(Ref. Unit 4 Exercise 1-A / Unit 5 Slides 7, 14-15) During the past 5-year, the monthly average return and standard deviation of Tesla (TSLA) stock were 6.55% and 22.11%, respectively. For the same period, the monthly average return and standard deviation of Exxon Mobil (XOM) stock were 1.39% and 10.11%, respectively. The correlation between TSLA and XOM was 0.09. Assume that the monthly risk-free rate is 0.14%.

Note: You can use the Excel template for 2-asset portfolio optimization posted on Canvas.

1. (1 point) What is the Sharpe ratio for TSLA? What is the Sharpe ratio for XOM?
   • Show your calculation steps briefly and clearly.
2. (1 point) Find the minimum-variance portfolio (MVP), i.e., the weight of TSLA and XOM in the MVP. Note that you must see a lower standard deviation for the MVP than TSLA and XOM by definition of the MVP.
   • You do not need to show your calculation steps for this subquestion.
3. (1 point) Find the optimal risky portfolio P*, i.e., the weight of TSLA and XOM in P*.
   • You do not need to show your calculation steps for this subquestion.
4. (1 point) Calculate the Sharpe ratio for the optimal risky portfolio P*. Note that you must see a higher Sharpe ratio for P* than TSLA and XOM by definition of P*.
   • Show your calculation steps briefly and clearly.
5. (1 point) Consider a portfolio that invests 30% in the risk-free asset and the rest in P*. What is the expected return on this portfolio?
   • Show your calculation steps briefly and clearly.