Optimal Portfolio Research Articles

A Novel Improved Genetic Algorithm for Multi-Period Fractional Programming Portfolio Optimization Model in Fuzzy Environment

The complexity of historical data in financial markets and the uncertainty of the future, as well as the idea that investors always expect the least risk and the greatest return. This study presents a multi-period fractional portfolio model in a fuzzy environment, taking into account the limitations of asset quantity, asset position, transaction cost, and inter-period investment. This is a mixed integer programming NP-hard problem. To overcome the problem, an improved genetic algorithm (IGA) is presented. The IGA contribution mostly involves the following three points: (i) A cardinal constraint processing approach is presented for the cardinal constraint conditions in the model; (ii) Logistic chaotic mapping was implemented to boost the initial population diversity; (iii) An adaptive golden section variation probability formula is developed to strike the right balance between exploration and development. To test the model’s logic and the performance of the proposed algorithm, this study picks stock data from the Shanghai Stock Exchange 50 for simulated investing and examines portfolio strategies under various limitations. In addition, the numerical results of simulated investment are compared and analyzed, and the results show that the established models are in line with the actual market situation and the designed algorithm is effective, and the probability of obtaining the optimal value is more than 37.5% higher than other optimization algorithms.

Risk Measurement and Portfolio Optimization Based on NASDAQ 100

Risk Measurement and Portfolio Optimization Based on NASDAQ 100

A dual-time dual-population multi-objective evolutionary algorithm with application to the portfolio optimization problem

The article proposes a dual-time dual-population multi-objective evolutionary algorithm, DTDP-EAMO, to address the challenges faced by multi-objective differential evolution algorithms in solving complex optimization problems, such as weakened late-stage search capability, susceptibility to local optima, and insufficient diversity. Firstly, DTDP-EAMO divides the population into three sub-populations using fast nondominated sorting. Then, it introduces a dual-stage and multi-population adaptive mutation strategy to maintain the convergence and diversity of each sub-population. Meanwhile, a dual external archive mechanism is introduced to enable the population to escape local optima and facilitate information exchange between sub-populations through archiving high-quality solutions from both stages. Finally, the individuals in the external archive are sorted, and high-quality solutions are selected and recombined to generate a new population. To demonstrate the effectiveness of DTDP-EAMO, fourteen test functions and a portfolio optimization problem are selected. Experimental results show that the algorithm's overall performance is superior to three comparative algorithms. Furthermore, practical application results demonstrate DTDP-EAMO's ability to reduce risk and increase returns in portfolio optimization problems, further confirming its effectiveness and feasibility. DTDP-EAMO outperforms comparative algorithms in convergence and distribution, indicating higher accuracy and superiority in solving portfolio models.

Financial awareness, risk aversion and portfolio choice

ABSTRACT “The financial market participation puzzle remains one of the most explored yet unanswered areas in finance. We extend the debate of portfolio choice by examining stock and derivatives market participation by focusing on two key investor traits: financial awareness and risk aversion. We use an investor survey conducted by the Securities and Exchange Board of India (SEBI), covering over 15,000 Indian investor responses. We find that risk aversion is associated with a 20% lower probability of market participation, whereas risk-averse individuals having high financial awareness are around 3.3% more likely to participate in financial markets. Furthermore, financial awareness and risk aversion are more significant in areas with higher economic freedom and lower social capital. Our findings suggest that policymakers may consider tailored financial awareness programmes based on differences in risk aversion among the investors as both these characteristics have a combined relationship with financial market participation.

Comparison of Markowitz Model and Index Model in Different Constraints

This paper reviews the application of Markowitz model and index model in portfolio optimization and focuses on comparing the performance under different constraints. The study covers the core concepts and theoretical framework of modern portfolio theory and the development of the two models. The Markowitz model employs quantitative analysis to consider the expected return and risk of assets and aims to maximize investor utility. The index model, on the other hand, achieves investment objectives by replicating the performance of a specific index. Comparative analysis shows that the Markowitz model is suitable for active management, while the index model is more suitable for passive investment. With the advancement of computing technology, the application of Markowitz model will be more accurate and extensive. Meanwhile, as the concept of passive investment becomes popular, the index model will continue to attract more investors. This study is of great significance to investors in choosing investment strategies, and will help academia and the industry to further optimize investment models.

A neural network framework for portfolio optimization under second-order stochastic dominance

Traditional portfolio optimization strategies often rely on statistical methods and linear programming tools to achieve a balance between return and risk. Despite their usefulness for portfolio optimization, they cannot efficiently capture the specific differences and complexity of real-world financial markets. Several modern approaches attempt to overcome these limitations by using nonlinear models, machine learning, and advanced risk measures. In this study, we propose a novel strategy for optimizing portfolios that incorporates second-order stochastic dominance constraints and solves them with neural networks. we show that portfolios subject to second-order stochastic dominance constraints outperform their traditional counterparts, especially in tail-risk situations.

Portfolio Management of Consumer Industry Based on Index Model

This paper explores the application of the index model in portfolio analysis, highlighting its significance in both macro and security analysis for the optimization of portfolios. Utilizing data spanning from October 2018 to November 2023, the study draws several key conclusions. Firstly, it identifies the optional consumption industry as particularly susceptible to market fluctuations, exhibiting higher sensitivity compared to the daily consumption industry. Secondly, an active portfolio comprising Costco, Walmart, Lululemon, and Under Armour, alongside short positions in risk-free securities, yields the optimal portfolio with a maximized Sharpe ratio. However, the study acknowledges limitations, notably the relatively small sample size and the impact of the COVID-19 pandemic, which introduces extreme risks and potential errors in the analysis. Future research directions include modifying the index model to incorporate volatility adjustments and exploring multi-factor investment models to mitigate errors and enhance portfolio efficiency. This study underscores the importance of continuous refinement and adaptation of analytical frameworks in portfolio management amidst dynamic market conditions.

Analysis of Periodic and Seasonal Characteristics in Time Series: Taking the Dow Jones Industrial Average as an Example

The objective of this research is to conduct a comprehensive analysis of the Dow Jones Industrial Average (DJIA) with a focus on identifying cyclical and seasonal patterns observed in long-term time series data. In order to accurately predict future market trends, this research employs a combination of fundamental and advanced forecasting techniques, including mean, naive, snaive, drift, Holt, Holt-Winters, and ARIMA models. Furthermore, the research explores the impact of return ratios on market investment opportunities. Customized portfolio optimization strategies are developed based on the risk profiles of different investors, along with quantitative trading strategies that effectively manage market risks using the Capital Asset Pricing Model (CAPM). The research shows that the price of Dow Jones Industrial Index has a gradual upward trend, and its return rate has a certain periodicity and seasonality. The aim of this research is to provide valuable insights into the fundamental framework of the American stock market, enabling economists, investors, and policymakers to make informed decisions.

An uncertain bi-objective mean-entropy model for portfolio selection with realistic factors

In the imprecise investment environment, there are many indeterminate factors impacting security returns. This paper introduces a portfolio optimization problem where cross-entropy is utilized to control portfolio risk within the framework of uncertainty theory and presents an uncertain bi-objective mean-entropy portfolio selection model. To be more realistic, some realistic factors such as minimum transaction lots, dividend factors and tax factors are also considered. By introducing a risk preference coefficient, the bi-objective model is converted into a single-objective model and some equivalents are discussed. Additionally, a hybrid intelligent algorithm integrating a genetic algorithm with uncertain estimation is designed to solve the proposed model. Finally, a case study is executed to confirm the practicability of the model and the performance of the algorithm, and an empirical analysis based on the proposed model and the uncertain mean–variance model is developed to illustrate the advantage of the uncertain mean-entropy model in practical investment.

A new distributionally robust reward-risk model for portfolio optimization

Abstract A new distributionally robust ratio optimization model is proposed under the known first and second moments of the uncertain distributions. In this article, both standard deviation (SD) and conditional value-at-risk (CVaR) are used to measure the risk, avoiding both fat-tail and volatility. The new model can be reduced to a simple distributionally robust model under assumptions on the measurements of reward, CVaR and SD. Furthermore, it can be rewritten as a tractable semi-definite programming problem by the duality theorem under partially known information of the uncertain parameters. Finally, the model is tested on portfolio problems and verified from numerical results that it can give a reasonable decision under only the first and second moments.

Human capital and portfolio choice: borrowing constraint and reversible retirement

Human capital and portfolio choice: borrowing constraint and reversible retirement

ESG integration in portfolio selection: A robust preference-based multicriteria approach

We present a framework for multi-objective optimization where the classical mean–variance portfolio model is extended to integrate the environmental, social and governance (ESG) criteria on the same playing field as risk and return and, at the same time, to reflect the investors’ preferences in the optimal portfolio allocation. To obtain the three–dimensional Pareto front, we apply an efficient multi-objective genetic algorithm, which is based on the concept of ɛ-dominance. We next address the issue of how to incorporate investors’ preferences to express the relative importance of each objective through a robust weighting scheme in a multicriteria ranking framework. The new proposal has been applied to real data to find optimal portfolios of socially responsible investment funds, and the main conclusion from the empirical tests is that it is possible to provide the investors with a robust solution in the mean–variance–ESG surface according to their preferences.

Portfolios Optimization Among Technology, Consumer Defensive, Consumer Cyclic and Entertainment

Nowadays in financial field, portfolio optimization is playing a key role in making decision of investment. This article taking about the asset allocation in seven companies in Technology, Consumer Defensive, Consumer Cyclic and Entertainment. The Markowitz and Index models are the primary tools utilized in this study to analyze the portfolio data. Then, three constraints will be set to see the difference between them. In more detail, comparing two different models in same constraint and find difference in same model when setting different constraints. The results shows that McDonald’s takes the highest Weight in two models when setting different constraints on models. In the meanwhile, compared to when there are no constraints, the performance of the minimal variance frontier and the capital allocation line is inferior. The research in this paper plays a reference role for investors to construct investment portfolios.

Bayesian Learning in an Affine GARCH Model with Application to Portfolio Optimization

This paper develops a methodology to accommodate uncertainty in a GARCH model with the goal of improving portfolio decisions via Bayesian learning. Given the abundant evidence of uncertainty in estimating expected returns, we focus our analyses on the single parameter driving expected returns. After deriving an Uncertainty-Implied GARCH (UI-GARCH) model, we investigate how learning about uncertainty affects investments in a dynamic portfolio optimization problem. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize her expected utility from terminal wealth under an Affine GARCH(1,1) model. The corresponding stock evolution, and therefore, the wealth process, is treated as a Bayesian information model that learns about the expected return with each period. We explore the one- and two-period cases, demonstrating a significant impact of uncertainty on optimal allocation and wealth-equivalent losses, particularly in the case of a small sample size or large standard errors in the parameter estimation. These analyses are conducted under well-documented parametric choices. The methodology can be adapted to other GARCH models and applications beyond portfolio optimization.

Towards Promoting the Efficiency of Enterprise Investment Management with Artificial Intelligence

With the continuous development and optimization of artificial intelligence, enterprises have begun to pay attention to the use of artificial intelligence for the optimization of work and the improvement of efficiency, and in the management of enterprise investment, a number of companies have begun to use a large number of artificial intelligence technologies in the integration and analysis of data, information processing and analysis, risk management, efficiency improvement, and so on. Enterprises encounter problems in analyzing data and information in investment management, and problems in risk management, all of which affect the improvement of their investment returns. Enterprises face a huge amount of data in the process of investment management, it is difficult to calculate a large number of data models in a relatively short period of time, and it is impossible to analyze and extract more information. In the face of investment risk, the control of risk in the past investment process is more based on experience to judge, there is a great deal of subjective assumptions in risk avoidance. And in the investment process companies also want to increase returns, improve efficiency, avoid risk, and achieve a more automated and intelligent trading process. Enterprises need to use artificial intelligence to technically solve the problems of data aggregation, arithmetic, and analysis; use artificial intelligence to optimize the problem of processing large amounts of information; use artificial intelligence technology to enhance risk management and predictive analysis, strengthen intelligent decision-making and portfolio optimization, and provide insights into big data analysis and market trends. The wide application of artificial intelligence technology in enterprises also has a certain impact on the development of enterprises, and it has a certain impact on the planning, feasibility, whole-process control, investment evaluation, investment report, and investment efficiency of investment in the investment link, which makes it widely concerned in the society and in enterprises.

Portfolio Analysis of Five Stocks Under Different Constraints Based on Markowitz Model & Index Model

Since the dawn of the 21st century, while there has been an abundance of talented fund managers, truly exceptional asset portfolios have been rare. Addressing this phenomenon, the study delves into the current state of asset management, employing two renowned financial models: the Markowitz model and the Index model. These models are utilized to analyze the returns and risks of five high-performing assets. Additionally, acknowledging the diversity of investor preferences, this paper incorporates five different constraints to cater to a wider spectrum of client needs. The crux of the research is the optimization of the asset portfolio, grounded in these models and constraints. The paper findings indicate that the integration of the Markowitz and Index models with the capital market line and the efficient frontier proves highly effective in the management of risk asset portfolios. In this paper, the Markowitz model consistently excels over the index model in both minvariance and maxsharpe scenarios. This study has important reference value for investors in related fields.

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.

Application Of Markowitz and Index Models to Real Markets

After Markowitz put forward the portfolio theory in the 1950s, the modern investment theory was developed, and more related theoretical models were created based on it. To find the optimal portfolio in the market, this paper randomly selects 7 stock types, uses three different constraint methods to show the investment characteristics of different group of investors, and uses Index model and Markowitz model to find efficient frontier and the proportion of asset allocation under the condition of maximum Sharpe ratio and minimum variance. The results show that to achieve the maximum Sharpe ratio and find the best combination, it is necessary to purchase AAPL primarily. Secondly, it chooses to purchase assets with less correlation and relatively large return rate, such as MSFT and WMT. The results in this paper shed lights for investor in selecting potential assets and may provide helpful insight for future investments.

Testing out-of-sample portfolio performance using second-order stochastic dominance constrained optimization approach

Second-order Stochastic Dominance (SSD) criterion can be used to support portfolio decision making under risk and uncertainty. In this paper, we develop novel robust SSD criteria to capture the strength of dominance and portfolio optimization models utilizing these criteria to identify portfolios whose in-sample SSD dominance over a given benchmark is likely to hold also out-of-sample. The developed models can incorporate incomplete probability information by allowing a set of feasible state probabilities. We also show that these portfolio optimization models can be formulated as linear programming problems. We report results from applying these SSD-based portfolio optimization models with different sets of state probabilities in an empirical application, with a focus on evaluating the out-of-sample portfolio performance of the optimized portfolios.

Teaching–Learning-Based Optimization Algorithm with Stochastic Crossover Self-Learning and Blended Learning Model and Its Application

This paper presents a novel variant of the teaching–learning-based optimization algorithm, termed BLTLBO, which draws inspiration from the blended learning model, specifically designed to tackle high-dimensional multimodal complex optimization problems. Firstly, the perturbation conditions in the “teaching” and “learning” stages of the original TLBO algorithm are interpreted geometrically, based on which the search capability of the TLBO is enhanced by adjusting the range of values of random numbers. Second, a strategic restructuring has been ingeniously implemented, dividing the algorithm into three distinct phases: pre-course self-study, classroom blended learning, and post-course consolidation; this structural reorganization and the random crossover strategy in the self-learning phase effectively enhance the global optimization capability of TLBO. To evaluate its performance, the BLTLBO algorithm was tested alongside seven distinguished variants of the TLBO algorithm on thirteen multimodal functions from the CEC2014 suite. Furthermore, two excellent high-dimensional optimization algorithms were added to the comparison algorithm and tested in high-dimensional mode on five scalable multimodal functions from the CEC2008 suite. The empirical results illustrate the BLTLBO algorithm’s superior efficacy in handling high-dimensional multimodal challenges. Finally, a high-dimensional portfolio optimization problem was successfully addressed using the BLTLBO algorithm, thereby validating the practicality and effectiveness of the proposed method.