The following probability distribution outlines the projected returns for a series of economic states over the next year for two stocks, X & Y, along with the probability of these states occurring.

State Pi Ri Stock X Ri Stock Y

Boom .40 13% 7.50%

Steady Growth .50 10% 6%

Recession .10 -5% 2%

a. Calculate the Expected returns of assets X and Y.

b. Calculate the standard deviation of returns of assets X and Y.

c. Given a correlation coefficient of +0.94 between X and Y calculate the expected returns AND standard deviation of a portfolio that includes 60% of X and 40% of Y.

d. Graphically illustrate the return and risk combinations that include two assets (e.g., stocks X an

Y). Briefly explain the efficient frontier and highlight the portfolios that a rational investor would never invest in.