Traditional Portfolio Selection Research Articles

Robust, extended goal programming with uncertainty sets: an application to a multi-objective portfolio selection problem leveraging DEA

AbstractThis study presents a two-phase approach of Data Envelopment Analysis (DEA) and Goal Programming (GP) for portfolio selection, representing a pioneering attempt at combining these techniques within the context of portfolio selection. The approach expands on the conventional risk and return framework by incorporating additional financial factors and addressing data uncertainty, which allows for a thorough examination of portfolio outcomes while accommodating investor preferences and conservatism levels. The initial phase employs a super-efficiency DEA model to streamline asset selection by identifying suitable investment candidates based on efficiency scores, setting the stage for subsequent portfolio optimization. The second phase leverages the Extended GP (EGP) framework, which facilitates the comprehensive incorporation of investor preferences to determine the optimal weights of the efficient assets previously identified within the portfolio. Each goal is tailored to reflect specific financial factors spanning both technical and fundamental aspects. To tackle data uncertainty, robust optimization is applied. The research contributes to the robust GP (RGP) literature by analyzing new RGP variants, overcoming limitations of traditional and other uncertain GP models by incorporating uncertainty sets. Robust counterparts of the EGP models are accordingly developed using polyhedral and combined interval and polyhedral uncertainty sets, providing a flexible representation of uncertainty in financial markets. Empirical results, based on real data from the Tehran Stock Exchange comprising 779 assets, demonstrate the superiority of the proposed approach over traditional portfolio selection methods across various uncertainty settings. Additionally, a comprehensive sensitivity analysis investigates the impact of uncertainty levels on the robust EGP models. The proposed framework offers guidance to investors and fund managers through a pragmatic approach, enabling informed and robust portfolio decisions by considering efficiency, uncertainty, and extended financial factors.

Is replacing standard investments with ESG substitutes a good choice?

We compare traditional portfolio selection strategies with traditional stock market indexes in their standard and ESG versions. In addition to the comparison of 12 indexes from different markets in their ESG and standard versions. To compare the portfolios we use conventional performance measures, and the results show that replacing the indexes with their ESG versions does not detract from performance in terms of the Shape ratio and other measures. In general, there is no statistically significant difference between the returns of the indexes and the portfolios built with these indexes compared to those using the standard versions. So that the investor concerned with environmental and social issues can replace their equity market investments with ESG assets without harming their financial performance.

A mental account-based portfolio selection model with an application for data with smaller dimensions

With the rapid development of Robo-adviser, behavioral portfolio theory (BPT) has been drawing good attention. However, the existing BPT models always assume the assets’ returns are normally distributed and cannot be solved efficiently when the number of assets is large. To circumvent these limitations, this paper proposes a new portfolio selection model with two mental accounts in which the lower-level (safety) is set up to avoid loss while the upper-level (self-actualization) need corresponding to the mental account is set up to get a good profit. To relax the normality assumption, we formulate our proposed model by replacing the probability terms with the expectation of indicator function and designing a sequential convex approximation algorithm to solve the proposed model. Also, we prove that the optimal portfolio obtained by our proposed algorithm converges when analyzing data with small dimensions.Last, we carry out empirical studies by using trading data with 30 stocks from the American stock market to demonstrate the superiority, effectiveness, and robustness of our proposed portfolio selection in a smaller dimension case because our method is suitable only for small dataset. By comparing the characteristics of the optimal portfolio and the out-of-sample performance of our proposed portfolio selection model with the corresponding traditional portfolio selection models, we find that our new model not only derives the optimal portfolio with moderate diversification, but also obtain the highest average return and the highest Omega ratio in the out-of-sample testing period. Extensive experiment results by using different sample sizes, different frequencies, and employing the rolling-time window approach also confirm that our proposed portfolio selection model performs the best when we compare both the highest cumulative return and the Omega ratio in the out-of-samples.

Portfolio Selection with respect to the Probabilistic Preference in Variable Risk Appetites: A Double-Hierarchy Analysis Method

Traditional portfolio selection models mainly obtain the optimized portfolio ratio by focusing on the prices of financial products. However, investors’ multiple preferences and risk appetites are also significant factors that should be taken into account. In consideration of these two factors simultaneously, we propose a double-hierarchy model in this paper. Specifically, the first hierarchy quantifies investors’ risk appetite based on a historical simulation method and probabilistic preference theory. This hierarchy can be utilized to describe investors’ variable risk appetites and ensure the obtained investment ratios meet investors’ immediate risk requirements. Then, using the cross-efficiency evaluation principle, the optimal investment ratios can be derived by fusing investors’ multiple preferences and risk appetites in the second hierarchy. Lastly, an illustrative example about evaluating the 10 largest capitalized stocks on the Shenzhen Stock Exchange is given to verify the feasibility and effectiveness of our newly proposed model. We make the theoretical contribution to improve the traditional portfolio selection model, especially considering investors’ subjective preferences and risk appetite. Moreover, the proposed model can be practical for assisting investors with their investment strategies in real life.

Ability parity model for optimal fund allocation: Evidence from China's mutual fund markets

We propose in this article a novel ability parity model for optimal fund allocation. Compared with the traditional portfolio selection methods which directly work on asset returns and/or risk (volatility), the proposed ability parity method focuses mainly on the allocation between the stock selection ability and market timing ability of fund managers, which essentially determines fund performance (Fama, 1972). Using the data of China's mutual fund markets, we find strong and robust evidence that the proposed ability parity model delivers significantly higher return, skewness, and Sharpe ratio than traditional models and the benchmark index, while having volatilities comparable with traditional models.

A New Adaptive Entropy Portfolio Selection Model.

In this paper, we propose an adaptive entropy model (AEM), which incorporates the entropy measurement and the adaptability into the conventional Markowitz’s mean-variance model (MVM). We evaluate the performance of AEM, based on several portfolio performance indicators using the five-year Shanghai Stock Exchange 50 (SSE50) index constituent stocks data set. Our outcomes show, compared with the traditional portfolio selection model, that AEM tends to make our investments more decentralized and hence helps to neutralize unsystematic risks. Due to the existence of self-adaptation, AEM turns out to be more adaptable to market fluctuations and helps to maintain the balance between the decentralized and concentrated investments in order to meet investors’ expectations. Our model applies equally well to portfolio optimizations for other financial markets.

A Mental Account-Based Portfolio Selection Model With an Application

To obtain better optimal portfolios, academics develop the behavioral portfolio theory (BPT) with two mental accounts by minimizing the risk as well as maximizing the return. However, there are some limitations to the existing BPT. To circumvent the limitations, this paper proposes a new portfolio selection (PPMPSM) model with two mental accounts in which the lower-level problem of the model is used to avoid from getting big loss while the upper-level problem corresponds to the mental account is used to get good profit. We formulate our proposed PPMPSM model by replacing the probability terms with the expectation of indicator function and then design a sequential convex approximation algorithm to obtain the optimal solution of our proposed model. We prove that the optimal portfolio obtained by our proposed algorithm converges. We demonstrate the superiority and applicability of our proposed PPMPSM models, including both Maslow (0.10) and Maslow (0.11) models, over the traditional portfolio selection models, including the model generated by using the naive equal-weighted (EW) strategy, the model satisfying investors' safety needs (Safety model), and the model satisfying the self-actualization needs (SA model) by using trading data from the American stock market. We find that our proposed PPMPSM model can obtain the highest expected return and generate the highest final cumulative wealth such that the cumulative wealth for both of our proposed PPMPSM models, Maslow(0.10) and Maslow(0.11), uniformly outperform those for the Safety and EW strategies in any week and perform the best among all the strategies in the last 2 weeks, including the SA strategy.

A Credibilistic Fuzzy DEA Approach for Portfolio Efficiency Evaluation and Rebalancing Toward Benchmark Portfolios Using Positive and Negative Returns

This paper proposes a data envelopment analysis (DEA)-based portfolio efficiency evaluation approach integrated with a rebalancing method to help investors acquire efficient portfolios. Two fuzzy portfolio selection models with value at risk (VaR) and conditional value at risk (CVaR) as objectives are proposed under the credibilistic framework. The models are constrained by realistic constraints of short selling/no short selling, capital budget, bounds on investment in an asset, and minimum return desired by the investor. These models are used to compute the benchmark portfolios, which constitute the portfolio efficient frontier. Furthermore, random sample portfolios are generated individually for each model in compliance with their constraints. These random sample portfolios are evaluated in terms of their relative efficiency with risk (VaR or CVaR) as an input and return as an output using DEA. Bearing in mind the volatile nature of the investment market, negative returns are also considered for portfolio efficiency evaluation using the range directional model. Moreover, an efficiency frontier improvement algorithm is used to rebalance the inefficient random portfolios to make them efficient. The proposed approach provides an alternative to the investors to acquire benchmark portfolios using the traditional portfolio selection models. A detailed numerical illustration and an out of sample analysis with the Nifty 50 index from the National Stock Exchange, India, are presented to substantiate the proposed approach.

Portfolio Selection Based on Bayesian Theory

The traditional portfolio selection model seriously overestimates its theoretic optimal return. Aiming at this problem, two portfolio selection models are proposed to modify the parameters and enhance portfolio performance based on Bayesian theory. Firstly, a Bayesian-GARCH(1,1) model is built. Secondly, Markov Chain is applied to curve the parameters’ state transfer, and a Bayesian Markov regime-Switching-GARCH(1,1) model is constructed. Both the two models can handle the overestimation problem and can obtain self-financing portfolios. In the numerical experiments, both the models are examined with data from China stock market, and their performances are compared and analyzed. The results show that BMS-GARCH(1,1) model is superior to the Bayesian-GARCH(1,1) model.

A chance-constrained portfolio selection model with random-rough variables

Traditional portfolio selection (PS) models are based on the restrictive assumption that the investors have precise information necessary for decision-making. However, the information available in the financial markets is often uncertain. This uncertainty is primarily the result of unquantifiable, incomplete, imprecise, or vague information. The uncertainty associated with the returns in PS problems can be addressed using random-rough (Ra-Ro) variables. We propose a new PS model where the returns are stochastic variables with rough information. More precisely, we formulate a Ra-Ro mathematical programming model where the returns are represented by Ra-Ro variables and the expected future total return maximized against a given fractile probability level. The resulting change-constrained (CC) formulation of the PS optimization problem is a non-linear programming problem. The proposed solution method transforms the CC model in an equivalent deterministic quadratic programming problem using interval parameters based on optimistic and pessimistic trust levels. As an application of the proposed method and to show its flexibility, we consider a probability maximizing version of the PS problem where the goal is to maximize the probability that the total return is higher than a given reference value. Finally, a numerical example is provided to further elucidate how the solution method works.

New model and method for portfolios selection

The portfolio selection problem has a venerable history. For example, Markowitz (1952), (1959), formulates the problem as a trade-off between the expected return and the expected risk of a portfolio. For his path breaking work that has revolutionized investment practice, he won the Nobel Prize in 1990. In this paper we proposed enhancement to the traditional portfolio selection problem. We enhance the formulation of the problem by introducing four additional constraints that take into account (a) the collinearity problem to decrease the portfolio risk, (b) the special preference of active stocks to control the systematic portfolio risk, (c) the special preference of stocks with outstanding performance to increase the un-expected return which it is special case of the non-efficient market, and (d) control the overall risk of the portfolio. Additionally, we propose enhancement method for GA (EGA). In the 264 Ali S. Hadi, Azza A. El Naggar and Mona N. Abdel Bary experiment, the proposal models and method are evaluated using both simulated and real data sets. Egyptian daily price index is used as the data set. The simulation shows that the proposal model is better than the traditional model. The EGA performs best among all the optimization methods. In this experiment, our model can be adapt to aggressive changes in the market, like the Egypt’s events at 25 January 2011.

An analytical derivation of the efficient surface in portfolio selection with three criteria

In standard mean-variance bi-criterion portfolio selection, the efficient set is a frontier. While it is not yet standard for there to be additional criteria in portfolio selection, there has been a growing amount of discussion in the literature on the topic. However, should there be even one additional criterion, the efficient frontier becomes an efficient surface. Striving to parallel Merton’s seminal analytical derivation of the efficient frontier, in this paper we provide an analytical derivation of the efficient surface when an additional linear criterion (on top of expected return and variance) is included in the model addressed by Merton. Among the results of the paper there is, as a higher dimensional counterpart to the 2-mutual-fund theorem of traditional portfolio selection, a 3-mutual-fund theorem in tri-criterion portfolio selection. 3D graphs are employed to stress the paraboloidic/hyperboloidic structures present in tri-criterion portfolio selection.

A Mean-Variance Hybrid-Entropy Model for Portfolio Selection with Fuzzy Returns

In this paper, we define the portfolio return as fuzzy average yield and risk as hybrid-entropy and variance to deal with the portfolio selection problem with both random uncertainty and fuzzy uncertainty, and propose a mean-variance hybrid-entropy model (MVHEM). A multi-objective genetic algorithm named Non-dominated Sorting Genetic Algorithm II (NSGA-II) is introduced to solve the model. We make empirical comparisons by using the data from the Shanghai and Shenzhen stock exchanges in China. The results show that the MVHEM generally performs better than the traditional portfolio selection models.

Chinese Corporate Social Responsibility by Multiple Objective Portfolio Selection and Genetic Algorithms

ABSTRACTIn this paper, we study corporate social responsibility (CSR) in China through the prism of investments. We work with large stocks and assess their CSR performance from agency CSR data. We formulate Chinese CSR by a multiple objective extension of a traditional portfolio selection model and analytically solve the extension. We also solve the extension by a genetic algorithm and directly evaluate the algorithm's performance against the analytical solution. The multiple objective formulation is tested by randomly choosing nondominated portfolios with out‐of‐sample data to identify nondominated portfolios that outperform the 1/n portfolio (equally weighted portfolio). Copyright © 2013 John Wiley & Sons, Ltd.

Computing the Nondominated Surface in Tri-Criterion Portfolio Selection

Computing the nondominated set of a multiple objective mathematical program has long been a topic in multiple criteria decision making. In this paper, motivated by the desire to extend Markowitz portfolio selection to an additional linear criterion (dividends, liquidity, sustainability, etc.), we demonstrate an exact method for computing the nondominated set of a tri-criterion program that is all linear except for the fact that one of its objectives is to minimize a convex quadratic function. With the nondominated set of the resulting quad-lin-lin program being a surface composed of curved platelets, a multiparametric algorithm is devised for computing the platelets so that they can be graphed precisely. In this way, graphs of the tri-criterion nondominated surface can be displayed so that, as in traditional portfolio selection, a most preferred portfolio can be selected while in full view of all other contenders for optimality. Finally, by giving an example for socially responsible investors, we demonstrate that our algorithm can outperform standard portfolio strategies for multicriterial decision makers.

In This Issue

In This Issue

Mean-Variance-Skewness-Entropy Measures: A Multi-Objective Approach for Portfolio Selection

In this study, we present a multi-objective approach based on a mean-variance-skewness-entropy portfolio selection model (MVSEM). In this approach, an entropy measure is added to the mean-variance-skewness model (MVSM) to generate a well‑diversified portfolio. Through a variety of empirical data sets, we evaluate the performance of the MVSEM in terms of several portfolio performance measures. The obtained results show that the MVSEM performs well out-of sample relative to traditional portfolio selection models.

Desempenho Fora-da-Amostra da Otimização Robusta de Carteiras

A otimização robusta de carteiras tem recebido grande interesse nos últimos anos devido a possibilidade de considerar o erro de estimação dentro do problema da seleção de carteiras. Uma questão abordada por poucos estudos é se esta nova abordagem é capaz de gerar uma performance fora-da-amostra superior aos métodos tradicionais. Além disso, é importante saber esta abordagem é capaz de gerar carteiras mais estáveis ao longo do tempo, contribuindo assim para reduzir os custos de administração e facilitando a implementação na prática. Este estudo analisa a performance fora-da-amostra e a estabilidade das composições ótimas das carteiras obtidas com otimização robusta e com métodos tradicionais. Os resultados indicam que, para dados simulados, a otimização robusta obtém uma performance superior aos métodos tradicionais tanto em termos de índice de Sharpe como em termos de portfolio turnover. Os resultados para dados reais de indicam que a performance ajustada ao risco foi estatisticamente equivalente, entretanto as composições ótimas foram mais estáveis do que as obtidas através de métodos tradicionais de otimização.

Estimation Risk Modeling in Optimal Portfolio Selection: An Empirical Study from Emerging Markets

Efficient portfolio is a portfolio that yields maximum expected return given a level of risk or has a minimum level of risk given a level of expected return. However, the optimal portfolios do not seem to be as efficient as intended. Especially during financial crisis period, optimal portfolio is not an optimal investment as it does not yield maximum return given a specific level of risk, and vice versa. One possible explanation for an unimpressive performance of the seemingly efficient portfolio is incorrectness in parameter estimates called “estimation risk in parameter estimates”. Six different estimating strategies are employed to explore ex‐post‐portfolio performance when estimation risk is incorporated. These strategies are traditional Mean‐Variance (EV), Adjusted Beta (AB) approach, Resampled Efficient Frontier (REF), Capital Asset Pricing Model (CAPM), Single Index Model (SIM), and Single Index Model incorporating shrinkage Bayesian factor namely, Bayesian Single Index Model (BSIM). Among the six alternative strategies, shrinkage estimators incorporating the single index model outperform other traditional portfolio selection strategies. Allowing for asset mispricing and applying Bayesian shrinkage adjusted factor to each asset′s alpha, a single factor namely, excess market return is adequate in alleviating estimation uncertainty.

Multiple objectives in portfolio construction

In this article we attempt to expand the limited framework of single-objective optimisation and broaden Markowitz's market standard, within which the problem of portfolio selection is conventionally addressed. The decision maker's Investment Policy Statement (IPS) is formulated through a multiobjective mixed-integer linear programming model. The model is then solved through the augmented e-constrained (AUGMECON) method, a novel a posteriori Multiobjective Mathematical Programming (MMP) technique. Our purpose for transforming the traditional two-dimension portfolio selection problem into a mixed-integer multiobjective optimisation problem in space is twofold: 1) to incorporate three objective functions in the decision process beyond the mean-variance approach, i.e., an additional measure of return, the portfolio's relative dividend yield, 2) to model even the most complex preferences that the investor may express, regarding specific cardinal constraints. The proposed model is tested through an illustrative application in the Athens Stock Exchange (ASE).