Please answer all work in detail and please show formulas you use, thank you.
You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 40% and 60%, respectively. X has an expected rate of return of 0.12 and variance of 0.0081, and Y has an expected rate of return of 0.09 and a variance of 0.0016. The coefficient of correlation, rho, between X and Y is 0.45. If you decide to hold a complete portfolio that has an expected outcome of $1,180
a. What will be the dollar values of your positions in X, Y, and Treasury bills, respectively? (10%)
b. What is the risk for the risky portfolio P (10%)?
c. What is the SR for the risky portfolio P (5%)?
d. What is the risk for this complete portfolio C (5%)? (Hint: risk in complete portfolio C is the product of y (the weight in P) and the risk of P.
e. What is the SR for this complete portfolio C (5%)?