You have $20,000 available for investment in two securities A and B and a one-year investment horizon. Security A has an expected return of 8% and a standard deviation of 30% while security B has an expected return of 6% and a standard deviation of 20%.

If the returns on these securities are perfectly negatively correlated calculate the dollar amounts that you would need to invest in securities A and B to form the minimum variance portfolio . Also Calculate the expected dollar value of your portfolio at the end of the year.