Calculate the standard deviation of the stock return using

Question

Problem 1

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?

Problem 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:

r_ABC=0.08-0.55F₁+1.2F₂+e_ABC

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

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

R_HD =0.02+0.80R_M+e_HD

R-squared =0.6

R_ML =-0.03+1.50R_M+e_ML

R-squared =0.4

σ_M =0.20

where M is S&P/TSX Comp Index, R_X 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

Using theYahoo! 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 EXCELdoes 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

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 R² =β²σ_M²/σ²,and the individual regression results).

iv. Calculate systematic risk and firm specific risk for the stock.

Answer 1

We have some issues that is based on correlation coefficient between portfolio P Problem 1: Assume the return on portfolio P has the subsequent probability distribution: 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, correspondingly. The correlation coefficient between portfolio P and the market portfolio M is 0.6. Answer the subsequent issues: 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: Think a 2 feature economy. Assume the risk-free rate = 3%, and the risk premiums are RP1 = 10%, RP2 = 8%. The return on stock ABC is produced according to the subsequent equation: rABC=0.08-0.55F1+1.2F2+eABC Suppose that the stock is at present priced at $50 per share. 1. What is the expected return for stock ABC using the APT?