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If I understand correctly what you are after is the marginal volatility contribution of a single asset to the portfolio. This is given by $$ \sigma(X_j;X) = \sigma(X_j)\ \rho(X_j, X) $$ See here for details.


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If I understand your problem correctly you are trying to search for the optimal basket of 5 pairs (without worrying about weighting). The problem is computationally there are too many combinations to sort through. So I will propose a simple algorithm: Calculate correlation matrix, grab the pair that has the least avg correlation as a seed for your basket, ...


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Correlation is not an asset allocation measure and thus should have nothing to do with the weights in the portfolio. What you want to do is to figure out the correlation between the two portfolios using: p = cov(x,y) / stdev(x) * stdev(y) and depending on the results, you can then run a solver function to find out the weights in each sub portfolio that ...


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I think Cholesky on correlation matrix is better because it makes code apply more generally in case we don't have full rank. For example, suppose we want to simulate three correlated normals with covariance matrix [[a^2,0,0], [0,b^2,0], [0,0,c^2]] i.e. variables are uncorrelated and have vols a, b, and c. Because this is positive definite, we can do ...



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