% Given {F XOM INTC} Returns = [-0.12 0.39 -0.09] STDs = [sqrt(0.00115) sqrt(0.0003438) sqrt(0.000314382)] Correlations = [1 0.3931 0.3512; 0.3931 1 0.2554; 0.3512 0.2554 1] %Variance / Covariance Matrix format short V = zeros(3) for i=1:3 for j = 1:3 V(i,j) = Correlations(i,j)*STDs(i)*STDs(j); end end V %Make N random portfolios N = 1000; Weights = rand(N,3) %Normalize Total = sum(Weights,2) Weights = Weights./Total %Expected Return of Portfolios PortReturn = Weights*Returns' %Variance of Portfolios for i = 1:N PortVar(i) = Weights(i,:)*V*Weights(i,:)'; end PortVar = PortVar'; %Plot Random Portfolios plot(sqrt(PortVar),PortReturn,'.b') hold on %Plot Pure Portfoli Problem 1: On the above Monte Carlo simulation of 1000 portfolios ,plot the efficient frontier using the KKT conditions (allows shorting). If there was something wrong with your Monte Carlo simulation on the midterm, fix it. Problem 2: On the same graph, plot the efficient frontier without allowing shorting (you can use fmincon or your favorite convex optimization software). Problem 3: Comment on the results