1. Required Rate of Return
AA Industries stock has a beta of 0.8. The risk-free rate is 4% and the expected return on the market is 12%. What is the required rate of return on AA's stock?

2. Portfolio Required Return

Suppose you manage a $4 million fund that consists of four stocks with the following investments:

Stock                           Investment                 Beta______________

   A                                 $  400,000                   1.50

   B                                    600,000                    -0.50

   C                                 1,000,000                   1.25

   D                                 2,000,000                   0.75

If the market's required rate of return is 14% and the risk-free rate is 6%, what is the fund's required rate of return?

3. Historical Realized Rates of Return

You are considering an investment in either individual stocks or a portfolio of stocks. The two stocks you are researching, stock A and B, have the following historical returns:

Year                            rA                               rB_________

2009                            -20.00%                       -5.00%

2010                            42.00%                        15.00%

2011                            20.00%                        -13.00%

2012                            -8.00%                         50.00%

2013                            25.00%                        12.00%

a. Calculate the average rate of return for each stock during the 5-year period.

b. Suppose you had held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would have been the realized rate of return on the portfolio in each year? What would have been the average return o the portfolio during this period?

c. Calculate the standard deviation of returns for each stock and for the portfolio.

d. If you are a risk-averse investor, then, assuming these are your only choices, would you prefer to hold Stock A, Stock B, or the portfolio? Why?

4. Historical Returns: Expected and Required Rates of Return

You have observed the following returns over time:

Year                Stock X                       Stock Y                       Market_____

2009                14%                             13%                             12%

2010                19                                7                                  10

2011                -16                               -5                                 -12

2012                3                                  1                                  1

2013                20                                11                                15

Assume that the risk-free rate is 6% and the market risk premium is 5%.

a. What are the betas of Stocks X and Y?

b. What are the required rates of return on Stock X and Y?

c. What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y?

5. Two-Asset Portfolio

Stock A has an expected return of 12% and a standard deviation of 40%. Stock B has an expected return of 18% and a standard deviation of 60%. The correlation coefficient between Stock A and B is 0.2. What are the expected return and standard deviation of a portfolio invested 30% in Stock A and 70% in Stock B?