Question 1: Portfolio Risk and Return Today, the stock price of company A is $40 and the stock price of company B is $50. You estimate that the two stocks will have the following prices one year from now, conditional on the state of the economy: State of Economy Probability Price of A Price of B Good .80 $50 $50 Bad .20 $30 $60 Please assume that both stocks will not pay any dividends in the next year and consider the one-year returns of each stock. a. Calculate the expected return of each stock. b. Calculate the standard deviation of each stock return. c. Calculate the covariance between returns of stocks A and B. d. A portfolio AB containing stocks A and B has an expected return of 12.8%. What is the standard deviation of the return of this portfolio? e. Suppose you buy 100 shares of stock A and 10 shares of stock B. What is the expected return of this portfolio? f. Is it possible to construct a portfolio containing A and B that has an expected return of 20%? Please be specific. g. Is it possible to construct a riskless portfolio containing A and B? Please be specific. 2
Question 2: Minimum Variance Portfolio a. Can you find the portfolio weights for IBM and Microsoft that correspond to the MVP in the case of perfect positive correlation (shown on slide 32 of lecture notes 07-08)? b. Can you find the portfolio weights for IBM and Microsoft that correspond to the MVP in the case of perfect negative correlation (shown on slide 33 of the lecture notes 07-08)?
Question 3: Efficient Portfolios, Capital Market Line a. Suppose the following 8 risky portfolios (A, B, …, H) represent your investment opportunities. Please plot them on a graph showing return versus risk. A B C D E F G H E[r], % 10 12.5 15 16 17 18 18 20 SD[r], % 23 21 25 29 29 32 35 45 b. Which of these portfolios are inefficient? c. Suppose you can also borrow and lend at an interest rate of 12%. Which of the above portfolios has the highest Sharpe ratio? d. What is your optimal investment strategy if you can borrow and lend at 12% and are willing to tolerate a standard deviation of 25%?
Question 4: CAPM, Security Market Line Information is provided for the common stock of company X, an efficient portfolio Q, the market portfolio M, and the riskless asset. Please assume the correlation between the return of stock X and the return of the market portfolio is 0.4. Can you fill in the values of the 5 empty cells? Expected Return Beta Standard Deviation Stock X 1.2 Efficient Portfolio Q 2.0 Market Portfolio M 8% 20% Riskless Asset 3% 0.0 0