● The classic Markowitz model that optimizes for the Sharpe ratio has proven to be suboptimal. ○ Summary is used directly as prediction. ○ Variance is not a good risk measurement since it penalizes positive shocks and says little about tail risks ● Other risk measurements such as Value-at-Risk and Expected Shortfall introduce non-linear, non-convex risk constraints and render the mean-variance ...

We show that the efficient frontier for a portfolio in which short positions precisely offset the long ones is composed of a pair of straight lines through the origin of the risk-return plane. This unique but important case has been overlooked because the original formulation of the mean-variance model by Markowitz as well as all its subsequent elaborations have implicitly excluded it by using ...

This paper studies the state-of-art constrained portfolio optimisation models, using exact solver to identify the optimal solutions or lower bound for the benchmark instances at the OR-library with extended constraints. The effects of pre-assignment, round-lot, and class constraints based on the quantity and cardinality constrained Markowitz model are firstly investigated to gain insights of in...

Financial Economics researches have become active since 1950’s and many prominent theories regarding asset pricing and corporate finance have been proposed (Markowitz, 1952; Modigliani, Miller, 1958; Sharpe, 1964; Shleifer, 2000). The assumption of the efficiency of financial markets plays an important role in the literature in traditional financial theory and many research have been conducted ...

The fundamental purpose of investing in stocks is to make a profit. But the stock investment, income always accompanies risk. In order reduce risk greater returns, investor will be two or more portfolio together invest. This study examines return and using minimal variance maximum Sharpe ratio model, based on Markowitz mean-variance theory, identify best for given preference. model risk-averse ...

We describe a fill-reducing ordering algorithm for sparse, nonsymmetric LU factorizations, where the pivots are restricted to the diagonal and are selected greedily. The ordering algorithm uses only the structural information. Most of the existing methods are based on some type of symmetrization of the original matrix. Our algorithm exploits the nonsymmetric structure of the given matrix as muc...

The mean-variance approach is an influential theory of decision under risk proposed by Markowitz (1952). Unfortunately, the mean-variance approach allows for violations of the first-order stochastic dominance. This paper proposes a new model in the spirit of the classical mean-variance approach but without violations of stochastic dominance. The proposed model represents preferences by a functi...

The mean-variance model proposed by Markowitz has received greatly acceptance as a practical methodology to manage portfolio selection, and has been widely extended in a variety of literatures. The aim of this paper is to extend the mean-variance model in uncertain decision systems. We present a new mean-TVaR model for portfolio selection when the returns of securities are described as uncertai...

The mean-variance-leverage (MVL) optimization model (Jacobs and Levy [2012, 2013]) tackles an issue not dealt with by the mean-variance optimization inherent in the general mean-variance portfolio selection model (GPSM) — that is, the impact on investor utility of the risks that are unique to using leverage. Relying on leverage constraints with a conventional GPSM, as is commonly done today, is...