How to calculte Efficient Frontier for Markowitz Portfolio

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Spyridon Papaspyrou
Spyridon Papaspyrou 2020-10-20
编辑： Spyridon Papaspyrou 2020-10-21
Hi, I'm trying to construct an optimized portfolio with 3 risk free assets. I have found the minimum vriance portfolio's weights, but I have a problem constructing thw effiient frontier. I would like some help if anyone knows..
My data (Excel File) comprises monthly closing prices of three Dow Jon Composite stocks from June 2010 until May 2020.
Thanks!
--Edit: Attached is the code that I'm using
Data=Untitled;
prices=Data(2:end,2:4);
% Calculation of returns
returns=tick2ret(prices);
% Convert table to homogeneous array
returns=table2array(returns);
%Summary Statistics
Std=std(returns);
Mean=mean(returns);
Cov=cov(returns);
% Use of Quadprog Solver for quadratic objective functions with linear constraints. Quadprog finds a minimum for a problem specified
f=zeros(numel(Mean),1);
Aeq=ones(1,numel(Mean));
beq=1;
[min_weights min_var]=quadprog(Cov,f,[],[],Aeq,beq)
% Smallest and Bigger Return of these 3 assets portfolios
Smallest_Mean=min_weights'.*Mean;
Largest_Mean= max(Mean);
% We define how many portfolios will be include in the Effeicient Frontier
Expected_Ret=Smallest_Mean:(Largest_Mean-Smallest_Mean)/1000:Largest_Mean;
% Use of Quadprog Solver for quadratic objective functions with linear constraints. Here is used to find the Efficient Frontier
a=numel(Mean);Mean'
Aeq1=[ones(1,a)]
for i=1:length(Expected_Ret);
beq1=[1;Expected_Ret(i)];
[x y]=quadprog(Cov,f,[],[],Aeq1,beq1);
pMean=Mean'.*x;
pVar=sqrt(y);
Port_Return(i,1)=pMean;
Port_Std(i,1)=pVar;
weight(1,i)=x(1,1);
weight(2,i)=x(2,1);
weight(3,i)=x(3,1);
pmean=o;
pvar=o;
end
From MatLab i get:
Error using quadprog (line 304)
The number of rows in Aeq must be the same as the number of elements of beq.

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