Wen lei, Lixia Loh for some great insights into
the subject. Their timely comments and suggestions on empirical tests helped
me 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 data
providers. In the end i’ll like to thank my parents and my sister for constant
support and motivation without which it would have been impossible to climb
this arduous path.
Regards,
Saurabh YADAV
EDHEC Business School 5

6. CONTENTS
Contents
1 Introduction 7
2 Literature Review 9
3 Data 13
3.1 Description of Macroeconomic Indicators . . . . . . . . . . . . . 13
3.2 Description of Stock Market Indices . . . . . . . . . . . . . . . . 14
4 Methodology 15
4.1 Construction of Time Series . . . . . . . . . . . . . . . . . . . . 15
4.2 Unit Root Test and Stationarity . . . . . . . . . . . . . . . . . . . 15
4.2.1 Mathematical representation of Stationary series and unit
root test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.2.2 Augmented Dickey Fuller Unit Root Test . . . . . . . . . 17
4.3 Testing Long Term Relationships . . . . . . . . . . . . . . . . . . 18
4.3.1 Johansen test for Cointegration . . . . . . . . . . . . . . . 18
4.4 Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5 Results 21
6 Conclusions 24
7 Graphs and Tables 25
7.1 Graphs of Time series . . . . . . . . . . . . . . . . . . . . . . . . 25
7.2 Graphs of Time Series - Differenced . . . . . . . . . . . . . . . . 29
7.3 Correlograms of Time series . . . . . . . . . . . . . . . . . . . . . 33
7.4 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
7.4.1 Table for Unit root test of Time series . . . . . . . . . . . 40
7.4.2 Tables for Unit root test of Differenced time series . . . . 40
7.4.3 Tables for Residual based test of cointegration . . . . . . . 40
7.4.4 Johansen cointegration test . . . . . . . . . . . . . . . . . 43
7.4.5 Impulse response tests . . . . . . . . . . . . . . . . . . . . 46
7.4.6 Granger causality test between IP and BSE . . . . . . . . 49
8 Bibliography 50
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7. 1 INTRODUCTION
1 Introduction
In the past few decades there has been a growing interest among academicians
and practitioners about the relationship between macroeconomic variables and
asset 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 expectation
of large future cash flows/ profits for the companies and various role players
in the economy. Similarly, during a bad or downward spiralling economy the
expectation of large future cash flows and profits decrease and consequently the
price 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 as
idiosyncratic factors related to each company or industry. As Stock prices are
real time and are more frequent than macroeconomic releases they are better
reflector of changes in domestic and global economy and can predict the move-
ment of macroeconomic indicators. In other words stock markets are a leading
indicator of the economy.
Markets respond to different macroeconomic indicators in different ways. The
response of Stock markets to any macroeconomic news is dependent on how the
news will effect the profits and interest rates. The price of the stock according
to the Discounted Cash Flow formula is:
Div1 Div2 Divt
Pt = + + ... + (1)
(1 + r1 )1 (1 + r2 )2 (1 + rt )t
As both dividends and interest rates enter into the formula for value of a
stock the reaction of stock price to a macro news will depend on how the news
effect the discounting factor ( Interest rates ) and future profits of the com-
panies. Macro economic factors that project brighter times and more profits
for the companies like, increasing Industrial production, Increasing M1 money
supply, good consumer confidence levels will have a positive effect on the stock
prices. Whereas, macro news that point to economic recession or slow growth
like, decreasing Industrial production coupled with Rising interest rates, Rise
in inflation, rise in unemployment, etc. will have a downward effect on stock
prices.
First people to do an empirical study on this subject were Eugene Fama and
Kenneth French. In their 1981 paper ”Stock returns, Real activity, Inflation
and money” they analysed the relationship between stock returns, real activity
inflation and money supply using macro economic data. After that study there
has been a barrage of studies on relationship between stock returns and macro
economic factors based on US and UK data. Another important paper pub-
lished on this research was by Chen,Roll and Ross (1986) who analysed whether
innovations in the macroeconomic variables are risks that are awarded in the
stock markets. They found that macroeconomic variables like, spread between
long and short interest rates, expected and unexpected inflation, Industrial pro-
duction are some of the factors that are awarded by the markets. Further, the
Arbitrage pricing theory (APT) of Ross (1976) posits relation between stock
prices and certain macro-economic variables. In the last decade or so the focus
for these kind of studies have started to shift from developed world economies to
developing world economies. As developing world economies have shown signs
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8. 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 study
will 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 stock
markets are related to its macroeconomic variables and global macro/micro eco-
nomic factors. This study will also help us in analysing whether the Indian stock
markets have become coupled to global factors or are they still dominated by
domestic economic factors.
The focus of this study is on relation between Indian stock market, represented
by BSE Sensex, and domestic macroeconomic factors and global factors repre-
sented by Standard and Poor’s 500 Index. This study builds on earlier studies
done 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 micro
factors and econometrics tools used in previous studies but at the same time it
differentiates itself from earlier studies in a sense that it is done on a market
that is still developing. Also, the time period used in the analysis is a period
where Indian market has undergone lot of regulatory changes that has created
a structural change in the market. Further, in this study I’ll analyse whether
the Indian markets are driven mainly by Domestic factors or do global factors
have more influence on Indian markets. To analyse the impact of international
factors I’ll use Standard and Poor’s 500 Index and USDINR exchange rate as a
substitute of global factors and to model domestic demand I’ll use macro factors
like Industrial production, M1 money supply, Consumer Price Index and Pro-
ducer price Index. The outline of the thesis is as followings: Section 2 provides
a literature review of the studies done earlier in this area, Section 3 provides a
detailed description of the data used in the study Section 4 provides a detailed
description of the methodology and various econometric tools that will be used
in the study, Section 5 provides the results of the study and Section 6 provides
the conclusion of the study.
EDHEC Business School 8

9. 2 LITERATURE REVIEW
2 Literature Review
Many studies and researchers have tried to find factors that can explain stock
returns. 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 stock
returns 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 sensitiveness
of each stock to change in overall market, which is measured by Beta. According
to CAPM, the market factor is the only factor determining the stock returns.
CAPM was a revolutionary model. It changed the way people looked at the
stock 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 stock
return in most of finance textbooks and used by many practitioners in stock
market.
However, the numerous set of assumptions made in deriving CAPM made it
inconsistent with the real world and led to criticism of CAPM. To overcome
the limitations and assumptions made in CAPM many scholars came up with
multi- factor models like Fama-French three factor model, APT model, etc. In
Fama-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 explain
the returns based on these risk factors for some time before it failed. There
have been many studies on failure of Fama-French model and markets where it
is 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 and
Ross (1980). APT is a multi-factor model and claims that the stock return can
be explained by unexpected changes or shocks in multiple factors. Chen,Roll
and Ross (1986) perform the empirical study for APT model and identify that
surprise 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 change
in 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 rises
and consequently the stock price rises. On the other hand if a firm is performing
bad for couple of years then the expectation of big future cash flows decrease
and in turn the stock price fall. This is a micro and idiosyncratic explanation of
stock prices and returns. But, the future cash flows of a stock does not depend
solely on the company’s performance or profits/loss. The systematic factor can
have a huge impact on the cash flows of not only one but many companies. The
systematic factor here refers to macro economic variables. The state of Macro
economic conditions lead to changes in Monetary and regulatory policies by the
government and which in turn affects the stock prices. For example a country
with good economic conditions, represented by its Industrial production index,
GDP, CPI, Interest rates will create an environment that is conducive for the
growth of companies by lowering borrowing rates and other open market opera-
tions. So, all macroeconomic factors that can influence future cash flows or the
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10. 2 LITERATURE REVIEW
discount rate by which the cash flows are discounted should have an influence
on the stock price.
Many researcher have studies the relationship between stock prices and macro
economic 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 relation
with real output and money supply but a negative relation with inflation. He
explains that negative relation between stock returns and inflation is induced by
negative relation between real output, approximated by Industrial production,
and inflation. This negative relationship between inflation and real activity
is explained by money demand theory and quantity theory of money. Fama
(1990) explains that measuring the total return variation explained by shocks
to expected cash flows, time-varying expected returns, and shocks to expected
returns is one way to judge the rationality of stock prices. In his paper he
finds that growth rates of production, used to proxy for shocks to expected cash
flows, explain 45% of return variance. Chen,Roll and Ross (1986) explored the
relationship between a set of economic variables and their systematic influence
on stock market returns. They found that Industrial production, changes in
risk premium, twists in yield curve had strong relationship and impact on stock
returns. A somewhat weaker effect was found for measures of unanticipated
inflation and changes in expected inflation during periods when these variables
were 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 forecast
changes in the investment and consumption opportunity set. According to his
research, default spread, the term spread, the one-month T-Bill rate, the lagged
industrial production growth rate, and the dividend-price ration are important
determinants of future stock market returns. Bulmash and Trivoli (1991) show
the effect of business cycle movements on the relationship between stock returns
and 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 strong
link between stock prices and real economic activity:
“First, information about the future real activity may be reflected in stock
prices well before it occurs — this is essentially the notion that stock prices
are a leading indicator for the well-being of the economy. Second, changes
in discount rates may affect stock prices and real investment similarly, but
the output from real investment doesn’t appear for some time after it is
made. Third, changes in stock prices are changes in wealth, and this
can 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 previous
works do not address the channels through which the macroeconomic activity
influences the stock prices. One example could be that industrial production
could 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
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11. 2 LITERATURE REVIEW
in determining both industrial production (due to change in investment) and
stock 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 among
macroeconomic variables like money supply, CPI,IPI, and foreign exchange rate
and stock markets in Pakistan. The results show that there are causal relation-
ship among the stock price and macroeconomic variables. He uses data from
1974 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 Hussian
and Tariq Massod (2001) used variables like investment, GDP and consumption
employing Granger’s causality test to find relationship between macro factors
and stock markets. They show that at two lags all macroeconomic variables
have highly significant effect on stock prices. James et al. (1985) use a VARMA
analysis for investigating relationship between macro economy and stock mar-
ket. Using VARMA analysis for finding causal relationship between factors is
a better technique as the procedure does not preclude any causal structure a
priori since it allows feedback among variables. Thus, the VARMA approach
allow whatever causal relationship exist to emerge from the data. They find
linkages between real activity and stock returns and real activity and inflation.
Also, they find that stock returns signal changes in the monetary base. Since
stock returns also signal changes in expected real activity, this suggests a link
between the money supply and expected real activity that is consistent with the
money supply explanation offered by Geske and Roll.
In recent years the focus of these kind of studies have shifted from developed
economies to developing economies. As developing economies are the economies
that 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 analyse
the 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 also
finds that for Thailand unemployment rate and inflation rate are insignificant to
determine the stock returns. The reason he provides is that the unemployment
rate and inflation rate are not timely and there could be some lags before the
data becomes available. Also, Granger’s test to examine lead-lag relationship
among the factors reveal that only few macroeconomic variables could predict
the future stock returns whereas the stock returns can predict most of future
macro economic variables. This implies that performance of stock markets can
be a leading indicator for future macroeconomic conditions. Ali (2011) study of
impact of macro and micro factors on stock returns reveals that inflation and
foreign remittance have negative influence and industrial production index have
positive 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 of
Granger’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 stock
markets and four macro economic variables namely crude oil prices, Money sup-
ply, Industrial production and inflation rate in China and India. They used a
period of 1999 to 2009 for analysis. As most of the economic time series have unit
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12. 2 LITERATURE REVIEW
root, they first used the Augmented Dickey Fuller unit root test and found the
underlying series to be non-stationary at levels but stationary after in difference.
Also, the use of Jhonson-Juselius (1990) Multivariate cointegration and Vector
Error Correction model technique, indicate that there are both long and short
run linkages between macroeconomic variable and stock market index in each of
the two countries. Their analysis shows that in long run the impact of increase
in prices of crude oil for China is positive but for India is negative. In terms
of 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 only
in China. In addition the effect of increases in inflation on these stock markets
is positive in both countries. Wickremasinghe (2006) analysed the relationship
between stock prices and macroeconomic variables in Sri Lanka. He used the
Unit root tests, Jhonson’s test, Error-correction model, variance decomposi-
tion and impulse response to analyse the relationships. His findings indicate
that there is both long term and short term causal relationship between stock
prices and macroeconomic variables in Sri Lanka. The result indicate that the
stock prices can be predicted from certain macroeconomic variables and hence
violate 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 Nifty
Index and BSE Sensex. For finding the long term relationship he applies Jo-
hansen’s cointegration and Toda and Yamamoto Granger Causality tests. For
analysing the Impulse response and variance decomposition he uses bivariate
VAR. His findings reveal that stock prices in India lead macroeconomic activity
except 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 outcome
of behaviour of key macro economic variables but it is also one of the causes
of movement in other macro dimensions in the economy. An important paper
by Bilson et al. (2001) argues that emerging markets local factors are more
important than global factors. They find that for emerging markets are at least
partially segmented from global capital markets. The global factors are proxied
by world market returns and local factors by set of macro economic variables
like money supply, prices, real activity and exchange rate. Some evidence is
found that local factors are significant in their association with emerging equity
market returns above than that explained by the world factor. When they use
a 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 for
most emerging markets.
EDHEC Business School 12

13. 3 DATA
3 Data
3.1 Description of Macroeconomic Indicators
One of the biggest problems when conducting a research with macroeconomic
data is the frequency of the data. Most of the macroeconomic indicator time
series are yearly,quarterly or monthly time series. This low frequency of the
macroeconomic 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 periods
to incorporate more data points for macroeconomic variables. But, another
problem that we face when we look at the macroeconomic indicators for Asian
countries 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 history
of Indian macroeconomic variables. So, in this research we have used a time
period for which we can find data for most of the macroeconomic indicators. In
this paper we use a time period of 20 years starting from 1990 to 2011. This
time period in Indian economy is representative of many structural and mone-
tary policy changes like liberalization of India markets. Also as the time period
is long it gives us enough data point for each macroeconomic factors to do a
robust 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 the
myriad of macro indicators available for an economy which factors to choose
to incorporate in the model. If one chooses macroeconomic factors that are
highly correlated among themselves then the power of test results decrease as
it may result in a model where the macro indicators are able to explain most
of 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 earlier
researches and that have been proven to have effect on stock markets. I also
test 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) study
on Indian markets specifically show that Industrial Production, Exchange rate,
Inflation index are macro economic indicators that have a strong positive or
negative relationship with the stock markets. So, in our study we test 5 macro
economic variables namely M1 money supply, Consumer and Producer price In-
dex, Industrial production, Exchange rate. The time period for these indicators
is from 1990-2011. The data for Inflation indices, Industrial production and
exchange rate has been pulled from Bloomberg c and Datastream c . The data
has been processed for errors and missing values. Data for M1 money supply
has been pulled from RBI website. For most of the indices like inflation and
Industrial production index, the base year has been changed to 1990. Also, as
some 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).
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14. 3 DATA
3.2 Description of Stock Market Indices
Compared to Macro Indicators, stock market data is relatively easy to find and
has considerably long history. Also, the stock market data is a real time data so
it has a very high frequency of seconds. Here, in our analysis we will make use of
BSE (Bombay Stock Exchange) as representation of Indian markets and SP500
(Standard and Poor’s 500 Index) as representation of global factors. BSE is a
market 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 is
the Index that represent the most liquid and traded stocks of the Indian stock
market. Also, the index is most traded index in India and a good representation
of trade prices of the stocks. Even in terms of an orderly growth, much before
the actual legislations were enacted, BSE Limited had formulated a compre-
hensive set of Rules and Regulations for the securities market. It had also laid
down best practices which were adopted subsequently by 23 stock exchanges
which were set up after India gained its independence. Our choice of SP500 is
based on the fact that it has a long history and many researchers have used
this 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 1990-2011
in accordance with data frequency of macro economic variables. Also, as the
indices have different levels at beginning of 1990 we rebase both the indices to
base year of 1990 starting at a level of 100.
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15. 4 METHODOLOGY
4 Methodology
4.1 Construction of Time Series
The first step in constructing an econometric model is constructing time series
all of which are in same units. Most of the time series used in our analysis are in
different formats. For example CPI, PPI, BSE Index, SP500 are in levels. M1
money supply, USDINR exchange rate is in absolute current format. Industrial
production is in absolute production levels. So, first we convert all of the given
time series to level. The way we construct time series in levels is firstly taking
the initial data point of each time series as 100. We then find the percentage
change from one period to the next one for each time series using a continuous
compounding 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 t
to be It and at time t+1 to be It + 1. Then we can compute the new rebased
index by formula:
RIt+1 = RIt ∗ (1 + ln(It+1 /It ))
where,
RIt = Rebased Index at time t
RIt+1 =Rebased Index at time t+1
We 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. A
strictly stationary process is one where, for any t1 , t2 ,...., tt ∈Z, any k ∈Z and
T=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 as
yt+k for all k. In other words a series is stationary if the distribution of its value
remain the same as time progresses. Similar to the concept of strict stationary
is weakly stationary process. A weakly stationary process is one which has a
constant mean, variance and autocovariance structure. Stationary is a necessary
condition for a time series to be tested in regression. A non-stationary series
can have several problems like:
1. The shocks given to the series would not die of gradually, resulting in
increase of variance as time passes.
2. If the series is non stationary then it can lead to spurious regressions. If two
series are generated independent of each other then if one is regressed on
other it will result in very low R2 values. But if two series are trending over
time then a regression of one over the other will give high R2 even though
the series may be unrelated to each other. So, if normal regressions tools
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16. 4 METHODOLOGY
are used on non stationary data then it may result in good but valueless
results.
3. If the variables employed in a regression model are not stationary, then
it can be proved that the standard assumptions for asymptotic analysis
will not be valid. In other words, the usual ’t-ratios’ will not follow a
t-distribution, and the F-statistic will not follow an F-distribution, and so
on.
Stationarity is a desirable condition for any time series so that it can be used
in 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 partial
correlation function of the series. If the series is stationary then the autocorre-
lation function should die off gradually after few lags and the partial correlation
function will me non zero for some lags and zero thereafter. Also we can use
the Ljung-Box test for testing that all m of σk autocorrelation coefficients are
zero using Q-statistic given by formula:
σk 2
Q = T (T + 2)Σm
k=1 ∼ χ2
T −k
where, T = Sample size and m = Maximum lag length
The lag length selection can be based on different Information Criteria like
Akaike’s Information criteria (AIC), Schwarz’s Bayesian information criteria
(SBIC), Hannan-Quinn criterion (HQIC). Mathematically different criteria are
represented as:
2k
AIC = ln(σ 2 ) + T
k
SBIC = ln(σ 2 ) + T lnT
2k
HQIC = ln(σ 2 ) + T ln(ln(T ))
For a better test for stationarity we use augmented Dickey fuller Unit root
test on each time series separately. Augmented Dickey Fuller test is test of
null hypothesis that the time series contains a unit roots against a alternative
hypothesis that the series is stationary.
4.2.1 Mathematical representation of Stationary series and unit root
test
Assume a variable Y whose structure can be given by AR process with no drift
equation:
yt = φ1 yt−1 + φ2 yt−2 + φ3 yt−3 + ... + φn yt−n + ut (2)
where, ut is the residual at time t. Using a Lag operator L we can write eq.(1)
as:
yt = φ1 L1 yt + φ2 L2 yt + φ3 L3 yt + ... + φn Ln yt + ut (3)
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17. 4 METHODOLOGY
Rearranging eqn. (2) we get,
yt − φ1 L1 yt − φ2 L2 yt − φ3 L3 yt + ... − φn Ln yt = ut (4)
1 2 3 n
yt (1 − φ1 L − φ2 L − φ3 L + ... − φn L ) = ut (5)
or,
φ(L)yt = ut (6)
The time series is stationary if we can write eqn.(5) in form,
yt = φ(L)−1 ut (7)
with φ(L)−1 converging to zero. It means the autocorrelation function would
decline as lag length is increased. If eqn. (6) is expanded to a MA(∞) process
the coefficients of residuals should decrease such that the the residuals that the
effect of residuals decrease with increase in lags. SO, if the process is stationary
the coefficients of residuals will converge to zero and for non-stationary series
they will and converge to zero and will have long term effect. The condition for
testing 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 root
test,
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 less
than zero Augmented Dickey-Fuller test is similar to normal Dickey-Fuller tests
except, it takes the lag structure of more than one into account.
p
∆y = ψyt−1 + αi ∆yt−i + ut (10)
i=1
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 make
these 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 these
series in the analysis.
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18. 4 METHODOLOGY
4.3 Testing Long Term Relationships
Engle and Granger (1987) in their seminal paper described cointegration which
forms the basis for testing for long term relationship between variables. Accord-
ing to Engle and Granger two variables are cointegrated if they are integrated
process in their natural form (of the same order), but a weighted combination
of the variables can be found such that the combined new variable is integrated
of order less than the order of individual time series. Mathematically, assume
yt to be a k X 1 vector of variables, then the components are cointegrated or
integrated 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 restrict
ourselves to case d=b=1. Two or more variables are said to be cointegrated if
there exist a linear combination of these variables that is stationary. Many of
the series are non-stationary but ’move together’ over time which implies two
series are bound by some common force or factor in long run. We will test for
cointegration by a residual-based approach and Johansen’s VAR method.
Residual Based approach Consider a model,
yt = β1 + β2 x2t + β3 x3t + ... + 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 else
there 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 and
under alternate hypothesis the residuals are I(0).
4.3.1 Johansen test for Cointegration
Johansen test for cointegration presents a better model for testing multiple
cointegration among multiple variables. The Residual based approach can only
find 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 use
Jhoansen VAR based cointegration for testing more than one cointegration.
Suppose that a set of g variables are under consideration that are I(1) and
which are thought to be cointegrated. A VAR with k lags containing these
variables could be set up.
yt = β1 yt−1 + β2 yt−2 + · · · + βk yt−k + ut (15)
g×1 g×g g×1 g×g g×1 g×g g×1 g×1
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19. 4 METHODOLOGY
In order to use the Johansen test, the VAR above should be turned into a
vector error correction model of form,
∆yt = Πyt−k + ℘1 ∆yt−1 + ℘2 ∆yt−2 + · · · + ℘k−1 ∆yt−(k−1) + ut (16)
where, Π = (Σk βi ) − Ig and ℘i = (Σi βj ) − Ig
i=1 j=1
The Johansen’s test centers around testing the Π matrix which is the matrix
that represents the long term cointegration between the variables. The test for
number of cointegration is calculated by looking at the rank of the Π matrix
through 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 be
less than 1 in absolute value and positive. If the variables are not cointegrated
the rank of the matrix will not be significantly different from zero i.e. λi ≈ 0.
There are two test statistics for Johansen test λtrace r and λmax
g ˇ
λtrace (r) = −T i=r+1 ln(1 − λi )
and,
ˇ
λmax (r, r + 1) = −T ln(1 − λr+1 )
λtrace is a test statistic for joint test where the null hypothesis is that the
number of cointegration vector is less than or equal to r against an alternative
that there are more than r.
λmax conducts another separate test on eigenvalues and has null hypothesis that
the number of cointegrating vector is r against r+1.
4.4 Impulse Response
Once we have determined whether the variables have long term relationship or
not we can form a multivariate VAR model for the variables. A multivariate
VAR model between g variables is a model where the current value of a variable
depend on differnt combinations of the previous k values of all the variables and
error terms. A general representation of the model can be:
yBSEt = α + βBSE yBSE + φIP yIP + γCP I yCP I + δM 1 yM 1 + κSP 500 ySP 500 + 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 + ψ1 at−1 + ψ2 at−2 + . . . (18)
where µ = [φ(1)]−1 φ0 provided that the inverse exists, and the coefficient ma-
trices ψi can be obtained by equating the coefficients of B i in the equation
(I − φ1 B − . . . − φP B P )(I + ψ1 B + ψ2 B 2 + . . .) = I (19)
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20. 4 METHODOLOGY
where I is the Identity martix. This is a moving average representation of rt
with the coefficient matrix ψi being the impact of the past innovation at−i on
rt . 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 impulse
response we will use equation of variables in first differnce form like,
k k
∆BSEt = αt + α11 (i)∆BSEt−i + α12 (j)∆M It−j + BSEt (20)
i=0 j=1
k k
∆M It = αt + α21 (i)∆M It−i + α22 (j)∆BSEt−j + M It (21)
i=0 j=1
Granger’s causality and Block’s F test of a VAR model will suggest which of
the variables have statistically significant impacts on the future values of other
variables 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 information
will, however, be given by an examination of the VAR’s impulse responses and
variance decompositions. Impulse response is a technique that trace out the
responsiveness of the dependent variable in the VAR to shocks of each of the
other variables. So for each variable from each equation separately we will apply
a 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 is
the BSE stock index to Indian macro indicators and SP500. This will help us
determine whether the BSE index is more reactive to domestic news or global
news.
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21. 5 RESULTS
5 Results
Before we use the time series for VAR analysis or cointegration tests we need to
determine whether the series are Stationary or not. If the series are stationary
in 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 graphs
of the various time series used. Section 7.1 shows the graphs of variables we
use for our analysis. As we can see from the graphs all of the time series have
a trend in long run which points to an integrated process. As a second step
we plot the graphs of differenced time series in Section 5.2. We can see that
the differenced graphs in Section 7.2 don’t show a long term trend and cross
the X-axis frequently. This is usually a property of I(1) processes. So we check
the 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 the
tables the Q-stat for all lags is zero and we can reject the joint null hypothesis
that all the autocorrelations up to 36 lags are zero. Table 7.4.1 shows that if
we conduct a Unit root test on levels of the series we find that all the 7 series
are integrated as we cannot reject the t-stat for unit root at 1% level. But if
we conduct the same test on differenced values of the series we find that we can
reject the null hypothesis of unit root at 1% significance level for all the series
except CPI. This tells us that all the series are I(1) as there first difference series
are I(0).
As our series are I(1) we will work with index levels of time series to determine
if there exist one or more cointegrating relationships between the series. Tables
in subsection 7.4.3 are based on residual approach where we run a regression of
BSE and various macroeconomic indicators and test the residuals for unit root
using 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 are
cointegrated then the errors should not have any trend or intercept. We see that
we 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 USDINR
we can’t reject the null hypothesis of unit root at even 5% level. This points
to the fact that BSE has a strong long term relationship with IP, M1 money
supply, 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 VAR
based cointegration test. The results of the test are displayed in subsection
7.4.4. The first panel of the test results displays the value of λt race andλm ax
of Johansen test with different assumptions about intercept and trend. We can
see from this panel that when we consider a functional form of intercept and no
Trend we have atleast and atmost three cointegrating relationships. The second
panel of the results display the value of information criteria for lag lengths. For
most of the models we see that Akalike criteria points to a lag of three and
Schwarz criteria points to a lag of one. To estimate the cointegrating model we
choose the model with intercept and no trend and run a cointegration test.Test
results are shown in Table 2 of subsection 7.4.4. At 5% significance level we
can reject the null of atmost two cointegrating factors for λt race and same for
λm ax. Now to test which all variables have a long tern relationship we perform a
Restricted cointegration with vector error correction model. As we had already
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22. 5 RESULTS
seen in our residual based test of cointegration that BSE has no cointegrating
relationship with SP500 and USDINR we create a restricted cointegration model
where we set coefficients of SP500 and USDINR as zero. The test results are
displayed 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 the
p-value for the test is 13.33 % which tells us that the restrictions are supported
by data at 10% level of significance. So we can conclude that the BSE has a
long term relationship with CPI,IP,PPI,M1 money supply but has no long term
relationship with SP500 and USDINR exchange rate. One interpretation of this
result can be that the Indian stock market, represented here by BSE Sensex,
moves more in accordance with domestic factors like Industrial production, M1
money supply, Consumer price index and Producer Price index than with global
factors or in other words, as BSE is representation of largest market cap Indian
companies we can say that the biggest companies in India are ones that are
more dependent on domestic demand rather than exports. This result presents
an opportunity for international investors to diversify their portfolio by invest-
ing in BSE Sensex as it is decoupled with global markets and macroeconomic
factors.
We use A bivariate Vector Autoregression (BVAR) technique to analyze the
dynamic interaction between real asset prices and macro economy. VAR is
preferred 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 with
cointegration relationship, VAR is performed at levels whilst for those that are
not cointegrated VAR is performed at first difference. Constant term is ignored
with loss of generality. We use the Bivariate Autoregression analysis for both
impulse response and Granger’s causality tests.
Impulse response results are displayed in subsection 7.4.5. From first graph of
impulse response of BSE to USDINR we can see that USDINR has a negative
impact 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 value
w.r.t USD, will have a negative effect on BSE for few lags and will disappear
after few lags. If we look at the constituents of BSE Index over time we see
that 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 sector
like Infosys, TCS, etc that are hugely dependent on services provided to clients
from Europe and U.S.. So, an appreciation of INR compared to USD makes
these firms costlier for the global clients and in turn reduces the income of these
companies. As the firm’s revenue/ profit decreases the value of the stock also
decreases 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 economy
which in turn results in higher trade between countries. The positive response
of BSE to one unit shock to SP500 indicates a spillover effect of global factors
on 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, PPI
make economic sense. As for M1 money supply one unit shock means increase
in 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
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23. 5 RESULTS
in profitable projects and generating larger cash flows. For Inflation indicators
one unit shock means increase in inflation. This increase in inflation results in
higher costs for the companies that in turn reduces their profit margins and as
a result value of stocks.
By looking at the graphs we can also see that shocks to Indian macroeconomic
indicators creates stronger response by BSE as compared to global factors like
SP500 or USDINR. This indicates that BSE Index is driven by companies that
depend hugely on domestic demand rather than exports. Response of BSE to
shocks to Industrial Production are contradictory to theory. In theory an in-
crease in industrial production should result in positive response from BSE but
our analysis shows the other way. A possible reason for this response could be
that 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 test
between BSE and IP. The result in section 6.4.6 shows that at a lag length
of 4 we can reject the Null hypothesis of BSE does not Granger cause IP at
1% significance level. This proves that BSE is a leading indicator of industrial
production and there exist a lead/lag relationship between the two indicators.
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24. 6 CONCLUSIONS
6 Conclusions
In this paper I tested the relations between Indian stock market, represented by
BSE, and domestic and global macro economic factors. The research concludes
that the India stock markets are mainly driven by domestic demand and the
influence of global macro factors on the stock market is weak. I also tested for
Granger causality between BSE and IP and found that BSE is a leading indicator
of Industrial production and can help in predicting the industrial climate in
India.
The research is insightful for investors and professionals who are looking for
investment opportunities to diversify their risks. As Indian stock markets are
more dependent on domestic factors one can invest in Indian indices and stocks
to 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 variance
decomposition technique to see how much variance of BSE can be explained my
various domestic and global macro factors. Also one can use different global
factors like sovereign CDS spreads, T-Bill rates, a composite indicator of global
economy for further research on interaction between Indian stock market and
global economy.One can also research on how various global macroeconomic
news affects India stock markets and for how long the effects persists.
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25. 7 GRAPHS AND TABLES
7 Graphs and Tables
7.1 Graphs of Time series
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26. 7 GRAPHS AND TABLES
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27. 7 GRAPHS AND TABLES
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28. 7 GRAPHS AND TABLES
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29. 7 GRAPHS AND TABLES
7.2 Graphs of Time Series - Differenced
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30. 7 GRAPHS AND TABLES
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31. 7 GRAPHS AND TABLES
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32. 7 GRAPHS AND TABLES
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33. 7 GRAPHS AND TABLES
7.3 Correlograms of Time series
BSE
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34. 7 GRAPHS AND TABLES
IP
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35. 7 GRAPHS AND TABLES
SP500
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36. 7 GRAPHS AND TABLES
USDINR
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37. 7 GRAPHS AND TABLES
CPI
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38. 7 GRAPHS AND TABLES
PPI
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39. 7 GRAPHS AND TABLES
M1
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40. 7 GRAPHS AND TABLES
7.4 Tables
7.4.1 Table for Unit root test of Time series
Variables T-Stat p-value
BSE -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-value
BSE -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 -1.94204
10% level -1.615891
Table 2:
BSE - IP
t-Statistic Prob.*
ADF test statistic -3.738802 0.02%
Test critical values: 1% level -2.574513
5% level -1.942136
10% level -1.615828
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41. 7 GRAPHS AND TABLES
Table 3:
BSE - M1
t-Statistic Prob.*
ADF test statistic -2.875518 0.41%
Test critical values: 1% level -2.573784
5% level -1.942035
10% level -1.615894
Table 4:
BSE - PPI
t-Statistic Prob.*
ADF test statistic -2.399055 1.62%
Test critical values: 1% level -2.573784
5% level -1.942035
10% level -1.615894
Table 5:
BSE - SP500
t-Statistic Prob.*
ADF test statistic -1.427184 14.30%
Test critical values: 1% level -2.573784
5% level -1.942035
10% level -1.615894
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42. 7 GRAPHS AND TABLES
Table 6:
BSE - USDINR
t-Statistic Prob.*
ADF test statistic -1.659522 9.17%
Test critical values: 1% level -2.573818
5% level -1.94204
10% level -1.615891
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43. 7 GRAPHS AND TABLES
7.4.4 Johansen cointegration test
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44. 7 GRAPHS AND TABLES
Table 2
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45. 7 GRAPHS AND TABLES
Table 3
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46. 7 GRAPHS AND TABLES
7.4.5 Impulse response tests
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47. 7 GRAPHS AND TABLES
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49. 7 GRAPHS AND TABLES
7.4.6 Granger causality test between IP and BSE
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50. 8 BIBLIOGRAPHY
8 Bibliography
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