Quesiton:
a) You have just been appointed a portfolio manager of Malou investment. An investor has two assets available from which to form his desired portfolio. Asset X has an expected return of 4% and standard deviation of 9%. Asset Y has an expected return of 8% and standard deviation of 12%.
i) Assume that the returns of the two assets are perfectly positively correlated. If the investor wishes to place portfolio weight 1/3 on asset X and weight 2/3 on asset Y compute the expected return and standard deviation of the portfolio.
ii) Assume now that the two asset returns are perfectly negatively correlated. If the investor places portfolio weight of α on asset X, write down an expression for the variance of the portfolio. Demonstrate that, in this scenario, the investor can form a portfolio with zero variance and find the appropriate weights associated with this portfolio.