Due by 4pm on March 25 Problem 1 Consider the following information about three stocks: Rate of Return if State Occurs State of Economy Probability of Stock A Stock B Stock C State of Economy Boom 0.2 40% 15% 7% Average 0.3 15% 30% 7% Poor 0.3 5% -5% Recession 0.2 -20% 5% 7% Your portfolio manager has invested 30% of your money in Stock A, 50% in Stock B, and 20% in Stock C. a) What is the expected return of your portfolio? b) What is the covariance between Stocks A and B? c) What is the correlation coefficient between Stocks B and C? d) What is the standard deviation of your portfolio? Hint: Instead of using the portfolio variance formula for three stocks, you can save time by calculating the return on the portfolio for all four states of the economy, and then calculate the standard deviation of these portfolio returns. Problem 2 You are given the following information about Stocks A and B: Rate of Return if State Occurs State of Economy Probability of Stock A Stock B State of Economy Boom 0.25 18% 20% Normal 0.50 6% 15% Recession 0.25 -5% 2% Stock A has a beta of 0.325 and Stock B has a beta of 1.000. Assuming that neither of these stocks is over or undervalued: What is the market risk premium and risk-free rate? b) What would be the beta of a portfolio consisting of 40% of Stock A and 60% of Stock B? ") What would be the expected return of the portfolio under b)? Problem 3 a) A portfolio consisting of Stocks 1 and 2 has an expected return of 14%. What is the standard deviation of this portfolio given the information about Stocks 1 and 2 in Table 3.1? Table 3.1 Stock 1 Stock 2 Expected Return 10% 15% Standard Deviation 12% 18% Correlation (piz) 0.35 b) A portfolio consisting of Stocks 3 and 4 has zero variance. What is the weight of Stock 4 in this portfolio given the information about Stocks 3 and 4 in Table 3.2? Table 3.2 Stock 3 Stock 4 Standard Deviation 7% 16% Correlation (p34) -1.00