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...this technique works only when returns are generated from normal distributions? Yes and no. Multiplying them by $C$ will produce the correlation that you wanted, but it won't preserve the distribution in general. Remember that when we apply $C$ to a vector of i.i.d. random variables $\boldsymbol{x}$ that the resultant vector element is $\sum_j C_{ij}x_j$,...

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Let’s put it this way. Classic MV is still used, but its shortcomings are universally appreciated. In its favour, the process is logical, conceptually intuitive, and non-quants easily understand it. But the optimisation produces some very unintuitive results, no different to multicollinearity effects in regression analysis. That’s a harder one for the non-...

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You can probably also do this with scipy but there is a specific convex optimiser cvxopt that suits this problem. from cvxopt import solvers, matrix For your problem suppose you seek $N$ variables $w$, then let $x$ be a vector where the first $N$ elements are $w$ and the latter $N$ elements are slack variables $t$. i.e. $x=[w,t]^T$ For your problem \$P = \...

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Your problem formulation is wrong, you must use the Charnes and Cooper transformation. This means that your constraint (mu-mu0)@y==1 must be (mu-mu0)@y==k and w=y/k, which implies that k==cp.sum(y).

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