Suppose there are three assets: A, B, and C. Asset A's expected return and standard deviation are 1 percent and 1 percent. Asset B has the same expected return and standard deviation as Asset A. However, the correlation coefficient of Assets A and B is 0.25. Asset C's return is independent of the other two assets. The expected return and standard deviation of Asset C are 0.5 percent and 1 percent.

(a) Find a portfolio of the three assets that has the smallest variance among all portfolios that yields the expected return of 0.9 percent.

(b) Find a portfolio of the three assets that has the smallest variance among all portfolios that yields the expected return of rp percent. Find the variance of the portfolio.

(c) Suppose the risk-free rate is zero. Find the tangency portfolio.

(d) Suppose an investor's mean-variance utility function is E(r) 0.005 A 2 , where A = 500. Find the investor's optimal portfolio of the three risky assets and the risk-free asset.