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...

Herein is an incomplete collection of facts about the Sharpe ratio, and the Sharpe ratio of the Markowitz portfolio. Connections between the Sharpe ratio and the t-test, and between the Markowitz portfolio and the Hotelling T 2 statistic are explored. Many classical results for testing means can be easily translated into tests on assets and portfolios. A ‘unified’ framework is described which c...

modern portfolio theory is based on harry markowitz's 1952 work on mean-variance portfolios. he stated that a rational investor should either maximize his expected return for a given level of risk, or minimize his risk for a given expected return. in this study the markowitz model with cardinality constraints was studied. we extend the standard model to include cardinality constraints that...

Despite having become firmly established as one of the major cornerstone principles of modern finance, traditional Markowitz mean-variance analysis has, nevertheless, failed to gain widespread acceptance as a practical tool for equity management. The Markowitz optimization enigma essentially centers on the severe estimation risk associated with the input parameters, as well as the resultant fin...

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...

short-selling prohibition has been one of the primary assumptions of markowitz mean-variance model. solving markowitz quadratic model creates investment efficient frontier by considering only two return and budget constraints. in order to develop a more realistic portfolio selection model, in this paper, a new mathematical model is developed to allow short-selling under some practical constrain...

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...

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...