Use yearly returns for Microsoft (MSFT), Raytheon Technologies (RTX), and Caterpillar (CAT) from December 31, 1991 to December 31, 2021 to answer the following questions. Assume risk-free rate to be 3.00%. Yearly returns from 1992 to 2021 are required to answer the following questions.

1. 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)
2. Find the optimal portfolio (i.e., weight of the three assets) by maximizing the Sharpe ratio of all feasible portfolios. Use yearly mean returns and variance-covariance matrix for this. (7 points)
3. Find a portfolio (i.e., weight of the three assets) on the efficient frontier with the expected return of 15%. Use yearly mean returns and variance-covariance matrix for this. (7 points)