Mean Semivariance Portfolio Research Articles

Portfolio Optimization Using Mean-Semi Variance approach with Artificial Neural Networks: Empirical Evidence from Pakistan

Purpose: The challenge of managing a portfolio effectively is allocating capital among numerous stock holdings to achieve maximum profit. Therefore, the purpose of this study is to guide investors in developing optimal portfolios in the stock market of Pakistan.
 Design/Methodology/Approach: To pick and optimize a portfolio in the most effective way possible, we used the daily closing stock prices of a sample of listed firms at the Pakistan stock exchange. The study applied the mean semi-variance approach and compared the performance of portfolios with equally weighted portfolios under artificial neural networks and historical-based return estimation in Pakistan.
 Findings: The result shows that artificial neural network-based estimation of the expected return vector has outperformed the historical return estimation under mean semi-variance portfolio optimization and constrained mean semi-variance portfolios based on the Sharp ratio in Pakistan.
 Implications/Originality/Value: The study suggests that investors, fund managers, and portfolio analysts should focus on the more sophisticated neural network-based choice for the development of portfolios in the equity market of Pakistan.

An automatic trading system for fuzzy portfolio optimization problem with sell orders

This paper deals with a portfolio optimization problem with sell orders, in which the investor will immediately sell the risky assets once their prices reach the preset sell thresholds. Departing from the traditional portfolio models, the investor needs to determine not only an investment proportion but also a sell threshold for each risky asset. We formulate the portfolio problem as a sequential decision problem and propose an automatic trading system with three stages to determine the investment strategy at the beginning of each period. In Stage 1, we formulate the return of an investment strategy as an LR-power fuzzy number based on the historical data and propose a fuzzy mean–semi-variance portfolio optimization model with sell orders. In Stage 2, we design a multi-objective genetic algorithm to solve the proposed model. In Stage 3, we select an optimal investment strategy among the efficient solutions based on the fuzzy Value-at-Risk ratio. Moreover, we conduct two case studies in the real stock market to illustrate the effectiveness and practicability of the proposed model and algorithm. The comparison results show that the proposed trading system has a better out-of-sample performance than the other ones.

Portfolio Selection Using Data Envelopment Analysis Cross-Efficiency Evaluation with Undesirable Fuzzy Inputs and Outputs

In this paper, we discuss a portfolio selection problem based on fuzzy data envelopment analysis cross-efficiency evaluation wherein both undesirable fuzzy inputs and outputs have been considered. We first propose a data envelopment analysis cross-efficiency model, in which both undesirable inputs and outputs are considered. Furthermore, considering the imprecision of the data, we extend the crisp model to the fuzzy environment and propose a fuzzy data envelopment analysis cross-efficiency model with coexisting undesirable input and output data. We then apply the proposed model to the portfolio selection problem and present a novel mean-semivariance portfolio selection model based on fuzzy data envelopment analysis cross-efficiency scores, in which several realistic constraints are considered, including a budget, cardinality, buy-in thresholds, and no short selling constraints. After that, we employ the genetic algorithm (GA) to solve the proposed model. Finally, a real-life case study is presented to demonstrate the effectiveness of the proposed approaches.

Time-consistent multiperiod mean semivariance portfolio selection with the real constraints

In this paper, a new multiperiod mean semivariance portfolio selection with the transaction costs, borrowing constraints, threshold constraints and cardinality constraints is proposed. In the model, the return and risk of assets are characterized by mean value and semivariance, respectively. Because the semivariance operator is not separable, the optimal solution of the model is not time-consistent. The time-consistent strategy for this model can be obtained by using game approach. The time-consistent strategy, which is a mix integer dynamic optimization problem with path dependence, is approximately turned into a dynamic programming problem by approximate dynamic programming method. A novel discrete approximate iteration method is designed to obtain the optimal time-consistent strategy, and is proved linearly convergent. Finally, the comparison analysis of trade-off parameters is given to illustrate the idea of our model and the effectiveness of the designed algorithm.

A CREDIBILISTIC MEAN-SEMIVARIANCE-PER PORTFOLIO SELECTION MODEL FOR LATIN AMERICA

Many real-world problems in the financial sector have to consider different objectives which are conflicting, for example portfolio selection. Markowitz proposed an approach to determine the optimal composition of a portfolio analysing the trade-off between return and risk. Nevertheless, this approach has been criticized for unrealistic assumptions and several changes have been proposed to incorporate investors’ constraints and more realistic risk measures. In this line of research, our proposal extends the mean-semivariance portfolio selection model to a multiobjective credibilistic model that besides risk and return, also considers the price-to-earnings ratio to measure portfolio performance. Uncertain future returns and PER ratio of each asset are approximated using L-R power fuzzy numbers. Furthermore, we consider budget, bound and cardinality constraints. To solve the constrained portfolio optimization problem, we use the algorithm NSGA-II. We assess the proposed approach generating a portfolio with shares included in the Latin American Integrated Market. Results show that this new approach is a good alternative to solve the portfolio selection problem when multiple objectives are considered.

Credibilitic Multiperiod Mean Semivariance Portfolio Selection with Transaction Costs

This paper proposes a credibilitic multiperiod mean-simivariance portfolio selection model with transaction costs, borrowing constraints, threshold constraints and cardinality constraints. In this model, the return rate of asset and the risk are quantified by credibilitic expected value and credibilitic semivariance, respectively. Threshold constraints limit the amount of capital to be invested in each stock and prevent very small investments in any stock. Based on credibilitic theories, the model is transformed into a mix integer dynamic optimization problem with path dependence. The proposed model is approximated to dynamic programming model. A novel discrete iteration method is designed to obtain the optimal portfolio strategy, and is proved linearly convergent. Finally, an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from the Shanghai Stock Exchange.

A Two-Stage Method for Considering Cardinality in Portfolio Optimization of Mutual Funds

Mutual funds are important financial institutes. There are several methods for performance evaluation of mutual funds such as portfolio optimization. Portfolio optimization has a basic model that has completed up to now. One of completions is adding cardinality constraint to the model. Considering cardinality in portfolio optimization model makes it an integer programming problem that solving it, is hard and makes the efficient frontier discontinuous. In current study in first stage we rank the mutual funds with VIKOR method and based on 5 characteristics: rate of return, variance, semivariance, Treynor ratio and Sharpe ratio. In second stage according to cardinality level best ranked mutual funds are chosen. A mean-semivariance portfolio optimization model is written using chosen funds. This model is solved using fuzzy technique programming and efficient frontier is obtained. Real data from NASDAQ based on 92 mutual funds are used to illustrate the effectiveness of proposed methodology. Results show that the efficient frontier obtained from our methodology is continuous and near to unconstrained efficient frontier.

Multi-period Possibilistic Mean Semivariance Portfolio Selection with Cardinality Constraints and its Algorithm

In this paper, we consider a multi-period portfolio selection problem in a fuzzy investment environment, in which the return and risk of assets are characterized by possibilistic mean value and possibilistic semivariance, respectively. Based on the theories of possibility, a new multi-period possibislistic portfolio selection model is proposed, which contains risk control, transaction costs, borrowing constraints, threshold constraints and cardinality constraints. the proposed model can be transformed into a crisp nonlinear dynamic optimization problem by using fuzzy programming approach. Because of the transaction costs and cardinality constraints, the multi-period portfolio selection is a mix integer dynamic optimization problem with path dependence A forward dynamic programming method is designed to obtain the optimal portfolio strategy. Finally, a comparison analysis of the different cardinality constraints is provided to illustrate the efficiency of the proposed approaches and the designed algorithm.

A multi-period fuzzy portfolio optimization model with minimum transaction lots

Abstract In this paper, we consider a multi-period fuzzy portfolio optimization problem with minimum transaction lots. Based on possibility theory, we formulate a mean-semivariance portfolio selection model with the objectives of maximizing the terminal wealth and minimizing the cumulative risk over the whole investment horizon. In the proposed model, we take the return, risk, transaction costs, diversification degree, cardinality constraint and minimum transaction lots into consideration. To reflect investor’s aspiration levels for the two objectives, a fuzzy decision technique is employed to transform the proposed model into a single objective mixed-integer nonlinear programming problem. Then, we design a genetic algorithm for solution. Finally, we give an empirical application in Chinese stock markets to demonstrate the idea of our model and the effectiveness of the designed algorithm.

Mean–semivariance portfolio selection under probability distortion

We formulate and study a mean–semivariance portfolio selection problem in continuous time when the probability is distorted by a nonlinear transformation. We give necessary and sufficient conditions for the feasibility and the existence of optimal strategies, respectively, and present the general form of optimal solutions when they exist. In sharp contrast with the previously established result that the infimum of the problem is not attainable when there is no probability distortion, we show that the infimum can be achieved with proper probability distortions. Finally, for a number of interesting cases we derive the optimal solutions in closed forms whenever they exist.

The Constrained Mean-Semivariance Portfolio Optimization Problem with the Support of a Novel Multiobjective Evolutionary Algorithm

The paper addresses the constrained mean-semivariance portfolio optimization problem with the support of a novel multi-objective evolutionary algorithm (n-MOEA). The use of semivariance as the risk quantification measure and the real world constraints imposed to the model make the problem difficult to be solved with exact methods. Thanks to the exploratory mechanism, n-MOEA concentrates the search effort where is needed more and provides a well formed efficient frontier with the solutions spread across the whole frontier. We also provide evidence for the robustness of the produced non-dominated solutions by carrying out, out-of-sample testing during both bull and bear market conditions on FTSE-100.

A NOTE ON SEMIVARIANCE

In a recent paper (Jin, Yan, and Zhou 2005), it is proved that efficient strategies of the continuous‐time mean–semivariance portfolio selection model are in general never achieved save for a trivial case. In this note, we show that the mean–semivariance efficient strategies in a single period are always attained irrespective of the market condition or the security return distribution. Further, for the below‐target semivariance model the attainability is established under the arbitrage‐free condition. Finally, we extend the results to problems with general downside risk measures.

Otimização robusta de carteiras utilizando desigualdades matriciais lineares

O objetivo deste trabalho é formular um problema de seleção robusta de ativos utilizando média-semivariância em termos de um problema de otimização com desigualdades matriciais lineares (LMI). O modelo de média-semivariância usa como função risco uma combinação convexa das semivariâncias (acima e abaixo do retorno esperado) do erro de rastreamento (a diferença entre os retornos da carteira considerada e um benchmark). Consideramos diferentes formas de calcular a média e a semivariância do erro de rastreamento. Iremos então minimizar uma função objetivo definida como uma combinação convexa da função risco menos o retorno esperado de erro de rastreamento. Chamamos de solução robusta a carteira factível que minimiza o valor da função objetivo no pior caso. Serão apresentadas simulações numéricas com dados de ações negociadas na Bolsa de Valores de São Paulo (BOVESPA).

Computation of mean-semivariance efficient sets by the Critical Line Algorithm

The general mean-semivariance portfolio optimization problem seeks to determine the efficient frontier by solving a parametric non-quadratic programming problem. In this paper it is shown how to transform this problem into a general mean-variance optimization problem, hence the Critical Line Algorithm is applicable. This paper also discusses how to implement the critical line algorithm to save storage and reduce execution time.