Assignment 2

Instructions

Assignment 2 should be submitted after you have completed Unit 3. This assignment is worth 15 percent of your final grade.

Assignment 2 contains four problems. The maximum mark for each problem is noted at the beginning of the problem. This assignment has a total of 100 marks.

Read the requirements for each problem and plan your responses carefully. Although your responses should be concise, ensure that you answer each of the required components as completely as possible. If supporting calculations are required, present them in good form.

When you receive your graded assignment, carefully review the comments the marker has made. This review component is an important step in your learning process. If you have any questions or concerns about the evaluation, please contact the Student Support Centre.

Problem 1 (15 marks)

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:

• Is P efficient? What is the beta of portfolio P?
• What is the alpha of portfolio P? Is P overpriced or underpriced?

Problem 2 (20 marks)

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:

r_ABC.08-0.55F₁+1.2F₂+e_ABC

Assume that the stock is currently priced at $50 per share.

• What is the expected return for stock ABC using the APT? Is stock ABC underpriced or overvalued? If the expected price next year will be $55, what is the stock price now that will not allow for arbitrage profits?
• Assume that the risk free rate increases to 4%, with the other variables remaining unchanged. Would you recommend to buy or sell stock ABC?

Problem 3 (15 marks)

Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results:

R_HD .02+0.80R_M+e_HD

R-squared .6

R_ML =-0.03+1.50R_M+e_ML

R-squared .4

?_M .20

where M is S&P/TSX Comp Index, R_X is the excess return of stock X.

• What is the standard deviation of each stock? What is the systematic risk of each stock? What are the covariance and correlation coefficient between HD and ML?
• 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.

Assignment 2 Instructions Assignment 2 should be submitted after you have completed Unit 3. This assignment is worth 15 percent of your final grade. Assignment 2 contains four problems. The maximum mark for each problem is noted at the beginning of the problem. This assignment has a total of 100 marks. Read the requirements for each problem and plan your responses carefully. Although your responses should be concise, ensure that you answer each of the required components as completely as possible. If supporting calculations are required, present them in good form. When you receive your graded assignment, carefully review the comments the marker has made. This review component is an important step in your learning process. If you have any questions or concerns about the evaluation, please contact the Student Support Centre. Problem 1 (15 marks) Suppose the return on portfolio P has the following probability distribution: Probability Return on P Bear Market 0.2 -20% Normal market 0.5 18% Bull market 0.3 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? Problem 2 (20 marks) FNCE 401v6 Assignment 2 Revised March 2014 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: rABC=0.08-0.55F1+1.2F2+eABC 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 arbitrage profits? 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? Problem 3 (15 marks) Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =0.02+0.80RM+eHD R-squared =0.6 RML =-0.03+1.50RM+eML R-squared =0.4 M =0.20 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? 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. FNCE 401v6 Assignment 2 Revised March 2014 FNCE 401v6 Assignment 2 Revised March 2014