Question

Suppose there are three risky assets (A, B, and C), with volatilities of 40, 50 and 66.7%, respectively.

a) If the assets’ returns are all uncorrelated, what are the weights of the minimum variance portfolio?

b) If A is uncorrelated with B and C, but B and C have a correlation of -0.3, then what are the weights of the minimum variance portfolio?

c) To help understand the difference in your answers to a) and b), recalculate the answers by first calculating the minimum variance portfolios of assets B and C, and then calculating the minimum variance portfolio of A with the B/C combination. You can do this because B and C are both uncorrelated with A, so adding A to a portfolio of B and C does change the relative weights of the two.

Answer 1

Summary: In the above 'a' and 'b' parts of the problem we calculated the minimum varaince portfolio weights given in a parts all the asstes were uncorrelated but in b part B and C were negatively correlated. So we saw that when B and C were negatively correlated their comparitve weight(as compared to wieghts calcuated in a part) increased which leads us to the conclusion of diversification of portfolio where the investor chooses to be risk averse and in order to minimize its risk it increases its amount invested in assests that are negavtively correlated. So wieghts are not only affected by the variance as well as the correlation between assests. And the main motive of the investor is always to minimise the risk and maximize the return and the answers calculated justify this condition.