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)

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?

2

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)

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:

?

? Independent Variable

? Intercept

? Dependent Variable

Beta Value

? Firm Specific Risk

i.

ii.

What is the alpha of the BNS stock?

iii.

Calculate the standard deviation of the stock return (using the equation for R2 =?2?M2/?2, and the individual regression results).

iv.

4

How well does the S&P/TSX Comp Index movement explain the variability of the return on BNS stock?

Calculate systematic risk and firm specific risk for the stock.