This is the full question, please solve the 4th question.

1) 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.

2) 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)

3) 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.

4) There are two firms. One is a firm which exports most of its products and uses raw materials produced in Turkey. The second firm sells most of its products in Turkey and most of its raw materials come from China and firm pays dollars to buy these raw materials. What may be the sign of the correlation coefficient between the stock prices of these two companies in the last three months if dollar was continously increasing in the last three months? Justify your conclusion by a short explanation. (Export proceeds are realised in dollars)