The Mean-variance framework proposed by Markowitz is the most common model for portfolio selection problem. The most important concept in his theory is diversification. Diversification means designing an investment portfolio that reduces exposure risk by combining a variety of investments. But actually, the portfolios’ weights are often extremely concentrated on few assets when using mean-varia...

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...

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 propose a model for portfolio optimization extending the Markowitz mean–variance model. Based on cooperation with Standard and Poor s we use five specific objectives related to risk and return and allow consideration of individual preferences through the construction of decision-maker specific utility functions and an additive global utility function. Numerical results using customized local...

Our approach preserves the form of the original problem in that an investor minimizes portfolio variance for a given level of the expected return. However, inputs are now given by the generalized expressions for mean and variance-covariance matrix involving moments of the random exit time in addition to the conditional moments of asset returns. While efficient frontiers in the generalized and t...

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...

Robust portfolio optimization has been developed to resolve the high sensitivity to inputs of the Markowitz mean-variance model. Although much effort has been put into forming robust portfolios, there have not been many attempts to analyze the characteristics of portfolios formed from robust optimization. We investigate the behavior of robust portfolios by analytically describing how robustness...

Over sixty years ago, Markowitz introduced the mean-variance efficient frontier to finance. While mean-variance is still the predominant model in portfolio selection, it has endured many criticisms. One serious one is that it does not allow for additional criteria. The difficulty is that the efficient frontier becomes a surface. With it now possible to compute such a surface, we provide an over...