Mathematical Model for Evaluation of Assets Returns in a Volatile Economy
CHAPTER ONE
Aims and Objectives of the Study
Aims
The aim of this study is to critically investigate the macroeconomic factor model in order to identify the effects of macroeconomic variables on the performance and efficiency of Nigerian Stock Exchange Market in a Volatile economic situation.
Objectives
The objectives of this study are to
- formulate a model for the macroeconomic variables,
- use macroeconomic factor model to analyze the effects of the macroeconomic variables on the 114 companies listed on the Nigerian stock exchange market and
- determine the liquidity of the Nigerian stock
Chapter Two
Literature Review
The state of the art focusing on problems of assets return, risk and the effectiveness of market volatility on the expected returns shall be covered in this chapter. Macroeco- nomic variables are indicators signaling the current trends in the economy. Therefore it is necessary to study, analyze and understand the major variables that determine the current situation of the economy. The quality to which these policies are applied differ from one country to another as the different political process from which these policies emerge are unique to each country. Therefore it is essential for an investor and/or financial analyst to be aware of the effect of news on the assets return in order for them to optimize their portfolio.
Chen et al (1986), studied economic forces and the stock market using Arbitrage pricing theory(APT) framework. They found a significant relationship between the industrial production , inflation rate US ,interest rate , bond yield and the US stock exchange. Fama et al (1992) investigated the cross-section expected stock return to test whether the average stock returns are positively related to market beta’s. They concluded that β does not seem to help explain the cross-section of average stock returns and that the combination of size and book-to-market equity seems to absorb the roles of leverage and earnings to price ratio in average stock returns during the period of study (1963–1990). They Their studies revealed that stock risk are multidimensional if assets are priced rationally and that the risk is proxied by size, market equity and by the ratio of the book value of common equity to its market value. They used the returns of all non-financial firms listed on NYSE, AMEX and NASDAQ.
Taulbee(2000) examined the effect of economic variables on the US economy using S&P 500 in order to determine hoe the performance of the economy influences the success of the stock market and vice versa. He studied hoe interest rates, real GDP and the Fisher effect impact theS&P 500 and various industries including utilities, transport, financial, and technology index. The result of his studies showed that the real GDP is the greatest economic determinant of stock market prices. He also discovered that unemployment rate significantly influence the performance of the overall stock market but does not indicate which industry to invest in and more so inflation and interest rate affects stock market significantly.
Cagnetti (2001) investigated the Italian stock market (ISM) using monthly data from 1990 to 2001, he applied both the Capital Asset Pricing Model and the Arbitrage pricing theory to establish the relationship between the ISM returns and the macroeconomic variables. His studies showed that the relationship between the macroeconomic vari- ables and the stock return was very weak and that the shares and/or portfolio in ISM are significantly influenced by a number of systematic forces which behavior can be explained by the macroeconomic variables. The focus of his paper was to test and compare the CAPM and APT in the Italian stock market in order to determine the model that performs better in explaining the behavior of share prices in the ISM. He resolved that the APT performs better than the CAPM in the overall tests considered.
Maysami et al(2004), examined the long term equilibrium relationship between selected macroeconomic variables and Singapore stock market as well as the hotel index using co integration analysis. They concluded that Singapore’s stock market and property index formed co-integration relationship with changes in the short and long-term in- terest rates, industrial production price level, exchange rate and money supply. The finance index and Hotel index form insignificant relationship with money supply and long term interest rate.
Jechche (2005) examined the arbitrage price theory within a vector autoregressive (VAR) framework theory for the case of Zimbabwe stock market and three macroe- conomic variables; (CPI) inflation, exchange rate, and Gross domestic product using Granger causality test with impulse response and variance decomposition. Granger causality show that there is unidirectional causality from consumer price index to stock price, but no causality between GDP, exchange rate and stock price. Variance decomposition indicated that GDP explains deviations in the stock prices while im- pulse response function reveal a significant relationship between exchange rate and stock market price of Zimbabwe.
Shenken et al (2006) re-examined the pricing models of Chen, et al (1986) and found a significant relationship between the industrial production growth factor and the VW market while the cooperate government bond return spread was insignificantly negative for the period of study which corroborate the cross section regression results.
Humpe et al (2007) examined the influence of macroeconomic variables on the stock prices in the US and Japan using standard discounted value model, they used cointegration analysis to model the long term relationship between industrial production, consumer price index, money supply, long term interest rate and stock prices in the US and Japan. The stock prices positively related to industrial production index and neg- atively related to both the consumer price index and long term interest rate based on the US stock market data. Whereas, the Japanese data indicated that stock prices are influenced positively by the industrial production index and negatively by the money supply and also the industrial production was negatively influenced by the consumer price index and long term interest rate.
Chapter Three
Method
Theoretical framework
Assets and Returns
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 benefit. We shall be investigating equity oriented assets that’s the stock market; a type of security that signifies ownership in a corporation and represents a claim on part of the corporation’s assets and earnings which may either be a gain or loss of a security in a given period. Most investors are concerned with financial risk. The return on an investment is expressed as a fraction of its revenue and the initial investment. If an investor buy an asset at the end of a holding period t1 with price Pt1 and later sold the asset at Pt2 at the end of the holding period t2, then the net return over the holding period from t1 to t1 is given by;
Research Method
This study is going to employ the macroeconomic variables factor model to determine the relationship between stock prices and the selected macroeconomic variables and shall use the unit root test (the Augmented Dickey Fuller test) to verify the stationarity of the stock data. Factor models for assets returns are used to;
- Decompose risk and return into explainable and unexplainable components,
- Generate estimates of abnormal return (performance measurement),
- Predict returns in specified stresss cenarios,
- Describe the variability and co-variability structure of returns(diversification),
- Provide a framework for portfolio risk
Macroeconomic factor model use observable economic time series like interest rate, inflation and consumer price index as measures of pervasive or common factors in assets returns. The factor models for asset returns have the general form below;
Chapter Four
Results and Discussion
Results
In this section we describe the statistical properties of the asset returns data and the macroeconomic variables. The purpose of this section is to apply the techniques of exploratory data analysis for financial time series and document facts about the assets and macroeconomic variables.The final dataset used in this work comprises of one hundred and fourteen (114) companies stock returns (from 2005 to 2013) and seven (7) selected macroeconomic variables. These time series data of eighty (80) companies started from 2005; twenty one (21) companies series started from 2006; eleven (11) companies series started from 2007 and two (2) companies series started from 2008. We use this series without truncating in order to ensure a better understanding of the effects of the selected macroeconomic variables on each of the companies stock returns. The dataset includes also a fair selection of various companies from the different sectors of the economy but because of secrecy and image of the companies, we use anonymous names in order to avoid legal issues.
Chapter Five
Summary, Conclusion and Recommendation
Introduction
This chapter presents the summary of the thesis, conclusion and recommendations based on the research carried out.
Summary
In this thesis, we considered the mathematical framework of the macroeconomic factor model to determine the effect of macroeconomic variables on the Nigerian Stock market returns. This work was motivated by the possibility that the model could improve our understanding of the volatility of the Nigerian economy, particularly the influence of inflation, interest rate, money supply, exchange rate, crude oil prices, gross domestic product and unemployment on the the Nigerian stock market return.
Conclusion
We investigated the impact of macroeconomic variables on the stock market return data of 114 companies in Nigeria using a macroeconomic multi-factor model with each of the individual returns as the dependent variable. In this study, we tested the im- pact of macroeconomic variables on the stock returns of 114 from January 2005 to December 2013. The macroeconomic variables used in the study are inflation, inter- est rate, money supply, exchange rate, crude oil prices, gross domestic product and unemployment. The empirical results revealed that there is a significant relationship between stock returns of the stock market returns of each of the 114 companies and the selected macroeconomic variables. For company C1,β0=218.15,β1=0.5657,β2=- 45.95,β3=-4.59,β4=19.66,β5=-10.047,β6=0.08,β7=-0.85 and using INF = 2.37, FER =
4.87, GDP = 2.14, UER = 2.5, IR = 2.9, OP = 4.15, M2 = 2.82 which on substitution
yields a return of 149.3 on the asset. Some companies reacted positively to the macroe- conomic variables while others reacted negatively. Thus an increase in a particular macroeconomic variable will yield a corresponding increase or decrease in the return of some company stocks. The hedge ratio of some companies were negative which implies that such companies were operating on borrowed funds within the period of study.
Recommendations
Based on the results of this research, it is recommended that investors in the stock market should use this information as a basis for evaluating and selecting the stocks to trade on. Thus, we recommend economic policies that will keep the exchange rate stable and the interest rate reduced to a single digit to encourage availability of resources for investors. Also, inflation, unemployment and the gross domestic product should be optimized with a corresponding level of money supply. Nonetheless, the Nigeria economy should be diversified so as to utilize other sectors to stabilize the economy and also crude oil should be refined locally in order to reduce the effect of exchange rate. This will improve the balance of trade and payment which will help in stabilizing the volatility of the other macroeconomic variables.
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