The Markowitz Wobble

Markowitz scheme for the sparse WZ factorization

In this paper the authors present problems which can appear when a sparse square matrix (without any special structure) is factorized to a product of matrices W and Z. The fill-in problem is considered, and the manners of its solving – by permuting both rows and columns with a modified Markowitz scheme among others. The results of numerical experiments for sparse matrices of various sizes are p...

Sparse and stable Markowitz portfolios.

We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the objective function a penalty proportional to the sum of the absolute values of the portfolio weights. This penalty regularizes (stabilizes) the optimization problem, encourages sparse portfolios (i.e., por...

Prospect and Markowitz Stochastic Dominance

Levy and Levy (2002, 2004) develop the Prospect and Markowitz stochastic dominance theory with S-shaped and reverse S-shaped utility functions for investors. In this paper, we extend Levy and Levy’s Prospect Stochastic Dominance theory (PSD) and Markowitz Stochastic Dominance theory (MSD) to the first three orders and link the corresponding S-shaped and reverse S-shaped utility functions to the...

Asymptotic Distribution of the Markowitz Portfolio

The asymptotic distribution of the Markowitz portfolio, Σ̂μ̂, is derived, for the general case (assuming fourth moments of returns exist), and for the case of multivariate normal returns. The derivation allows for inference which is robust to heteroskedasticity and autocorrelation of moments up to order four. As a side effect, one can estimate the proportion of error in the Markowitz portfolio du...

On Inverse Markowitz' Eventological Problem