You consider investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with 2 risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081. The coefficient of correlation, rho, between X and Y is 0.45.
a. If you desire to form a portfolio with an expected rate of return of 0.11, what percentage of your money must you invest in the T-bill and P?
b. What would be the dollar values of your positions in X and Y, respectively, if you decide to hold 40% of your money in the risky portfolio and 60% in T-bills?
c. If you desire to form a portfolio with a standard deviation of 5.59%, what percentage of your money must you invest in the T-bill, X, and Y?
d. What would be the dollar value of your positions in X, Y, and the T-bills, if you decide to hold a portfolio that has an expected outcome of $1,200?