Individual Market Return - Coursework Example

Statistical assignment Introduction Purpose ment The focus of this study will include two variables, one dependent and one independent variables. The study wishes to determine if there is significant relationship in the time series regression CAPM. The study will run a time series regression on each of the selected companies. The primary independent variable is Rm- Rf which is the return of the company. In this study these variables will be explored and the correlation between the dependent variable, and the independent variables. Definitions of Variables The dependent variable, market return is defined to be the amount of resources the business will be generating over a given accounting period. Individual market return is said to have a relationship with the market return. The independent variable, market return, is referring to the amount of company around the business environment are receiving in their day to day activities. In this case, the relationship between the individual market return they receive and the market return the business generate in the area is said to have a positive relationship. The independent variable, market return, refers to the other businesses that are involved in the same product or closely related products that are substitute of the products. Data description The data contain two variables; market return, and individual market return. The data is obtained after randomly sampling 160 companies and obtaining their financial data. That is, the market return, and the individual stock return Regression analysis  Represent the multiple regression models, and are model parameters referred to as regression coefficient. Such model describes the hyper plane in the k-dimensional space of the regression variable. The parameters  represent the expected change in the response variable y per a change in, while all the repressor remains constants. Checking if the assumptions are justified The residual analysis For the regression analysis to be used, several assumptions are made. The assumption that the errors are normally distributed can be justified by making a normal probability plot or by constructing a histogram of the residuals. In this study, we will check if the errors of the dependent variables and independent variables are normally distributed by making the checks. From the above histogram, the variables; market return and individual market return are normally distributed. The variable market return has outliers and are removed to ensure that the do not influence the inference and conclusion. The normal probability plot From above analysis of normal probability, the variables, revenue, people, income. Competitors and price are normally distributed. From the two analyses that check the assumption of normality, we conclude that the data is normally distributed and hence the regression analysis can be conducted. The regression equation The regression equation is Revenue = -0.001491517+0.965969024 market return Since the regression model is a linear regression, the best estimation method for the coefficient predictor variables is the least square method. Merit and demerits of CAPM regression The primary drawbacks are reflected in the models inputs and assumptions. Risk-free Rate (Rf): The commonly accepted rate used as the Rf is the yield on short term government securities. The issue with using this input is that the yield changes daily, creating volatility. Return on the Market (Rm): The return on the market can be described as the sum of the capital and dividend for the market. A problem arises when at any given time; the market return can be negative. As a result, a long-term market return is utilized to smooth the return. Another issue is that these returns are backward-looking and may not be representative of future market returns. Ability to Borrow at a Risk-free Rate: CAPM is built on four major assumptions, including one that reflects an unrealistic real-world picture. This assumption, that investors can borrow and lend at a risk-free rate, is unattainable in reality. Individual investors are unable to borrow (or lend) at the rate the US government can borrow at. Therefore, the minimum required return line might actually be less steep (provide a lower return) than the model calculates. Determination of Project Proxy Beta: Businesses that use CAPM to assess an investment need to find a beta reflective to the project or investment. Often a proxy beta is necessary. However, accurately determining one to properly assess the project is difficult and can affect the reliability of the outcome. The merits of CAPM are; CAPM is a simplistic calculation that can be easily stress-tested to derive a range of possible outcomes to provide confidence around the required rates of return. Diversified Portfolio: The assumption that investors hold a diversified portfolio, similar to the market portfolio, eliminates unsystematic risk. Systematic risk (beta): CAPM takes into account systematic risk, which is left out of other return models, such as the dividend discount model. Systematic or market risk is an important variable because it is unforeseen and often cannot be completely mitigated because it is often not fully expected. Business and Financial Risk Variability: When businesses investigate opportunities, if the business mix and financing differ from the current business, then other required return calculations, like weighted average cost of capital cannot be used. From above regression analysis, there is a relationship between the dependent variable revenue and the independent or the predictor variables. This is because the p-value is equal to 0.000 which is less than 0.05 level of the confidence. We thus conclude that dependent variable has a relationship with the independent variable. The f-statistic is equal to 108.3215. From the CAPM regression analysis we can observe that the regression has a coefficient of determination is equal to 0.396315263. This means that the cross section regression can account for 39.6315263% of the errors in the regression model. The analysis of variance of the regression model indicate that the value of the f (1,165) = 108.3215 which has a p- value of 0.0000. This implies that the regression analysis is significant at 95%. SUMMARY OUTPUT Regression Statistics Multiple R 0.629535752 R Square 0.396315263 Adjusted R Square 0.392656568 Standard Error 0.032631603 Observations 167 ANOVA   df SS MS F Significance F Regression 1 0.115343 0.115343 108.3215 8.06278E-20 Residual 165 0.175696 0.001065 Total 166 0.291039         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -0.001491517 0.002527 -0.59025 0.555832 -0.006480804 0.003498 -0.00648 0.003498 -0.00121 0.965969024 0.092812 10.40776 8.06E-20 0.782716022 1.149222 0.782716 1.149222 Conclusion In the analysis of individual independent variable, the independent variable, individual return, is significant since the p-value is equal to 0.000 which is less than the 0.05 level of confidence. Thus we conclude that the independent variable individual stock return has no relationship with the dependent variable market return. The value of the t-statistics of the independent variable individual stock return is 10.40776. 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