Use yearly returns for Caterpillar (CAT), Microsoft (MSFT) and Raytheon Technologies (RTX) for 1990 to 2019 (returns for 30 years) to answer the following questions. Assume risk-free rate to be 2.00%.

a. Find the variance-covariance matrix using yearly returns. All entries in the variance-covariance matrix should be calculated using the yearly returns and should be linked to the yearly returns as well. (6 points)

b. Find the optimal portfolio by maximizing the Sharpe ratio of all feasible portfolios. Use yearly mean and covariance matrix for this. Clearly indicate weights for each stock in the optimal portfolio. (7 points)

c. Find a portfolio on the efficient frontier with the expected return of 20%. Use yearly mean and covariance matrix for this. Clearly indicate weights for each stock in the target portfolio. (7 points)