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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 Stock A Stock B Boom 0.1 25% -3% Normal 0.6 15% 9% Recession 0.3 -5% 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%2 ). (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. (2 marks)

ii) determine whether Stock A is under, fairly or over-valued.