Question

Consider two risky securities, A and B. They have expected returns E[Ra], E[Rb], standard deviations σA, σB. The standard deviation of A’s returns are lower than those of B (i.e. σA < σB and both assets are positively correlated (ρA,B > 0). Consider a portfolio comprised of positive weight in both A and B and circle all of the true statements below (there may be multiple true statements).

(a) The expected return of this portfolio cannot exceed the average of E[Ra] and E[Rb].

(b) The variance of the portfolio may be greater than σA.

(c) There are only gains from diversification if ρA,B 6= 1.

(d) With the proper weights, a portfolio of zero variance can be formed

Answer 1

(a) False - Assuming E[Ra] > E[Rb], and w_a > w_b, the expected return of this portfolio will be more inclined towards E[Ra] and will be greater than average of E[Ra] and E[Rb].

(b) True - given that ρ_A,B > 0, The variance of the portfolio will lie between σA < σB and hence might be greater than σA.

(c) False - we have to look for gain per unit of risk which is not possible with the given data.

(d) False - since ρ_A,B > 0.

Please do rate me and mention doubts, if any, in the comments section.