Intermediate Corporate Finance
Assignment
1. The following information is available on the percentage rates of return on various assets under the three possible states of the world, each of which has a probability of occurring of one third:
State 1 2 3
Share A -6% -18% 60%
Share B 32% -22% 35%
Market Portfolio 50% -10% 20%
Risk-free Asset 10% 10% 10%
i) What is the numerical equation for the Capital Market Line (CML) for the market?
ii) Do shares A and B lie on the CML, and what, if anything, do you conclude from this?
iii) What are the beta values for share A and B?
iv) Are the expected returns for shares A and B consistent with the Security Market Line and, if not, what equilibrating changes would you expect to occur?
2. Mary Johnson decides to invest $10,000 on financial market. She is allowed to invest on only two stocks IBM and GE if the money is invested in stock market. Mary can also invest on government risk-free security with rate of interest 8%. She can also borrow
money at 8%. Using historical data, Mary estimates the following statistics:
IBM GE
Expected Return % 30 15
Variance % 100 25
The correlation between the returns of IBM and GE is estimated to be 0.5. What is the optimal investment strategy for Mary who is risk averse?
3. There are only two investors and two risky assets (Stock A and B) in the market. The investors are Mr. Black and Mrs White. Mr. Black invests 6 billion dollars on Stock A, $4 billion on Stock B and $1 billion on risk-free bank deposit while Mrs White spends $7.5 billion buying stock A, $5 billion buying B and $10 billion on risk-free bank deposit. The returns of A and B are as follows:
A B
Expected Return % 10 15
Standard Deviation % 10 20
The correlation between two returns is 0.
i) What is the market portfolio (of risky assets)?
ii) Suppose the CAPM holds, what is the risk-free return in equilibrium?
iii) What are the numerical equations for the CML and SML of the market?
iv) Draw the diagrams of CML and SML. Do Asset A and B lie on them?
4. Imagine that we are in 22nd century. After hundreds of waves of mergers and acquisitions, there are only two listed companies in the market: West Co. and East Co.
There are only two investors (sovereignty wealth fund managers), Mr. Hussein and Miss Wang, who do investment management for individuals. Mr. Hussein's investment on risky assets is $10 billion on Stock West and $4 billion on Stock East. Miss Wang's portfolio on risky assets is $11 billion on West and $10 billion on East.
They also invest on risk-free assets by borrowing or saving. The returns of West and East are as follows:
West Co. East Co.
Expected Return % 8 13
Standard Deviation % 5 10
The correlation between two returns is 0.
We assume that the market is in equilibrium. What is the slope of the capital market line (CML) of the market? (Hint: borrowing and lending interest rates may be different)
5. Write risky asset i's return as ??~??. In the standard deviation-expected return (??, ??) space, the coordinates of ??~?? are denoted by (????, ????). The correlation coefficient of ??~?? with the market return ??~?? is denoted by ????,??. The risk-free return is assumed to be ????.Suppose all assumptions for CAPM hold.
i) The standard deviation measures the total risk of a risky asset's return. If only systematic risk is included, what are the coordinates of ??~?? in the standard deviationexpected return space?
ii) If we link all the points across different assets i with each point's coordinates being given in 1), prove that these points form a straight line. Give the mathematical equation of the straight line. (Hint: you may refer to the proof on pages 27-28 in lecture note 2).
iii) What is the mathematical equation for SML in the beta-expected return (??, ??) space?
iv) Compare the slope of the two mathematical equations given in ii) and iii). What is the relationship between the two mathematical equations?
v) Provide economic interpretation/intuition for the above results.