You are analyzing the returns of stock A and stock B and have collected the following information about stock As returns.

State of the economy	Probability	Stock A's return
Boom	0.3	20%
Normal	0.5	15%
Bust	0.2	1%

Additionally, your analysis shows the following information:

• The correlation between stock A and the market portfolio is equal to 0.3
• The standard deviation of the market portfolio is equal to 5%
• The expected return of stock B is equal to 10%
• The standard deviation of stock B is equal to 13.89%
• Stock B has twice as much systematic risk as the market portfolio
• The covariance between stock A and stock B is equal to 0.93%

1. Calculate the expected return and standard deviation of the returns of Stock A. (4 marks)

2. Calculate the expected return and standard deviation of the returns of an equally-weighted portfolio of stock A and stock B. (4 marks)

3. Calculate the correlation between the returns of stock A and the returns of stock B. (2 marks)

4. What is the beta of stock B. (2 marks)

5. What is the beta of stock A. (2 marks)

6. You would like to form a portfolio by investing in stock A, stock B, and a risk-free asset. Your objective is to allocate a 20% portfolio weight to the risk-free asset and at the same time to ensure that your portfolio has the same level of systematic risk as the market portfolio. What are the weights of stock A and stock B in this portfolio? (5 marks)

7. Assume that the market risk premium is equal to 4%, and the risk free rate is equal to 2%. Do stock A and stock B plot on the Security Market Line (SML)? Are they correctly priced? Briefly explain. (6 marks)