Over the 20-year period (1997–2016), U.S. stocks have averaged 7.7%

in annual return, with an STD risk of 15.3%. During the same period, U.S. bonds have averaged 5.3% in annual return, with an SD risk of 3.4%. An investor is considering a portfolio with proportion α in stocks and (1 − α) in bonds, where α varies between 0 and 1.

a. What will be the optimal portfolio that maximizes average return, ignoring risk? What will be the portfolio’s average return and STD risk?

b. Suppose the investor splits the investment capital equally between stocks and bonds by choosing α = 0.5. Determine the portfolio’s average return and its STD risk.

c. Determine the optimal value of α that will produce a portfolio with minimum variance. Formulate this as an optimization problem and solve. What is the average return and STD risk of the minimum variance portfolio?