markowitz, in his portfolio selection theory, stated that investors select their portfolios according to two criteria of risk and return. accordingly, he presented his mathematical model. one of the criticisms of this model is that while investors, practically, consider different criteria in forming their portfolios, it only considers the return mean and return standard deviation. liquidity is ...

We propose a new approach to portfolio optimization by separating asset return distributions into positive and negative half-spaces. The approach minimizes a so-called Partitioned Value-atRisk (PVaR) measure by using half-space statistical information. Using simulated and real data, the PVaR approach generates better risk-return tradeoffs in the optimal portfolios when compared to Markowitz mea...

Select 59 concept stocks in the chip industry for quantitative analysis, use principal component analysis method and k-means clustering to process our financial indicators; historical simulation method, variance-covariance Monte Carlo calculate VaR value of each stock effective risk management. Based on Markowitz theory, frontier five is constructed, combined with utility investors different av...

In the introductory lectures, we have discussed Markowitz’ theory of mean-variance optimization (MVO) for the selection of portfolios of securities (or asset classes) in a manner that trades off the expected returns and the perceived risk of potential portfolios. Consider assets S1, S2, . . . , Sn (n ≥ 2) with random returns. Let μi and σi denote the expected return and the standard deviation o...

The literature on portfolio analysis assumes that the securities returns are random variables with fixed expected returns and variances values (see Bachelier [1], Briec et al. [4] and Markowitz [10]). However, since investors receive efficient or inefficient information from the real world, ambiguous factors usually exist in it. Consequently, we need to consider not only random conditions but a...

This paper presents two meta-heuristic algorithms to solve an extended portfolio selection model. The extended model is based on the Markowitz's Model, aiming to minimize investment risk in a specified level of return. In order to get the Markowitz model close to the real conditions, different constraints were embedded on the model which resulted in a discrete and non-convex solution space. ...

We consider the problem of online learning in settings in which we want to compete not simply with the rewards of the best expert or stock, but with the best trade-off between rewards and risk. Motivated by finance applications, we consider two common measures balancing returns and risk: the Sharpe ratio [7] and the mean-variance criterion of Markowitz [6]. We first provide negative results est...

Keywords: Robust optimization Mean–variance portfolio theory Ellipsoidal uncertainty Equilibrium price system a b s t r a c t In a financial market composed of n risky assets and a riskless asset, where short sales are allowed and mean–variance investors can be ambiguity averse, i.e., diffident about mean return estimates where confidence is represented using ellipsoidal uncertainty sets, we de...