Bauer has $1,000,000 to invest and is considering the merits of the following two stocks Co. A and B Inc. The possible monthly rate of return of stocks is shown as below: Monthly Rate of Return of Stocks A and B for the coming month (Dec 2021): State of Affair Probability Boom 0.1 Normal 0.6 Recession 0.3 Stock A 25% 15% -5% Stock B -3% 9% 13% (a) Calculate the expected rate of return and variance of rate of return of Stock A and Stock B. (12 marks) (b) Bauer plans to construct a portfolio consisting of 10,000 shares of Stock A and 6,000 shares of Stock B. At the end of the Dec 2021, Stocks A and B are currently trading at $70 and $50 respectively. Calculate the weight of the Stock A and Stock B in the portfolio. (3 marks) (c) Calculate the expected rate of return and variance of the portfolio as stated in part (b), given the covariance is -0.0018 (or -18%). (6 marks) (d) Bauer has collected the following market data: Risk-free rate: 3% Expected market return: 13% Beta of Stock A: 1.5 i) calculate the required rate of return of Stock A. ii) determine whether Stock A is under, fairly or over-valued. (2 marks) (2 marks)