To invest, you want to create a portfolio of three companies (A, B and C) with stocks. The expected monthly returns of these shares are 1%, 2% and 3% respectively. Standard deviations are 1%, 1.5% and 2%, respectively. There is a positive correlation of 0.5 between the returns of shares of companies A and B. There is no correlation between A and C and between B and C.
a) If you only want to create a portfolio consisting of A and B shares, find the portfolio weights that minimize the risk (standard deviation) of this portfolio. Calculate the expected the result of this portfolio.
b) Find the weight of the active portfolio which provides the expected monthly return of 5%. Calculate the standard deviation of the portfolio. Compare it with the risk of the portfolio in (a).
c) If you are investing $ 100,000 in the portfolio in (b), calculate how much you want to buy or sell from each individual.