Bivariate and Univariate Analysis and Effect of Firms Variables on Stock Return Test of Normality - Assignment Example

Name: Lecturer: Course name: Course code: Date Table of content Part A Introduction Graphical presentation of stock return Bivariate and univariate analysis and effect of firm’s variables on stock return test of normality Multivariate Analysis Table showing the Multicollinearity between variables Coefficient of variation Part B Report to directors of Goodvalue References PART A Introduction Capital asset pricing model under the condition of risks is the key factor that determines the stock return. The model hypothesize that the anticipated stock return on assets beyond the risk free rate of return is linearly correlated to the non-diversifiable risks as ascertained by the beta of the assets. The capital assets pricing model is the easy and realistic method in application on condition of the market restiveness Normal hypothesis. In hypothetical and practical study in finance is that, appropriate variables such as the capital asset pricing model (capm), price earnings ratio as well as the dividend yield portray the multivariate normal distribution. where a random variable does not correspond to univariate normal distribution, it means that the random variable did not emanate from multivariate normal distribution and hence, the test procedure as well the equivalent proof not in favor of the multivariate normal distribution is relevant and because returns are correlated, statistics will be dependent. Key approach in ascertaining stock market behavior is to perform classical statistics where stock rates of return are normally distributed. All the traits of stock return are ascertained in the mean and the variance of the data collected. By employing the standard normal distribution, it is easy to forecast the behavior of stocks return. Some of the variables affecting stock return are explained in details as follows. The required rate of return Required rate of return is a return in percentage form in which investors desires to achieve from an investment so as to purchase the security in the stock market. The required rate of return will have effect on the stock price in that; it will alter the value of the stock price in which an individual is eager to pay for a specified security. Dividend yield A dividend yield depicts how much an investor will realize income from the price of the security. Stock containing a high dividend yield might provide a better channel of income. Dividend paying securities might rapidly decline in value since, there is a threat that the future dividend will decline. Where a corporation announces a decline in dividend, the value of the stock will respond rapidly. Market capitalization Market capitalization merely means the worth an investor will get when he multiply all the outstanding shares of a security by the price of a sole share. High market capitalization depicts high value of stock of the company since; the company is having a dividend held leading to high payout ratio. This will attract investors into the company consequently increasing the value of stock return. Market cap= {share price per unit*total shares in the company} Beta of the firm (capm) Beta of a venture is an assessment of the risk consequential from exposure to broad market trends. Beta less than one depict a venture with low volatility than the market or the investment is volatile and has the trend of its prices less correlated with the market trend. where an investment is having a better of greater than one implies that the assets is volatile and moves up and down in relation to the market trends. Beta is vital since, it ascertains the threats of non- diversifiable investment. In capm, beta risk is the single kind of risk for which an investor must receive a high expected return as compared to the risk free rate of return. Capm=risk free rate of return+ (market premium)*beta Price earnings ratio (P/E) p/e= {net income/average shares] This approach employs the net income and divides by the average number of common share in issue during the period. In making comparison between the value of the stock and the earning per share for a company, an investor can ascertain the market stock valuation of the corporation and its sharers in relation to its income. High stock forecast earnings growth have a higher price earnings ratio and with low earning growth depicts low price earnings ratios. Price earnings ratio is dependent on the leverage of the company. The debt ratio of the company affects both the earning and the share price in many ways. a) Graphical representation of the market stock return the above graphical presentation depicts cyclical trend of security returns, it can be observed that the maximum stock return is $ 0.6 while the lowest stock return is -0.6.it is therefore apparent that an investor wishing to invest in any company listed in the stock market ought to invest in security that is not overvalued or undervalued (-0.6 to.6 range)this is the acceptance region in which a return will be expected from investment as well as the extent to which a potential investor should tolerate on the risk of stock return. Majorly the securities of these companies do not portray adverse effect and hence it is worthwhile to invest on these shares of any company listed. Graphical presentation of beta return segmenting beta returns and making a correlation between beta and the stock retuns,a slight correaltion is depicted implying that beta estimates provides a relibale corlinearity between the anticipated return and the beta estimator.a beta less than one represent a business enterprise with small unpredictability as compared to the market or the venture is unpredictable and has the tendency of its prices less correlated with the market drift. A speculation with better of greater than one implies that the assets are volatile and moves up and down in relation to the market trends. Beta is vital because, it ascertains the pressure from non- diversifiable speculation agraphical preasentation of price earning ratio Price earnings ratio depicts a cyclical trend that is correlated with the market stock return and hence it is probable to ascertain the performance of the stock price as well anticipating the future trend of stock performance. . In making judgment involving the price of the stock and the earning per share for a business, and shareholder can establish the market stock valuation of the business as well as the sharers in relation to its income. High stock estimates the earnings growth has advanced value earnings ratio, low earning growth depicts a low price earnings ratios. In these cases, it can be concluded that there is multivariate normal distribution among the variables affecting the stock returns. BIVARIATE AND UNIVARIATE ANALYSIS AND EFFECT OF FIRM’S VARIABLES ON STOCK RETURN b) Univariate analysis’s of stock return and bivariate analysis of capital asset pricing model on stock return Univariate analysis is relevant when the data has no correlation with each other. From the above data analysis, the univariate distribution will be enough to depict how much return will be anticipated if the historical return does not have effect on the future return. Where a random variable is not univariate normally distributed, then it cannot have emanated from the a multivariate normal distribution and thus it implies that the test method and equivalent proof against the multivariate normality suitable Capital asset pricing model (capm) creates a connection involving risks and returns in the efficient capital markets. Though beta by itself is not an appropriate determinant of asset pricing and that several other factors could clarify the cross-section of returns. capital asset pricing model (capm)is analyzed by running the regressions on the actual returns of the individual .the security/portfolio’s cross-sectional analysis regression is performed in order to assess the degree of autonomous variable’s pressure on the security/portfolio returns. Test for univariate normality It is evident that if a vector of assets return is multivariate normal distributed, then every assets return is univariate normally distributed. Though univariate normality do not merely means multivariate normality, dismissal of univariate normality is adequate to discard the multivariate normality situation. Kurtosis and skewness are the two relevant measures of normality. This statistical measure concentrates on properties of distribution which do not have effect on assets return as well as the derivative securities. Relevant deviation from the univariate normal null will point towards alternative distribution which assures the skewness and kurtosis figures. Skewness and kurtosis Skewness evaluates evenness of the anticipated distribution of a random variable about the mean. The value can either be positive or negative. Where the value equals to zero, it implies that the data are absolutely balanced. Kurtosis ascertains the peakedness of the anticipated distribution of a random variable. Effects of (capm) capital asset pricing model on stock return. {Normality test) root mean square (rams): 1.167 std error of mean: 0.01537 skewness: -0.6124 kurtosis: 5.971 coefficient of variation: 0.1901 relative standard deviation: 19.01% Capital assets pricing model depicts a skewness of -0.6124 and kurtosis of 5.971.it therefore implies that there is a good return from investment for investors since, stock will have a higher returns from investment. Normality of dividend yield on the stock return root mean square (rms): 1.859 std error of mean: 0.09709 skewness: 3.12 kurtosis: 17.12 coefficient of variation: 1.098 relative standard deviation: 109.8% Dividend yield has positive skewness of 3.12 implying that median is greater than mode {point at the top of the curve) Price earnings ratio analysis and its effect on the stock return absolute deviation: 4.386 root mean square (rms): 24.67 std error of mean: 0.5577 skewness: 1.578 kurtosis: 9.71 coefficient of variation: 0.3383 relative standard deviation: 33.8 The above table depicts the variables single kurtosis and skewness test for the 200 companies over the same sample period. the variables depicts excess kurtosis due to the fact that the stock return are in fact drawn from the substitute distribution to the multivariate normal distribution and also, the kurtosis trend in stock return might be unauthentic because, if stock are multivariate normally distributed then ascertaining the kurtosis of every stock return would generate different kurtosis and where there is no correlation of assets return, then any superfluous might be interfered in terms of the univariate statistics with placid modification. where the stock return are correlated, it implies therefore that under the null assumptions of the multivariate normal distribution that other assets will as well display the kurtosis to some degree and consequently, cross-sectional correlation might creates other cross-sectional prototype of the kurtosis in a diminutive proportion. However, where a small number of stock returns depict kurtosis, it implies that the multivariate normal distribution hypothesis is superior estimate for stock return. This is not satisfactory enough to proof of stock returns. the estimate of superfluous kurtosis in a small number of stock give consistent proof against multivariate normal distribution since, the correlation provide information regarding the correctness and exactitude of every kurtosis estimates in the combined system. c) Multivariate test analysis Multi-variety time series analysis is envisaged where multiple related a variable occurs at the same time. In hypothetical as well as the observed study in finance depicts that relevant variables have portrays multivariate normal distribution. The multivariate normality of stock returns is a decisive hypothesis in several tests of beta (capm). Univariate test statistics are unpredictable for testing the multivariate normality in view of the fact univariate test statistics do not take into account the simultaneous correlation connecting asset returns. the return of a stock under the normal distribution is the asymptotically very proficient estimator 0f the anticipated return and its insertion of extra assets will not change the approximation .distinguishing with multivariate t distribution, the anticipated returns encloses relevant information on predicting the expected stock return. The multivariate normal distribution expresses its normality by way of relatively little parameters that is the mean, variance of the return and the correlation of return between r1---rz. discriminate analysis is a technique of multivariate analysis that relate a categorical autonomous variable with metric autonomous variable and thus the linear joint of discriminate analysis is ascertained by an equation as follows. {Zx=a+zcx+zcx2+….zcxn} Where, Zx is the is the discriminate Z score for the stock return x A is the intercept, C, c2---cn are the coefficient of stock return for the autonomous variable x, x2...xn After separating the dependent and independent variable on the basis of higher and lower return assumptions, the stock return was analyzed using the formulae RI= {x1] x1-1]-1)*100 X1 is the closing stock returns Where a multicolliniearity is observed among the autonomous variables and correlation is depicted, then those variables that discriminate are chosen as the model and it is concluded that none of the variable portrays correlation. Table showing the Multicollinearity between variables .In understanding the importance of every variable that affect the stock return, it is appropriate to observe the standardized coefficient of the function as well since, The coefficient of variation are the product of the non coefficient by the roots of the covariance. Coefficient of variation Dividend yield 1.098 CAPM 0.1901 Price earnings ratio 0.3383 From the above table analysis, it is apparent that coefficient that contribute majorly to discriminate amongst the group of variables in downward manner is the dividend yield, followed by the Beta and hence the price earnings ratio. The outcome of the analysis implies that, dividend yield is the factor which portrays the highest weight in providing an understanding concerning the stock returns. Beta is the single excluded factor since it has a capital asset pricing model restriction in providing an understanding as to the stock return and once cannot be relied fully for decision making. This result implies that, Potential investor considers other external factors other than risks to value the anticipated stock price. The above coefficient analysis of variables depicts that, a correlation exist items of the stock returns and the variables itself that affect the stock return. Capital assets pricing model is one of the key indicator of stock performance as much as it has a restriction from the beta, its risk free rate of return provide a tolerable error in which an analyst should allow in order to Place reliance on the information provided by the beta (capm) in concluding whether to purchase a security or dispose. the security of Goodvalue therefore is performing well since, the market efficiency is semi-strong and hence potential investors willing to acquire the securities in this company should consider making a decision in order to capitalize o the market discrepancies and to make a supernormal profit before other external factor affects the general trend so stock performance, PART B Report to directors of Goodvalue Limited It is hard to understand single test statistics for univariate normality in stock return though it is possible to test the assumption that stock return is normally distributed. The test limits themselves, consequently, to study marginal distribution of the stock, deviation from multivariate normality might be established in the combined distribution of stock (assets).kurtosis and skewness are tools used to ascertain the returns of stock. In applying these techniques to stock returns as well as the market model residuals, it is evident that non-normality exists in the distribution assets. The multivariate normal hypothesis cannot give a good reason as per the alternative multivariate normal distribution, the technique employed to test the relevance of these alternative distribution. As compared to other practical capital assets pricing model as well as the finance research, it is presumed that the assets return portrays a multivariate normality continuously although the t multivariate distribution is still off-putting; it is sensible unlike the normality hypothesis. in statistics, multivariate t distribution are employed extensively for data analysis which exhibit fat tails since, the stock return do not portray fat tails. The only limitation with multivariate hypothesis is that, they entail a lot of many parameters commanding numerical study in order to make the most of the objective function and hence it will be hard to apply large dimensional troubles. It is apparent that researches employees the univariate estimates to conduct multivariate analysis. From the above date analysis, can be observed that a multivariate normality exist and thus it is evident that this variables affect the returns of the assets (Jan Bebbington, 2001). The stock returns performing well in the market since it can be observed clearly that the highest the price of the stock is $0.6 while the least tolerable price decline is $-0.6.in this case, an investor is having good platform to make verdict whether to buy or disposal a security given the prevailing economic conditions. Therefore the general performance of the 200 companies is quite promising and hence a return will be realized from investment Bibliography Jan Bebbington, ‎Rob Gray, ‎Richard Laughlin. Financial Accounting: Practice and Principles. 2001. . The standard error of estimates is quite low implying that the security is having a favorable tolerable error in which an investor should tolerate before disposing the returns due to poor returns, in this case, a potential investor should consider ascertaining the performance of this securities in the stock market and capitalize on the marker discrepancies as well as efficiency of stock market in buying a security in order to earning profit. Reference list E. Altman, Financial ratios, discriminant analysis and the prediction of Business failure, Journal of Finance, 23 (1968), 589-609 W. C. Barbee, S. Mukherji and G. A. Raines, Do sales-price and debt equity Explain stock returns better than book-market and firm size? Financial Analysts Journal, 52 (1996), 56-60. M. S. Bartlett, Multivariate Analysis, Journal of the Royal Statistical Society, 9 (1947), 176-197. K. C. Chan, Y. Hamao and J. Lakonishok, Fundamentals and stock Returns in Japan, Journal of Finance, 46 (1991), 1739-1764 E. 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