The two-fund separation theorem tells us that an investor with quadratic utility can separate her asset allocation decision into two steps: First, find the tangency portfolio (TP), i.e., the portfolio of risky assets that maximizes the Sharpe ratio (SR); and then, decide on the mix of the TP and the risk-free asset, depending on the investor’s attitude toward risk. In this paper, we describe an...

In portfolio selection models, uncertainty plays an important role. The parameter’s uncertainty leads to getting away from optimal solution so it is needed to consider that in models. In this paper we presented a two-stage robust model that in first stage determines the desired percentage of investment in each industrial group by using return and risk measures from different industries. One rea...

We study the coupling of basic quantitative portfolio selection strategies with a financial news article prediction system, AZFinText. By varying the degrees of portfolio formation time, we found that a hybrid system using both quantitative strategy and a full set of financial news articles, performed the best. With a 1-week portfolio formation period we achieved a 20.79% trading return using a...

Organizations need to evaluate project proposals and select the ones that are the most effective in reaching the strategic goals by considering sustainability issue. In order to enhance the effectiveness and the efficiency of project oriented organizations, in this paper a new multi-objective decision making (MODM) approach of sustainable project portfolio selection is proposed which applies in...

Portfolio management in finance is more than a mathematical problem of optimizing performance under risk constraints. A critical factor in practical portfolio problems is severe uncertainty – ignorance – due to model uncertainty. In this paper, we show how to find the best portfolios by adapting the standard risk-return criterion for portfolio selection to the case of severe uncertainty, such a...

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...

On the basis of Markowitz mean-variance framework, a new optimal portfolio selection approach is presented. The portfolio selection model proposed in the approach includes the expected return, the risk, and especially a quadratic type transaction cost of a portfolio. Using this model may yield an optimal portfolio solution that maximizes return, and minimizes risk, as well as also minimizes tra...

In this paper, we address the problem of maximizing expected return subject to a worst case return constraint by composing a portfolio that may consist of cash, holdings in a stock market index and options on the index. We derive properties of optimal and feasible portfolios and present a linear programming model to solve the problem. The optimal portfolios have pay-off functions that reflect a...

Let the random (stock market) vector X 2 0 be drawn according to a known distribution function F(x), x E R ". A log-optimal portfolio b* is any portfolio b achieving maximal expected log return W* = sup,, E In b'X, where the supremum is over the simplex b 2 0, Cr, b, = 1. An algorithm is presented for finding b*. The algorithm consists of replacing the portfolio b by the expected portfolio b', ...

We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose a new portfolio optimization model involving stochastic dominance constraints on the portfolio return. We develop optimality and duality theory for these models. We construct equivalent optimization models with utility functions. Numerical illustra...