Finance Assignment -
We will use monthly returns from Jan 1970 to Dec 2014 of 49 US industry portfolios, the US market portfolio and the risk-free rate provided by Kenneth French. All the data we need is provided in the excel file "industry portfolios.xlsx". Solve everything in excel and present your results clearly, i.e. create a spreadsheet with the name \Results" (where the answers to all questions can be found) and clearly indicate which cells belong to which question.
(a) Estimate expected returns and the covariance matrix of the 49 industry portfolios. Multiply expected returns and covariance matrix by 12 to annualize them.
(b) Plot the expected returns and volatilities of all 49 industry portfolios in a scatter plot.
(c) Construct the minimum-variance frontier for desired expected returns ranging from 0% to 50%. Add the minimum-variance frontier to the scatter plot.
(d) Calculated the global minimum-variance portfolio and add it to the scatter plot.
(e) Suppose for now the annual risk-free rate is constant and equal to 5% per year. Calculate the tangency portfolio and add it to the scatter plot.
(f) Construct the Capital Allocation line and add it to the scatter plot.
(g) Calculate the optimal portfolio for an investor with mean-variance preferences u (r) = E [r] - γ/2 Var[r], with γ = 5. Draw an indifference curve which passes through the optimal portfolio in the scatter plot.
(h) Use the market return and risk-free rate data in the excel file to estimate CAPM-αs and CAPM-βs for all 49 industry portfolios. Multiply CAPM-αs by 12 to annualize them; CAPM-βs do not have to be annualized. (Use actual excess returns using the risk-free interest rate data instead of the above assumed constant risk-free interest rate of 5%.) You will find that most CAPM-αs do not statistically significantly differ from zero, except for "Food", "Smoke" and "Other".
(i) Set the market premium (risk premium of market portfolio) equal to the average excess return of the market over the risk-free rate in the data. Assuming the CAPM holds (CAPM-α=0 for all assets), estimate the expected returns of the 49 industry portfolios.
(j) Construct the covariance matrix assuming the Single Index Model, i.e. assuming the errors in the CAPM regressions are uncorrelated across assets.
(k) We now create an optimal portfolio using the Single Index Model. We assume that the CAPM-αs of all industry portfolios are zero (since they are all insignificant), except for the three industries "Food", "Smoke" and "Other". For the three industries "Food", "Smoke" and "Other" we use the estimated CAPM-αs. That is, we only include the three industry portfolios "Food", "Smoke" and "Other" in our active portfolio. Follow the simple 7 step approach in the lecture notes on pages 231-233 to construct the optimal risky asset portfolio.
(l) Find the optimal weight in the risky asset portfolio in (k) and the risk-free asset (assume again the risk-free rate is 5% per year) for an investor with mean-variance preferences u (r) = E [r] - γ/2 Var [r], with γ = 5.
Attachment:- Assignment Files.rar