Suppose the return on portfolio P has the following probability distribution:
Bear Market Normal market Bull market
Probability 0.2 0.5 0.3
Return on P -20% 18% 50%
Assume that the risk-free rate is 9%, and the expected return and standard deviation on the market portfolio M is 0.19 and 0.20, respectively. The correlation coefficient between portfolio P and the market portfolio M is 0.6.
Answer the following questions:
1. Is P efficient?
2. What is the beta of portfolio P?
3. What is the alpha of portfolio P? Is P overpriced or underpriced?
2.Consider a two factor economy. Assume the risk-free rate = 3%, and the risk premiums are
RP1 = 10%, RP2 = 8%. The return on stock ABC is generated according to the following equation:
Assume that the stock is currently priced at $50 per share.
1. What is the expected return for stock ABC using the APT?
2. Is stock ABC underpriced or overvalued?
3. If the expected price next year will be $55, what is the stock price now that will not allow for
4. Assume that the risk free rate increases to 4%, with the other variables remaining unchanged. Would you recommend to buy or sell stock ABC?
3.Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results:
where M is S&P/TSX Comp Index, RX is the excess return of stock X.
1. What is the standard deviation of each stock?
2. What is the systematic risk of each stock?
The systematic risk of a stock is measured by its beta
The beta is determined by regressing the returns of stock against the returns on the market
The slope of the regression is the beta
3. What are the covariance and correlation coefficient between HD and ML?
4. For portfolio P with investment proportion of 0.3 in HD and 0.7 in ML, calculate the systematic risk, non-systematic risk and total risk of P.