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4. With the same information as in problem 3 (which is down below), find analytically an optimal sets of weights that maximize Sharpe ratio, max () , subject to the same constraint. (Hint: Use Lagrange Multipliers.)

3. An investment firm, SHB-BC Fund, would like to construct a portfolio. The risk-free rate equals 1.5% and a covariance matrix is, [ 0.001 0.07 0.02 0.07 0.03 0.09 0.02 0.09 0.002 ] Answer each question for the SHB-BC fund using the following data: Stocks Weights Returns GM 0.3 0.7% IBM 0.3 2.0% MCD 0.4 1.4% 1) Compute a portfolio return using matrix multiplication. 2) Compute a portfolio standard deviation using matrix multiplication. 3) Find analytically an optimal set of weights to minimize portfolio risk subject to the constraints: = 1 3 =1 and > 0. 8 7. With the same information as in problem 6, find analytically an optimal sets of weights that maximize Sharpe ratio, max () , subject to the same constraint. (Hint: Use Lagrange Multipliers.)