Jack is considering investments in two stocks, X and Y. He expects a return of 12% from stock X and a return of 18% for stock Y. The standard deviation of the return is 20% for stock X and 30% for stock Y. The correlation coefficient between the returns is .30.

a. Compute the expected return and standard deviation of a portfolio with 50% inested in stock X and 50% invested in stock Y

b. Compute the expected return and standard deviation of a portfolio with 75% invested in stock X and 25% invested in stock Y

c. Plot the expected returns and standard deviations of the portfolios in parts (a) and (b) along with the expected returns and standard deviations for each of the two stocks ( ie. for portfolios invested entirely in stock X and Y.)

d. Assume that Jack can borrow or lend at an interest rate of 6%. Sketch the impact on Jack's investment opportunities. Given the borrowing and lending opportunities available to Jack, determine approximately the proportions of the stock portfolio that should be invested in stock X and in stock Y.