(a) The rate of return in each week for each stock and for the stock market index for the 27 weekly periods. Calculate the discrete rate of return. Calculate the arithmetic mean return and the geometric mean return of each stock for the entire period. Use only the discrete returns for your calculations and for the calculations in the questions that follow. (10 marks)
(b) The variance of returns for each stock and the index and the covariances of returns between each pair of stocks, the covariance between each stock and the stock market index, and the corresponding correlation coefficients. (5 marks)
(c) Compare your results in (a) and (b) for each stock and the stock market index and comment on the risk return characteristics and performance of each of your stocks and the index. Illustrate with tables/charts as appropriate. Comment on the results, relating to what you have learnt in this course. Relate the risk return pattern and the performance of the market index and your stocks to relevant events that took place during this period. Draw on economic, political, industry and company related events that took place over this period that may have impacted on the performance of your stocks and the market index. Give bibliographic references to the sources of your information. (15 marks)
Part 2 (10 marks)
(a) Based on the discrete returns calculations in Part 1, compute the weekly rate of return and the variance of an equally weighted portfolio formed from the three stocks. Make use of your knowledge of matrix algebra in your calculations. (5 marks)
(b). Examine and compare the pattern of the returns of your portfolio with those of the individual stocks, and the stock index. Compare the corresponding variances. Comment on your observations, relating to material learnt in this course. (5 marks)
Part 3 (45 marks)
(a) Extract for each week, the yield of the 26-week Treasury bill (or equivalently the 90 day or 180-day bank accepted bill from the financial media (i.e. Federal Reserve Bank: http://www.federalreserve.gov/default.htm) over your sample period. (Remember sometimes reported yields are usually annualised figures. Convert the yields to weekly numbers. Use these as a proxy for the risk free rate).
(b) Estimate the Security Characteristic Line (SCL) for each of your stocks and the equal weighted portfolio, based on the ‘Market Model’, using excess returns (discrete returns less the risk free rate), using Excel regression analysis functions. Show your results graphically. From your results, compute the Beta and the Jensen’s Alpha of each stock and the portfolio. (15 marks)
(c) Calculate the total risk (the return variance) of each stock and the portfolio. Partition the total risk to their respective systematic and unsystematic risk components. (10 marks)
(d) Based on your observations and results in parts (b) and (c) above, comment on each of your stock’s and portfolio’s performance, and on their risk characteristics, comparing and contrasting the magnitude and the proportions of their systematic and unsystematic risk components. What further insights can you gain on the characteristics and behaviour of your stocks and portfolio compared to the analysis and observations you made in Part 1 (c) and Part 2 (b)? (15 marks)
Part 4 (15 marks)
From the point of view of an investor who wishes to evaluate whether the stocks that you examined are worth investing in, how useful was the analysis you carried out on these stocks? What limitations do you see in your analysis and results for investment decision making purposes? What further analysis would you wish to carry out? Explain.