The Sampling and Data Collection Procedures used in market research - Free Essay Example

This study is based on 60 monthly observations from April 2005 to March 2010 inclusive. The period was chosen to provide enough observations to obtain reliable parameter estimates. The totality of the data was obtained from Yahoo Finance, Bank of England, and Office for National Statistics. Despite that historical Stock data is available on daily, weekly and monthly basis; monthly data was obtained because historical data for some other independent variables like inflation and money supply were only available monthly. FTSE100 Index was selected amongst the London Stock Exchange (LSE) FTSE group as it represents the share index of the 100 most highly capitalized UK companies and constitute about 80% of the market capitalisation of the entire LSE thus it is likely to lead to more robust estimates. For the selected macroeconomic variables, Interest rate data was obtained from Bank of Englands Monetary Policy Statistics, and Money supply data were sourced from Bank of England Publications: Bankstats (Monetary Financial Statistics). UK representative of Inflation rate, Consumer Price Index (CPI) data were obtained from Office for National Statistics (ONS). CPI for all items based on monthly percentage change was used. Data for Inflation rate, Money supply and Interest rate are measured by rates of change rather than absolute values as this facilitates comparison with stock returns. 3.2 Measure of Variables 3.2.1 Stock Return (SR) Dependent Variable LSE FTSE 100 Index Monthly Close Stock data adjusted for dividends and splits were downloaded from Yahoo Finance. From the monthly adjusted close data, the monthly stock return was calculated as follows: SR = log (Qt/Qt-1) 1 Where Qt is adjusted close price of t time, and Qt-1 = adjusted close price of t-1 time. Stock return was used as dependent variable to determine how the three macroeconomic variables (Inflation rate, Interest rate and Money supply) affect it. 3.2.2 Money Supply Independent Variable There is an abundance of literature which treats deposit modeling from a macroeconomic point of view. By money supply we mean the total stock of monetary media of exchange available to a society for use in connection with the economic activity of the country Ahuja (2004). According to the standard concept of money supply, it is composed of two elements (1) currency with the public and (2) demand deposit with the public. Central banks introduced monetary aggregates to monitor the money supply in the economy and the different monetary aggregates are M0, M1, M2, M3, M4 and MZM as defined below: M0 The physical currency (coins and bank notes) and the accounts of Central Bank exchangeable into physical currency; M1 M0 plus the amount in the demand accounts (checking accounts, current accounts, etc) M2 M1 plus the amount in savings account, money market accounts and small certificate of deposit accounts (CDs under $100,000). M is called the quasi-money, i.e the deposits wi thout maturity that could without any risk and quasi instantly be converted in cash; M3 M2 plus large CDs, repurchase agreements and currency deposit (Eurodollars in the US). In some countries, M3 takes into account all the ultra liquid and risky investments easy to sell into the market: institutional money funds, short term investment funds, term deposits, etc. M4 M3 plus medium term treasury bonds. In UK, M4 is defined as M3 plus private sector holdings of building society shares and deposits and sterling certificates of deposits. MZM represents the Money Zero Maturity i.e all the deposits without any maturity. In the US, MZM is M less small-demonian. Money Supply is the amount of money in an economy at a given time. The simplest definition is the actual amount of bank notes and coins in circulation. There are various variations on the above listed types and the exact definition of money supply varies from country to country. In the UK, there are only two Money S upply measures: M0 and M4. The exact definitions are revised from time to time by the Bank of England. M0 represents notes and coins in circulation with the public plus UK private sectors non-interest bearing sterling sight deposits with banks in the UK; plus UK private sectors interest-bearing retail sterling deposits with banks in the UK and is referred to as the wide monetary base, or narrow money. M4 represents UK private sectors holdings of: Sterling notes and coins; plus Sterling deposits with banks in the UK; plus Building society shares, deposits, and sterling certificates of deposit and is referred to as broad money or simply the money supply. Seasonally adjusted and non-seasonally adjusted broad money supply M4 are published monthly by Bank of England in its Quarterly Bulletin (BEQB). Thus the seasonally adjusted broad money aggregate M4 is a measure of the quantity of UK money supply and will be used in this study as one of the independent variables. Monthly seas onally adjusted growth rate data (percentage) were obtained from Bank of England, Bankstats (Monetary Financial Statistics) Tables Growth rates of M4 monthly seasonally adjusted data (Table A2.1.1). 3.2.3 Interest Rate Independent Variable Mankiw (2000) defines interest rate as, the market price at which resources are transferred between the present and the future. He further adds that interest rate is the return of saving and the cost of borrowing. A rise in interest rate could influence investors decision to switch from the stock market to the money market. Reduced interest rates also encourage demand for cash mainly for speculative purposes. Thus, the lower the yield on bonds and debt instruments, the higher the stock returns and the higher the yield on bonds and debt instruments, the lower the stock returns. The interest rate used in this study is the official bank rate that Bank of England charges banks for secured overnight lending as most bank lending rates are tied to the official bank rate. Data were obtained from Bank of England, Statistical Interactive Database Official Bank Rate history. In the UK, changes to the official bank rate are based on recommendations made by the Monetary Policy Committ ee and subsequently enacted by the Governor, Bank of England. Changes in interest rates are thereafter announced after a decision has been made following the Thursday meeting of the Monetary Policy Committee. Such change becomes effective after the announcement thus, there were instances where interest rates are changed within the month. To harmonize the monthly data for interest rates, data were adjusted where there is a change within a month by calculating the number of days based on the old rate and number of days based on the new rate. Results for the two rates are thereafter added to arrive at the interest rate for the month and used as an independent variable in this study. 3.2.4 Inflation Rate Independent Variable Inflation is a rise in the general level of prices of goods and services in an economy over a period of time. Inflation rate is the measure of price inflation. Inflation rate affects investors attitude and decisions on where to invest funds. Where inflation rate is high, real income would decline; investors will sell their assets which includes stocks and shares to improve their purchasing power as each currency buys fewer goods and services. However, where inflation rate is low, real income increases and investors will buy assets with their strong purchasing power. High inflation rate and hyperinflation can be caused by excessive growth of the money supply. High inflation rates negatively affect stock returns while low inflation rate boost stock returns. Inflation rate data was obtained from Office for National Statistics, Consumer Price Index monthly percentage change data. 3.3 Models Models used in this study are: The Unit root test Granger Causality test Multiple Regression analysis test. 3.3.1 Unit Root Test It is important to check whether a time series variable is stationary or non-stationary for the following reasons: To avoid spurious regressions. Where two variables are trending over time, a regression of one on the other could lead to a high R2 even when the two are totally unrelated. To avoid misleading results as the stationarity or non-stationarity of a series could influence its behavoiur and properties strongly. Also, where variables in the regression model are not stationary, standard analysis assumptions will not hold, thus the hypothesis test of the regression parameters would be invalid. As different unit root test can be employed, the Augmented Dickey-Fuller test was employed in this study. The objective of the test is to test the hypothesis H0: ÃÆ'Ã… ½Ãƒâ€šÃ‚ ´ = 0 (Unit Root) H1: ÃÆ'Ã… ½Ãƒâ€šÃ‚ ´ ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã‚ °Ãƒâ€šÃ‚   0 Where ÃÆ'Ã… ½Ãƒâ€šÃ‚ ´ = p 1 The Dickey-Fuller unit root test was based on the following regression forms: ÃÆ'  ¢Ãƒâ€¹Ã¢â‚¬  Ãƒ ¢Ã¢â€š ¬Ã‚  Yt = ÃÆ'Ã… ½Ãƒâ€šÃ‚ ´Yt-1 + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ¼t ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã‚  Ãƒ ¢Ã¢â€š ¬Ã¢â€ž ¢ Yt is a random walk (without constant and trend) ÃÆ' ¢Ãƒâ€¹Ã¢â‚¬  Ãƒ ¢Ã¢â€š ¬Ã‚  Yt = ÃÆ'Ã… ½Ãƒâ€šÃ‚ ± + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ´Yt-1 + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ¼t ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã‚  Ãƒ ¢Ã¢â€š ¬Ã¢â€ž ¢ Yt is a random walk with drift (with constant) ÃÆ' ¢Ãƒâ€¹Ã¢â‚¬  Ãƒ ¢Ã¢â€š ¬Ã‚  Yt = ÃÆ'Ã… ½Ãƒâ€šÃ‚ ± + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²T + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ´Yt-1 + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ¼t ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã‚  Ãƒ ¢Ã¢â€š ¬Ã¢â€ž ¢ Yt is a random walk with drift around a stochastic trend (with constant and trend) The Augmented Dickey-Fuller unit root test was based on the following regression forms: ÃÆ' ¢Ãƒâ€¹Ã¢â‚¬  Ãƒ ¢Ã¢â€š ¬Ã‚  Yt = ÃÆ'Ã… ½Ãƒâ€šÃ‚ ± + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²T + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ´Yt-1 + yi ÃÆ'Ã… ½Ãƒâ€šÃ‚ £ÃƒÆ' ¢Ãƒâ€¹Ã¢â‚¬  Ãƒ ¢Ã¢â€š ¬Ã‚  Y t-1 + ÃÆ'Ã… ½Ãƒâ€šÃ‚ µt Where ÃÆ'Ã… ½Ãƒâ€šÃ‚ µt is a pure white noise error term ÃÆ' ¢Ãƒâ€¹Ã¢â‚¬  Ãƒ ¢Ã¢â€š ¬Ã‚   Y t-1 = (Y t-1 Y t-2), ÃÆ' ¢Ãƒâ€¹Ã¢â‚¬  Ãƒ ¢Ã¢â€š ¬Ã‚  Y t-2 = (Y t-2 Y t-3) etc To test if ÃÆ'Ã… ½Ãƒâ€šÃ‚ ´ = 0, Decision rule: Where t ÃÆ'†¹Ãƒâ€ Ã¢â‚¬â„¢ Augumented Dickey-Fuller critical value ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã‚  Ãƒ ¢Ã¢â€š ¬Ã¢â€ž ¢ do not reject null hypothesis, i.e. unit root exists. Where t ÃÆ'†¹Ãƒ ¢Ã¢â€š ¬Ã… ¡ Augumented Dickey-Fuller critical value ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã‚  Ãƒ ¢Ã¢â€š ¬Ã¢â€ž ¢ reject null hypothesis, i.e. unit root does not exists. To transform data from non-stationary to stationary, the Difference-Stationary Process (DSP) was used. The regression equation is: ÃÆ' ¢Ãƒâ€¹Ã¢â‚¬  Ãƒ ¢Ã¢â€š ¬Ã‚  (ÃÆ' ¢Ãƒâ€¹Ã¢â‚¬  Ãƒ ¢Ã¢â€š ¬Ã‚  Yt) = ÃÆ'Ã… ½Ãƒâ€šÃ‚ ± + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ´ÃƒÆ' ¢Ãƒâ€¹Ã¢â‚¬  Ãƒ ¢Ã¢â€š ¬Ã‚  Yt-1 + ÃÆ'Ã… ½Ãƒâ€šÃ‚ µt Differencing was applied to render the series stationery. The use of 1st difference or 2nd difference generated the stationarity. 3.3.2 Granger Causality Test Despite that multiple regression analysis deal with the dependence of one variable on other variables, it does not imply causality. Granger causality test is implemented to identify how much one factor is significant in forecasting the other one. Granger (1969) discussed the important problem of apparent instantaneous causality and suggested that the problem often arises due to slowness in recording information or non usage of sufficiently wide class of possible causal variables. Thus, the results are not coefficients of the real dependence or indicators of the actual causality; rather it is just a sign of existing linear interdependency of one factor on another. The hypothesis is to hold only if one factor follows the other and the initial is a potential reason for the follower. Granger (1969) proposed a time-series data based approach to determine causality. In this study, Granger causality test was conducted to examine the direction of causality between Inflation rate, Intere st rate, Money supply and Stock returns. For example, does Inflation rate granger-cause Stock returns (INFR ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã‚  Ãƒ ¢Ã¢â€š ¬Ã¢â€ž ¢ SR) or does Stock return granger-cause Inflation rate (SR ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã‚  Ãƒ ¢Ã¢â€š ¬Ã¢â€ž ¢ INFR) with the arrow indicating the direction of causality. In a simple Granger-causality test, there are two variables and their lags. As required by the Granger test, each variable was first transformed to achieve stationarity and then lagged. Based on the above illustration, the following two equations can be specified where it is assumed that the disturbances ÃÆ'Ã… ½Ãƒâ€šÃ‚ ¼1t and ÃÆ'Ã… ½Ãƒâ€šÃ‚ ¼2t are uncorrelated: (INFR)t = ÃÆ'Ã… ½Ãƒâ€šÃ‚ ± + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²i(INFR)t-1 + Tj(SR)t-j + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ¼1t (SR)t = ÃÆ'Ã… ½Ãƒâ€šÃ‚ ¸ + Øi(SR)t-1 + ÃÆ' Ãƒâ€¹Ã¢â‚¬  j(INFR)t-j + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ¼2t Subsequently, four different hypotheses can be formulated: Unidirectional causality from SR to INFR. Here, INFR i ncreases the prediction of SR but not vice versa i.e. Tj ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã‚ °Ãƒâ€šÃ‚   0 and ÃÆ' Ãƒâ€¹Ã¢â‚¬  j = 0. Unidirectional causality from INFR to SR. Here, SR increases the prediction of INFR but not vice versa. Thus, Tj = 0 and ÃÆ' Ãƒâ€¹Ã¢â‚¬  j ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã‚ °Ãƒâ€šÃ‚   0. Bilateral or Feedback causality. Here, the sets of SR and INFR coefficients are statistically significantly different from zero in both regressions i.e. an increase in SR increases the prediction of INFR and vice versa. Thus, Tj ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã‚ °Ãƒâ€šÃ‚   0 and ÃÆ' Ãƒâ€¹Ã¢â‚¬  j = 0. Independence. Here, the sets of SR and INFR coefficients are not statistically significant in both the regressions i.e. an increase in SR increases the prediction of INFR and vice versa. Thus, there are no granger causalit in any direction i.e. Tj = 0 and ÃÆ' Ãƒâ€¹Ã¢â‚¬  j = 0. Granger causality was tested using EViews Pairwise Granger Causality Test. A common difficulty in perfor ming Granger-causality test is the lag length as results are not independent from the chosen lag structure. Since Granger causality test is very sensitive to the number of lags, lag 2 and lag 10 was used along with the conventional 5 percent level of significance value to confirm that lagged terms are important in the causality test, and also because I did not use Akaike or Schwarz information criterion to select the lagged terms. 3.3.3 Multiple Regression Analysis test Regression analysis test is a statistical analysis utilized for the investigation of relationships between variables i.e. it is used to ascertain the causal effect of one variable on another variable. In this study, correlation and multiple regression analysis was used to predict the direction of change and estimate the quantitative effect of the causal variables on the variable that they influence. Thus, the study investigated the relationship between Inflation rate, Interest rate, Money supply, and Stock returns by examining the relationship between the dependent and explanatory variables using regression analysis. Regression analysis helps to understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. The method to be performed is outlined below: Estimated regression model Response variable and regression coefficient Estimating the coefficient of multiple determination 3.3.3.1 Estimated Regression Model Three explanatory variables: Money supply (X1); Interest rate (X2); and Inflation rate (X3), were investigated for their relationship with a response variable FTSE 100 Index returns (Y) model. According to Studenmund (2006), the multivariate regression model with K independent variable is represented as detailed below: Yi = ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²0 + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²1X1i + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²2X2i + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²3X3i ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¦ÃƒÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¦ÃƒÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¦. ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²KXKi + i Where i goes from 1 to N and indicates the observation number. ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²0 indicates the constant term ÃÆ'Ã… ½Ãƒâ€šÃ‚ ² indicates the coefficient of the function. X1i indicates the ith observation of independent variable X1. X2i indicates the ith observation of another independent variable X2 X3i indicates the ith observation of another independent variable X3 i indicates the error term. The coefficient ÃÆ'Ã… ½Ãƒâ€š  ²1 measures the impact on Y of a one-unit increase in X1, holding constant X2, X3, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¦ÃƒÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¦.. and XK but not holding constant any relevant variables that might have been omitted from the equation. Multivariate regression coefficient indicates that a change in the dependent variable associated with a one-unit increase in the independent variable in question holding constant the other independent variables in the equation. In this study, where there are three independent variables -money supply, interest rate and inflation rate, the above equation will be written as follows: SR = ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²0 + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²1MS + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²2INTR + ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²3INFR + i Where, SR = Monthly percentage change in adjusted close in the FTSE 100 Index MS = Monthly seasonally adjusted M4 INTR = Monthly Bank of England Base rate. INFR = Monthly CPI rate. With ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²0 as the constant term, where MS, INTR and INFR = 0, then SR = ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²0. Since Beta is the coefficient of the function, it therefore predicts the variance in SR from MS, INTR and INFR. Thus a negative beta coefficient indicates that MS, INTR and INFR affect SR negatively and a unit increase in MS, INTR and INFR will decrease SR by the coefficient amount. Also, a positive beta coefficient indicates that MS, INTR and INFR affect SR positively and a unit decrease in MS, INTR and INFR will increase SR by the coefficient amount. p-value was used to measure how reliable MS, INTR and INFR can predict SR. Were the p-value is greater than 0.05, it implies no statistical significant relationship with SR. 3.3.3.2 Testing the response variable and Regression Coefficients I used student t-test to examine if explanatory variables are significant predictor of the response variable. The t-statistics is given as: Where is given as: Sb = ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²iÃÆ'â„ ¢Ãƒâ€šÃ‚ ­ is the hypothesised value, K is the number of parameters and n is the number of sample observation. Then we set the hypothesis: H0: ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²iÃÆ'â„ ¢Ãƒâ€šÃ‚ ­= 0 H1: ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²iÃÆ'â„ ¢Ãƒâ€šÃ‚ ­ÃƒÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã‚ °Ãƒâ€šÃ‚   0 If the hypothesised value is ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²iÃÆ'â„ ¢Ãƒâ€šÃ‚ ­= 0, then the testing amounts to deciding if the explanatory variables are a significant predictor of the response variable. However, in testing the overall significance of the regression we set the hypothesis: H0: ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²1 = ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²2 = ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²3 = 0 H0: ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²1 ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã‚ °Ãƒâ€šÃ‚   ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²2 ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã‚ °Ãƒâ€šÃ‚   ÃÆ'Ã… ½Ãƒâ€šÃ‚ ²3 ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã‚ °Ãƒâ€šÃ‚   0 This t est aims at finding out whether the explanatory variables do actually have any significant influence on the response variable. The easiest way to reach a decision is by means of p-values. A p-value less than 5% suggests that the estimated model is significant. 3.3.3.3 Estimating coefficient of multiple determination The coefficient of multiple determination (denoted by R2), in the four variable-model shows the percentage of the total variation of the response variable, Y that is explained by changes in the explanatory variables,X1, X2 and X3. Therefore: R2Y.X1X2X3 = ÃÆ'Ã… ½Ãƒâ€šÃ‚ £( The value of lies between 0 and 1. The higher the greater the percentage of the variation of response variable (the better the goodness of fit) explained by the regression plane (Koutsoyiannis 2003). At this point, we need to note that our model has not been check for the assumptions about the random variable and the explanatory variables. Therefore, I did not check if our data has presence of seasonality, serially correlated, heteroscedasticity, multicollinearity and autocorrelation. Chapter 4 Empirical Results and Analysis 4.1 The Unit Root Augmented Dickey Fuller unit root stationarity test are presented below: Table 1 Unit Root and Stationarity Test for FTSE 100 at level Null Hypothesis: FTSE100 has a unit root Exogenous: Constant, Linear Trend Lag Length: 3 (Automatic based on SIC, MAXLAG=10) t-Statistic   Ãƒâ€šÃ‚  Prob.* Augmented Dickey-Fuller test statistical -1.921036   0.6304 Test critical values: 1% level -4.130526 5% level -3.492149 10% level -3.174802 The computed Augmented Dickey-Fuller test-statistic (-1.921036) is greater than the critical values (-4.130526, -3.492149 and -3.174802 at 1%, 5% and 10% significant level respectively). I cannot conclude to reject H0. This implies that FTSE 100 has a unit root problem and the series is a non-stationery series i.e. not stationery at level. This position requires further testing at 1st level. Table 2 Unit Root and Stationarity Test for FTSE 100 at 1st Difference Null Hypothesis: D(FTSE100) has a unit root Exogenous: Constant, Linear Trend Lag Length: 2 (Automatic based on SIC, MAXLAG=10) t-Statistic   Ãƒâ€šÃ‚  Prob.* Augmented Dickey-Fuller test statistic -10.51879   0.0000 Test critical values: 1% level -4.130526 5% level -3.492149 10% level -3.174802 The computed Augmented Dickey-Fuller test-statistic (-10.51879) is smaller than the critical values (-4.130526, -3.492149 and -3.174802 at 1%, 5% and 10% 1st significant level respectively). Thus, I can reject H0. This implies that FTSE 100 does not have a unit root problem and the FTSE 100 series is a stationery series at 1%, 5% and 10% 1st significant level i.e. stationery at 1st difference Table 3 Unit Root and Stationarity Test for Inflation at level Null Hypothesis: INFLATIONRATE has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Automatic based on SIC, MAXLAG=10) t-Statistic   Ãƒâ€šÃ‚  Prob.* Augmented Dickey-Fuller test statistic -8.527799   0.0000 Test critical values: 1% level -4.121303 5% level -3.487845 10% level -3.172314 The computed Augmented Dickey-Fuller test-statistic (-8.527799) is smaller than the absolute critical values (-4.121303, -3.487845 and -3.172314 at 1%, 5% and 10% significant level respectively). Therefore, I can reject H0. This implies that INFLATIONRATE does not have a unit root problem and the series is a stationery series at 1%, 5% and 10% significant level i.e. stationery at level. Table 4 Unit Root and Stationarity Test for Interest rate at level Null Hypothesis: INTERESTRATE has a unit root Exogenous: Constant, Linear Trend Lag Length: 1 (Automatic based on SIC, MAXLAG=10) t-Statistic   Ãƒâ€šÃ‚  Prob.* Augmented Dickey-Fuller test statistic -1.936709   0.6226 Test critical values: 1% level -4.124265 5% level -3.489228 10% level -3.173114 Computed Augmented Dickey-Fuller test-statistic (-1.936709) is greater than the critical values (-4.124265, -3.489228 and -3.173114 at 1%, 5% and 10% significant level respectively). Thus, I cannot conclude to reject H0. This implies that INTERESTRATE 100 has a unit root problem and the series is a non-stationery series at level i.e. not stationery at level. This result requires further testing at 1st level. Table 5 Unit Root and Stationarity Test for Interest rate at 1st Difference Null Hypothesis: D(INTERESTRATE) has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Automatic based on SIC, MAXLAG=10) t-Statistic   Ãƒâ€šÃ‚  Prob.* Augmented Dickey-Fuller test statistic -2.960972   0.1520 Test critical values: 1% level -4.124265 5% level -3.489228 10% level -3.173114 Computed Augmented Dickey-Fuller test-statistic (-2.96092) is greater than the critical values (-4.124265, -3.489228 and -3.173114 at 1%, 5% and 10% significant level respectively). This implies that (D)INTERESTRATE 100 has a unit root problem and the series is a non-stationery series at 1st level i.e. not stationery at 1st level. Again, I cannot conclude to reject H0 at this point as the result requires further testing at 2nd difference. Table 6 Unit Root and Stationarity Test for Interest rate at 2nd Difference Null Hypothesis: D(INTERESTRATE,2) has a unit root Exogenous: Constant, Linear Trend Lag Length: 1 (Automatic based on SIC, MAXLAG=10) t-Statistic   Ãƒâ€šÃ‚  Prob.* Augmented Dickey-Fuller test statistic -6.816662   0.0000 Test critical values: 1% level -4.130526 5% level -3.492149 10% level -3.174802 At 2nd level, the computed Augmented Dickey-Fuller test-statistic (-6.816662) is smaller than the absolute critical values (-4.130526, -3.492149 and -3.174802 at 1%, 5% and 10% significant level respectively). Therefore, I can reject H0. This implies that DINTERESTRATE2 does not have a unit root problem and the series is stationery at 1%, 5% and 10% 2nd significant level. Thus the 2nd-difference of INTERESTRATE becomes stationery. Table 7 Unit Root and Stationarity Test for Money Supply at level Null Hypothesis: MONEYSUPPLY has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Automatic based on SIC, MAXLAG=10) t-Statistic   Ãƒâ€šÃ‚  Prob.* Augmented Dickey-Fuller test statistic -5.787052   0.0001 Test critical values: 1% level -4.121303 5% level -3.487845 10% level -3.172314 Computed Augmented Dickey-Fuller test-statistic (-5.787052) is smaller than the absolute critical values (-4.121303, -3.487845 and -3.172314 at 1%, 5% and 10% significant level respectively). Therefore, I can reject H0. This implies that MONEYSUPPLY does not have a unit root problem and the series is a stationery series at 1%, 5% and 10% significant level i.e. stationery at level. Unit root test conducted on the four variables: Stock Returns; Interest Rate; Inflation Rate; and Money Supply were reliable as they all passed the Durbin-Watson test. The Durbin-Watson statistics were quite significant to reject the autocorrelation at 1.933634 for FTSE100 (1st difference); 1.935061 for Interest Rate (2nd difference); 1.984945 for Inflation Rate; and 1.978578 for Money Supply. 4.2 Granger Causality Augmented Dickey-Fuller test has been calculated as Granger causality requires that the series should be covariance stationary. .Granger Causality test was computed using EViews for lagged 2 terms at 5% level of significance with the following results. Table 8 Pairwise Granger Causality Test between FTSE100 DINTERESTRATE Lags: 2   Null Hypothesis: Obs F-Statistic Prob. Â  DINTERESTRATE does not Granger Cause DFTSE100   55   4.84185 0.0120   DFTSE100 does not Granger Cause DINTERESTRATE   5.29129 0.0082 At lagged term 2, I will accept the null hypothesis that Interest rate does not granger-cause FTSE100 and that FTSE100 does not granger-cause Interest rate as the p-values are both below 0.05. However, the fact that Interest rate does not granger-cause FTSE100 does not imply that FTSE100 is independent of Interest rate and vice versa as granger causality refers to the ability of Interest rate to forecast FTSE100. Table 9 Pairwise Granger Causality Test between FTSE100 INFLATIONRATE Lags: 2   Null Hypothesis: Obs F-Statistic Prob. Â  INFLATIONRATE does not Granger Cause DFTSE100   56   1.40244 0.2553   DFTSE100 does not Granger Cause INFLATIONRATE   0.32788 0.7220 The p-values above 0.05 suggest that Inflation rate granger-cause FTSE100 and vice versa. Thus I reject the null hypothesis H0. Table 10 Pairwise Granger Causality Test between FTSE100 MONEYSUPPLY Lags: 2   Null Hypothesis: Obs F-Statistic Prob. Â  MONEYSUPPLY does not Granger Cause DFTSE100   56   0.59881 0.5533   DFTSE100 does not Granger Cause MONEYSUPPLY   1.99209 0.1469 Similar to the results in Table 9 above, I reject the null hypothesis H0 because the p-values are higher than 0.05 in both regressions. Money supply does granger-cause FTSE100 and FTSE100 does granger cause Money Supply. Table 11 Pairwise Granger Causality Test between DINTERESTRATE INFLATIONRATE Lags: 2   Null Hypothesis: Obs F-Statistic Prob. Â  INFLATIONRATE does not Granger Cause DINTERESTRATE   55   3.78624 0.0294   DINTERESTRATE does not Granger Cause INFLATIONRATE   2.31506 0.1093 Table 11 postulates that Inflation rate does not granger-cause interest rate but Interest rate does granger-cause Inflation rate. P-value of 0.0294 is less than 0.05 (accept the null hypothesis) while p-value of 0.1093 is higher than 0.05 (reject the null hypothesis). Table 12 Pairwise Granger Causality Test between DINTERESTRATE MONEYSUPPLY Lags: 2   Null Hypothesis: Obs F-Statistic Prob. Â  MONEYSUPPLY does not Granger Cause DINTERESTRATE   55   1.52566 0.2274   DINTERESTRATE does not Granger Cause MONEYSUPPLY   0.47661 0.6237 Money supply does granger-cause interest rate and Interest rate does granger cause Money supply. The null hypothesis is rejected in the two regressions because the p-value in the two instances are more than 5% level of significance. Table 13 Pairwise Granger Causality Test between MONEYSUPPLY INFLATIONRATE Lags: 2   Null Hypothesis: Obs F-Statistic Prob. Â  MONEYSUPPLY does not Granger Cause INFLATIONRATE   58   1.04867 0.3576   INFLATIONRATE does not Granger Cause MONEYSUPPLY   0.25617 0.7750 Similar to the result in Table 12 above, since the p-values are higher than the 5% level of significance, the null hypothesis H0 is rejected in the two situations. Thus, Money Supply granger-cause Inflation rate and vice versa. Granger causality test carried out with lag 10 produced a different result as illustrated in Table 14. 4.4 REGRESSION TABLE 15 CORRELATION USING EVIEWS FTSE100 INTERESTRATE INFLATIONRATE MONEYSUPPLY DFTSE100   1.000000 INTERESTRATE -0.233544   1.000000 INFLATIONRATE   0.172117 -0.002656   1.000000 MONEYSUPPLY -0.316644   0.400237 -0.278901   1.000000 Correlation matrix amongst FTSE 100, Inflation rate, Interest rate and Money supply are listed in Table 12 above. The result shows that there is negative correlation between FTSE 100 and the macroeconomic variables Money supply and Interest rate. However, there is a positive correlation between FTSE 100 Index and Inflation rate. Also, among the macroeconomic variables, there is negative relationship between Interest rate Inflation rate, and Inflation rate Money supply. These are in line with what is generally explained in economic theory. As inflation increases the market reacts negatively (Varian, 2003). There is a positive correlation between Interest rate and Money supply. Results were further analysed using Excel and similar results were obtained In all macroeconomic variables, the pair-wise correlation was very low which suggest that there are no collinearity problems. With above result, there is need to verify the existence of multi collinearity by running the regression. Table 15: Regression results without testing for stationarity and unit root in Excel SUMMARY OUTPUT Regression Statistics Multiple R 0.352636386 R Square 0.124352421 Adjusted R Square 0.077442729 Standard Error 0.043224995 Observations 60 ANOVA  Df SS MS F Significance F Regression 3 0.014858768 0.004952923 2.650889742 0.057519925 Residual 56 0.104630409 0.0018684   Total 59 0.119489177     Coefficients Standard Error t Stat P-value Intercept 0.027716505 0.014080199 1.968473987 0.05397107 MS -0.017252571 0.010733585 -1.607344751 0.11360312 INTR -0.003263929 0.00317997 -1.026402297 0.30911525 INFR 0.012988814 0.015847688 0.819603093 0.41591714 From Table 15 above, Inflation rate affects Stock return positively as shown by ÃÆ'Ã… ½Ãƒâ€šÃ‚ ² coefficient 0.01298. This further indicates that one unit increase of Inflation rate would cause Stock return to increase by 0.01298 units. However, Money Supply and Interest rate affects Stock return negatively with ÃÆ'Ã… ½Ãƒâ€šÃ‚ ² coefficient of -0.01725 and -0.00326 respectively. This also indicates that a unit increase in Money supply and Interest rate would result to reduction in Stock returns by 0.01725 and 0.00326 units respectively. The statistical significance of Money supply, Interest rate and Inflation rate on Stock return is 0.11, 0.31 and 0.42 r espectively. Since the p-values are more than 0.05, it is a sign of low significance. R2 of 0.124 represents the prediction level of variance in Stock returns by Money Supply, Interest rate and Inflation rate. This also implies that only 12% of stock returns are predicted by combination of the three macroeconomic variables and other macroeconomic variables not covered in this study predicts stock return by 88%. Table 16: Regression results after testing for stationarity and unit root in EViews Dependent Variable: DFTSE100 Method: Least Squares Date: 08/23/10 Time: 16:16 Sample (adjusted): 4 60 Included observations: 57 after adjustments Coefficient Std. Error t-Statistic Prob.  Ãƒâ€š CONSTANT -0.024102 0.026751 -0.900944 0.3717 DINTERESTRATE -0.126212 0.049943 -2.527110 0.0145 INFLATIONRATE 0.014430 0.037484 0.384960 0.7018 MONEYSUPPLY 0.023353 0.021515 1.085388 0.2827 R-squared 0.162273   Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Mean dependent var 0.000545 Adjusted R-squared 0.114854   Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  S.D. dependent var 0.096607 S.E. of regression 0.090890   Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Akaike info criterion -1.890737 Sum squared resid 0.437835   Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Schwarz criterion -1.747365 Log likelihood 57.88599   Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Hannan-Quinn criter. -1.835017 F-stat istic 3.422132   Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Durbin-Watson stat 3.065866 Prob(F-statistic) 0.023644 Results from Table 16 above, where data was tested for unit root and stationarity, differs from what obtains in Table 15. Inflation rate and Money supply affects Stock return positively as shown by ÃÆ'Ã… ½Ãƒâ€šÃ‚ ² coefficient 0.0144 and 0.0233 respectively. This implies that one unit increase of Inflation rate and Money supply would cause Stock return to increase by 0.0144 and 0.0233 units respectively. However, only Interest rate affects Stock return negatively with ÃÆ'Ã… ½Ãƒâ€šÃ‚ ² coefficient of -0.1262. Thus, a unit increase in Interest rate would result to reduction in Stock returns by 0.01262 units. The statistical significance of Interest rate, Inflation rate and Money supply on Stock return is 0.01, 0.70 and 0.28 respectively. Since the p-values for Interest rate on Stock return is 0.01, which is less than 0.05, it implies that Interest rate predi cts effect on Stock return. Statistical significance of Inflation rate and Money supply is more than 0.05 and indicates a sign of low significance. R2 of 0.162 represents the prediction level of variance in Stock returns by Money Supply, Interest rate and Inflation rate. This implies that only 16% of stock returns are predicted by combination of the three macroeconomic variables and other macroeconomic variables not covered in this study predicts stock return by 84%.