(15 marks) (a) Download at least 15 years of daily market price data for 10 shares from the same country, and convert each of the observation to a yearly return. Plot a histogram of the returns for a few of the shares. (b) Determine the sample covariance matrix as well as sample average return vector for the set of 10 shares. Consider the problem of nding a portfolio that minimizes variance over all portfolios that have an expected annual return of r = 5%. Write down the 12 linear equations that need to be solved, or alternatively give the A and b in the linear equation Ax = b. (c) Solve the system of equations and check your solution. (d) Plot the ecient frontier in r space. 2. (10 marks) Repeat each of (b)-(d) of Question 1 but instead of just the sample covariance matrix, using a shrinkage estimator approach for the covariance matrix, using a choice of \shrinkage target matrix" that is referenced from the academic literature. 3. (15 marks) Set up a factor model for these 10 asset returns using the same data set. Plot the 10 principal values and select the three factors that explain most of the variance in the returns. Then set up the 1010 covariance matrix from this factor model and do Questions (b)-(d) of Question 1 using this covariance matrix. Hint: cov(ri + i1f1 + i2f2 + i3f3; rj + j1f1 + j2f2 + j3f3) =i1j1var(f1) + i2j2var(f2) + i3j3var(f3): 4. (10 marks) Compare the dierences between your results in Questions 1-3, and explain whether the dierences are signicant. Also, comment on whether you expect the dierences to become more pronounced if the number of shares is increased. Page