 |
Center for Nonlinear Studies |
We consider the variance portfolio optimization problem supplemented by an asymmetric L1 regularizer. We carry out analytical calculations with the replica method borrowed from the physics of disordered systems. We present results for the relative estimation error, the distribution of optimal portfolio weights and the fraction of weights set to zero by the regularizer. We study in particular the dependence of these quantities on the ratio r between the number of assets and the length of the time series used to estimate the covariance matrix. We find that regularization extends the interval where the optimization can be carried out and suppresses the infinitely large sample fluctuations, and that beyond the critical ratio r=2 the variance cannot be optimized.
Host: Francesco Caravelli