Suppose that the S&P 500, with a beta of 1.0, has an expected return of 10% and T-bills provide a risk-free return of 4%.

a. How would you construct a portfolio from these two assets with an expected return of 8%? Specifically, what will be the weights in the S&P 500 versus T-bills?

b. How would you construct a portfolio from these two assets with a beta of 0.4?

c. Find the risk premiums of the portfolios in (a) and (b), and show that they are proportional to their betas.