MULTIPLE REGRESSIONS ON SOME SELECTED MACROECONOMIC VARIABLES ON STOCK MARKET RETURNS FROM 1986-2010

Advances in Economics and International Finance AEIF Vol. 1(1), pp. 1-11, December 2014 Available online at http://www.academiaresearch.org Copyright 2014 Academia Research Full Length Research Paper MULTIPLE REGRESSIONS ON SOME SELECTED MACROECONOMIC VARIABLES ON STOCK MARKET RETURNS FROM 1986-2010 Abstract Accepted 25 November, 2014 There is a consensus among macroeconomists and finance theorists that stock market prices are driven by macroeconomic variables, the so called fundamentals in the economy. The question of whether the stock market can predict the economy has been widely debated. Those who support the market s predictive ability argue that the stock market is forward looking and current prices reflect the future earnings potential, or profitability of firms. Since stock prices reflect expectations about profitability and profitability is directly linked to economic activity, fluctuations in stock prices are thought to lead the direction of the economy. In this study, a multiple regression analysis is applied in order to model the long term relationship between macroeconomic variables (Inflation rate, interest rate, and exchange rate) and stock prices (All shares index) in Nigeria. Our estimation reveals that only exchange rate was significant while interest rate and inflation rate were not significant in estimating All share index for the period under study. Furthermore, our results also shows that there was high correlation coefficient between All share index and macroeconomics variables. It was also observed that 54.2% of the total variation in the All share index can be explained by the inflation rate, interest rate and Exchange rate. Key words: Macroeconomic variables, stock market, multiple regressions, Anova. Authors` Affiliation M.S. Ladan 1, A.M. Karim 1, K.S. Adekeye 2 1Department of Statistics, Yaba College of Technology, Yaba, Lagos. Email: sm_ladan@yahoo.com 2Department of Mathematical Sciences, Redeemer's University, Km. 46, Lagos-Ibadan Expressway. Ogun State, Nigeria. Email: samadek_2017@yahoo.co.uk INTRODUCTION There is a consensus among macroeconomists and finance theorists that stock market prices are driven by macroeconomic variables, the so called fundamentals in the economy. Moreover, it is also agreed that the linkage is two ways that is; feedback exists between the stock market and real activity. The question of whether the stock market can predict the economy has been widely debated. Those who support the market s predictive ability argue that the stock market is forward looking and current prices reflect the future earnings potential, or profitability of firms. Since stock prices reflect expectations about profitability and profitability is directly linked to economic activity, fluctuations in stock prices are thought to lead the direction of the economy. The characteristics which all stock market have in common are the uncertainty which is related with the short and long term future state. This feature is undesirable for the investor but it is also unavoidable whenever the stock market is selected as the investment tool. The best that one can do is to try to reduce this uncertainty. Stock market prediction (or forecasting) through macroeconomic variables is one of the instruments in the process. The stock market prediction task divides researcher and academics into two groups: those who believe that we can devise mechanisms to predict the market and those who believe that the market is efficient and whenever new information comes up the market absorbs it by correcting itself, thus there is no place for prediction. Furthermore, they believe that the stock market follows a random walk which implies that the best prediction you can have about tomorrow s value is today s value. The finance and economic literatures have been devoted to studies on the relationship between stock market returns and macroeconomic variables in developed economies, with little or no attempt in unfolding this relationship in a developing economy like Nigeria. This study therefore attempts to examine the relationship (if any) between economic fundamentals and stock prices in Nigeria. Researchers to a large extent focus on studying the interactions between the financial and macroeconomic variables on stock markets in different countries with widespread econometric methods. However, very little has been conducted in Nigeria and this study seeks to analyze specifically the relationship that exist among the highly

Ladan et al. 2 volatile financial markets specifically short term interest rate, exchange rate and inflation on stock market returns due to the increased focus on the African stock market in recent times. LITERATURE REVIEW The dynamic relationship between macroeconomic variables and share returns have been widely discussed and debated. Several studies have investigated the relationship between stock prices and level of economic activities in developed countries. Studies on non- US markets have mostly been based on the (Chen et al., 1986) approach. Hamao (1988) tested the Japanese market and found strong pricing evidence except for the case of Japanese monthly production. (Kwon and Shin, 1999) applied Engle-Granger co integration and the Granger- causality tests from the Vector Error Correction Model (VECM) and found that the Korean stock market is co integrated with a set of macroeconomic variables. Poon and Taylor (1991) are also unable to explain stock returns in the UK by factors used by (Chen et al., 1986). Kaneko and Lee (1995) have reexamined the US and Japanese markets by employing the (Chen et al. 1986) factors to evaluate the effects of systematic economic news on stock market returns. Since there exists a long-term relationship between the changes in stock prices and leading economic variables as indicated by many finance experts. Fama (1981) documents a strong positive correlation between common stock returns and real economic variables like capital expenditures, industrial production, real GNP, money supply, exchange rate, inflation and interest rates. Chen et al (1986) found that changes in aggregate production, inflation, short term interest rates and risk premium are the economic factors which explain and predict stock prices. Sill (1995) documents that the industrial production output, T-bill rate and inflation are statistically significant in explaining the US stock market excess returns. In addition, the conditional variance - covariance of macroeconomic factor are important drivers of the conditional stock return volatility Solnik (1987) studied the effect of a number of variables including exchange rate, interest rate and changes in inflation expectations and stock prices. The study utilised data from nine developed economies, namely, the US, Japan, Germany, France, the UK, Switzerland, Belgium, Canada and the Netherlands. Among the findings of the study was that a fall in the exchange rate impacted positively on the US stock market as against changes in inflation expectations. Adjasi and Biekpe (2005) investigated the relationship between stock market returns and exchange rate movements in seven African countries. Cointegration tests showed that in the long-run exchange depreciation leads to increases in stock market prices in some of the countries, and in the short-run exchange rate depreciations reduce stock market returns. Subair and Salihu (2010) employed a data set comprising annual stock market capitalization, GDP, inflation rate, IR and EXR volatility for the period between 1981-2007. Through the ECM, the study investigated the effects of EXR volatility on the Nigeria stock markets. It was found that the EXR volatility exerts a stronger negative 20 impact on the Nigeria Stock markets. However the rate of inflation and interest rate did not have long run relationship with stock market capitalization since the major participants in the market is the government. They further concluded that, the EXR volatility has a very serious implication on the Nigeria Stock market thus for any serious development of the stock market there is a need to stabilize the movement of the EXR. METHODOLOGY In statistics, regression analysis is a statistical process for estimating the relationship between variables. It includes many techniques for modeling and analyzing several variables when the focus is on the relationship between a dependent variable and one or more independent variables. The linear multiple regression model estimates is: Y = β 0 + β 1 X i + β 2 X 2 + β 3 X 3 + e Where Y is the All share index (dependent variable) X 1 is the Inflation Rate X 2 is the Exchange Rate X 3 is the Interest rate Β 0 is the Y-intercept e is the random error component. For ease of computation, the model is estimated in the vector-matrix notation shown below.

Adv. Econ. Int. Finance 3 a) LINEAR REGRESSION MODEL IN MATRIX NOTATION Y= XB + ᶓ Y is the response variable vector X is the matrix of the explanatory variables B is the vector of parameters ᶓ represent the random error term vector showing the unpredicted or unexplained variation. Where Y 1 X 11 X 12 X 1p β 1 ε 1 Y 2 = X 21 X 22 X 2p β 2 + ε 2 Y n X n1 X n2 X np β P ε n n x 1 n x p p x 1 n x 1 b) Estimating B The estimated values of the parameters B can be given as B= (x x) -1 x Y c) Estimating the Residual The residual representing observed minus calculated quantities are useful to calculate or analyze the regression. Residual are determined from ᶓ = y xb Where ᶓ is the estimated vector of error Y is the observed vector of y X and B are as defined above. d) Standard Deviation (δ) The standard deviation (δ), for the model is determined from (ᶓ 1 ᶓ) = (y 1 y b 1 x 1 y) (n p) (n p) e) Confidence Interval for B The 100 (1-α) % confidence interval for the parameters, B i s, Is computed as B i ± tα 2, n-p α (x 1 x)ii -1 )

Ladan et al. 4 Where t follows the Student's t- distribution with n-p degrees of freedom and (x 1 x) -1 denotes the value located in the i th row and j th column of the matrix. ANALYSIS OF VARIANCE (ANOVA) ESTIMATION The regression sum of squares (SSR) is given by: SSR = (yi y) 2 = b 1 x 1 y -1 / n (y 1 uuy) Where u is an n x 1 unit vector, the error sum of squares (ESS) is given by ESS = (yi y) 2 = y 1 y 1/n ( y 1 uu 1 y) = SSR + ESS ANOVA TABLE SOURCE OF VARIATION df SS MS F-RATIO REGRESSION P-1 SSR SSR/(P-1) MSR/MSE ERROR n-p ESS ESS/(n-p) TOTAL n-1 TSS F 0 = MSR/MSE against F α (v 1 v 2) Decision rule: if F 0 F α (p 1, n-p), reject H 0 ADEQUACY TEST FOR REGRESSION MODEL a. Coefficient of Determination (R 2 ) The value of R 2 measures the percentage / ratio of the total variability in the dependent variable explained by the explanatory variables altogether. R 2 = SSR /TSS = 1 (ESS / TSS) Recall 0 R 2 1 b. Residual Analysis Residual analysis is helpful in checking the assumption that the errors are normally independent distributed with mean zero and variance δ 2 i.e. ᶓ NID (0, δ 2 ) and in determining if additional terms in the model would be useful. ᶓ = y xb. c. Approximate Check of Normality A frequency histogram of the residuals or normal probability plot constructed will show normality or otherwise. Residuals are plotted in time sequence i. Against fitted values y The standardized residuals is D = ᶓ MSE For an NID (0, δ 2 ), approximate 95 % of the standardized residuals falls in the interval (-2, +2). ii. Plotting the residual against the previous residuals i.e. lagging.

Adv. Econ. Int. Finance 5 The model assumptions are checked and verified if no pattern exists in the plot. CHECKING THE MODEL VALIDITY The model validity is checked using the confidence interval includes zero, then the parameter can be removed from the model. Hence, a new regression model excluding that parameter would need to be performed and continued until there are no more parameters to remove. RESULTS The data used in this research work was collected from CBN Statistical Bulletin (2010). The data covers a period of twentyfour (24) years. The data was analyzed using the statistical package for social sciences (SPSS17.0) employing the tool of multiple regression analysis as discussed in the methodology. Table 1: Data Presentation Year All share Index Exchange Rate Interest Rate Inflation Rate 1986 149.82 2.0206 9.63 5.39 1987 176.92 4.0179 15.28 10.18 1988 210.81 4.5367 13.38 56.04 1989 273.87 7.3916 20.78 50.47 1990 423.66 8.0378 21.3 7.5 1991 671.62 9.9095 18.25 12.7 1992 931.02 17.2984 21.43 44.81 1993 1229.03 22.0511 24.72 57.17 1994 1913.23 21.8861 15 57.03 1995 3815.12 81.0228 13.88 72.81 1996 5955.14 81.2528 13.28 29.29 1997 7638.59 81.6494 7.35 10.67 1998 5961.88 83.8072 10.19 7.86 1999 5264.19 92.3428 13.08 6.62 2000 6701.18 100.1194 10.5 6.94 2001 10185.08 111.5166 10.19 18.87 2002 11631.87 120.4700 16.34 12.89 2003 15559.90 129.2230 13.08 14.03 2004 24738.65 133.0010 12.92 15.01 2005 22876.72 131.1004 10.1 17.85 2006 25343.55 128.1420 8.92 8.24 2007 48773.31 125.0660 9.4 5.38 2008 50424.70 117.7772 11.9 11.6 2009 23091.55 147.2718 9.96 11.5 2010 24775.59 148.3085 10.18 13.72 Source: Central Bank of Nigeria, Statistical Bulletin, 2010 Edition. An explanatory data analysis (EDA) was carried out on the data and the graph are presented in Figures 1 through 4.

Ladan et al. 6 Figure 1: Line graph of ALL Share Index against year Figure 2: Line graph of Exchange rate against year Figure 3: Line graph of Interest rate against year

Adv. Econ. Int. Finance 7 Figure 4: Line graph of Inflation rate against year The historical yearly behavior of the nominal ( and real), All share index, exchange rate, interest rate, and inflation rate for the periods of 1986(1) - 2010(24) are presented in Figure 1 to 4. Using the model described in the methodology, the obtained results from the SPSS software are presented below. Table 2: Model Parameters Estimation Model Unstandardized Coefficients B Std. Error Beta Standardized Coefficients T Sig. (Constant) -644.505 11283.181-0.057 0.955 Inflation Rate -77.004 121.605-0.109-0.633 0.533 Exchange Rate 184.281 51.688 0.687 3.565 0.002 Interest Rate 18.974 636.997 0.006 0.030 0.977 Coefficients a. Dependent Variable: All Share Index b 0 = -644.505, which shows All share index when inflation rate, Exchange rate and interest rate are zero b 1 = -77.004, which shows All share index with a unit decrease in inflation rate. b 2 = 184.281, which shows All share index with a unit increase in Exchange rate b 3 = 18.974, which shows All share index with a unit increase in Interest rate Therefore, the regression equation that is used to forecast the market returns is given by All Share Index = -644.505 77.004Inflation rate + 184.281Exchange rate + 18.94Interest rate The model summary is presented in Table 3. Table 3: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate Durbin- Watson 1 0.736 a 0.542 0.477 10419.78083 0.809

Ladan et al. 8 From Table 3, the correlation coefficient (R) for the fitted model was 0.736 which shows a strong relationship between All Share Index and the explanatory variables (Inflation Rate, Exchange Rate, and Interest Rate). Furthermore, the adjusted coefficient of determination (R 2 ) obtain was 0.477 which shows that 47.7% of the variability in All share index can be explained by the explanatory variables (Inflation Rate, Exchange Rate, and Interest Rate). The ANOVA for the fitted regression model is Table 4: ANOVA b Sum of Squares df Mean Square 2.701E9 3 9.005E8 2.280E9 21 1.086E8 4.981E9 24 a. Predictors: (Constant), Interest Rate, Inflation Rate, Exchange Rate b. Dependent Variable: All Share Index The Fishers value (F- value) obtain was 8.294 with a p-value of 0.001 which implies that all the three explanatory variables (Inflation Rate, Exchange Rate, and Interest Rate) were significant in estimating All share Index at 99% confidence level during the period under consideration. In assessing which of the explanatory variables is actually significant in estimating All share index, the t-value obtained with corresponding p-value were as follows Inflation rate Exchange rate Interest rate t-value -0.633 3.565 0.030 p-value 0.533 0.002 0.977 This shows that only Exchange rate is significant at 95% confidence level in estimating All share index during the period of study because p-value was less than 0.05, while the p-value for inflation rate and interest rate was greater than 0.05 Table 5: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 0.965 a 0.931 0.905 777.24772 Correlation Coefficient (R) was 0.965 which shows a strong relationship between All Share Index and the explanatory variables (Inflation Rate, Exchange Rate, and Interest Rate) Adjusted Coefficient of Determination (R 2 ) obtain was 0.905 which shows that 90.5% of the variability in All share index can be explained by the explanatory variables (Inflation Rate, Exchange Rate, and Interest Rate) Table 6: ANOVA b Model Sum of Squares Df Mean Square F Sig. Regression 6.479E7 3 2.160E7 35.749 0.000 a Residual 4832912.123 8 604114.015 Total 6.962E7 11 a. Predictors: (Constant), interest Rate, inflation rate, Exchange Rate b. Dependent Variable: All Share Index

Adv. Econ. Int. Finance 9 The Fishers value (F- value) obtain was 35.749 with a p-value of 0.000 which implies that all the 3 explanatory variables (Inflation Rate, Exchange Rate, and Interest Rate) were significant in estimating All share Index at 95% confidence level during the period under consideration Table 7: Coefficients a Model Unstandardized Coefficients B Std. Error Beta Standardized Coefficients T Sig. (Constant) 1051.711 969.900 1.084 0.310 inflation rate -16.584 10.715-0.161-1.548 0.160 Exchange Rate 72.557 8.588 0.939 8.449 0.000 interest Rate -36.608 55.339-0.076-0.662 0.527 a. Dependent Variable: All Share Index b 0 = 1051.711, which shows All share index when inflation rate, Exchange rate and interest rate are zero b 1 = -16.584, which shows All share index with a unit decrease in inflation rate. b 2 = 72.557, which shows All share index with a unit increase in Exchange rate b 3 = -36.608, which shows All share index with a unit increase in Interest rate The regression equation that is used to forecast the market returns is given by All Share Index = 1051.711 16.584Inflation rate + 72.557Exchange rate - 36.608Interest rate In assessing which of the explanatory variables is actually significant in estimating All share index, the t-value obtained with corresponding p-value were as follows : Inflation rate Exchange rate Interest rate t-value -1.548 8.449-0.662 p-value 0.160 0.000 0.527 This shows that only Exchange rate is significant at 95% confidence level in estimating All share index during the period of study because p-value was less than 0.05, while the p-value for inflation rate and interest rate was greater than 0.05 BETWEEN 1997 2010 Table 8: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 0.619 a 0.383 0.198 13085.40157 a. Predictors: (Constant), interest Rate, Exchange Rate, inflation rate Correlation Coefficient (R) was 0.619 which shows a relationship between All Share Index and the explanatory variables (Inflation Rate, Exchange Rate, and Interest Rate) Adjusted Coefficient of Determination (R 2 ) obtain was 0.198 which shows that 19.8% of the variability in All share index can be explained by the explanatory variables (Inflation Rate, Exchange Rate, and Interest Rate)

Ladan et al. 10 Table 9: ANOVA b Model Sum of Squares Df Mean Square F Sig. Regression 1.062E9 3 3.541E8 2.068 0.168 a Residual 1.712E9 10 1.712E8 Total 2.775E9 13 a. Predictors: (Constant), interest Rate, Exchange Rate, inflation rate b. Dependent Variable: All Share Index The Fishers value (F- value) obtain was 2.068 with a p-value of 0.168 which implies that all the 3 explanatory variables (Inflation Rate, Exchange Rate, and Interest Rate) were not significant in estimating All share Index at 95% confidence level during the period under consideration. Table 10: Coefficients a Model Unstandardized Coefficients B Std. Error Beta Standardized Coefficients T Sig. (Constant) -10944.984 25281.384-0.433 0.674 inflation rate -1067.629 958.089-0.305-1.114 0.291 Exchange Rate 455.579 185.909 0.668 2.451 0.034 interest Rate -930.081 1639.169-0.143-0.567 0.583 a. Dependent Variable: All Share Index b 0 = -10944.984, which shows All share index when inflation rate, Exchange rate and interest rate are zero b 1 = -1067.629, which shows All share index with a unit decrease in inflation rate. b 2 = 455.579, which shows All share index with a unit increase in Exchange rate b 3 = -930.081, which shows All share index with a unit increase in Interest rate The regression equation that is used to forecast the market returns is given by All Share Index = -10944.984 1067.629Inflation rate +455.579Exchange rate - 930.081Interest rate In assessing which of the explanatory variables is actually significant in estimating All share index, the t-value obtained with corresponding p-value were as follows: Inflation rate Exchange rate Interest rate t-value -1.114 2.451-0.567 p-value 0.291 0.034 0.583 This shows that all the 3 explanatory variables were not significant at 95% confidence level in estimating All share index during the period of study because p-value was all greater than 0.05. FINDINGS There was a significant linear relationship between All share index and all the explanatory variables (IF, EXR, and INR) even though only the exchange rate is individually significant in the year 1986 1997 and 1986-2010. There was a linear relationship between All Share index and all the three explanatory variables (IF, EXR, and INR) and

Adv. Econ. Int. Finance 11 and none were significant in estimating All share Index in the year 1997-2010. This Research work shows that exchange rate influences All share index while interest rate and inflation rate is not statistically significant in explaining All share index. R (0.736) which is the correlation coefficient, meaning, there is high correlation between the dependent variable (All share index) and the independent variables (inflation rate, Exchange rate and interest rate). Also, the Adjusted co-efficient of determination which is frequently used to described the goodness of fit or the amount of variability explained by a given set of explanatory variables. In our study, Adjusted R 2 value was 0.477, which indicates that 47.7% of the variability in the dependent variable is explained by the independent variables while the remaining 52.3% is explained by the elements not included in the model but are taken care of by the stochastic error term ε The model fitted was All Share Index = -644.505 77.004Inflation rate + 184.281Exchange rate + 18.94Interest rate CONCLUDING OBSERVATION Premised on our findings we conclude that there was high correlation between the macroeconomics variables and stock market returns and it was also observe that there was a linear relationship between the macroeconomics variables and stock market returns between the years 1986 to 2010. A lot of studies have been done on the relationship between macroeconomic variables and stock market prices in previous years. A few studies have investigated the relationships between exchange rate and stock price across a range of countries, with mixed conclusions. (Solnik,1987) finds a significantly positive relationship between stock prices and exchange rates and this result is consistent with (Ajayi and Mougoue, 1996) The main thrust of this paper is an empirical investigation of the relationship between the stock market returns and some major macroeconomics factors as reflected in the general business and financial conditions evidence from Nigeria. The results and findings of our study corroborated the findings of other studies in similar areas. Although it is now well recognized that stock market returns react to fluctuations in macroeconomic variables, any definite prediction of the relationships between the expected risk factors is difficult if not impossible. However our results will help investors and portfolio managers deepen their understanding of the risk-return relationship, pricing of macroeconomic risk as well as diversification implications in Nigerian stock market. Additionally, policy makers may play a major role in influencing the expected risk premium and volatility on stock markets through the use of macroeconomic policy. One of the limitations of the study is that we have used four macroeconomic variables only. so further research needs to be explored by including more macroeconomic variables to know the relationships between these factors and the nature of stock market volatility. Secondly, it is also possible that the macroeconomic variables have different impact on stock market volatility depending on the trading mechanisms and regulatory environments. REFERENCES Adjasi CKD, Biekpe BN (2005). Stock Market Returns and Exchange Rate Dynamics in Selected African Countries: A bivariate analysis, The African Finance Journal, July, Cape Town, South Africa. Ajayi RA, Mougoue M (1996). On the Dynamic Relation between Stock Prices and Exchange Rates, Journal of Financial Research 19, 193-207. Chen N, Roll R, Ross S (1986). Economic Forces and Stock Market, Journal of Business, 59, 383-403. Fama E (1981). Stock Returns, Real Activity, Inflation and Money, American Economic Review, 71. Kaneko T, Lee BS (1995). Relative Importance of Economic Factors in the US and Japanese Stock Markets Journal of the Japanese and International Economies Vol. 9 Kwon CS, Shin TS (1999). Co-integration and causality between macroeconomic variables and stock market returns. Global Finance Journal, 10: 1: 71-81. Poon S, Taylor SJ (1991). Macroeconomic Factors and the UK Stock Market Journal of Business and Accounting Vol. 18. Sill K (1995). Macroeconomic risk and the determination of expected returns on Stocks Management Finance Vol. 21 No 7. pg. 43-56. Solnik B (1987). Using financial prices to test exchange rate models: a note, Journal of Finance.