Question:
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
b) ‘If correlation among security returns were perfect-if returns of all securities moved up and down together in perfect unison, diversification could do nothing to eliminate risk. The fact that security returns are highly correlated, but not perfectly correlated, implies that diversification can reduce risk but not eliminate it' Markovitz(1981).
c) Discuss the assumptions underlying the diversification theory.