% Given {F XOM INTC}Returns =-0.12 0.39 -0.091STDs = [sqrt(0,00115) sart(0.0003438) sqrt(0.000314382)1Correlations = [1 0.3931 0.3512; 0.3931 1 0.2554; 0.3512 0.2554 1]%Variance / Covariance Matrixformat shortV = zeros (3)for i=1:3for j = 1:3V(i,j) = Correlations(i,j) *STDs (i)*STDs(j) ;endendV*Make N random portfoliosN = 1000;Weights = rand(N,3)*NormalizeTotal = sum(Weights, 2)Weights = Weights. /Total*Expected Return of PortfoliosPortReturn = Weights*Returns'%Variance of Portfoliosfor i = 1:NPortVar(i) = Weights(i, : )*V"Weights (i,:)';endPortVar = PortVar";%Plot Random Portfoliosplot(sqrt(PortVar),PortReturn,'.b')hold on%Plot Pure Portfoliosplot (STDs, Returns, 'OR')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.

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 Make N random portfolios N = 1000; Weights = rand (N, 3) Normalize Total = sum(Weights, 2) Weights = Weights. /Total Expected Return of Portfolios ortReturn = Weights*Returns' "Variance of Portfolios for i = 1:N PortVar (i) = Weights(i, : )*V*Weights(i,!)"; end PortVar = PortVar' ; Plot Random Portfolios