# Exercise 1

Given the following table of returns for financial assets A and B

Probability __r _{A}__

__r___{B}0.1 | 10% | -2% |

0.3 | 8% | 14% |

0.2 | 20% | 3% |

0.1 | 7% | 12% |

0.2 | -2% | 7% |

0.1 | 0% | 2.5% |

- Calculate expected return and standard deviation for each of the two securities
- Plot the frontier of portfolios obtained by changing the proportion of wealth invested in each of the two securities. In doing so, assume that the percentage of wealth invested in asset
*A*, call it*w*, and the percentage invested in asset_{A}*B*,*w*, add up to 1._{B} - Determine the efficient frontier.

# Exercise 2

Suppose that two assets have identical variance. Show that the minimum variance portfolio always assigns a weight 1/2 to each asset, independently of their covariance.

# Exercise 3

(from Ross et al.): Holup, Inc., makes pneumatic equipment. The beta of Holup’s stock is 1.2. The expected market risk premium is 8.5 percent, and the current risk- free rate is 6 percent. Assume the capital-asset-pricing model holds. What is the expected return on Holup’s stock?

# Exercise 4

(from Ross et al.): Suppose you observe the following situation:

State of Economy | Probability | Stock A Return | Stock B Return |

Bust | 0.25 | -0.1 | -0.3 |

Normal | 0.5 | 0.1 | 0.05 |

Boom | 0.25 | 0.2 | 0.4 |

- Calculate the expected return on each stock.
- Assuming the capital-asset-pricing model holds and stock A’s beta is greater than stock B’s beta by 0.25, what is the expected market risk premium?

# Exercise 5

(from Ross et al.): The risk-free rate is 7.6%. Potpourri Inc. stock has a beta of 1.7 and an expected return of 16.7 percent. Assume the capital-asset-pricing model holds.

- What is the expected market risk premium?
- Magnolia Industries stock has a beta of 0.8. What is the expected return on the Magnolia’s stock?
- Suppose you have invested $10,000 in a combination of Potpourri and Magnolia stock. The beta of the portfolio is 1.07. How much did you invest in each stock? What is the expected return on the portfolio?

# Exercise 6

(from Ross et al.): The returns for the past five years on Douglas stock and on the New York Stock Exchange Composite Index (NYSE) are listed below :

- What are the average returns on Douglas and on the market?
- Compute the beta of Douglas’ stock.

Douglas | NYSE |

-0.05 | -0.12 |

0.05 | 0.01 |

0.08 | 0.06 |

0.15 | 0.10 |

0.10 | 0.05 |

# Exercise 7

(from Ross et al.): The following table lists possible rates of returns on Compton Technology’s stock and debt and on the market portfolio. The probability of each state is also listed.

State | Probability | Stock Return (%) | Debt Return | Mkt Return |

1 | 0.1 | 3% | 8% | 5% |

2 | 0.3 | 8% | 8% | 10% |

3 | 0.4 | 20% | 10% | 15% |

4 | 0.2 | 15% | 10% | 20% |

- What is the beta of Compton Technology debt?
- What is the beta of Compton Technology stock? If the debt-to-equity ratio of Compton Technology is 0.5, what is the asset beta of Compton Technology? Assume no taxes.

# Exercise 8

(from Ross et al.): Lipzaz Inc. is a levered firm with a debt-to-equity ratio of 0.25. The beta of the common stock is 1.15, while the beta of the debt is 0.3. The market risk premium is 10 percent and the risk-free rate is 6 percent. The corporate tax rate is 35 percent.

- What is the firm’s cost of equity capital?
- If a new company project has the same risk as the overall firm, what is the weighted average cost of capital for the project ?

# Exercise 9

(from Ross et al.): Calculate the weighted average cost of capital for the Luxury Porcelain Company. The book value of Luxury’s outstanding debt is $60 million. Currently, the debt is trading at 120 percent of book value and is priced to yield 12 percent. The 5 million outstanding shares of Luxury stock are trading at $20 per share. The required return on Luxury stock is 18 percent. The tax rate is 25 percent.