The Efficient Frontier and CAPM:

2. Supposethat: =5%, ( )=12%and =0.18

a.What is the risk premium in the market?

b.Present the CML equation (use for the standard deviation of the portfolio).

c.What will be the expected return that investors demand in order to invest in a portfolio with standard deviation of 12%? What should the expected return be if the standard deviation of the portfolio is 25%?

5.The market portfolio has an expected return of 8% and a SD of 10%. The risk free rate in the market is 5%. Consider the following two efficient investors: Lionel and Cristiano. You know that the expected return in Lionels portfolio is 6%, and the Standard Deviation in Cristianos portfolio is 12%

a. Calculate Lionels and Cristianos investment weight (proportion) in the market out of their portfolio.

b. Jose (another investor) decided to invest all of its money in one stock. The expected return of the stock is 15% and the standard deviation of the stock is 60%. Can he improve his portfolio? Specifically, how should Jose construct his portfolio?

c. Following b, if he still wants the same standard deviation, what will be his expected return?

6.The following table presents data of four portfolios, traded in a CAPM model market:

Expected return

Standard Deviation

Beta

Specific variance

Portfolio 1 Portfolio 2 Portfolio 3 Portfolio 4

8% 10% 12% ? ? 0 2 0.49 10 0 0.36? ? 5% ?

Using the given information, please complete the missing data in the table.

7.The risk free rate is 3% and the expected return of the market portfolio is 9%. The expected return of stock Y is 6% and the standard deviation of stock Y is 10%. The correlation between stock Y and the market return is 0.8.

Calculate the beta of stock Y.

Calculate the standard deviation of the market portfolio.

Stock Z has similar expected return as stock Y (6%) and standard deviation of 0.2. What is the correlation between stock Z and the market portfolio?

8. Consider the following three stocks in the market.

Which of the following sentences is True?

CML A

B

B1.The total risk of C is higher than the total risk of A

2.The systematic risk of B and C is similar.

3.The specific risk of A and C is similar.

4.B has higher correlation with the market than A.

5.The systematic risk of A is higher than the systematic risk of C.

10. Your firm is considering an investment in a new project. The project requires an initial investment of $10,000. Based on the probability below, the project is expected to produce the following cash flow in one year:

Probability Cash Flow

25% 10,000

50% 12,000

25% 25,000

Further, according to your analysis, you found that the beta of the firms stock is 1.5. Additionally, you are given the following information to help with your investment decision:

- The beta of the new project is 2.

- The expected return on the market portfolio is 15%.

- The risk free rate in the market is 3%.

Based on the above information, should the firm undertake the project?