Replica approach to mean-variance portfolio optimization

Istvan Varga-Haszonits, Fabio Caccioli and Imre Kondor ()

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Abstract: We consider the problem of mean-variance portfolio optimization for a generic covariance matrix subject to the budget constraint and the constraint for the expected return, with the application of the replica method borrowed from the statistical physics of disordered systems. We find that the replica symmetry of the solution does not need to be assumed, but emerges as the unique solution of the optimization problem. We also check the stability of this solution and find that the eigenvalues of the Hessian are positive for $r=N/T

Date: 2016-06
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