Portfolio Optimization Model Research Articles

Enhancing Portfolio Optimization: A Two-Stage Approach with Deep Learning and Portfolio Optimization

The portfolio selection problem has been a central focus in financial research. A complete portfolio selection process includes two stages: stock pre-selection and portfolio optimization. However, most existing studies focus on portfolio optimization, often overlooking stock pre-selection. To address this problem, this paper presents a novel two-stage approach that integrates deep learning with portfolio optimization. In the first stage, we develop a stock trend prediction model for stock pre-selection called the AGC-CNN model, which leverages a convolutional neural network (CNN), self-attention mechanism, Graph Convolutional Network (GCN), and k-reciprocal nearest neighbors (k-reciprocal NN). Specifically, we utilize a CNN to capture individual stock information and a GCN to capture relationships among stocks. Moreover, we incorporate the self-attention mechanism into the GCN to extract deeper data features and employ k-reciprocal NN to enhance the accuracy and robustness of the graph structure in the GCN. In the second stage, we employ the Global Minimum Variance (GMV) model for portfolio optimization, culminating in the AGC-CNN+GMV two-stage approach. We empirically validate the proposed two-stage approach using real-world data through numerical studies, achieving a roughly 35% increase in Cumulative Returns compared to portfolio optimization models without stock pre-selection, demonstrating its robust performance in the Average Return, Sharp Ratio, Turnover-adjusted Sharp Ratio, and Sortino Ratio.

Modeling risky portfolios with guaranteed maximize returns under a patent race

This paper studies the patent race problem of communication enterprises investing in communication technologies, and constructs a portfolio optimization model which considers the expected returns, investment risks, and replacement costs, in order to achieve the dual goals of maximizing the net investment income of backward enterprises and minimizing the expected investment risk. Through numerical experimental analysis, the optimal investment portfolio strategy under different risk levels and the impact of different risk levels on the net income of lagging company are obtained. The research results show that due to the backward research in the first stage of the backward enterprises, when their own investment decision-making power is relatively high, they can focus on the development of self-interested key technology areas in order to achieve the victory of the patent race.

Cryptocurrency Portfolio Allocation under Credibilistic CVaR Criterion and Practical Constraints

The cryptocurrency market offers attractive but risky investment opportunities, characterized by rapid growth, extreme volatility, and uncertainty. Traditional risk management models, which rely on probabilistic assumptions and historical data, often fail to capture the market’s unique dynamics and unpredictability. In response to these challenges, this paper introduces a novel portfolio optimization model tailored for the cryptocurrency market, leveraging a credibilistic CVaR framework. CVaR was chosen as the primary risk measure because it is a downside risk measure that focuses on extreme losses, making it particularly effective in managing the heightened risk of significant downturns in volatile markets like cryptocurrencies. The model employs credibility theory and trapezoidal fuzzy variables to more accurately capture the high levels of uncertainty and volatility that characterize digital assets. Unlike traditional probabilistic approaches, this model provides a more adaptive and precise risk management strategy. The proposed approach also incorporates practical constraints, including cardinality and floor and ceiling constraints, ensuring that the portfolio remains diversified, balanced, and aligned with real-world considerations such as transaction costs and regulatory requirements. Empirical analysis demonstrates the model’s effectiveness in constructing well-diversified portfolios that balance risk and return, offering significant advantages for investors in the rapidly evolving cryptocurrency market. This research contributes to the field of investment management by advancing the application of sophisticated portfolio optimization techniques to digital assets, providing a robust framework for managing risk in an increasingly complex financial landscape.

Combining transformer based deep reinforcement learning with Black-Litterman model for portfolio optimization

Combining transformer based deep reinforcement learning with Black-Litterman model for portfolio optimization

A three-level nested portfolio optimization model with position allocation

Existing portfolio optimization models cannot well capture the real position allocation requirement, leading to limited impact in practice. To overcome this challenge, we propose a three-level nested portfolio optimization model with position allocation. Within this model, the inner and middle levels collaboratively determine the optimal portfolio, while the outer level focuses on optimizing the holding proportion of each stock in the optimal portfolio. Compared with existing models with portfolio weights, the proposed model imposes the position allocation constraint that precisely characterizes the limitations on holding each stock. This constraint is crucial for investors to obey securities trading regulations involving position limitations and to mitigate the potential impact of market risks. To address the nonlinear and nonconvex nature of the novel model, we develop an intelligent optimization algorithm by effectively hybridizing the support vector regression and the enhanced grey wolf optimizer. We comprehensively evaluate its performance using eight metrics, including accumulative return, annual return, Sharpe ratio, maximum drawdown, absolute and relative win ratios, predictive precision and accuracy. The experimental results indicate that (i) the proposed model can achieve more excess returns than those stock selection models not considering position allocation, especially for the large-cap stocks; (ii) compared with other state-of-the-art meta-heuristics, the enhanced grey wolf optimizer can yield better portfolio in conjunction with the support vector regression; (iii) in the context of the Chinese A-share stock market, specific financial indicators such as return on equity, inventory turnover rate, net income growth rate, and debt-to-equity ratio should be given greater consideration compared to other financial metrics.

Robust portfolio optimization model for electronic coupon allocation

Currently, many e-commerce websites issue online/electronic coupons as an effective tool for promoting sales of various products and services. We focus on the problem of optimally allocating coupons to customers subject to a budget constraint on an e-commerce website. We apply a robust portfolio optimization model based on customer segmentation to the coupon allocation problem. We also validate the efficacy of our method through numerical experiments using actual data from randomly distributed coupons. Main contributions of our research are twofold. First, we handle six type of coupons, thereby making it extremely difficult to accurately estimate the difference in the effects of various coupons. Second, we demonstrate from detailed numerical results that the robust optimization model achieved larger uplifts of sales than did the commonly-used multiple-choice knapsack model and the conventional mean–variance optimization model. Our results open up great potential for robust portfolio optimization as an effective tool for practical coupon allocation.

Computational analysis of expectile and deviation expectile portfolio optimization models

Computational analysis of expectile and deviation expectile portfolio optimization models

Sparse portfolio optimization via [formula omitted] over [formula omitted] regularization

Sparse portfolio optimization, which significantly boosts the out-of-sample performance of traditional mean–variance methods, is widely studied in the fields of optimization and financial economics. In this paper, we explore the ℓ1/ℓ2 fractional regularization constructed by the ratio of the ℓ1 and ℓ2 norms on the mean–variance model to promote sparse portfolio selection. We present an ℓ1/ℓ2 regularized sparse portfolio optimization model and provide financial insights regarding short positions and estimation errors. Then, we develop an efficient alternating direction method of multipliers (ADMM) method to solve it numerically. Due to the nonconvexity and noncoercivity of the ℓ1/ℓ2 term, we give the convergence analysis for the proposed ADMM based on the nonconvex optimization framework. Furthermore, we discuss an extension of the model to incorporate a more general ℓ1/ℓq regularization, where q>1. Moreover, we conduct numerical experiments on four stock datasets to demonstrate the effectiveness and superiority of the proposed model in promoting sparse portfolios while achieving the desired level of expected return.

Machine Learning for liquidity classification and its applications to portfolio selection

Liquidity refers to the ease of asset conversion into cash, playing a crucial role in investment decisions for achieving optimal returns. This study proposes a novel stock liquidity classification method using machine learning algorithms, trained, and tested on ten years of Brazilian stock market (B3) data. Achieving an accuracy of 99.2%, the classifier, when integrated with the mean-variance portfolio optimization model, reduces portfolio uncertainty by preventing an average of 11.5% of illiquid asset sales.

Application of Financial Mathematical Models Combined with Root Algorithms in Finance

Investors in the financial markets must deal with various hazards, for which they must create prudent investment portfolios and risk management plans. A multi-objective optimisation approach is proposed using the root algorithm to create a multi-objective root system growth model based on many clusters. An investment risk management optimisation model based on root system growth is built into the study using distributed decision-making. To create a multi-objective root algorithm-based portfolio optimisation model, the Markowitz mean-variance model and a multi-objective root algorithm are employed. Accordingto the findings, the multi-group multi-objective root system method has a real Pareto frontier solution that is more accessible, has a faster convergence rate, and has lower fitness values. The root algorithm’s solutions are workable, and the final risk values of 0.0105, 0.0082, and 0.4623 for the 2, 4, and 6 investment objectives are all in the low-risk class range. The optimal set of solutions discovered by the algorithm had better distributivity and convergence. The Hypervolume values for the multi-group multi-objective root algorithm were 5.5298 and 3.9628 for the dual-objective portfolio and the tri-objective portfolio of investment return costs, respectively. The findings of this study can guide the development of portfolio and risk management strategies.

Modeling of Mean-Value-at-Risk Investment Portfolio Optimization Considering Liabilities and Risk-Free Assets

This paper aims to design a quadratic optimization model of an investment portfolio based on value-at-risk (VaR) by entering risk-free assets and company liabilities. The designed model develops Markowitz’s investment portfolio optimization model with risk aversion. Model development was carried out using vector and matrix equations. The entry of risk-free assets and liabilities is essential. Risk-free assets reduce the loss risk, while liabilities accommodate a fundamental analysis of the company’s condition. The model can be applied in various sectors of capital markets worldwide. This study applied the model to Indonesia’s mining and energy sector. The application results show that risk aversion negatively correlates with the mean and VaR of the return of investment portfolios. Assuming that risk aversion is in the 5.1% to 8.2% interval, the maximum mean and VaR obtained for the next month are 0.0103316 and 0.0138270, respectively, while the minimum mean and VaR are 0.0102964 and 0.0137975, respectively. The finding of this study is that the vector equation for investment portfolio weights is obtained, which can facilitate calculating investment portfolio weight optimization. This study is expected to help investors control the quality of appropriate investment, especially in some stocks in Indonesia’s mining and energy sector.

Leveraging probability and statistical algorithms for enhanced financial risk management

This paper explores the foundations and applications of quantitative analysis in financial risk management. It examines the pivotal role of probability theory, statistical inference, and advanced algorithms in identifying, quantifying, and mitigating financial risks. Key concepts such as the Normal, Poisson, and Binomial distributions are discussed in the context of risk analysis, alongside statistical inference methods like hypothesis testing and confidence intervals. Furthermore, the paper investigates the application of portfolio optimization models, credit risk evaluation techniques, and market risk assessment methodologies in practical risk management scenarios. Additionally, it addresses the challenges posed by model risk, data quality, and regulatory compliance, emphasizing the need for rigorous validation, robust data governance, and ethical considerations in risk management practices. By integrating sophisticated quantitative techniques with real-world applications, financial institutions can enhance their ability to navigate the complexities of modern financial markets and achieve more effective risk management strategies.

On the sensitivity of some portfolio optimization models using interval analysis

On the sensitivity of some portfolio optimization models using interval analysis

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.

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.

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.

Research on Portfolio Optimization Model based on Machine Learning Algorithm in Stock Market

This study aims to explore portfolio optimization models based on machine learning algorithms in the stock market and evaluate their effectiveness and performance in practice. The paper combines various machine learning algorithms such as Long Short Term Memory Network (LSTM), Convolutional Neural Network (CNN), and Reinforcement Learning (RL) to design a complex and innovative portfolio optimization model. Through training and testing using historical stock data, the paper verifies the accuracy and yield performance of the model in predicting the direction of stock price change. The experimental results show that our model performs well in forecasting accuracy and yield, and can get higher returns under the same risk, with better risk-adjusted returns. In addition, the paper also discusses the advantages of multi-algorithm combination in portfolio optimization, and analyzes the practicability and operability of the model. Our research provides a new portfolio optimization method for investors in the stock market, and has important theoretical and practical significance.

Optimal Portfolio Analysis of Listed Companies in IDX 30

Investors face the dual considerations of return and risk when making investment decisions. Therefore, proper analysis is crucial, especially during the COVID-19 crisis, to achieve maximum returns while minimizing risk. This research used three portfolio optimization models, the Mean-Variance Model, the Mean-Absolute Deviation Model and the Value-at-Risk Model, to construct a stock portfolio. The findings indicated that the Mean-Variance Model can yield an expected return of 16.55% and a portfolio risk of 258.66%. The result from the Mean-Absolute Deviation Model was that the target return is 16%, along with a portfolio risk of 282.43%. Keywords: Portfolio Optimization, Mean-Variance, Mean Absolute Deviation, Value at Risk, R Language, IDX30

A robust ordered weighted averaging loss model for portfolio optimization

In this paper we will propose a Robust Ordered Weighted Averaging (ROWA) optimization model to find a portfolio according to different attitudes towards risk of a decision maker. The rationale of our model is supported by the idea of measuring risk through conditional means of losses from a database of past returns. The way in which these means of extreme losses affect to the final decision may be different according to the risk perception of the decision maker (scenarios). In this context, a compromise portfolio is identified to reconcile the admisible risk attitudes of a decision maker according to different paradigms. We will also link the robustness of the proposed solution with its efficiency from a multi-criterion decision making viewpoint (Pareto optimality). Both concepts have been connected previously in the literature in different contexts. The paper ends with an extensive numerical experiment in order to check the applicability of our model to real data on six financial markets.

Comparison of the Markowitz Model and Index Model in Capital Markets

This paper examines two widely used portfolio optimization models: the Markowitz Model (MM) and the Index Model (IM). We collected and processed historical data on ten stocks for 2001-2021 that included four different sectors, one P500 stock index, and a proxy for a risk-free rate (1-month Fed Funds rate). By computing all properly optimized inputs for the full Markowitz and index models, we find the regions allowing the portfolio under five additional realistic constraints. The study shows that the minimum variance combination and the maximum Sharp ratio are better than the Index Model. In addition, this paper further complements the empirical research of two models and provides some valuable investment suggestions for building the portfolio.