How to compute n bivariate copulas in modern portfolio theory?

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Enrico Trogolo
Enrico Trogolo 2017-11-17
Hi everyone, i'm trying to explain the dependance structures between n financial stock returns. Instead of using a single n-variate copula, I tried to use n*(n-1)/2 copulas to explain the dependance structures one-to-one. But how can I find an optimal portfolio of stocks (using modern portfolio theory) using these bivariate copulas? I already found the best family and the correspondent parameter(s) for each bivariate copula. But now I don't know how to manage them... Here I'm finding the simulated returns of each one-to-one stock.
nPoints = 100;
R = zeros(nAsset,nAsset,nPoints,2);
for i=1:nAsset
for j=1:i-1
if strcmp(copula_type(i,j),'t')==1
U = copularnd(copula_type(i,j), [1 copula_coefficients(i,j,1); copula_coefficients(i,j,1) 1], copula_coefficients(i,j,2), nPoints);
R(i,j,:,:) = [marginal{i}.icdf(U(:,1)) marginal{j}.icdf(U(:,2))];
elseif strcmp(copula_type(i,j),'Gaussian')==1
U = copularnd(copula_type(i,j), [1 copula_coefficients(i,j,1); copula_coefficients(i,j,1) 1], nPoints);
R(i,j,:,:) = [marginal{i}.icdf(U(:,1)) marginal{j}.icdf(U(:,2))];
else
U = copularnd(copula_type(i,j), copula_coefficients(i,j,1), nPoints);
R(i,j,:,:) = [marginal{i}.icdf(U(:,1)) marginal{j}.icdf(U(:,2))];
end
end
end
I'd like to create a Markowitz's frontier using Expected Shortfall as risk measure, but I don't know how to manage these n*(n-1)/2 copulas :(
Please help me :)
Thanks, Enrico.

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