We consider the mean-variance (M-V) model of Markowitz and the construction of the risk-return efficient frontier. We examine the effects of applying buy-in thresholds, cardinality constraints and transaction roundlot restrictions to the portfolio selection problem. Such discrete constraints are of practical importance but make the efficient frontier discontinuous. The resulting quadratic mixed...

We consider the l1-regularized Markowitz model, where a l1-penalty term is added to the objective function of the classical mean-variance one to stabilize the solution process, promoting sparsity in the solution and avoiding short positions. In this paper, we consider the Bregman iteration method to solve the related constrained optimization problem. We propose an iterative algorithm based on a...

in this paper, linear data envelopment analysis models are used to estimate markowitz efficient frontier. conventional dea models assume non-negative values for inputs and outputs. however, variance is the only variable in these models that takes non-negative values. therefore, negative data models which the risk of the assets had been used as an input and expected return was the output are uti...

Since the 1960s, lots of scholars had begun to research in the portfolio selections based on the theory of mean-variance of Markowitz portfolio and relevant methods. All of these studies are under certainly of the assumption term, and then the researchers can get efficient set of portfolio selection. However, alone with the finance environment increasing of complexity, it is becoming more compl...

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 ...

The Markowitz Mean Variance model (MMV) and its variants are widely used for portfolio selection. The mean and covariance matrix used in the model originate from probability distributions that need to be determined empirically. It is well known that these parameters are notoriously difficult to estimate. In addition, the model is very sensitive to these parameter estimates. As a result, the per...

The inclusion of transaction costs is an essential element of any realistic portfolio optimization. In this paper, we consider an extension of the standard portfolio problem in which transaction costs are incurred to rebalance an investment portfolio. The Markowitz framework of mean-variance efficiency is used with costs modelled as a percentage of the value transacted. Each security in the por...

In conventional mean-variance model of portfolio optimization problem the expected return is taken as the mean of the past returns. This assumption is not correct and hence the method leads to poor portfolio optimization performance. Hence an alternative but efficient method is proposed in which the mean and variance of expected return are first predicted with a low complexity functional link a...

In this paper we tackle the optimal portfolio selection problem (PSP). Many research has been made around this subject mainly in two ways, whether extending the Markowitz model by taking into account real-world constraints (floor-ceiling, class and cardinality) or introducing different risk measures like semivariance, value at risk, absolute desviation, etc. Here, we present the preliminary res...