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.

Problem 4 (50 marks)

Using the Yahoo! Finance website, search the Bank of Nova Scotia (BNS.TO) by finding its stock symbol. If you are unable to locate the prices for BNS.TO, use prices for BNS (the Bank of Nova Scotia observed in US dollars at the New York Stock Exchange). For the purpose of this question, assume that the Canadian dollar and the US dollar had been exchanged one for one. Find historical prices for the stock (on the left-hand menu) and complete the following:

• Download historical data for the stock prices (adj. close) from January 1, 2004 through January 1, 2012, on a monthly basis. You will also need to download corresponding monthly prices for the S&P/TSX Comp index (also available on the Yahoo! Finance site) as well as 3-month T-Bill rates (download this attachment: T-Bill Rates.xlsx). Calculate returns for both series of prices downloaded from Yahoo site (BNS and S&P /TSX Comp Index). Prior to that, make sure the data is sorted in ascending order (i.e., first row has the oldest data). The final spreadsheet should have the two series of returns you downloaded and calculated from Yahoo! Finance. Make sure all data is expressed in same units. Using the Tools menu in EXCEL, (Tool Pack has to be installed if EXCEL does not show it) perform regression analyses using the Market Model for BNS.
• Clearly provide the regression results in a table with an explanation for the coefficients obtained, and clear interpretation. Specifically, for each regression provide:
• 1. Dependent Variable
• 2. Independent Variable
• 3. Intercept
• 4.Beta Value 5. Firm Specific Risk Q1. How well does the S&P/TSX Comp Index movement explain the variability of the return on BNS stock? Q2. What is the alpha of the BNS stock? Q3. Calculate the standard deviation of the stock return (using the equation for R

² =?²?_M²/?²,and the individual regression results). Q4. Calculate systematic risk and firm specific risk for the stock. 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. Problem 4 (50 marks) FNCE 401v6 Assignment 2 Revised March 2014 Using the Yahoo! Finance website, search the Bank of Nova Scotia (BNS.TO) by finding its stock symbol. If you are unable to locate the prices for BNS.TO, use prices for BNS (the Bank of Nova Scotia observed in US dollars at the New York Stock Exchange). For the purpose of this question, assume that the Canadian dollar and the US dollar had been exchanged one for one. Find historical prices for the stock (on the left-hand menu) and complete the following: 1. Download historical data for the stock prices (adj. close) from January 1, 2004 through January 1, 2012, on a monthly basis. You will also need to download corresponding monthly prices for the S&P/TSX Comp index (also available on the Yahoo! Finance site) as well as 3-month T-Bill rates (download this attachment: T-Bill Rates.xlsx). 2. Calculate returns for both series of prices downloaded from Yahoo site (BNS and S&P /TSX Comp Index). Prior to that, make sure the data is sorted in ascending order (i.e., first row has the oldest data). The final spreadsheet should have the two series of returns you downloaded and calculated from Yahoo! Finance. Make sure all data is expressed in same units. 3. Using the Tools menu in EXCEL, (Tool Pack has to be installed if EXCEL does not show it) perform regression analyses using the Market Model for BNS. 4. Clearly provide the regression results in a table with an explanation for the coefficients obtained, and clear interpretation. Specifically, for each regression provide: Dependent Variable Independent Variable Intercept Beta Value Firm Specific Risk FNCE 401v6 i. How well does the S&P/TSX Comp Index movement explain the variability of the return on BNS stock? ii. What is the alpha of the BNS stock? iii. Calculate the standard deviation of the stock return (using the equation for R 2 =2M2/2, and the individual regression results). iv. Calculate systematic risk and firm specific risk for the stock. Assignment 2 Revised March 2014