Assume that the S&P 500 is the market portfolio and is also the tangency portfolio. The S&P 500 has an expected return of 12%, with a standard deviation of 25% per year. Apple's stock has an expected return of 16%, with a standard deviation of 40% per year. The risk-free rate is 4%. Assume that CAPM holds for the remainder of this problem.

1a) (7 points) Is this combination of expected returns and standard deviations possible according to the CAPM? Why or why not?

1b) (8 points) Now, suppose, contrary to above, that we do not know the expected return of Apple's stock or the standard deviation of its return. However, we do know that its covariance with the S&P 500 is 0.1. What is the expected return on Apple's stock?

1c) (7 points) Suppose that the expected return on Apple's stock is as in part a (i.e., 16%). Suppose that the expected return on Intel's stock is half of the expected return on Apple's stock. What is the beta of Intel's stock?

1d) (8 points) Suppose that the expected return on Apple's stock is as in part a (i.e., 16%). Calculate the expected return and beta of a portfolio that invests in the following five assets in the following proportions: 30% in Apple 30% in Intel 30% in the S&P 500 -20% in GM (expected return = 5%) 30% in the risk-free asset.