Descriptive Statistics of Abbott Laboratories and Unilever - Essay Example

MODULE: NBS-3F3Y WORK Colin al affiliation: Descriptive Statistics Part 1A Descriptive statistics involves the analysis of data that helps describe, show and summarize data in a meaningful way that patterns may emerge from the data. With reference to the descriptive statistics, the location and dispersion were taken into considerations in analyzing the Abbotts Laboratories together with two other companies, including Unilever and S & P 500. Abbott Laboratories has a relatively higher average return and lower risk when compared to Unilever and S & P 500 which has a higher average return than it but a higher risk rate. Therefore Abbott Laboratories is a better company to invest in based on its lower risks rate. But if the average is considered, then S & P 500 is a better company to invest in. Mean and median are two types of averages and are the most common. Mean is the average which is realized when you add up all the numbers and then divide by the count of the numbers, in this case after calculating the mean value for each of the firms, we realized the following data outputs, Abbots Laboratories 34.51503, Unilever realized a mean of 37.05433 while S & P500 realized a mean of 1654.891. The median is the middle value in the list of various numbers, to obtain median the numbers are listed in numerical order, after calculations we realized the following data, Abbotts Laboratory a median of 34.75, Unilever realized a median of 38.11 and S&P 500 realized 1649.6. The range on the other hand is the difference between the largest and the smallest values in a group of data, the range of the firms were as follows, Abbotts Laboratory realized a range of 21.14, the Unilever realized a range of 16.57 and finally S&P 500 realized a range of 810.96. Mean = where X is the scores and N is the number of scores Median =where L is the lower limit of the interval containing the median, N the total number of scores, FW is the frequency or the number of scores within the interval containing the median, and I is the range of the interval. In finance and accounting, variance is a term used to measure the degree of risk in an investment. It is obtained by calculating the average of the squared deviations from the mean rate of return. The standard deviation is the representation of the risk associated with a given security (stocks, bonds) or the risk of a portfolio of securities and it is obtained by taking the square root of the variance. Table below shows the report on the mean, median, range, variance and Standard deviation based on the weekly returns of each of the three assets.   Abbott Labs Unilever S&P 500 Mean 34.51503 37.05433 1654.891 Median 34.75 38.11 1649.6 Range 21.14 16.57 810.96 Variance 28.72163 20.6085 57890.58 Standard D. 5.359257 4.539659 240.6046 Statistically these value returns helps investors understand he financial market empirically. Financially investors who seek incomes have several alternatives to choose from that can offer superior payouts with minimal risk rates. It is thus vital to know that there is nothing like risk-free investment but that different investments carry different types of risk. With reference to the data descriptive analysis above and based on their risk investment returns, out of the three companies, I would recommend the Abbott Laboratories to any potential investor due to its lower risks rate. PART 1B In statistics, the correlation coefficient r measures the strength and direction of a linear relationship between two variables, in this case Abbott Laboratories and Unilever on a scatterplot. The value of r is always between +1 and -1, thus at 0.1383 results to a weak uphill and it’s a positive linear correlation. The value y=0.3395x shows the gradient of the linearity and 0.0009 is the point at which the linear crosses the y axis. Increasing the value of Unilever would lead to either a moderate or strong uphill, positive linear correlation which would eventually end up in a perfect positive correlation. From the above XY plot it is clearly observed that there is a positive correlation between the two return series between Unilever and Abbott Laboratories returns. The average return of Abbott laboratories is 0.41% while the average return of Unilever returns at 0.23% thus giving the Standard Portfolio return of 1.85%, which is the portfolio standard deviation and it’s realized by finding the square root of the variance value. The table above shows the calculated covariance between the weekly returns of Abbott laboratories and Unilever Company. These includes the standard deviation and the average return of the portfolio With reference to the statistics, it is observed that the variations in the returns is higher for my portfolio than the Abbotts laboratories, but has a lower return than that of Abbott laboratories. This implies that there is a higher risk investment on my portfolio than that of Abbott laboratories. Below are the results of the covariance and correlation between the weekly returns of Abbott laboratories and Unilever. Count 157 SUMPRODUCT 204180.8     COVARIANCE 21.72162 CORRELATION 0.892821 The formula for calculating the covariance data is as shown below. x = the independent variable Y = the dependent variable n = the number of data points in the sample = the mean of the independent variable x = the mean of the dependent variable y The formular of finding correlation is as follows, to calculate correlation, you must know the covariance for the two variables and the standard deviations of each variable. 2 Capital Asset Pricing Model This is a pricing model that describes the relationship between risk and expected return and that is used in the pricing of risky securities. On this section, an XY plot has been created for excess returns of the S & P 500 against the excess returns of Abbott laboratories based on a constant weekly risk rate of 0.05% as indicated in figure below. The Capital Asset Pricing Model (CAPM) regression line was fitted as well as the R –squared and regression equations were displayed on the plot. Based on the above plots, it is observed that there is strong positive correlation between S&P 500 and Abbott laboratories excess returns. The coefficient of correlation is 0.9972 which is the alpha coefficient and it is considered to be very high, hence, a strong positive correlation. Explanatory power of the model: This can well be explained by R squared which is considered to be the statistical measure that measures how close the given data are to the regression line that is fitted (Kan and Zhang 1999). It is as well referred to as coefficient of determination and it is usually between 0 to 100%. In this case, 42.1%, which is the ratio of the explained variation to the total variation and is the measure of how good the regression line is. This shows that the model does explain any the response data variability around its mean. On the other hand, 100% means that the model explains all the variability (Kandel and Stambaugh 1995). The regression model above represents a 42.1% of the variance and the more the variance is accounted for the closer the data points fall on the fitted regression line. PART 2B Estimation of the CAPM regression The aim of this section is to test the hypothesis using the dataset provided of the weekly returns of S & P 500 and Abbott laboratories for the past 3 years. It was investigated whether the Abbot Laboratories excess returns are influenced by the S & P 500 excess returns. The model that corresponds to this is: Where Yt represents the current excess return of Abbott laboratories and X1 represents the excess returns on the S & P 500. Basing on the regression summary (at 95 % and 90% confidence interval) below (table 3), it is observed that the intercept on the Abbott laboratories is statistically significant while the excess return on the Abbott laboratories ( is not statistically significant. This is because the p value of the Abbott laboratory excess return is greater than 0.05 while that of the intercept is less than 0.05. Therefore, this equation or model can be used in forecasting the Abbott excess returns using the S & P 500 excess returns. The excess returns falls between 0.10846 and 0.2925 at 95% confidence level. The R squared is small and it could be due to the Abbott laboratories excess return is influenced by many factors other than S & P 500. When the regression analysis is run at 90% confidence interval as shown in table 3, it is still observed that the intercept is statistically significant but the excess return on the Abbott laboratories is not significant due to the p value being greater and less than (WT 7 talking about) 0.05 respectively. Regression Results Intercept 0.0009 Read More