Discuss what is meant by the mean-variance framework in the context of portfolio choice

Consider a portfolio problem with n risky assets. Explain how one can construct the mean-variance frontier using the data on the expected returns and their standard deviations. Explain what is meant by the effcient frontier.

Two stocks have the following expected returns and standard deviations:

Suppose that the correlation between the two expected returns is equal to zero. An investment manager has constructed a portfolio made up of 50% of stock X and 50% of stock Y. Another manager makes the following comment: "Since the expected returns and standard deviations of the two stocks are the same and their returns are not correlated, it does not make sense to combine A and B in a portfolio."

 State whether you agree with this statement and provide a proof of your argument using the numbers in the table.

Suppose that the correlation between the two expected returns is equal to one. Would you agree in this case that combining these stocks in a portfolio does not bring any benefit in terms of risk reduction? Provide proof of your argument using the numbers in the table.

Stock Expected return Standard Deviation X 10% 20% Y 10% 20%