Exercise 1 Problem: Suppose we have two assets, ABC and XYZ, with: Mean E[R] = 1.0% E[R] = 15.0% ABC (1) XYZ (2) and correlation between assets P1,2 = 70% Volatility 01 0% 0 = 23% Questions: a) If an investor holds w = 50% in the ABC and W = 50% in XYZ what is the mean and volatility of the portfolio return? b) Suppose that an investor wants to minimize the volatility of its portfolio. What would be the optimal w and w? Additionally, calculate the volatility and portfolio return and compare it with a) Suppose that an investor wants to maximize the expected returns of its portfolio. What would be the optimal w and w? Additionally, calculate the volatility and portfolio return and compare it with a) c) d) Using the graph of the investment opportunity set, show where should a), b) and c) belong. e) Redo parts a, b, c, and d assuming that P1,2 = -70% 3

ABC(1)XYZ(2)E[R1]=1.0%E[R2]=15.0%1=0%2=23% and correlation between assets 1,2=70% Questions: a) If an investor holds w1=50% in the ABC and w2=50% in XYZ what is the mean and volatility of the portfolio return? b) Suppose that an investor wants to minimize the volatility of its portfolio. What would be the optimal w1 and w2 ? Additionally, calculate the volatility and portfolio return and compare it with a) c) Suppose that an investor wants to maximize the expected returns of its portfolio. What would be the optimal w1 and w2 ? Additionally, calculate the volatility and portfolio return and compare it with a) d) Using the graph of the investment opportunity set, show where should a), b) and c) belong. e) Redo parts a, b, c, and d assuming that 1,2=70%