1. When solving the optimal portfolio problem with two risky assets and the risk-free asset, all investors will
A] Hold the same risky portfolio
B] Invest the same amount in the risk free asset
C] Minimize the slope of the CAL
D] Hold the same complete portfolio
2. Consider the following four assets that are all trading in the market. Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz?
A] W: E[r]= 15%, Sigma=36%
B] X:E[r] = 12%, Sigma=15%
C] Y=E[r] = 5%, Sigma=7%
D] Z=E[r] =9%, Sigma=21%
E] All of the above can lie on the efficient frontier
3. You determine that the beta of Costco (COST) is 0.85. Also, you determine that the E[rcost]=10.5%, E[rm]=11%, rf=5%, sigma m =16%, sigma cost=28%. To figure out the effect of hedging the market risk you think of the following scenario: over the next year the market experiences a -10% rate of return. What is the return on Costco if the firm specific return is 1% and what is the return on your trading strategy?
A] -6.30%---1.35%
B] -6.35%---1.35%
C] -6.30%---1.40%
D]-6.35%---1.40%
4. Dale the farmer and his brother Jake decide to sell the family farm. They will use the proceeds to invest in the stock market. As they cannot agree on an investment choice, they split their money. Dale buys stock "Bull" with his half million and "Bull" currently sells for $45 per share. Dale decides that he wants to earn money faster and his broker will allow him to buy on margin. His broker requires a 50% initial margin and charges a 3% annual fee on the loan amount. While Jake is certain his brother is always wrong and decides to short "Bull." His brother requires a 50% initial equity position, which does not gain interest. At what price would each of the brothers receive a margin call if their brokers require a 30% maintenance margin or equity position?
5. You would like to invest in a stock called WOWZA, currently priced at $1200. Your broker requires a 50% initial margin requirement and a 35% maintenance margin.
A] If you have 30,000 dollars today, how many shares can you purchase.
B] What price of WOWZA will lead to a margin call. Then calculate the percent change in the price of WOWZA that leads to a margin call.
C] If the price rises $200 dollars over a one year period, what is your holding period return? Assume you pay 2% annual on the original loan.
6. If the optimal risky portfolio has an expected return of 12% and a standard deviation of 35%, using a risk free rate of 0.05.
A] Write down your utility function you will need to maximize to determine the optimal complete portfolio.
B] Take the derivative of this to maximize utility, show each step. Use this to come up with a formula for the optimal allocation to the optimal risky portfolio.
C] Solve for Y (allocation to the risky portfolio), if A=2 or 5 and give a thorough explanation what these optimal Y values mean. Solve for the Sharpe ratio for A=2 and A=5.
7. Assuming the assumptions of the CAPM, with E[rm]=0.15, sigma m=0.25 and the rf=0.05
A] If you have a well-diversified stock(k) with beta 0.25, what is your expected return on this stock?
B] Now using the same stock but in the index model context: if you expect the return on k to be 0.08, what is k's alpha?
C] Create a tracking portfolio to capture this gain. Explain what your tracking portfolio is made up of. Explain how you use it to make a profit. Be specific.
D] Is the gain risk free, why?