16) In this problem, you will analyze the optimality of the S&P 500 as a market portfolio for the tech market given in the table below. 1. Compute the covariance matrix. 2. What is the composition of the no-leverage portfolio that holds the 4 tech stocks and the S&P 500 and maximizes the portfolio Sharpe ratio? 3. What is the composition of the potentially levered portfolio that holds the 4 tech stocks and the S&P 500 and maximizes the portfolio Sharpe ratio? 4. Suppose that an investor holds the S&P 500 portfolio and wishes to add only one of the 4 tech stocks to this portfolio. Which stock would yield the highest Sharpe ratio for the investor? You can assume that the latest risk-free rate is 0.08%. Correlations Marke Price Expected Volatilit Alphabet Amazon Apple Microsoft t Caps return (trillio n) $1.75 $2,653.6 20.90% 40.60% 1 0.87 0.75 0.92 4 Alphabet Amazon 24.50% 49.20% 0.87 1 0.81 0.88 $1.49 $2,936.3 5 Apple $2.59 $158.52 25.40% 35.20% 0.75 0.81 1 0.85 16) In this problem, you will analyze the optimality of the S&P 500 as a market portfolio for the tech market given in the table below. 1. Compute the covariance matrix. 2. What is the composition of the no-leverage portfolio that holds the 4 tech stocks and the S&P 500 and maximizes the portfolio Sharpe ratio? 3. What is the composition of the potentially levered portfolio that holds the 4 tech stocks and the S&P 500 and maximizes the portfolio Sharpe ratio? 4. Suppose that an investor holds the S&P 500 portfolio and wishes to add only one of the 4 tech stocks to this portfolio. Which stock would yield the highest Sharpe ratio for the investor? You can assume that the latest risk-free rate is 0.08%. Correlations Marke Price Expected Volatilit Alphabet Amazon Apple Microsoft t Caps return (trillio n) $1.75 $2,653.6 20.90% 40.60% 1 0.87 0.75 0.92 4 Alphabet Amazon 24.50% 49.20% 0.87 1 0.81 0.88 $1.49 $2,936.3 5 Apple $2.59 $158.52 25.40% 35.20% 0.75 0.81 1 0.85