A Mathematical Model For Evaluation Of Assets Returns In A Volatile Economy – Complete project material

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ABSTRACT

In recent years, advance in technology have made it possible for the stock markets
to trade in real time and also for large dataset to be available for statistical analysis.
Thus, we examined the impact of macroeconomic variables on the stock returns of
114 companies listed on the Nigerian Stock Exchange Market. We have established
the mathematical framework required to solve our model and perform various empir-
ical analysis on the stock market data and macroeconomic variable. The formulated
Macroeconomic Factor models are deployed to evaluate the eects of the macroeco-
nomic variables on a volatile economy and Ordinary Least Square procedure are de-
ployed to estimate the parameters of the model. We apply the model to the available
data and discovered that the stock market return volatility is in uenced by the selected
macroeconomic variables; Gross Domestic Product, In ation, Foreign Exchange Rate,
Unemployment, Interest Rate, Price of Crude Oil and Money supply.
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TABLE OF CONTENTS

Approval i
Certication ii
Dedication iii
Acknowledgments iv
Abstract v
1 Introduction 1
1.1 Background of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Hypothesis of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Aims and Objectives of the Study . . . . . . . . . . . . . . . . . . . . . 6
1.4.1 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Scope and Limitations of the Study . . . . . . . . . . . . . . . . . . . . 6
1.6 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.7 Main Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.8 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Literature Review 10
3 Method 21
3.1 Theoretical framework . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.1 Assets and Returns . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.2 Assets Pricing Models . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.3 Macroeconomic Variables Description . . . . . . . . . . . . . . . 28
3.2 Research Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3 Formulation of the Model . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.1 Existing Model by Izedonmi et al (2011) . . . . . . . . . . . . . 37
3.4 Macroeconomic Factor Model for Returns . . . . . . . . . . . . . . . . 37
3.5 Unit Root Test for the Stock Data and the Macroeconomic Variables . 39
3.5.1 Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5.2 Non-Stationarity and Stationarity Test . . . . . . . . . . . . . . 40
3.6 Data and Data Source . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
x
4 Results and Discussion 44
4.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.1.1 Descriptive Statistics of the Stock Data . . . . . . . . . . . . . . 44
4.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2.1 Discussion of the Hedge Ratio (i0
) . . . . . . . . . . . . . . . . 47
4.2.2 Eects of In ation (i 1t) . . . . . . . . . . . . . . . . . . . . . . 47
4.2.3 Eects of Exchange Rate (i 2t) . . . . . . . . . . . . . . . . . . 48
4.2.4 Eects of Gross Domestic Product (i 3t) . . . . . . . . . . . . . 48
4.2.5 Eects of Unemployment Rate (i 4t) . . . . . . . . . . . . . . . 48
4.2.6 Eects of Interest Rate (i5
t) . . . . . . . . . . . . . . . . . . . 48
4.2.7 Eects of Price of Crude Oil (i 6t) . . . . . . . . . . . . . . . . 49
4.2.8 Eects of Money Supply, M2 (i 7t) . . . . . . . . . . . . . . . . 49
5 Summary, Conclusion and Recommendation 50
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.4 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Appendix A 52
Appendix B 109
Appendix C 117
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CHAPTER ONE

Introduction
1.1 Background of the Study
Nigeria is supposed to be one of the world’s richest nation if the natural reserve were
used as a measure of wealth. In reality, oil reserve have been a curse to Nigeria instead
of a blessing as the Agricultural, solid minerals and other non-oil sectors which were
the main source of export have been neglected. This has made crude oil to be the main
product of Nigerian export, thus giving an unfavorable balance of trade and payment
which greatly aects the Nigerian economy in particular exchange rate, unemployment
rate and in ation.
In recent years Nigeria has become a crude oil exporting and nished products (from
crude oil) importing country, the balance of payment for the import and export may
either be favourable or unfavourable. This volatility of oil prices have varying conse-
quences on Nigeria as will reap the benet of high oil prices as well as experience the
unfavorable terms of trade in our external sector that can be transferred into the econ-
omy in the long run from oil imports. This situation makes the value of the exchange
rate to increase thereby reducing the purchasing power of local currency and increas-
ing the cost of importing raw materials and production. This change in exchange rate
makes trade and investment more challenging since the decision makers cannot predict
the approximate value of the exchange rate, thus resulting to in ation as the prices
of most commodities will rise rapidly with little or no incentive to search for cheaper
substitute that could help keep the production cost low.
1
The uncertainty about the future value of Naira and real interest rates makes busi-
nessmen or decision makers less willing to take risk in investing in long term projects.
As in ation rises businessmen shift their investments to gold and real estate instead
of holding of stocks and bonds. The interest rate volatility results to less business in-
vestment and a reduction in the real economic growth as the supply of funds available
for businessmen to borrow reduces thereby raising the cost of investment and maybe
eventually the closure of the business. This is evidenced in the increase in interest rate
to account for in ationary uncertainty, thus the cost of borrowing by businessmen and
consumers increases substantially.
Investors always react to changes in market news so as to minimize the risk of in-
vesting in order to maximize prot. Thus they tend to select the stock to invest in
based on looking at the historic data of the adjusted closing price of the various stocks
and trying to predict the future outcome. This has increased the interest of nancial
analyst, policy makers and academics in nancial markets and the quest to forecast
their performance with the increasing impact of macroeconomic variables. However,
in Nigeria there is less attention in the study of the relationship between stock prices
and fundamental economic activities.
The relationship between macroeconomic variables and stock market has been discussed
in previous research papers such as Chen et al (1986), Abraham (2010) that deal with
this topic in various ways. It is expected that the macroeconomic factors should aect
the prices of stocks which in turn should in uence the real economy. During the last
two decades, empirical studies relating to this subject matter began to be a topic of
interest with new improved methods to analyze the correlation between scal and real
economic world. The major problem is distinguishing the magnitude in terms of size
and direction of the relationship that exist between some macroeconomic variables and
stock market. The results achieved from previous research by Chen et al (1986), Gay
(2008), Zhu (2012) among others which will be discussed more in literature review show
no signicant change over time, though the evidence remains relevant for new markets
trying to enter global nancial world. They considered risk and returns as the two
factors that can determine the value of nancial assets. For emerging economy, these
2
two factors are not enough determinant as to whether or not to invest in a particular
asset. Markowitz (1952) stated the golden rule underlining the theory of investment
that investors seek either to maximize returns at a given level of risk or to minimize
risk at a given level of returns on their investment.
Generally speaking, Capital Asset Pricing Model (CAPM) and Arbitrage Pricing The-
ory (APT) are the two broad frameworks for pricing nancial assets. In particular, the
CAPM is a one factor model which relies mostly on a measure, beta, which stresses
the sensitivity of asset unpredictability to the unpredictability of the entire market.
On the other hand, the APT is a multi-factor model, which traces the expected return
on a number of securities to their sensitivities. The Nigerian Stock Exchange (NSE)
was established in 1960 as the Lagos Stock Exchange. As of December 31, 2013, it has
about 200 listed companies with a total market capitalization of about N12.88 trillion
(80.8 billion USD). The NSE is regulated by the Securities and Exchange Commission
(SEC), which has the mandate of Surveillance over the stock exchange market in order
to forestall violation of market rules and to deter and detect unfair manipulations and
trading practices.
Data on listed companies performances are published daily, weekly, monthly, quar-
terly and annually. The Nigerian Stock Exchange has been operating an Automated
Trading System (ATS) since April 27; 1999; with dealers trading through a network
of computers connected to a server with facility for remote trading and surveillance.
Consequently, many stock brokers trade on-line from their oces in Lagos and from all
the thirteen branches across the country. The Exchange is in the process of establishing
more branches for on-line real time trading. Trading on the Exchange starts at 9.30
a.m. every business day and closes at 2.30 p.m.
In order to encourage direct foreign investment into Nigeria, the government have to
review the legislation preventing the ow of foreign capital into the country. This
has allowed foreign brokers to enlist as dealers on the Nigerian Stock Exchange, and
investors of any nationality are free to invest. Nigerian companies are also allowed
multiple and cross border listings on foreign markets. It is expected that an eective
and ecient market should re ect the real economy; that is to say, that the stock
3
market prices should incorporate the eect of changes in the macroeconomic variables
such as in ation, GDP, exchange rate among others. This thesis does not use NSE
all share prices index as the measure of stock market movements as dierent sectors
and/or companies within the same sector respond dierently to changes in the macroe-
conomic variables. Several research work mostly in the developed countries deal with
recent economic development and problems, especially about the relationship between
returns and macroeconomic variables. However, stock market interactions with macroe-
conomic variables remain a topic of interest to the developing countries. As the market
is not perfectly integrated with global nancial world, local macroeconomic factors can
in uence the stock market returns more than global risk factors. In the light of previ-
ous empirical evidence this research work purposes to model empirically the eect of
macroeconomic variables and the selected stock data of 114 companies from dierent
sectors of the economy using microfoundations. According to Jerey(2012), the advan-
tage of building macroeconomic models from microfoundations is that we can begin
to understand the relationship between macroeconomic outcomes and the individual
decisions of the agents in the economy.
1.2 Statement of the Problem
The rate of uctuation in the returns on stocks and the continuous decrease and/or
increase in several macroeconomic variables has created panic in the Nigeria Stock
Market. Studies on the interactions among the selected macroeconomic variables and
selected stock market returns in Nigeria Stock Exchange market is the main purpose of
this research. The presence of correlations between the stock price and macroeconomic
variables can be explained, conversely, if the results support signicance of macroeco-
nomic variables and stock market returns, we can use them as a price determination
tool for share prices. Most researchers have focused on systematic risk such as con-
sumer price index, in ation, interest rate and so on as sources of risk. This means
that in the long run, the returns on an asset should re ect the true situation of the
economy. Many studies carried out in the developed world such as the US, the UK
among others have attempted to establish the relationship between assets returns and
4
economic indicators (Chen et al (1986), Gay (2008), Zhu (2012)).
The importance of establishing these relationships to investors is extremely imperative
given that the risk faced by investors may be traced to the changing values of these
economic variables. Several empirical studies have tested these relationships using the
CAPM and APT on stock data of various countries and their results show that the
theory has the possibility of explaining the returns on such capital markets. In devel-
oping and emerging capital markets of Africa including that of Nigeria, there are no
widespread studies relating stock markets returns with macroeconomic variables such
as interest rates, in ation, price of crude oil and money supply among others which
to a large extent are expected to aect stock market activities. We seek to nd out if
macroeconomic variables have any eect on the Nigeria stock exchange (NSE) returns?
We shall use the factor model which is based on the arbitrage pricing theory (APT)
framework to examine the relationship between selected macroeconomic variables and
the Nigerian stock market.
1.3 Hypothesis of the Study
Based on general intuitive theory suggested by Fama (1981) and previous literatures
on this topic, we hypothesis that there is no relationship between the selected macroe-
conomic variables such as in ation, money supply, consumer price index, exchange
rate, price of crude oil, gross domestic product and the returns of the 114 companies.
Mathematically,
0 = 1 = 2 = 3 = 4 = 5 = 6 = 7 = 0
Where
0 is the eect of hedge ratio (a measure for liquidity),
1 is the eect of in ation rate,
2 is the eect of exchange rate,
3 is the eect of gross domestic product,
4 is the eect of unemployment rate,
5 is the eect of interest rate,
6 is the eect of price of crude oil,
5
7 is the eect of money supply.
1.4 Aims and Objectives of the Study
1.4.1 Aims
The aim of this study is to critically investigate the macroeconomic factor model in or-
der to identify the eects of macroeconomic variables on the performance and eciency
of Nigerian Stock Exchange Market in a Volatile economic situation.
1.4.2 Objectives
The objectives of this study are to
formulate a model for the macroeconomic variables,
use macroeconomic factor model to analyze the eects of the macroeconomic
variables on the 114 companies listed on the Nigerian stock exchange market and
determine the liquidity of the Nigerian stock exchange.
1.5 Scope and Limitations of the Study
The specic goal of this work is to determine the eect of selected macroeconomic
variables on the historic data of asset returns of 114 rms listed on the Nigeria stock
exchange (NSE). The results from this research may not give an accurate replication of
what goes on in all other markets because the features of two dierent markets or group
of stock markets diers hence their reaction to the selected macroeconomic variables
will dier. The macroeconomic variables selected namely; Money supply, Exchange
rate, Gross Domestic Product, In ation, interest rate, unemployment rate and crude
oil prices are factors that we have applied to the macroeconomic factor model. We
have used the R statistical programming language to analyze the nancial data and in
estimating the macroeconomic factor model.
6
1.6 Motivation
We saw that previous models on the eect of macroeconomic variables and stock returns
such as in studies by Chen et al (1986), Maysami et al(2004), Kuwornu et al (2011),
Izedonmi et al (2011) among others, were based on either the all share index or the
sectoral index and used a selection of less than six (6) macroeconomic factors. However,
we discovered through research that the macroeconomic variables are the determinant
of the state of an economy. For instance, a close investigation of the developed country
shows that unemployment is inversely proportional to in ation because the developed
economy are ecient and they engage all available resources including human skills in
production using the principle of comparative advantage. Nigeria has suered socio-
political and economic setbacks which has aected the quality of the macroeconomic
policy and thus tends not to follow most of these economic principles as postulated by
the developed countries.
In light of the above, we see that the existing models may not have properly taken
care of the situation of addressing the eect of macroeconomic variables on the stock
returns bearing in mind the volatility of the Nigerian economy. Hence, our desire
to remodel the multifactor model taking into account more macroeconomic variables
and liquidity. More so, our model build bridges between micro-level structures and
macro-level relationships among variables.
1.7 Main Contributions
We combined the macroeconomic variables and the individual stock returns in order
to achieve a better understanding of how the Nigerian economy behaves. Also, we con-
sidered the volatility of the macroeconomic variables and liquidity. This model builds
bridges between the underlying micro-level structures and macro-level relationships
among the variables.
7
1.8 Glossary
Stock: A share of a company held by an individual or group.
Asset: refers to a resource with economic value that an individual, corporation, state
or country owns or controls with the expectation that it will provide future benet.
Return: The gain or loss of an asset in a particular period.
Volatility: is a measure for the variation of price of a nancial asset over time.
Macroeconomics: the study of the economy as a whole, and the variables that con-
trol the macro-economy.
Portfolio: A grouping of nancial assets such as stocks, bonds and cash equivalents
among others held by an investor.
Risk: means uncertainty in future returns from an investment.
Idiosyncratic risk: risk that is associated with an individual asset.
Exports: The Amount of Domestically Produced Goods Sold on Foreign Soil.
Imports: The Amount of Goods Produced on Foreign Soil Purchased Domestically.
Option: In nance, an option is a contract which gives the buyer (the owner) the
right, but not the obligation, to buy or sell an underlying asset or instrument at a
specied strike price on or before a specied date.
NYSE: New York Stock Exchange.
AMEX: American Express Financial Services Company
NASDAQ: National Association of Securities Dealers Automated Quotations
SENSEX: is an abbreviation of the Bombay Exchange Sensitive Index
FMCG: Fast-moving consumer goods
FII: Foreign Institutional Investment
CMR: Call Money Rate
ADF: Augmented Dickey Fuller
DF: Dickey Fuller
AR(p): Autoregressive Process of order p, p=1,2, . . .
MA(q):The q Order Moving Average
ISE: Istanbul Stock Exchange
8
APT: Arbitrage Pricing Theory
CAPM: Capital Assets Pricing Model
9

 

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