Question Convert the assets' monthly adjusted closing prices into discrete monthly returns compounding per month and also into monthly continuously compounding returns. Report both the discrete and continuously compounded monthly returns' historical arithmetic average, standard deviation and variance for each of the stocks. Report your results in a clearly labeled table with units.
Question 2 For this and all of the following questions, use the discretely compounded monthly returns. Report the assets' covariance of returns matrix in a table. Also report the assets' correlation of returns matrix in a table. Note that the assets include the stocks, market portfolio and bond.
Question 3 Comment on the bond's risk and discuss if it can be seen as a risk free security. Use academic references to support your answer.
Question 4 Construct an equally-weighted portfolio of the stocks and report its return, variance and standard deviation.
Question 5a: Graph 3 Markowitz bullets on the same chart using the stocks only, the stocks and the market, and all assets. Do not assume that the bond is risk free. Label each portfolio possibility frontier appropriately. Depict the stocks and the equally-weighted portfolio as points on the graph and label them too. Assume that all assets can be short-sold.
Question 5b Repeat with short selling not allowed.
Question 6: In this question only, assume that the bond is a risk free security in the sense that its standard deviation of returns is zero and its expected yield is the historical average total return.
Question 6a Construct a tangency portfolio that only includes the stocks. Ignore the ASX200 market portfolio. Assume that the bond is risk free and short selling is allowed. Report the tangency portfolio's return, variance, standard deviation and weight in each stock using a table.
Question 6b Repeat with short selling not allowed.
Question 6c Report the current weights of your stocks in the market portfolio (ASX200) using a table.
Question 6d Calculate the Sharpe ratios of both the short-selling and non-short selling tangency portfolio's, and the ASX200 market portfolio. Report your results in a table. Plot the three Capital Allocation Lines (CAL's) from the bond through the two tangency portfolios and the market portfolio on a graph of return versus standard deviation.
Question 6e How useful are the calculations that you've made in this question for an investor who is considering an investment into the stocks that you've discussed? Use academic references.
Question 6f Which of the problems that you identified in the previous question can be alleviated by applying the Black-Litterman model? Describe how the Black-Litterman model helps correct these problems. Outline how the Black-Litterman model could be applied to help an investor decide on his portfolio allocation into the stocks that you've discussed. You do not have to actually complete a Black-Litterman analysis, just state how it could be done.
Question 7 Using the Single Index Model, report the assets' betas in a table. Assume that the ASX200 is the factor.
Note that the Single Index Model has the formula:
R_it=α_i+β_i (R_mt )+Ïµ_it
The variable Ïµ_it is the error term which averages to zero. R_mt is the index, in this case the ASX200 market portfolio. The β_i is the slope and the α_i is the y-intercept (the return when the beta is zero). Note that the Single Index Model is not the Capital Asset Pricing Model (CAPM). There is no risk free rate or market risk premium in the Single Index Model. See lecture 3 for more details.
Question 8 Report the Single Index Model's systematic, idiosyncratic and total variances for each asset and the equally-weighted portfolio in a table, with the ASX200 as the index, the only factor.
Question 9 For one of the stocks and the market portfolio, present two histograms of the discrete monthly returns and the continuously compounded monthly returns (4 histograms in total).
Calculate the arithmetic mean, mode and median returns and label these on the distributions. Define the mode as the midpoint of the most popular histogram bucket since the ordinary definition of the most popular value is not useful for high-precision floating point numbers with lots of decimal places.
Comment on the apparent distributions of the four histograms. You may wish to calculate the skew and kurtosis of each distribution to aid your explanation.
Question 10 Report the standard errors of each assets' historical arithmetic average discretely compounded monthly returns. Using the theory set out by James-Stein and others who followed, present the assets' future expected returns in a table. Outline how the calculations were done for one of the stocks. Use academic references.