Mean Variance Skewness Research Articles

ESG portfolio for TDFs with time‐varying higher moments and cardinality constraint

AbstractPension funds are crucial in supporting environmentally sustainable and socially responsible investments. This paper focuses on an essential product of pension funds, target date funds (TDFs), constructing its portfolio model that considers environmental, social, and governance (ESG) investment. Our model utilizes the mean–variance–skewness–kurtosis optimization framework and accounts for the time‐varying relationship between realized higher moments and subsequent TDFs performance. A cardinality constraint is included to prevent over‐diversification and reduce costs, controlling the number of constituent funds in the TDFs. Since the model is multiobjective, we transform it into a single‐objective optimization through the investment manager's preferences. The numerical experiments represent the most suitable time‐varying higher moment strategy for the Chinese market and demonstrate the model's applicability to managers prioritizing risk over returns, which resonates well with the conservative investment of pension funds. We prove that controlling the number of constituent funds with cardinality constraint is advantageous for improving TDFs' performance. By selecting ESG funds as underlying assets, we highlight that green TDFs have better long‐term performance in terms of higher moment risk.

A closed-form mean–variance–skewness portfolio strategy

This paper analyzes portfolio selection problems with multivariate normal-gamma distributed risky returns. We obtain a partial elliptic cone-shaped mean–variance–skewness (MVS) frontier and a closed-form MVS portfolio strategy for investors with a cubic utility function. We show that the utility improvement and Sharpe ratio loss of our MVS strategy relative to the traditional mean–variance strategy depend on the investor’s prudence and risk-aversion levels, and the mean and variance of a max-skewness portfolio. Moreover, we obtain a three-moment capital asset pricing model, and propose a max-skewness factor in addition to the market factor.

A novel finite-time q-power recurrent neural network and its application to uncertain portfolio model

This paper presents a novel finite-time q-power recurrent neural network (FT-QPNN) for uncertain portfolio model. An uncertain mean–variance-skewness model under concave transaction costs is discussed. This portfolio model is essentially a nonconvex nonlinear optimization problem with a non-positive definite Hessian matrix of the Lagrange function. The non-positive definite Hessian matrix leads to the failure of many recurrent neural network methods in solving the problem, and many recurrent neural networks cannot converge to the equilibrium point in finite time. To overcome these difficulties, the FT-QPNN is proposed. Combined with finite-time activation function and local convexification method, the FT-QPNN can solve the optimization problem with non-positive definite Hessian matrix and converge to the equilibrium point in finite time. The global finite-time stability and robustness properties of the FT-QPNN are proved theoretically and verified by numerical experiments. Furthermore, the proposed FT-QPNN is applied to solve the uncertain portfolio model. The application simulation results and comparative experiments with other methods respectively illustrate the feasibility and superiority of the FT-QPNN.

Uncertain random mean–variance–skewness models for the portfolio optimization problem

In the face of complex financial phenomena, describing the high uncertainties in financial markets remains a challenging issue in modelling and decision making. In this paper, chance theory is used to analyse the hybrid uncertainty that combines random returns and uncertain returns. We regard the total return as an uncertain random variable and study the uncertain random portfolio optimization problem. We first define the skewness of an uncertain random variable and derive some important properties and explicit expressions with deterministic distributions. These theoretical results help transform the model into a deterministic form. Then, uncertain random mean–variance–skewness portfolio optimization models and their corresponding equivalents are established to meet the diverse needs of investors. Finally, we provide two numerical experiments to illustrate the applicability of the proposed model, one of which demonstrates that the model can be applied in the area of energy finance. It is shown that when uncertain asset returns are asymmetric, this model can be used to make investment decisions for investors. We also find that a higher return is accompanied by higher risk and higher skewness.

Credibilistic variance and skewness of trapezoidal fuzzy variable and mean–variance–skewness model for portfolio selection

The fuzzy set theory is widely used to describe the uncertainty of financial markets in modern portfolio selection problems. In this study, the credibility theory (a popular branch of the fuzzy set theory) is applied to extend Markowitz’s mean–variance portfolio selection model into mean–variance–skewness portfolio selection model. For this, the returns on risky stocks are regarded as trapezoidal fuzzy variables. The credibilistic skewness is obtained originally for trapezoidal fuzzy variable, and the incorporation of the credibilistic variance of trapezoidal fuzzy variable enables the estimation of risk on portfolio return. To solve the proposed multi-objective optimization problem, a polynomial goal programming approach is suggested in this study. In addition, a dominant numerical analysis of the proposed work and its comparison with existing works are presented.

Regret theory-based fuzzy multi-objective portfolio selection model involving DEA cross-efficiency and higher moments

This paper deals with fuzzy portfolio selection problems under the framework of bounded rationality, in which the higher moments and DEA cross-efficiency are taken into consideration. To this end, a regret cross-efficiency (RCE) evaluation model is first proposed to evaluate cross-efficiency scores of all assets by integrating several important financial information: return on equity, earnings per share, current ratio, price/earnings ratio, price/book ratio, and beta value. Then, by incorporating cross-efficiency into the mean–variance–skewness framework, a regret theory-based multi-objective portfolio selection model is developed. The model aims to maximize investor’s perceived utility (composed of utility, regret, and rejoice functions) with respect to the four objectives, namely mean–variance–skewness-efficiency, bounded by several realistic constraints. Additionally, considering the inherent uncertainty in data, the criteria related to RCE evaluation as well as asset returns are characterized as fuzzy variables. The current study not only empowers investors with an overall control over the preferences regarding all portfolio objectives, but also gives investors an opportunity to tweak their intrinsic behavioral tendencies from the perspective of regret aversion and rejoice preference, thus achieving the results that are compatible with the actual preferences of investors. A real-world empirical application is presented to demonstrate the effectiveness of the proposed model.

ASSET PRICING WITH HIGHER CO-MOMENTS AND CVAR: EVIDENCE FROM PAKISTAN STOCK EXCHANGE

The development of asset pricing model is attributed to Markowitz (1952) which initiated towards Modern Portfolio Theory (MPT). The whole concept of MPT based on normality of returns assumption but in emerging economies volatility of returns is an important issue and sometimes markets only behave in either bullish or bearish patterns. Moreover, the volatility cannot be attributed and explained by variance rather it can be a result of extreme events (profits / losses) referred to as none elliptical distributions of returns. The objective of this study is to incorporate additional dimensions of risk in Markowitz Mean-Variance framework through inclusions of skewness kurtosis and coherent risk measure CVaR to obtain optimal portfolio with PGP approach. The study analyzes the portfolio returns of Mean-Variance (MV), Mean Variance Skewness (MVS), Mean Variance Skewness Kurtosis (MVSK) & Mean CVaR Skewness Kurtosis (MCVaRSK) models by using selected stocks of KSE-100 index over the time period of 2009-2018. The empirical findings suggest that portfolio returns impacted through inclusion of higher moments and CVaR and generated higher returns over the benchmark portfolio. The results of study are immensely useful for the fund managers and investors for stocks selection and construction of alternative portfolios. Keywords: Portfolio optimization, Mean CVaR Skewness Kurtosis, Multi objective optimization, Pakistan JEL Classifications: C61, G10, G11 DOI: https://doi.org/10.32479/ijefi.10351

A Novel Hybrid ICA-FA Algorithm for Multiperiod Uncertain Portfolio Optimization Model Based on Multiple Criteria

This paper deals with a multiperiod portfolio selection problem in an uncertain investment environment, in which the returns of securities are assumed to be uncertain variables and determined by experts’ subjective evaluation. Based on uncertain theory, we present a novel multiperiod multiobjective mean–variance–skewness model by considering multiple realistic investment constraints such as transaction cost, bounds on holdings, cardinality, etc. For the proposed solution, we first apply a weighted max–min fuzzy goal programming approach to convert the proposed multiobjective programming model into a single-objective one. After that, we design a novel hybrid of an imperialist competitive algorithm (ICA) and a firefly algorithm (FA), termed ICA–FA, to solve it. Finally, we provide a numerical example to demonstrate the effectiveness of the proposed model and corresponding algorithm.

Unique closed-form solutions of portfolio selection subject to mean-skewness-normalization constraints

This paper originally proposes two unique closed-form solutions, respectively to risky assets only and a risk-free asset existing situations, of the mean-variance-skewness (MVS) optimization model subject to mean-sknewness-normalization constraints for portfolio selection. The efficient frontier and capital allocation surface (CAS) respectively derived from the two solutions are two hyperboloids, and tangent to each other at one hyperbola referred to as the market portfolio curve. Moreover, this curve intersects the mean-skewness plane of the portfolio return wtih zero-variance (zero-risk) at a line. Calculating the distance between a point on the coincident curve with the vertex of the CAS, we present a novel ratio to measure the performance of the risk-adjusted returns of market portfolio. The ratio is similar to the Sharpe ratio, moreover, under the more realistic assumption that portfolio returns follow a skew-normal distribution, the novel ratio can quantify the degree (or absence) of market portfolio exuberance.

Does skewness help in better investment decision making?

PurposeThe purpose of this paper is to examine the significance of skewness in maximizing the investor utility using the daily data for eight sectors listed on the National Stock Exchange of India.Design/methodology/approachThe analysis is carried out in three different steps. In the first part, the author analyzes the monthly stock returns and the important financial ratios – price-to-book (PB) ratio, price-earnings (PE) ratio and dividend yield (DY). Second, the author tests the sector-wise return predictability using Westerlund and Narayan (2012) flexible generalized least squares estimator. Third, the author compares the mean–variance–skewness (MVS) utility function with the mean–variance (MV) utility function.FindingsThe author forecasts the sectoral stock returns using three financial ratios – PB ratio, PE ratio and DY – as predictors. The results indicate that sectoral stock returns are significantly predicted by these financial ratios. The author then formulates trading strategies by including skewness in the utility function and finds that the investor utility is high when the utility function includes skewness as opposed to when the skewness is excluded.Originality/valueThe author extends the MV utility function to the MVS utility function and shows that the Indian stock market is more profitable when the investor uses a MVS utility function which highlights the main contribution to the literature.

Nonlinear decision weights or moment-based preferences? A model competition involving described and experienced skewness

The predictive power of cumulative prospect theory and expected utility theory is typically compared using decisions from description, where lotteries’ outcome values and probabilities are explicitly stated. In decisions from experience, individuals sample (in the sampling paradigm without cost) from the return distributions to learn outcome values and their relative frequencies; here cumulative prospect theory and expected utility theory require the calculation of probabilities from experience. Individuals, however, may be more attuned to the experienced moments of outcome distributions, rather than the probabilities. We therefore test the mean–variance–skewness model, and retrieve the proportion of expected utility theory (over income), cumulative prospect theory, and mean–variance–skewness populations using a latent-class hierarchical Bayesian model across six large datasets. For simple lotteries (with 1–2 outcomes), we find a mixture of cumulative prospect theory and mean–variance–skewness populations in decisions from both description and experience. For more complex lotteries (with 2–3 outcomes), all participants are classified as cumulative prospect theory types in decisions from description, but as mean–variance–skewness types in decisions from experience. This suggests that in decisions from experience with more complex return distributions, preferences for skewness are more predictive than nonlinear probability weighting.

A Coskewness Shrinkage Approach for Estimating the Skewness of Linear Combinations of Random Variables*

Abstract Decision-making in finance often requires an accurate estimate of the coskewness matrix to optimize the allocation to random variables with asymmetric distributions. The classical sample estimator of the coskewness matrix performs poorly for small sample sizes. A solution is to use shrinkage estimators, defined as the convex combination between the sample coskewness matrix and a target matrix. We propose unbiased consistent estimators for the MSE loss function and include the possibility of having multiple target matrices. In a portfolio application, we find that the proposed shrinkage coskewness estimators are useful in mean–variance–skewness efficient portfolio allocation of funds of hedge funds.

A new comprehensive possibilistic group decision approach for resilient supplier selection with mean–variance–skewness–kurtosis and asymmetric information under interval-valued fuzzy uncertainty

Since resilient supplier selection problems (RSSPs) are regarded vague, uncertain and complex, interval-valued fuzzy sets (IVFSs) and possibilistic statistical theories can assist to deal with preferences and experience of group of experts into meaningful results to appraise the potential suppliers. This research presents a novel comprehensive possibilistic statistical group decision approach with IVFSs and asymmetric information to solve RSSPs in the supply chain networks (SCNs). Possibilistic statistical concepts, including mean, variance, skewness and kurtosis, are proposed for the first time in the literature of SCNs for the group decision process. Also, asymmetric information with IVFSs is provided in the presented approach along with introducing two new extensions of weighting methods for experts as well as evaluation criteria. In addition, new relations, new separation measures and novel distinguish indices are introduced regarding to the preference by similarity to ideal solutions with mean–variance–skewness–kurtosis modeling. Then, the proposed comprehensive decision approach is implemented to an application in automobile industry for the RSSPs to assess the resilience strategy in the SCNs under uncertain conditions.

Multi-objective mean–variance–skewness model for nonconvex and stochastic optimal power flow considering wind power and load uncertainties

This paper presents a multi-objective mean–variance–skewness (MVS) model for reliably assessing the problem of nonconvex and stochastic optimal power flow (NSOPF), considering valve-point effect, stochastic load and uncertain integrated wind power. The MVS model aims to maximize both the expected return and skewness while simultaneously minimizing the risk, which is formulated as a competing and conflicting three-objective optimization problem. Based on such a model, we propose a multi-objective optimization algorithm, multiple preys based evolutionary predator and prey strategy (MPEPPS), to provide Pareto solutions, which show the trade-off relationship among the expected return, the skewness and the risk of the dispatching objective. Subsequently, a multi-criteria decision making method, the technique for order preference by similarity to an ideal solution (TOPSIS), is applied for determining the final dispatch solution. The objective of this paper is to develop a reliable model to assess the NSOPF from the perspective of economics and reliability of power system operation, and propose an efficient algorithm to obtain a solution that considers all of the possible load and wind power simultaneously. Simulation results based on a modified IEEE 30-bus power system demonstrate the reliability and effectiveness of the MVS and MPEPPS in solving NSOPF.

Portfolio selection in a multi-moment setting: A simple Monte-Carlo-FDH algorithm

This paper proposes a non-parametric efficiency measurement approach for the static portfolio selection problem in a general inputs–outputs space, where inputs can include variance and kurtosis and outputs can include mean and skewness. Our work is in the vein of Briec, Kerstens, and Jokung (2007) and Jurzenko, Maillet, and Merlin (2006) who develop a directional distance (shortage function) approach to evaluate the performance of portfolios in Mean–Variance–Skewness and in Mean–Variance–Skewness–Kurtosis spaces. Our approach use the Free Disposal Hull (FDH) estimator to derive an algorithm avoiding the heavy and non-robust numerical optimization approaches suggested so far. This new approach is much faster, more robust to reach the optimum and more flexible since it can be extended to more general situations. We illustrate the algorithm with a data set on the French CAC 40 already used in the literature, to compare our method with the numerical optimization approaches. It appears that our approach is much more performant than the numerical optimization techniques, both in terms of computing time, but also in terms of robustness, avoiding the pitfall of local numerical optima.

Nonlinear Decision Weights or Skewness Preference? A Model Competition

An extensive literature exists comparing the predictive power of Cumulative Prospect Theory (CPT) and Expected Utility Theory (EUT) in decisions from description. CPT accommodates the empirically observed deviations from EUT primarily by assuming a nonlinear probability weighting function and loss aversion. An alternative explanation is that decision makers have preferences for higher-order moments, beyond the mean and variance of lotteries — we extensively test the Mean-Variance-Skewness (MVS) preference model. We estimate the proportion of EUT, CPT and the MVS populations using a latent-class hierarchical Bayesian model for six different datasets, including both decisions from description and experience. In decisions from description, subjects are explicitly presented with the probabilities and outcome values of the lotteries. In decisions from experience subjects must sample (without cost) from the lottery distributions to learn both the probabilities and outcome values. In the latter, CPT and EUT require the explicit calculation of probabilities from experience; however, the MVS model only requires that decision-makers hold estimates of the three moments of the outcome distributions. In decisions from experience and description with simple lotteries (one safe option and one risky lottery with only two outcomes), we find significant subject heterogeneity — some subjects are classified as CPT and others as MVS. In the remaining four datasets with multiple (two to three) outcomes per lottery, a single class is sufficient to characterize subjects. Specifically, in two datasets of decisions from experience all subjects are classified as MVS, thus implying that preferences for skewness are more predictive than nonlinear probability weighting. In two datasets with decisions from description all subjects are classified as CPT. We find no evidence of an EUT population in any of the datasets. We conclude that the scope of CPT is primarily limited to decisions from description, while the scope of MVS to decisions from experience. Furthermore, out of the four datasets with a CPT population, only in one dataset did we observe the standard inverse-S shaped probability weighting function; this was the only dataset with simple lotteries (as defined above) and no multi-outcome lotteries.

Multi objective mean–variance–skewness model with Burg’s entropy and fuzzy return for portfolio optimization

A new non-Shannon fuzzy Mean–Variance–Skewness-entropy model is proposed with stock returns are considered as triangular fuzzy numbers. The fuzzy stock portfolio selection models are presented with credibility theory that maximizes mean and skewness and minimizes portfolio variance and cross-entropy in terms of Burg. With addition of Burg’s entropy in the multi objective non linear models, focus is the generation of well diversified portfolios within the optimal allocation. For an imprecise capital market, this study facilitates a more reasonable investment decisions with four objective decision criteria including Burg’s entropy. Numerical examples with case studies are used to illustrate the entire method which can be efficiently used in practical purposes like national stock exchanges.

A stein type lemma for the multivariate generalized hyperbolic distribution

When two variables are bivariate normally distributed, Stein’s (1973, 1981) seminal lemma provides a convenient expression for the covariance of the first variable with a function of the second. The lemma has proven to be useful in various disciplines, including statistics, probability, decision theory and finance. In finance, however, asset returns do not always display symmetry but may exhibit skewness. This observation led Adcock (2007, 2010, 2014) to develop Stein’s type lemmas for certain multivariate distributions that are consistent with Simaan’s (1987, 1993) setting for asset returns. In this paper, we depart from Simaan’s setting and develop a new Stein’s type lemma in the setting of a mean–variance mixture model for returns. As a particular application, we show that expected utility maximizers select portfolios that are mean–variance–skewness efficient.

A novel group decision model based on mean–variance–skewness concepts and interval-valued fuzzy sets for a selection problem of the sustainable warehouse location under uncertainty

Recently, sustainable warehouse location has been regarded as one of the most critical and significant decision problems for long-term planning in the supply chain. This strategic decision can be effected by different quantitative and qualitative evaluation criteria via three dimensions of the sustainability. Main theme of the paper is to select the most optimal location decision from a number of potential sustainable warehouse candidates. For this purpose, this paper presents a novel multi-criteria decision-making model by a group of supply chain experts or decision makers with interval-valued fuzzy setting and asymmetric uncertainty information. Concepts of mean, variance and skewness are introduced into the proposed group decision model, and their mathematical relations are defined based on a fuzzy possibilistic statistical approach. Then, new relations in this model are presented for obtaining ideal solutions under uncertainty with two high and low values of the possibilistic mean and possibilistic standard deviation, along with the possibilistic cube root of skewness. In addition, novel separation measures and new fuzzy ranking index of hybridized relative closeness coefficients are presented to provide final preference order of warehouse location candidates under uncertain conditions. Finally, a sustainable warehouse location selection problem in a pharmaceutical company is presented and solved by the proposed group decision model to demonstrate its applicability and suitability.

Revealed preferences for portfolio selection – does skewness matter?

ABSTRACTIn this article, we consider the portfolio selection problem as a Bayesian decision problem. We compare the traditional mean–variance and mean–variance–skewness efficient portfolios. We develop bi-level programming problem to investigate the market’s preference for risk by using observed (market) weights. Numerical experiments are conducted on a portfolio formed by the 30 stocks in the Dow Jones Industrial Average. Numerical results show that the market’s preferences are better explained when skewness is included.