Impact of Macroeconomic Variables on NIFTY Index

Impact of Macroeconomic Variables on the
National Stock Exchange of India: NIFTY INDEX
By
CHIRAG Pankaj PATWA (K1440395)
Thesis submitted in partial and fulfilment of the requirements for
the degree of Master of Science in Applied Econometrics
Kingston University London
Supervised by
Dr. Daniil Kiose
September 2015

Impact of macroeconomic variables on the National Stock Exchange of India: NIFTY Index 1
Acknowledgments
This dissertation is a milestone in my academic career. I have been fortunate to learn
new theories and concepts which would have been impossible if I had not extensively
carried out the needed research. I am grateful to a number of people who have guided
and supported me throughout the research process and provided assistance for my
venture.
I would first like to thank my mentor and supervisor Dr. Daniil Kiose who guided me in
selecting the final theme for this dissertation. He was there throughout my
preparation of the proposal and the conceptualization of its structure. I would not
have been able to do the research and achieve learning in the same manner without
his help and support. His recommendations and instructions have enabled me to
assemble and finish the dissertation effectively.
I would also like to thank all my teacher and faculty members of arts and social
sciences, who throughout my educational career have supported and encouraged me
to believe in my abilities. They have directed me through various situations, allowing
me to reach this accomplishment.
Finally, my family and friends have supported and helped me along the course of this
dissertation by giving encouragement and providing the moral and emotional support I
needed to complete my thesis. To them, I am eternally grateful.

Contents
Acknowledgments......................................................................................1
Abstract......................................................................................................3
Introduction ...............................................................................................3
Literature review........................................................................................6
Theoretical framework.............................................................................12
Data Selection ..........................................................................................14
Research Methodology ............................................................................19
Limitations ............................................................................................20
Analysis and Interpretation of Results......................................................20
Autocorrelation function for Residuals:- ...............................................22
Worm Plots:-.........................................................................................25
Term Plots.............................................................................................31
Model Selection .......................................................................................34
Forecasting...............................................................................................37
Conclusion................................................................................................39
References ...............................................................................................40
Appendix ..................................................................................................43

Abstract
This paper examines the effect of macroeconomic variables on the stock price
movement on the NIFTY Index. Nine macroeconomic variables (Interest Rate,
Consumer Price Index, Exchange rate, GDP, Population, Unemployment rate,
NIFTYLAG, Industrial Production and Exchange rate) are used as explanatory variables
and the NIFTY Index is indicated as the dependent variable. The research for this
report is based on the GAMLSS technique that uses flexible regression to construct a
quantitative model. The time series uses monthly data gathered from the Bloomberg
terminal and the official website of the National Stock Exchange of India from 1991-
2010. The results of this paper indicated that there exists significant correlation
between eight explanatory variables and the NIFTY Index while Interest rate showed
no effect on the stock prices. The analysis for the forecasting is done for the period
from 2011-2015 on monthly basis and the results shows a fall in the market.
Introduction
Financial market plays a pivotal role in growing industries and commerce of a country
that eventually affects its economy. In 1991, government of India had introduced a
series of policy measures to liberalize its economy to cope up with the ongoing process
of globalization all over the world. Relaxation of licensing rule, rationalisation of tax
structure, enhancement of the ceiling of foreign direct investment and private
participation are some of the outcomes of liberalization which showed a great impact
on the integration of the Indian economy. An efficient capital market provides a
significant investment avenue that contributes to attract domestic and foreign capital.
If the efficient capital market hypothesis is true, then stock prices adjusts swiftly

according to the new information available and it reflects expectation of future
performances of corporate houses and financial institutions. The dynamic relationship
between stock prices and macroeconomic variables can be used to make a nation’s
macroeconomic policies. A strong perception of the macro dynamics of the Indian
stock market can helpful for traders, investors and policy makers of the country.
From an investor’s perspective, investors must be able to evaluate a country’s current
economic environment and to forecast its future economic environment in order to
identify asset classes and securities that will benefit from economic trends occurring
within that country.
If a country’s economy is performing well and expected to grow at vigorous pace, the
market is frequently expected to imitate the situation. The market index provides a
historical stock market performance which is used as the yardstick to compare the
performance of individual portfolios and also provides investors for forecasting future
trends in the market. Unlike the stock market of the advanced countries, emerging
economies are likely to be sensitive to factors such as changes in the level of economic
activities, changes in the political and international economic environment. Investors
evaluate the potential economic fundamentals and other firm specific factors to
formulate expectations about the stock market.
In the modern portfolio theory, the Arbitrage Pricing Theory (APT) developed by Ross
(1976) assumes that the return on asset is a linear function of various macroeconomic
factors or theoretical market indices, where sensitivity to changes in each factor is
represented by factor-specific beta coefficient. The APT states that the realized return
on asset is composed of the expected return on that asset at the beginning of a time
period and the unexpected realization krisk factors during that time period plus firm
specific risk.

The National Stock Exchange of India commonly known as NSE and is India’s leading
stock exchange all over the country. The main objective of NSE was to set a fully
modern automated trading platform within national reach. The exchange offers a wide
range of products to its investors which are Equities that includes indices, mutual
funds, ETF’s, IPO’S etc. it also deals with derivatives which includes currency, interest
rate futures. It also provides its investors to trade on debt market such as retail debt,
wholesale debt market and also on corporate bonds issued by companies and financial
institutions. Today the NSE has a network that stretches to more than 1500 locations
and supports around 2, 30,000 terminals which offers more than 10 asset classes.
The NSE has not a restricted its reach within the country but also cross boundaries, it
has signed a Memorandum of Understanding (MOU) with the Singapore Exchange
(SGX) which enables the products of NSE to be listed on the SGX and provides investors
in one country to trade on other country’s exchange. It also covers license agreements
for both benchmark indexes for US and Indian equities which were formed by NSE and
CME group.
The National Stock Exchange has nearly 1400 listed companies all covering the length,
breath and diversity of the Indian economy which includes industries like software,
refinery, public sector units, infrastructure and financial services. It not only provides
its users with safe and secure trading but also with additional services like Direct
market access, Cross margining, FIX capabilities and co-location facilities.

NSE Schematic.
Source: http://www.nseindia.com/technology/content/nse_schematic.htm
Literature review
This section of the paper discusses some of the past research works and their empirical
results that are related to our topic area. Many financial analysts, researcher made an
attempt to study and predict the relationship between stock prices and

macroeconomic variables. Different papers shows different results based on their
methodologies, time period and also the explanatory variables chosen.
Rajesh Pai and Dr. S. kareemulla Basha, (2014) did a paper on impact of
macroeconomic variables on NIFTY returns in India. This study examined the causal
relationship and impact of the macro variables on stock prices. The results for the
ARIMA output showed that there is 98.2% of variance which can be forecasted using
independent variable taken into account. According to the analysis Crude oil, M3, IIP
and Real GDP are positively correlated to the NIFTY index whereas, INR/USD, Exchange
rate, Unemployment rate, Interest rate are have a strong negative correlation.
In 1986 Chen studied relationship between stock prices to future expected cash flows
and future discount rate of the cash flow. His argument was based on the fact stock
returns should be affected by factors that influence future cash flows using the
discounted cash flow method or the present value model. His analysis showed that all
macroeconomic factors influences future expected cash flows or discount rate on stock
prices.
A study was conducted by Chatrath in 2007 to examine the relationship between stock
market returns and inflationary trends. The analysis showed a negative impact for
developed economies in Europe and North America.
Maysami and Howe (2004) chose macroeconomic variables over a seven-year time
zone from the 1988-1995 and tested the relationship between the Singapore stock
index. Their studies have found that there exists a positive relationship between
changes in money supply and stock returns but a negative relationship with prices
levels, interest rate and exchange rate.
Bhattacharya and J Mukherjee (2002) five economic variables that were money supply,
index of industrial production, national income, interest rate and inflation were tested

to check for causal relationship between BSE index using techniques of unit roots, co-
integration and long run Granger non- causality test for the period of 1992-1993 to
2000-2001. His analysis found concluding results in which it showed no causal links
between stock prices, money supply, national income and interest rate. Stock prices
were led by industrial production and a bilateral relationship between stock price and
inflation.
Maghayreh in 2003 examined a long run relationship between Jordanian stock prices
and macroeconomic variables. His analysis included testing co-integration using
monthly data from January 1987 to December 2000. The explanatory variables that
were chosen are exports, foreign reserves, interest rate, inflation and industrial
production. His findings concluded that all the variables are significant with the stock
prices.
Sarkar (2005) studied the relation between capital accumulation and growth of India.
Annual data was used between 1950-1951 to 2005 on different variables like nominal
and real share price, share market turnover ratio, number of listed firms in the stock
market, fixed capital formation, real GDP and industrial output. Both long run and
short run equilibrium shows no positive relationship between real and stock market
variables.
Basabi, Bhattacharya, Jaydeep Mukherjee (2001) tested the causal relationship
between the stock returns, foreign institutional investment and the exchange rate in
India. The results indicated that there exists a bi-directional relationship between
foreign institutional investment and stock prices while a unidirectional causality
relationship between stock prices and changes in exchange rate. There shows no
relationship between exchange rate and net investment by FII’s.

In 2007 Horobet Livia studied the relationship between stock prices and exchange rate
of Romania. The techniques used to study the analysis were bivariate co-integration
test, both the Engle- Granger and the Johansen methodology. The period that was
chosen involved from January 1999- June 2007. His findings showed no co-integration
between the exchange rate and the stock prices. While performing the non-co-
integrated through Granger causality test he identified unilateral causality relations
from the stock prices to exchange rate and one bilateral causality relation between the
stock prices and exchange rate against the US dollar.
Kandir in 2008 analysed the impact of macroeconomic factors in Turkish stock market.
Model was built from the period of July 1997 to June 2005 in which his research found
that exchange rate, interest rate and world market return affected the portfolio.
Inflation rate was the most significant which affected the market while industrial
production, money supply and oil prices have no effect on stock prices.
Mahmood and Dinniah (2009) examined the long run and short run relationship
between stock prices of six Asian Pacific selected countries like Malaysia, Korea,
Thailand, Hong-Kong, Japan and Australia. The explanatory variables that were chosen
are foreign exchange rate, consumer price index and industrial production on monthly
basis for the period of January 1993 to December 2002. There exists a long run
relationship between stock prices and macroeconomic variables of four countries that
is Japan, Korea, Hong Kong and Australia. On the other hand for short run no
relationship exists between stock prices and macroeconomic variables for Hong Kong
and Thailand.
In 2002 Wongbangpo and Sharma tested the effects of macroeconomic variables and
stock prices in five South East Asian countries namely- Indonesia, Malaysia, Philippines,
Singapore and Thailand. Data were collected from the period of 1985 to 1996 on a
monthly basis. The explanatory variables that were used in this study were GNP,

consumer price index, money supply, interest rate, exchange rate. Their results show
that exchange rate is positively related in countries like Indonesia, Malaysia and
Philippines and negatively affects stock prices in Singapore and Thailand. Whereas
Indonesia and Philippines have a high rate of negative relationship between stock
prices and money supply compared to countries like Malaysia, Singapore and Thailand
where there exists a positive relationship.
Gagan Deep Sharma (2010) used the multiple regression models to study the effects of
macroeconomic variables such as changes in exchange rate, foreign exchange reserve,
inflation rate and gold prices on stock prices. The main of the paper was to determine
the lead and lag relationship between the independent and dependent variables. The
findings showed that exchange rate and gold prices affects the BSE index. Variables like
inflation rate and foreign exchange reserve have a significant relation on stock prices.
Gan, Lee and Zhang conducted test in 2006 to analyse the relationship between seven
macroeconomic variables that are inflation rate, interest rate, real trade weighted
exchange index, GDP, money supply and domestic oil prices against the New Zealand
Stock Index (NZSE40). The study was done from January 1990 until January 2003. For
their paper they employed the co-integration test specifically the Johansen
Multivariate Granger causality test. The conclusion from these tests showed that
interest rate, money supply, and real GDP had a positive relationship with the NZSE40
and were constantly determined by these factors.
In 2011 Ali M. B tested the microeconomic and macroeconomic variables on stock
prices on Dhaka stock exchange (DSE). He conducted his analysis through a multiple
regression model using the standard Ordinary Least Square. Inflation and foreign
exchange have a negative influence while market P/E’s and monthly percentage
average growth in market capitalisation has a positive influence on DSE. Market P/E
and stock prices show one unidirectional causal relationship. Evidence of

informationally inefficient market exists due to lack of granger causality between stock
prices and some micro and macro variables.
In 2011 relationship between China Stock market and five macroeconomic variables
that is real GDP, CPI and short term interest rate was conducted by Xiufang Wang. The
main aim of his research was to estimate the volatility of variables using Exponential
Generalized Autoregressive Conditional Hetroskedasticity (EGARCH) and also test the
causal relationship using LAG- augmented VAR models. In conclusion of his findings
there is no causal relationship between stock prices and real GDP, whereas bilateral
causal relationship exists between inflation and stock price volatility.
Akbar et.al (2012) employed the co-integration test and VECM to study the
relationship between the Karachi stock exchange index and macroeconomic variables.
The time period that was chosen was from January 1999 to June 2008. His conclusion
was that there exists long run equilibrium between macroeconomic variables and
stock prices. Interest rate rates and money supply shows a positive influence on stock
prices while negative relationship between inflation and foreign exchange.
Sarbapriya Ray 2012 tests the effect of macroeconomic variables on stock prices using
multiple regression models and used granger causality test to examine the existence of
causal relationship between these factors. She analysed the data on the Indian stock
market using annual data from 1990-1991 to 2000-2011. The results showed no causal
relationship between stock prices, interest rate, industrial production, but there exists
a unidirectional association between stock prices, inflation, foreign direct investment,
GDP, exchange rate and gross fixed capital formation. Bidirectional relationship exists
between stock prices, foreign exchange reserve, money supply, crude oil and
wholesale price index. While testing the multiple regression models study indicated a
that oil prices, gold prices have a negative impact, while interest rate, balance of trade,
foreign exchange reserve, GDP, industrial production and money supply has a positive

influence on stock prices. There is no significant impact on stock prices by inflation
rate, foreign direct investment, exchange rate and wholesale price index.
Mohi-u-Din Sangmi and Mohd. Mubasher Hassan in 2013 studied the relationship
between three leading stock market indices namely Sensex, Nifty and BSE 100. They
examined six macroeconomic variables such as wholesale price index, changes in
exchange rate, index of production, money supply, gold prices and interest rates.
Empirical results showed that Sensex and Nifty were highly influenced by increase in
inflation rate which lead to higher returns on stock prices. On the other hand increase
in exchange rate lowered the returns on stock prices and factors also indicated a
change in stock prices based on the statistical analysis. Monthly data from the time
period of April 2008 to June 2012 were used for this research.
In 2014 Dr.Venkatraja. B analysed the relationship between the Bombay stock
exchange and five macroeconomic variables namely industrial production, wholesale
price index, gold prices, FII and exchange rate from April 2010 to June 2014 on a
monthly basis. His conclusion showed that inflation, inflow of FII, exchange rate and
gold prices has strong impact on stock market and significantly affects the
performance of the market.
Theoretical framework
The main focus of this study is to develop flexible regression model using the GAMLSS
technique that is used as the tool. It is a generalized class of statistical model for a
univariate regression response variable and is also known as generalized additive
model for location, scale and shape. This model was developed by Rigby and
Stasinopoulos (2001, 2005, p.509) and Akantziliotou et al. (2002, p.509) which was

used as a tool to overcome some of the limitations of the Generalized Linear Model
and Generalized Additive Model. The GAMLSS models assumes independent
observations y (i) for i = 1, 2, 3…n with probability (density) function f (yi |θi
)
conditional on θi
where θi
= (θi1, θi2…… θip) is a vector of p parameters each of which is
related to the explanatory variables. While implementing it in R at most it requires 4
distribution parameters (µi , σi , νi , τi). The parameters of µi and σi are the first two
population parameters and are characterized as location and scale, the remaining
parameters are specified as shape parameters. For this model any population
distribution of parameters can be applied. The GAMLSS model is also called as semi-
parametric model as it allows for random effect terms to be included in the model.
The GAMLSS model is usually fitted with two basic algorithms. The first one is CG and is
a generalization of Cole and Green (1992) which explains the algorithm and it uses the
first derivative and the expected values of the second and cross derivatives of the
likelihood function with respect to θ = (µ, σ, ν, τ). The second is the RS algorithm and is
generally known as Rigby and Stasinopoulos (1996a, 1996b). This algorithm is used for
fitting the Mean and Dispersion for Additive Model unlike CG the RS does not use the
expected values of the cross derivatives. The advantage of using the GAMLSS model is
well suited to modelling of response variable which does not follow an exponential
family distribution (e.g. leptokurtic or platykurtic and/or positively or negatively skew
response variable, or over dispersed counts response variable) or which exhibit
heterogeneity, (e.g. where the scale or shape of the distribution of the response
variable changes with explanatory variables(s). It uses a wide range of distribution to
describe our response variable and rather than just using a single parameter to model
it uses all the parameters of the distribution to independently be related with our
response variable it is quite handy in situation where our data is approximately
normally distributed and does not have a constant variance.

Advantages of using this framework:-
1) It is flexible in modular fitting procedure.
2) New distributions can be easily implemented.
3) New additive terms can also be implemented in the model.
4) Values such as (µ, σ, τ, ν) can be found.
5) Unlike the simple linear model, the GAMLSS are stable and reliable algorithm.
6) It does not separately model each distribution rather uses all the parameters.
7) It is a convenient framework to various distributional assumptions such as
Gumbel, Weibull and the student-t in addition to the standard natural
exponential family distributions.
8) It does not restrict its modelling to the location of distribution as in Generalised
Linear Model.
9) In the GAMLSS technique all distributional parameters can be explicitly
modelled using both fixed and random effects.
Data Selection
1) Nifty Index: - the index is owned and managed by India Index services and
product limited. It is the flagship of the National stock Exchange of India which
trades in the most liquid and largest Indian securities. It captures the highest
percentage of its float adjusted market capitalization which includes 50 of 1600
companies and tracks the portfolio of blue chip companies. This index is
computed using a market capitalization weighted methodology. The changes in
the index are caused due to the action of stock splits, rights issuance etc. The
CNX nifty has a highly governed structure which comprises of three-tier 1)
Board of Directors 2) index Policy Committee 3) Index maintenance

subcommittee. All common shares are listed on the index which covers 21
sectors of the Indian economy. Fixed income and preferred shares which
guarantee a certain amount of return is not eligible to trade. Changes in stock
prices reflect the market capitalization which changes the index level and sets a
trend. Hedging of the index uses monthly data and is observed that the
correlation (R square) for various other portfolios and indices on the CNX Nifty
was significantly higher than other benchmark index’s which to be better for
hedging securities
It is calculated using total market cap of the company or the market
capitalization is the product of the market price and the total number of
outstanding shares of the company.
Market capitalisation= Equity capital * Price
2) Consumer Price index: - inflation is measured by the changes in the CPI. Shifts
from investments to consumption are caused due to high rate of inflation
which causes demand to fall for the instrument and leads to reduction in
volume of stock traded. Government monetary policies quickly respond to
changes of high inflation. When inflation is moving upward it most likely
tightens the monetary policy which results in increase of discount rate. In times
of high inflation growth stocks will be more negatively impacted which shows
that value stocks are significantly correlated with inflation and negatively
correlated with growth stocks. For investors that are interested in income
generating stocks or stocks that pay a fixed amount of dividend will prefer low
inflation as dividends tends to keep up with inflation and makes it more
attractive when inflation is high. It is said that inflation is negative relationship
with equity prices.

3) Exchange rate: - the price of a nation’s currency in terms of another country’s
currency. US dollar/ Indian rupees exchange rate is used in this study. Factors
affecting the effect of exchange rate on stock prices 1) when country’s currency
is depreciating it cause the stock price to decrease because of expectations of
inflation. 2) Foreign investors will be reluctant to invest in country’s whose
currency depreciates as it reduces their return on investment. 3) Different
companies face different exchange rate depreciation depending on whether it
is importing or exporting. Companies that imports will suffer from high costs
due to due weaker domestic currency and will have lower earning and result in
lower stock prices. When the currency is depreciated it will boost the export
industry and the impact will be positive which lead the investors to invests
more and increase the share prices as a result of booming economy. Imports of
goods and services will have a negative impact on stock prices whereas exports
will have a positive impact.
4) Industrial production: - industrial production is a measure of output of the
industrial sector of the economy and is used as a proxy to calculate growth in
the real sector. Increased spending or capital equipment by industries is often
associated with increase in production and results in increased profits.
Investors from these increased profits will access the stock valuations and
begin to invest which will lead to higher stock prices and returns. The
relationship between the stock prices and industrial production is expected to
be positive according to economic theory i.e. as the dividends grow company
earnings increases which results in higher share prices.
5) Money supply: - money supply refers to the total amount of monetary assets
available in an economy at a specific time. Stock prices tend to move upwards

when the money supply in the economy is high. When the general demand in
the economy increases stocks tend to follow the money supply as it increases
and vice versa. Therefore money supply also has a positive relationship with
stock prices.
6) Interest rate: - it is the amount charged by the lender to a borrower for the use
of the assets and is expressed a percentage of the principal amount. Stock
prices and interest rates have a negative relationship. There are two reasons
for negative relationship between stock prices and interest rates 1) if the rate
of interest increases to depositors paid by banks then investors prefers to
deposit their capital in banks and switch from share market which will decrease
the demand for the share and lower the share price. 2) When the rate of
interest paid by banks to depositors increases, the lending also increases which
decreases the investments in the economy and leads to decrease in share price.
7) Unemployment rate: - as the unemployment rate increases the banks and
financial institutions will experience decrease in confidence in translating to a
downturn in the value of the stock market. Therefore stock prices and
unemployment rate have an inverse relationship i.e. as unemployment rate
rises stock prices decline and as unemployment decreases stock prices increase
this is due to the fact that investors have more disposable income and they
tend to invest in financial markets in anticipation to get higher returns.
8) GDP: - the Gross Domestic Product of a country is one of the main
macroeconomic variables and is used as a primary indicator to analyse the
health of a country’s economy. It is used to calculate the total value of goods
and services produced in a country. Many researchers have proved that there is

positive relationship between the stock prices and GDP. When the Economy is
booming investors are more confident about the future prospects and have
more wealth in turn encourages them to invest and increases sales and
corporate earnings. On the other hand when the Economy is contracting stock
prices are low, companies are forced to cut costs and increases there debt and
investors find it difficult to gather new sources of financing. In the previous
research Goldsmith studies the relationship between the economic growth and
the financial framework. His analysis concludes that there exists positive
correlation between the GDP and financial inter fix ratio (FIR)
9) Population: - the demographics of country play a very significant role in
determining the stock prices as well as its economic growth. Over the years not
much is research is done on population and stock prices, the reason being that
many analyst and investors believed that demographics does directly affect the
movement of stock prices. In 2004 Amit Goyal did a study on demographics,
stock market flows and stock returns which was published in the journal of
financial and quantitative analysis which concluded that demographics are
directly related to the stock market returns. The general notion is that
households invest different amount of money at different life cycles: a) young
investors substantially invest less amount of money as they do not own much
financial wealth b) the second group are the middle-aged population that are
the most prominent investors in financial markets c) the last category are the
old aged population that again invest less in the markets. At this point in time
they tend to have more of outflow than inflow as they start accumulating their
savings earned over the years.

Research Methodology
The study for this paper is focused on nine macroeconomic variables-CPI index IMF,
Exchange rate, industrial production, money supply, IMF India interest rate,
unemployment rate, IMF India population, GDP using exchange rate in billion in 2005
using USD. These variables are used as independent variable to investigate the
relationship in stock prices of NIFTY index. For this study monthly data from 1991-2010
which has been selected from the Bloomberg terminal and National stock exchange
website. By using the multiple regression models the paper is divided into subgroups
to test for correlation to check whether all the variables are significant with the Nifty
Index and whether those variables have a positive or a negative influence on the index
graphically representing it through term plots and checking for inadequacies in the
model using the worm plots. The GAMLSS techniques used in R is to examine the
general framework for fitting the regression models where the distribution of the
response variable does not belong to the exponential family and includes high skew
and kurtosis continuous and discrete distribution. And finally forecasting the Index for
the period from 2011 to 2015.
The current R implementation of the software allows us to use up to 4 parameters to
be modelled under this framework. Under this condition, we can derive the following
model when p=4.
𝑔1(𝜇) = 𝜂1 = 𝑋1 𝛽1
𝑔1(𝜎) = 𝜂2 = 𝑋2 𝛽2
𝑔1(𝜈) = 𝜂3 = 𝑋3 𝛽3
𝑔1(𝜏) = 𝜂4 = 𝑋4 𝛽4

Where 𝜇, 𝜎, 𝜈, 𝜏 are vectors of length 𝑛, 𝑋K are known design matrices, 𝛽K =𝛽1,K, 𝛽2,K, …
, 𝛽𝑗,𝑘 are parameter vectors,
In simpler terms the above equation simply means that the moments of response
variable in each data cell can be directly expressed as function of covariates after a
proper parameterization is done.
The above equation showed is the generalised formulation of GAMLSS method.
Limitations
1) As the data selected are secondary there might some discrepancies and the
result may not always be accurate
2) Variables such as GDP per capita, population and GDP are based on annual
basis and not on monthly basis due to lack of unavailable data.
Analysis and Interpretation of Results
In the previous section of the research methodology, a generalised formulation of
GAMLSS model was shown with 4 distribution parameters. In this study four models
are built. The first model is the conventional linear model (model 0), the second and
third and fourth models are built using the GAMLSS technique (model 1, model 2 and
model 3). For the GAMLSS technique different models were built and among them the
best model is chosen for forecasting. Selecting the best model is based on the residuals
using the Autocorrelation function, the worm plots and the AIC. The worm plots are
used to detect the inadequacies in the model or within a specific range of explanatory
variables. Another way of choosing the best model is through the Generalized Akaike
Information Criterion (GAIC) and the Schwarz Bayesian Criterion (SBC). The GAIC was

proposed by Akaike (1974) and measures the goodness of fit of the model and the log
likelihood function using the Global deviances which is regarded as measure of lack of
fit between the model and data. The general rule for the global deviance is that the
larger the deviance, the poorer the fit to data. The model with the lowest Akaike
Information Criterion is chosen. The global deviance is formulated through = - 2 x L + c
x edf, where the L stands for the log-likelihood function of the model and the edf is the
effective degrees of freedom of a fitted model i.e. it specifies the dimension of the
vector of model parameters.
Formulation of the three models is shown below:-
1) Conventional linear model:-
Part 1 of the model belongs to the normal distribution and it refers to family of
continuous probability distribution and is described by the normal equation.
2) GAMLSS model:- NIFTY~TF2 (µ, σ, υ ) (mu, sigma, nu)
The above GAMLSS models Implements t-family distribution with mean equal to mu
and standard deviation equal to sigma (nu/nu-2)) ^0.5 with the degrees of freedom nu.
The function TF2 is a different parametrization where sigma is the standard deviation.
The student t –family for - ∞ < y < ∞ (e.g. lange el al. (1989) explains the TF (µ, σ, υ),
and assumes that z has standard t-distribution with υ degrees of freedom, where z=(y -
µ)/ σ. The µ specifies the mean of y i.e. the NIFTY index and σ is the standard deviation
as a non-parametric function of the explanatory variables, while the parameter υ is
used to control the tails of the family distribution which shows its skewness and
kurtosis , g specifies the link function and can also be used as log.

Autocorrelation function for Residuals:-
The section below analyses the graph of the NIFTY Index which shows the correlation
between the series and its lagged values and shows the difference between the
observed values and its estimated values. For the series to be stationary there
shouldn’t be any significant correlation for any lag. For time series data is observed
with equally spaced intervals and ordered in time. With a positive autocorrelation,
there is a pattern that is constantly followed i.e. positive and negative errors are
directly proportional to counterparts. The dotted horizontal line shows the significance
level and the vertical lines gives the residuals in different time zones.
Figure 1

Figure 1 shows the autocorrelation for the conventional model that uses the normal
distribution in GAMLSS. As the residuals are correlated with its observed values and
are non-stationary. The autocorrelation is shown up to lag 5 which is not a good sign
and cannot be used for further analysis. The ACF is declining after lag 6. The data is
trended downwards which shows non randomness.
Figure 2
The above graph of ACF of figure 2 uses the GAMLSS technique of the TF family
distribution. All the explanatory variables are insignificant and none of the explanatory
variables have residual autocorrelation. Although on lags 6, 8 and 23 errors have
touched the horizontal line still this model can be considered for further analysis as
there has been no violation and this model 1 is stationary. This concludes that the data
are random and are near zero at all time lag separation.

Figure 3
In figure 3 the series are non-random and are significantly non zero up to lag 12 which
indicates that the explanatory variables are highly correlated with their past values.
The model also uses the GAMLSS technique with the TF family distribution but when
compared with model 1 of figure 2 the difference is that in this model the NIFTY lag
data has been removed which drastically affects the model. In conclusion this model is
incorrect and invalid for further analysis. The series are also trended downwards which
follows a specific path.

Figure 4
Figure 4 shows that the series are random and the residuals are not auto correlated.
Unlike figure 2 the ACF are higher in early lags 2, 6, 8 and 9. Although these lags are
insignificant and the model can be considered for further analysis. The auto correlation
is close to zero which indicates that the data are not repeated in this model.
Worm Plots:-
The diagnostic stage of the model selection process involves the use of worm plots and
was introduced by Van Burren et al (2001) in accordance to identify regions or intervals
of the explanatory variables within which the model does not adequately fit the data
and is also known as model violation. These plots are in effect de-trended normal QQ
plots of the quantile residuals. For the model to be accepted all the observations must

fall inside the two elliptic curves. The red curve in the plot is the fitted cubic
polynomial to the points on the plot this curve usually follows the direction of the
explanatory variable that is dominant in the analysis.
Figure 5
Figure 5 shown above has high levels of inadequacies in the data which shows that the
explanatory variable does not capture the dynamics of the NIFTY index market. From
the plot it is visible that the data follows certain amount of trend. Extreme deviations
are seen on both upper and lower bounds. Another reason might be due the fact that
it is a conventional linear model and belongs to the normal family distribution which
involves some assumptions. Increase in the interest rate policies, depreciation in
domestic currency, the money supply has decreased in the economy could be some of
the possibilities that the model is inadequate it is difficult to individually interpret
which explanatory variable has caused the inadequacies in the model and clearly
model NIFTY0 has been rejected.

Figure 6
The worm plot is applied to the model NIFTY 1 of figure 6 shown above and the
analysis indicates that the data perfectly capture the dynamics and the variability of
the market. The explanatory variables are adequate enough and the dotted yellow line
follows the path of the red horizontal line that shows the movement of the index. Very
few deviation are caused on the plot that maybe due some errors in the data but are
still very close to zero. The reason for these adequacies is that in this model GAMLSS
technique with the TF family distribution has been used which relaxes most of the
assumptions of the linear model. All the explanatory variables are fallen inside the
elliptic curve which is what we needed. There may be some explanatory variables that
are dominant and causes some deviations. This model is appropriate for further
analysis.

Figure 7
In figure 7 there are signs of extreme deviations on both the lower and higher bounds.
Most of the data as it can be seen have fallen in the elliptic curve which makes this
model inadequate for any further analysis. Although this model had also been
constructed using the GAMLSS technique of the TF family distribution, but the
difference in this model is that the NIFTY lag observation has been removed which
proves that this series becomes weak without the lag of its index. The deviation has
crossed both the extreme values of 0.5 and -0.5 which makes it inappropriate and
clearly it is rejected.

Figure 8
The plot of figure 8 is very similar as that of figure 6 shown above. That is also has
almost straight line with all the explanatory variables perfectly fitting the model and
adequately captures the overall dynamics of the market and its movement. Almost all
the deviations are on zero which makes this model perfect as it could be. Very few
minor setbacks have been caused but still are very low compared to any other plots
and it can be ignored as it does not fall in the elliptic curve. This model perfectly fits
the data.
This section has only focused on deciding which model is adequate that fits the data
and which is not, figure 6 and figure 8 are the two models that perfectly fits the data
but by just looking at the plots it is difficult to decide which is the best model. The
worm plots alone cannot decide which model is the best so the Akaike Information
Criteria and the global deviance are used. This is shown in the next section.

Global deviance AIC SBC
modelNIFTY0 -697.8803 -679.8803 -649.0955
modelNIFTY1 -1222.544 -1196.544 -1152.077
modelNIFTY2 -839.5362 -807.5362 -752.8076
modelNIFTY3 -1229.037 -1193.037 -1131.468
Table 1
Table 1 clearly shows that modelNIFTY0 and modelIFTY2 are rejected due to high
values in AIC and global deviance and was justified by the inadequacies in the worm
plots of figure 5 and figure 7. From modelNIFTY1 and modeNIFTY3 the AIC is lower for
modelNIFTY1 and higher for modelNIFTY3. But the global deviance is higher for
modelNIFTY1 compared to modelNIFTY3. The reason for this high deviation was
caused by dominant in some explanatory variables. Figure 8 showed nearly all values
close to zero which perfectly fit the model. But the best fit does not always guarantee
the best model. An argument can always be made which model to choose whether the
one that fits the data better or the one with the lowest AIC, but for this paper the
value with the lowest AIC is chosen that is modelNIFTY1.

Term Plots
The section discusses the term plots based on free scale that explains individual effects
of each explanatory variable with the NIFTY Index and its impact on the share prices.
Figure 9
Figure 9 is a graphical representation of modelNIFTY1 which show that the money
supply and exchange rate have a positive effect on the Index as expected the money
supply increases with stock prices due high demand in the economy. The reason for a
positive influence of exchange rate is due to the fact that the Indian Rupee has
depreciated and has boosts the export industry. The graph for the interest is not as
expected because it shows minor influence on the stock prices irrespective of the
changes in the interest rate although it should have a negative influence. The bottom
row of figure 6 clearly shows that the consumer price index is negatively related with
the index that was the expectation as inflation decreases the growth stocks becomes

more attractive to the investors and start investing in equities. The NIFTY lag has very
direct and proportional relationship with the NIFTY Index as it is its own lagged value
and has the highest influence. The industrial production keeps up with the expectation
of the economic theory and has a positive impact on the index that is as a company’s
dividends grow their earnings increases in turn increases their share prices. All the
variables has shown the expectation of the economic theory except for the interest
rate and this was the model that was chosen and had the lowest AIC value and was
adequate in fitting the data.
Figure 10
Figure 10 graphically shows that the money supply is as expected with economy theory
and has a positive influence on the stock prices but with less deviation and a more
direct proportion. The exchange rate also signifies a very straight and a strong
influence on the index with very little deviation. The population also shows an
influential negative relationship with stock market. This indicates that the investors are

mainly either in the young category that do not hold much of financial wealth or old
aged people that are using their investments made over the years. The consumer price
index beats the expectation of the general theory and investors prefer to consume
more rather than investing in the stock markets. The unemployment rate follows the
path of the economic theory which shows a negative relationship with the NIFTY index,
i.e. as the unemployment rate declines the stock prices increase because as people
have more jobs that increases there disposable income and are motived to invest in
the financial market in hope for a higher return. ALL of the variables have shown a very
direct relationship which is usually not the case and many have not kept up with
expectation of the economic theory this is due to the fact that this model did not
contain the NIFTY lag variable which was the determining force and also this model as
rejected by all the three criteria of the ACF, AIC and the worm plots and represents
modelNIFTY2
Figure 11

The above term plot of figure 11 is graphical representation of modelNIFTY3. The
industrial production shows a positive impact on the stock prices with high levels of
deviations as the prices increases which indicates that the companies are increasing
their production in anticipation of high demand which results in increased profits
which leads to payment of high dividends and increased share prices. Previous
research has proved that GDP has positive influence on the share price as it is an
indicator that analyses the health of a country. In this case the Indian economy is
booming due to liberalisation in the economic policies that was introduced in 1991
which has brought confidence in the investors for the growth of the economy and has
led to increase in the Index. Even in this plot the population is significantly decreasing
at a faster rate which points out that the middle-aged groups are still little reluctant in
investing in equities due to high risk. The inverse relationship with the CPI Index and
share price is as expected but the decline is slow which indicates that the economy is
slowly responding to the inflation rate and has a low impact. The NIFTY lag has the
same direct positive relationship shown as that of figure 9 and has the highest
influence on the share price. The exchange rate is influenced more by the export
industry and is positively increasing. All the variables have kept up the expectation of
the economic theory which indicates a good sign that the model correctly fits the data
and none of the series have caused drastic changes.
Model Selection
Based on the previous findings and model validation we conclude that modelNIFTY1 is
the best chosen model for interpreting the summary results and forecasting.
modelNIFTY1~
g (µ) = β11 -0.0196 + β12 0.0965 + β13 0.0178 + β14 0.00072 + β15 -0.1829 + β16 0.9427 +
β17 0.0585

g (σ) = β21 -4.7754 + β22 3.88219
g (υ) = β31 20.815+ β32 -7.329 + β33 -8.452 + β34 -14.941
In the above equation the g (µ) parameter which also known as the mu link parameter
explains the movement and the magnitude of each macroeconomic variable to the
share prices in the Index as this is the best chosen model using the AIC. This equation
summarises the term plot of figure 9. All the variables are statistically significant with
Index except for the Interest rate with its p value is way above the 0.05 mark this is
shown in the graph which indicated that it did not have any effect on the share price.
The money supply has a positive impact that is as the money supply in the economy
increases by 1 unit the share prices increases by 0.0965 units which is an indication
that the index quickly responds to the supply of monetary assets in the economy it is
also found that in order to continue driving the Index higher the market consistently
needs higher amount of money supply without which it will lose its momentum. As
Exchange rate increases by 1 unit it has positive effect of 0.0178 units on index which
has found that the currency has depreciated in terms of U.S dollar. The depreciation in
the currency has made it more attractive for foreign investors as they now can
purchase more volume of shares at a lower value. The interest rate has shown no
significance which gives a clear indication that changes in fiscal policy does not affect
the market. The consumer price index has an inverse relationship with stock prices, as
the consumer price index increased by 1 unit it showed a fall in share prices by -0.1829
units and is statistically significant. The decrease in the CPI is due to the decrease in
the inflation rate which indicates that the purchasing power has increased and
investors prefer to invest more in income generating stocks that are the dividend that
pay them more than what they could have earned from investing in value stocks such
as equities. The NIFTY lag is the most important variable in determining the movement
of the index. It has the highest positive impact of 0.9427 units. As the Industrial

production increased by 1 unit it is followed by a direct increase of 0.0585 in the stock
prices of the index. This positive impact shows that the manufacturing industry is
booming and as the demand increases the production increases which leads to
increase in corporate profits. As India is a developing economy industrial sector plays a
significant role and becomes an important tool for predicting the future GDP growth.
The g (σ) parameter is used as an indicator that explains the volatility of the index in
terms of the percentage change that is affected by the explanatory variable and is also
the standard deviation. The NIFTY lag is the only variable that has been chosen which is
statistically significant and is highly volatile with the index with a positive impact of
3.88%.
g (υ) is the nu link that signifies the skewness that measures the asymmetry in
probability distribution. It indicates whether the distribution is right tailed ore left
tailed depending on the signs of the coefficient. The general theory suggests that all
the explanatory variables should be normally distributed with its mean value being
zero, but in this case it will not be possible as this model uses the TF family
distribution. As shown in the above equation all the variables are left tailed with
unemployment and NIFTY lag being statistically significant at p values of 0.0069 and
0.0005. The skewness for these variables are -7.329 and -8.452 respectively and fall on
the left hand side. The third variable indicates the exchange rate although it is highly
skewed to the left compared to the other two variables with its coefficient value being
-14.941 it is insignificant with p value being 0.0771 > 0.05.

Forecasting
Figure 12
So far we have discussed different models and applied different techniques that would
be suited for an individual to invest in financial markets. But the integral part of any
investment lies in its future values. For this reason forecasting of the market is an
important part of any analysis. This section provides insights of the future prices of the
NIFTY Index that would be helpful tool for not only investors but also government
agencies in predicting the economic growth of the country. The vertical axis signifies
the forecast prices on point basis and the horizontal axis indicates the time. As shown
in the above figure 12 the black line tells us about the actual data and the red line
shows us the predicted values. The forecasting period is from January 2011 to
December 2015 on monthly basis. The overall market has shown a fall with very high
volatility and its prices constantly dropping this indicates that the market is bearish.
The predicated values shows signs of lag in comparison to actual data. This widespread
pessimism and negative sentiments has caused investors to hold back and are
reluctant in investing in any financial instruments. In these situations traders and
investors try to short sell their investments which are quite difficult for those holding
long term positions. The index is trended downwards for almost all the forecasting

period which is not a good sign for the economy. At the end of 2010 the nifty was well
above the 0.8 basis points and had a great fall just slight above 0.5 basis points. By
2013 end the nifty had crashed with it lowest value of 0.1 basis points, whereas the
actual data showed an increase, this trend almost lasts for long term forcing the
investors to change their strategic long term plans. This decline is due to decrease in
corporate profits or correction of overvaluation (i.e. stocks become too expensive and
fall to a more reasonable level).
Recommendation: - this section suggests some recommendation that would help
investors and policy maker’s deal with bearish market that has created lack of
confidence in the economy. There are several strategies that could be used and one of
them is to sell their investments into much more stable financial instrument or hold
cash. Shor term government bonds help reduce their risk in the stock market and
minimize the effects. These government bonds are inversely correlated with the stock
market and tend to rise in a falling economy. Savings and money market account
provides a strong platform and a medium to earn interest without the risk of market
fluctuations. In addition to these strategies investors can find stability in defensive
stocks that is shifting their portfolios to more established companies having strong
balance sheets commonly known as defensive companies this creates a hedge and
protects investors as they are paid regular dividends because eventually the market
will shift and it is the best strategy for long term investors willing to hold their financial
assets.

Conclusion
In this paper we analyse the long term and short term equilibrium relationships
between macroeconomic variables and the NIFTY Index of the National Stock Exchange
of India. These variables are represented by the Industrial Production, Interest Rate,
Exchange Rate, Consumer Price Index, Unemployment, GDP, Population and Money
Supply. We employed the GAMLSS technique that was used to construct 4 sets of
quantitative model using the normal and TF family distribution.
In the first part for our model validation we checked for auto correlation in the
residuals and found that modelNIFTY0 and modelNIFTY2 are highly correlated within
the explanatory variables which are rejected. By using the worm plots we test for the
inadequacies in the model and the results also showed that both the modelNIFTY0 and
modelNIFTY2 are very inadequate for modelling. The data. In the third part we used
the term plots to explain individuals effects of each macroeconomic variables on the
Index and concludes that figure 10 is clearly rejected as it did not satisfy any of the
other criteria plus the plots showed questionable results that were completely
opposite of the general economic theory. Among figure 9 and figure 11 both have
given reasonable conclusions that agree with the economic theories except for interest
rate in figure that showed minor effect, despite this set back figure 9 was chosen as
the best model because it satisfied all the criteria’s plus had the lowest value in AIC.
In the section for model selection Exchange Rate and Interest found insignificance with p
values 0.245 and 0.9008 respectively the volatility was very high with 3.88% with all the
variables being skewed on the left hand side. In context of forecasting it showed a fall in the
market which indicated that the market is bearish and should avoid investing in growth stocks.

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Appendix
modelNIFTY0~
g(µ) = β41 + β42 MS + β43 ExchRate + β44 InterestRate + β45 CPI + β46 Indprod + β47
Populaiton + β45 GDP
g(σ) = β51
Mu link function :Identity
Estimate Std. Error t value Pr(>ǀtǀ)
Intercept -0.349880 0.069291 -5.049 9.28e-07
MS -0.504923 0.235533 -2.144 0.033165
ExchRate 0.432936 0.063626 6.804 9.75e-11
InterestRate 0.006197 0.031774 0.195 0.845542
CPI 0.266982 0.332172 0.804 0.422423
IndProd 0.440578 0.125145 3.521 0.000525
Population -1.123593 0.180696 -6.218 2.55e-09
GDP 44.237383 7.089427 6.240 2.27e-09
Sigma link function : log
Intercept -2.96292 0.04704 -62.99 <2e-16

modelNIFTY1~
g(µ) = β11 + β12 MS + β13 ExchRate + β14 InterestRate + β15 CPI + β16 NIFTYLAG + β17
IndProd
g(σ) = β21 + β22 NIFTYLAG
g(υ) = β31 + β32 Unemployment + β33 NIFTYLAG + β34 ExchRate
Intercept -0.0196 0.0158 -1.239 0.2166
MS 0.0965 0.0412 2.339 0.0203
ExchRate 0.0178 0.0155 1.143 0.2545
InterestRate 0.00072 0.0058 0.15 0.9008
CPI -0.1829 0.0712 -2.567 0.0109
NIFTYLAG 0.9427 0.0265 35.464 <2e-16
IndProd 0.0585 0.0267 2.193 0.0294
Intercept -4.7754 0.07804 -61.195 <2e-16
NIFTYLAG 3.88219 0.45119 8.604 1.69e-15
Nu link function: logshiftto2
Intercept 20.815 8.619 2.415 0.0165
Unemployment -7.329 2.691 -2.724 0.0069
NIFTYLAG -8.452 2.409 -3.508 0.0005
ExchRate -14.941 8.414 -1.776 0.0771
modelNIFTY2~

g(µ) = β71 + β72 MS + β73 ExchRate + β74 Population + β75 CPI + β76 Unemployment
g(σ) = β81 + β82 GDP + β83 MS + β84 CPI + β85 Population
g(υ) = β91 + β92 CPI + β93 MS + β94 GDP + β95 InterestRate
Intercept -0.08118 0.03189 -2.545 0.01164
MS 1.33969 0.07209 18.584 <2e-16
ExchRate 0.17941 0.03514 5.105 7.39e-07
Population -0.52041 0.08115 -6.413 9.28e-10
CPI 0.54977 0.24389 2.254 0.02522
Unemployment -0.03865 0.01358 -2.846 0.00487
Intercept -3.4816 0.1651 -21.087 <2e-16
GDP 225.9923 133.4494 1.693 0.0918
MS 3.3624 4.9720 0.676 0.4996
CPI -0.7394 7.2165 -0.102 0.9185
Population -6.0262 3.4149 -1.765 0.0791
Intercept 19.7301 3.8861 5.077 8.44e-07
CPI -85.2017 31.3054 -2.722 0.00704
MS 2.8404 18.5194 0.153 0.87825
GDP -0.5047 388.8845 -0.001 0.99897
InterestRate -15.5032 3.0145 -5.143 6.19e-07
modelNIFTY3~
g(µ) = β101 + β102 IndProd + β103 GDP + β104 Population + β105 CPI + β106 NIFTYLAG + β106

ExchRate
g(σ) = β111 + β112 GDP + β113 MS + β114 CPI + β115 Population
g(υ) = β121 + β122 CPI + β123 MS + β124 GDP + β125 InterestRate + β126 ExchRate
Intercept -0.01150 0.02143 -0.537 0.5921
IndProd 0.08549 0.3237 2.641 0.0089
GDP 5.55027 1.32149 4.200 3.96e-05
Population -0.15743 0.02908 -5.414 1.69e-07
CPI -0.06075 0.09140 -0.665 0.5070
NIFTYLAG 0.87186 0.03100 28.124 <2e-16
ExchRate 0.01269 0.02471 0.514 0.6080
Intercept -4.0849 0.1584 -25.786 <2e-16
GDP 110.9443 131.3606 0.845 0.399
MS 6.1419 5.5433 1.108 0.269
CPI -8.0620 9.7744 -0.825 0.410
Population -2.7002 4.0122 -0.673 0.502
Intercept 64.26 111.52 0.576 0.565
CPI -31.56 78.71 -0.401 0.689
MS 8.87 35.77 0.248 0.804
GDP -993.92 1936.96 -0.513 0.608
InterestRate -24.38 36.91 -0.661 0.510
ExchRate -39.30 79.24 -0.496 0.620

Impact of Macroeconomic Variables on NIFTY Index

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