Question

A and B are two risky assets. Their expected returns are E[Ra], E[Rb], and their standard deviations are σA,σB. σA< σB and asset A and asset B are positively correlated (ρA, B > 0). Suppose asset A and asset B are comprised in a portfolio with positive weight in both and please check all the correct answers below.

() There are only gains from diversification if ρA, B is not equal to 1.

() The portfolio may have a zero variance

() σA may be smaller than the variance of the portfolio

() The portfolio's expected return cannot be larger than 0.5(E[Ra] + E[Rb]).

Answer 1

If we are adding two assets in the portfolio, in order to get the benefits of diversification there should be low correlation between them. A perfect correlation of + 1 , means that there would be no benefits of diversification in the portfolio in the form of risk reduction.

So, the correct option is the first option.

A portfolio cannot have zero variance, only the risk free asset has a zero variance.

The portfolio varaince and standard deviation is lesser than the individual asset.

the weights of the two asset is not necessarily equal,so the expected return of the portfolio cannot be the above mentioned , if the weights were equal, then the portfolio return can be calculated as 0.5* E(Ra) + 0.5*E(Rb).