-----There are two stocks which an investor wants to buy. The stock has an expected return of 25% and an expected variance of 16% while stock B has an expected return of 15% and expected variance of 9%. Find the portfolio return and portfolio variance assuming that the correlation coefficient between A and B is + 0.4 and assuming that investor invests 60% of his/her money in stock A.

----- In the problem above; let us assume that this investor who demands an expected return of 20% wants to minimize the variance by choosing optimal portfolio weights. Show the Lagrangian (using numbers that I gave) that may be used for that purpose and set the equation system which will lead to the optimal weights (just set the equation system, a numerical answer for optimal weights is not required)

-----Now suppose that the investor wants only to buy A (whose expected return and variance is given in Q1)but also wants to invest 40% of his/her money in a risk-free T-Bill whose return is 12%. The correlation coefficient between a T-Bill and stock A is +0.2. Given this find the portfolio expected return and portfolio variance.