Analyzing the Stocks of Four Companies in the FTSE 100 Index between January and March 2014 - Case Study Example

Number: Analyzing the stocks of four companies’ in the FTSE 100 index between January and March 2014 The paper analyzes the stock performance of International Consolidated Airlines Group SA (IAG.L), which is a consolidated airline group involved in the provision of passenger and cargo transport services in UK and Spain; The Sainsbury (J) PLC (SBRY.L) which is a UK based company engaged in grocery and related retailing activities; The Royal Mail PLC (RMG.L), which is involved provision of postal and delivery services in Europe; and The Intertek Group PLC (ITRK.L), which is a UK based company involved in the supply and provision of utilities such as in Industry & Assurance. The work also involves computation of the return and variance of a portfolio comprising of equal quantities of stock using the Single Index Model and the historical data; calculating the cumulative abnormal return of one of these stocks using a key date in its life such as a major announcement as an event on the four companies. (a) Alpha is the distance above or below the security market line. It measures the historical performance of the security relative to the expected return predicted by the security market line and thus used to compute the risk –adjusted return of a security. The alpha of a stock can be calculated as α = [(Sum of X) – (b * Sum of Y)]/ n Where; X is the rate of return for the fund Y is the rate of return for the market B is the beta of the stock N is the number of observations (Alpha ) The estimate of securities alpha has been determined as shown in the above table in the appendix. Security (IAG.L) has the largest alpha of 0.128% while stock (SBRY.L) has the lowest alpha of -0.190%. This implies that given the stated betas, the average daily return of stock (IAG.L) is 0.128% above that required by the security line while the average of security (SBRY.L) given its betas , was 0.190% below the security market line. (b) Beta for each stock Beta of a stock is the measure of its volatility due to market –wide risk and thus attempts to explain the stocks sensitivity to market risk. It is the sensitivity of the security’s return to the return of the market portfolio where the market portfolio is a combination of different stocks in the market. Beta is the expected percentage change in its return given a 1% change in the return of the market portfolio (Brealey, Myers, & Allen, 2011). Beta of a security can be calculated as [SD(R1) * Corr( R1, R mkt)]/ SDmkt Where SD(R1) : -Is the standard deviation of the security Corr( R1, R mkt)]:- Correlation between the security and the market SDmkt : -Standard deviation of the market Based on the data collected the betas for the four securities are as shown in the appendix table i and ii. The expected average market beta is 1. A stock with a beta of more than 1 is more risky compared to the market portfolio for which investors expect to be compensated with an expected return higher than expected market return. Therefore, based on returns of daily data, (IAG.L) security will be ranked highly be investors and based on weekly data, (SBRY.L) will be ranked highly by investors while securities (RMG.L) and (ITRK.L) will be ranked last by investors (Brealey, Myers, & Allen, 2011). The tables i and ii also show beta ranking changes according to measurement method and time period, raising questions about how to properly apply the theory of portfolio analysis in a practical setting. (c) The standard deviation of the residuals is a statistical measure that provides an indication of how far the sample averages might deviate from the expected return. It is the standard deviation of the estimated value of the mean of the actual distribution around its true values, that is, the standard deviation of average return. The standard error can be calculated as SD (Average of independent, identical risk) = SD( Individual Risk)/ Square root ( Number of observations) The standard deviations of the residuals for the four securities based on data from daily returns are as shown in the appendix table iii and iv. The standard error of the residual returns shows the extent of possible mis-measurement of the securities returns and can therefore be used to estimate a 95% confidence interval of the estimated returns plus or minus two standard errors (Ehrhardt & Brigham, 2011) (d) Correlation coefficient between each security and the market Correlation coefficient is the measure of the tendency of two variables to move together. The correlation coefficient between a security and the market is the measure of the tendency to which the security’s returns move together in relation to market returns (Ehrhardt & Brigham, 2011) . The correlation between the variables can be positively correlated if they tend to move up or down together, negatively correlated if the returns move inversely to those of the market, or zero when there is no correlation. The correlation coefficient is the magnitude through which the variables move together and can take values between -1 to +1. The correlation between a security and the market can be determined as; Corr (Ri, Rj) = Cov(Ri, Rj) / SD(Ri) SD(Rj) Where Cov(Ri, Rj); Covariance of security and the market SD(Ri); Standard deviation of the security SD(Rj); Standard deviation of the market The correlation coefficients based on data from daily and weekly returns are as shown in table v and vi below. From the data on the correlation coefficient of the four securities with the market for both the daily and weekly returns are positive, which means that the returns of the securities move together with the returns of the market. The different values are the magnitudes of the movement and thus (IAG.L) will be the most affected by changes in the market while (SBRY.L) will be the least affected by changes in market returns. Based on the weekly data stock (SBRY.L) will be the most affected by market changes while stock (ITRK.L) will be the least affected by market changes. The positive correlation of the stocks also means that their risks cannot be diversified. (e) Average return of the market Based on the daily returns, the average return for the market index is FTSE 100 Mean -0.034% Based on the weekly returns, the average returns for the market index is FTSE 100 Mean -0.140% The average returns from both daily and weekly data of the market, FTSE100 index, is negative, this implies that there has been a net decrease in the value of shareholders investment in securities making up the market index but of varying amounts with the average return on daily data having the least decrease. (f) The variance of the market Variance is one of the measures of volatility of securities. The variance of the market can be defined as the expected squared deviation from the expected return. The magnitude of deviation from the mean is a sign of volatility and acts to increase the variance. Daily Returns: FTSE 100 Sample Variance 0.005% Weekly Returns: FTSE 100 Sample Variance 0.03% The market variance based on the daily returns data is 0.005% while the market variance based on weekly returns is 0.03%. This implies that there are high variations in weekly returns than the variations in daily returns. (g) Compute the mean return and variance of each stock The mean and variances of stocks based on daily and weekly returns are as shown in the appendix table vii and viii. From the stocks means returns and variances based on daily and weekly returns, stock (IAG.L) has a positive return while stocks (SBRY.L), (ITRK.L) and (RMG.L) have negative returns implying that over the time period of analysis only stock (IAG.L) lead to increase in the wealth of shareholders through increase in share prices (Ehrhardt & Brigham, 2011). The variance can be defined as a measure of a return squared deviation from its mean return. From the analysis of the daily data, stock (IAG.L) has the highest variation of returns from the squared deviation implying that the returns are more risky compared to other stocks with stock (ITRK.L) has the lowest deviation. From the analysis of weekly data, stock (SBRY.L) has the highest variation in returns while stocks (ITRK.L) and (RMG.L) have the least variance in returns of 8% each. (h) Covariance matrix Covariance of stocks is the tendency of returns of stocks to move together at the same time. It is the expected product of the deviation of two returns from their means. Covariance matrix is combination of covariance of stocks with each other expressed in form of a matrix (Ehrhardt & Brigham, 2011). The covariance of stocks will be positive if their returns tend to be above or below at the same time. The covariance between two securities from historical data can be calculated as Ƿ(1,2) * SDev1* SDev2 Where, Ƿ(1,2) is the correlation between S1 and S2 SDev1 is the standard deviation of S1 SDev2 is the standard deviation of S2 The covariance matrices of the daily and weekly returns are as shown in table (ix) and (x) in the appendix. (i) Compute the return and variance of a portfolio comprising of equal quantities An equally weighted portfolio is combination of different stocks in which the same amount is invested in each stock. The return on a portfolio of n stock is the weighted average of the returns of the stock in the portfolio and the variance of a portfolio is equal to the weighted average covariance of each stock with the portfolio. The returns based on daily and weekly data is contained in the appendix table (xi) and (xii). It shows that based on daily returns the mean in –0.045% while based on weekly data it is 0.320%. The combination of different stocks in a portfolio with the intention of averaging out the risk is known as diversification. The variance of an equally weighted portfolio, assuming diversification can be calculated as Var (Rp) = (1/n) * Average Variance of the individual stocks + (1 – 1/n) * Average Covariance between the stocks Where n is the number of stock in the portfolio. The average variance o the individual stocks has been calculated as the sum of all variances divided by the number of stocks in the portfolio. The average covariance between the stocks has been calculated as the sum of all variances between stocks divided by the number of alternative combination of the stocks (Brealey, Myers, & Allen, 2011). Average Variance Average covariance between stocks 0.0230% 0.00489% (1/n) and (1 -1/n) 0.25 0.75 [(1/n)* Average Variance]/[ (1 -1/n) * Average covariance between stocks 0.0057% 0.0037% 0.0094% Therefore, the variance of a portfolio comprising of equal quantities of the four securities, based on daily returns is 0.0094%. This is lower than the variances for the individual stocks and this means that independent risks in the stocks have been average out in the portfolio (Brealey, Myers, & Allen, 2011). This lower variance also means that the combination of the four securities has a return risk of 0.0094%. (j) Cumulative abnormal return is the actual return over and above the expected stock return because of firm specific news. Abnormal returns can be calculated as Abnormal return = Actual stock return – expected stock return The Expected stock return = (α +β*return on market index) (Brealey, Myers, & Allen, 2011) Therefore Abnormal return = R – (α +β rm) International Consolidated Airlines Group SA (IAG.L) Abnormal returns = Actual Return -(Alpha + Beta( Market return)) Alpha Beta(Average Market return) Expected return Actual Return Abnormal return 13th Feb 2014 0.128% -0.35% -0.23% 2.886% 3.11% On, 13 February 2014, International Consolidated Airlines Group had an abnormal return that was caused by firm specific news. The company had a preview of their annual financial statements for the year ended December 2013 and had posted better financial results. This included a 5.5% increase in total revenue and 149.1% in profit after tax. The group did not intent to distribute dividend and thus the profit after tax would be used to invest in profitable investments to increase shareholders wealth (IAG, 2014). (Word count 2032) Appendix The alpha of stocks based on historical daily returns Sum of returns sum of market returns Beta Number of observations b*( Sum of Market returns Alpha International Consolidated Airlines Group SA (IAG.L) 4.850% -2.113% 1.51 63.00 -3.190% 0.128% Sainsbury (J) PLC (SBRY.L) -13.519% -2.113% 0.73 63.00 -1.532% -0.190% Intertek Group PLC (ITRK.L) -2.017% -2.113% 0.87 63.00 -1.841% -0.003% Royal Mail PLC (RMG.L) -0.626% -2.113% 0.72 63.00 -1.523% 0.014% Table (i) Daily Betas Securities Beta International Consolidated Airlines Group SA (IAG.L) 1.51 Sainsbury (J) PLC (SBRY.L) 0.73 Intertek Group PLC (ITRK.L) 0.87 Royal Mail PLC (RMG.L) 0.72 Table (ii) Weekly beta Securities Beta International Consolidated Airlines Group SA (IAG.L) 0.826 Sainsbury (J) PLC (SBRY.L) 1.456 Intertek Group PLC (ITRK.L) 0.622 Royal Mail PLC (RMG.L) 0.633 Table (iii) Daily Standard deviations of errors Securities Standard Error International Consolidated Airlines Group SA (IAG.L) 0.22% Sainsbury (J) PLC (SBRY.L) 0.21% Intertek Group PLC (ITRK.L) 0.15% Royal Mail PLC (RMG.L) 0.18% Table (iv) Weekly Standard deviation Securities Standard Error International Consolidated Airlines Group SA (IAG.L) 0.828% Sainsbury (J) PLC (SBRY.L) 1.083% Intertek Group PLC (ITRK.L) 0.798% Royal Mail PLC (RMG.L) 0.798% Correlation co –efficient Table (v) Daily returns data Securities Correlation coefficient International Consolidated Airlines Group SA (IAG.L) 0.58 Sainsbury (J) PLC (SBRY.L) 0.30 Intertek Group PLC (ITRK.L) 0.51 Royal Mail PLC (RMG.L) 0.35 Table (vi) Weekly Securities Correlation coefficient International Consolidated Airlines Group SA (IAG.L) 0.46 Sainsbury (J) PLC (SBRY.L) 0.62 Intertek Group PLC (ITRK.L) 0.36 Royal Mail PLC (RMG.L) 0.37 Table (vii) The mean and variances of stocks based on daily returns Securities Mean Variance International Consolidated Airlines Group SA (IAG.L) 0.077% 0.032% Sainsbury (J) PLC (SBRY.L) -0.215% 0.027% Intertek Group PLC (ITRK.L) -0.032% 0.014% Royal Mail PLC (RMG.L) -0.010% 0.020% Table (viii) The mean and variances of stocks based on weekly returns Securities Mean Variance International Consolidated Airlines Group SA (IAG.L) 0.22% 0.09% Sainsbury (J) PLC (SBRY.L) -1.21% 0.15% Intertek Group PLC (ITRK.L) -0.09% 0.08% Royal Mail PLC (RMG.L) -0.19% 0.08% Table (ix) The covariance matrix of the securities based on the daily returns Covariance Matrix (IAG.L) (SBRY.L) (ITRK.L) (RMG.L) FTSE100 (IAG.L) 0.00584% 0.00650% 0.00788% 0.00703% (SBRY.L) 0.00584% 0.00231% 0.00359% 0.00338% (ITRK.L) 0.00650% 0.00231% 0.00320% 0.00406% (RMG.L) 0.00788% 0.00359% 0.00320% 0.00336% FTSE100 0.00703% 0.00338% 0.00406% 0.00336% Table (x) The covariance matrix of the securities based on the weekly returns International Consolidated Airlines Group SA (IAG.L) Sainsbury (J) PLC (SBRY.L) Intertek Group PLC (ITRK.L) Royal Mail PLC (RMG.L) FTSE 100 International Consolidated Airlines Group SA (IAG.L) -0.00296% 0.01695% 0.04620% 0.02287% Sainsbury (J) PLC (SBRY.L) -0.00296% 0.03239% 0.01720% 0.04033% Intertek Group PLC (ITRK.L) 0.01695% 0.03239% -0.02107% 0.01722% Royal Mail PLC (RMG.L) 0.04620% 0.01720% -0.02107% 0.01737% FTSE 100 0.02287% 0.04033% 0.01722% 0.01737% Table (xi) Mean Return International Consolidated Airlines Group SA (IAG.L) 0.077% Sainsbury (J) PLC (SBRY.L) -0.215% Intertek Group PLC (ITRK.L) -0.032% Royal Mail PLC (RMG.L) -0.010% Sum of all returns -0.180% Portfolios average return -0.045% The portfolio’s return based on daily return’s data is - .0045% Table (xii) Mean International Consolidated Airlines Group SA (IAG.L) 0.22% Sainsbury (J) PLC (SBRY.L) -1.21% Intertek Group PLC (ITRK.L) -0.09% Royal Mail PLC (RMG.L) -0.19% Average portfolio’s return -0.320% Stocks Alpha Alpha determination Sum of returns sum of market returns Beta Number of observations b( Sum of Market returns Alpha International Consolidated Airlines Group SA (IAG.L) 4.850% -2.113% 1.51 63.00 -3.190% 0.128% Sainsbury (J) PLC (SBRY.L) -13.519% -2.113% 0.73 63.00 -1.532% -0.190% Intertek Group PLC (ITRK.L) -2.017% -2.113% 0.87 63.00 -1.841% -0.003% Royal Mail PLC (RMG.L) -0.626% -2.113% 0.72 63.00 -1.523% 0.014% Work cited Shim, Jae K, Joel G. 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