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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
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%
- Calculate the expected return and standard deviation of the returns of Stock A. (4 marks)
- Calculate the expected return and standard deviation of the returns of an equally-weighted portfolio of stock A and stock B. (4 marks)
- Calculate the correlation between the returns of stock A and the returns of stock B. (2 marks)
- What is the beta of stock B. (2 marks)
- What is the beta of stock A. (2 marks)
- 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)
- 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)
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