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% Naive MV Weights Comparasion
% Black-Litterman Min-Var Portfolio
[Min_Var_W]=Portfolio_Optimization(Ret_BL,Cov_BL,Lambda,2,0,[],[],[]);
Min_Var_Ret=Ret_BL’*Min_Var_W;
Min_Var_Vol=sqrt(Min_Var_W’*Cov_BL*Min_Var_W);
display(Min_Var_Ret);
display(Min_Var_Vol);
% Naive Min-Var Portfolio
[Min_Var_W_Naive]=Portfolio_Optimization(Pi,Covariance,Lambda,2,0,[],[],[]);
Min_Var_Ret_Naive=Pi’*Min_Var_W_Naive;
Min_Var_Vol_Naive=sqrt(Min_Var_W_Naive’*Covariance*Min_Var_W_Naive);
display(Min_Var_Ret_Naive);
display(Min_Var_Vol_Naive);
Min_Var_Ret =
0.0608194042429562
Min_Var_Vol =
0.157414163468075
Min_Var_Ret_Naive =
0.0693830642201692
Min_Var_Vol_Naive =
0.138025600602617
Taregt_Ret =linspace(Min_Var_Ret_Naive,max(Pi),20);
MV_Weights = zeros(Assets,Assets);
Port_Var = zeros(1,Assets);
Port_Ret = zeros(1,Assets);
Max=20;
for i = 1:Max
MV_Weights(:,i) = Portfolio_Optimization(Pi,Covariance,Lambda,3,0,[],[],Taregt_Ret(i));
Port_Ret(i) =Pi’*MV_Weights(:,i);
Port_Var(i) = sqrt(MV_Weights(:,i)’*Covariance*MV_Weights(:,i));
end
figure
area( Port_Var,MV_Weights’)
xlabel(‘Portfolio Volatility’ )
ylabel(‘Asset Allocation’ )
title(‘Markowitz’)
legend( ‘SPX ‘ , ‘MEXBOL’, ‘CAC’ , ‘DAX’,’NKY’ , ‘HSI’, ‘AS51′,’KOSPI’, ‘NIFTY’ , ‘SHCOMP’ )
figure
plot(Port_Var,Port_Ret)
xlabel(‘Volatility’ )
ylabel(‘Returns’ )
title(‘Portfolio Frontier – Markowitz’)
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