Abstract—Modern Portfolio Theory (MPT) according to Markowitz states that investors form mean-variance efficient portfolios which maximizes their utility. Markowitz proposed the standard deviation as a simple measure for portfolio risk and the lower semi-variance as the only risk measure of interest to rational investors. This paper uses a third volatility estimator based on intraday data and c...

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 ...

Portfolio allocation theory has been heavily influenced by a major contribution of Harry Markowitz in the early fifties: the mean-variance approach. While there has been a continuous line of works in on-line learning portfolios over the past decades, very few works have really tried to cope with Markowitz model. A major drawback of the mean-variance approach is that it is approximation-free onl...

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. ...

In this tutorial paper we introduce different approaches to Markowitz portfolio optimization, and we show how to solve such problems in MATLAB, R and Python using the MOSEK optimization toolbox for MATLAB, the Rmosek package, and the MOSEK Python API, respectively. We first consider conic formulations of the basic portfolio selection problem, and we then discuss more advanced models for transac...