You are provided the given information on a stock fund.
Question 1: Please compute the expected return and standard deviation for the stock fund.
Scenario Probability Rate of Return/Stock Fund
Recession 25.0% -7%
Normal 50% 12%
Boom 25.0% 28%
Question 2: You plan to form a portfolio with 50% invested in the Stock Fund and 50% invested in T-bills (the risk-free asset). T-bill offers a return of 5%. What's the portfolio return and portfolio risk?
Question 3: There is a Bond Fund which has a correlation coefficient of -1 with the Stock Fund mentioned in part a. The expected return and standard deviation for the Bond Fund are 6% and 10%, respectively. You plan to form a portfolio with the Stock Fund and the Bond Fund only (no T-bills in this part). What are the portfolio weights you need to choose such that the variance of the portfolio is minimized?