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Integration of asset preselection with appropriate portfolio optimization techniques can improve the performance of the portfolio optimization models. This paper morphed the potential asset selection and the optimal portfolio construction rather than focusing on one. A large volume of sample data from 25 stocks is used for the experiment from the National Stock Exchange, India, between January 2005 and December 2021. Initially, a 3-step screening approach, an asset selection method is applied to select potential assets. The 3-steps comprise data choice, fundamental screening, and the Long Short Term Memory model anticipating real-time stock prices to shortlist stocks with higher expected returns. The suggested approach is effective in determining the quality of assets. Further, the optimal asset allocation is done by introducing a novel exponentially weighted-mean-variance model. This exponential weighting scheme outperforms the classical Mean-Variance model when applied to the maximum Sharpe ratio model. The proposed model outperforms the five baseline techniques in terms of the Sharpe ratio and average potential returns and risks. Additionally, the proposed model's resilience across diversified time frames is tested through the incorporation of multiple time windows, demonstrating robustness of the performance. [ABSTRACT FROM AUTHOR]

Constructing the optimal portfolio by determining and selecting the best combinations of multiple portfolios is computationally challenging due to its exponential complexity. This paper considers the above issue and demonstrates an efficient portfolio selection method based on the sparse minimax Sharpe ratio model involving pre-selected stocks by an unsupervised machine learning approach. Different clustering techniques, such as k-means, fuzzy c-means, and ward linkage, have been used to cluster the stock market data into a finite number of clusters created based on their return rates and related risk levels. Several validity indices have been applied to arrive at the most appropriate number of groups to opt into the portfolio. Further, the sparse minimax Sharpe ratio model is implemented for the selection of the most efficient portfolio. Finally, the efficacy of the developed technique is justified and validated by illustrating a numerical example based on the historical dataset taken from the Bombay stock exchange (BSE), India. [ABSTRACT FROM AUTHOR]

As a model-free algorithm, deep reinforcement learning (DRL) agent learns and makes decisions by interacting with the environment in an unsupervised way. In recent years, DRL algorithms have been widely applied by scholars for portfolio optimization in consecutive trading periods, since the DRL agent can dynamically adapt to market changes and does not rely on the specification of the joint dynamics across the assets. However, typical DRL agents for portfolio optimization cannot learn a policy that is aware of the dynamic correlation between portfolio asset returns. Since the dynamic correlations among portfolio assets are crucial in optimizing the portfolio, the lack of such knowledge makes it difficult for the DRL agent to maximize the return per unit of risk, especially when the target market permits short selling (i.e., the US stock market). In this research, we propose a hybrid portfolio optimization model combining the DRL agent and the Black-Litterman (BL) model to enable the DRL agent to learn the dynamic correlation between the portfolio asset returns and implement an efficacious long/short strategy based on the correlation. Essentially, the DRL agent is trained to learn the policy to apply the BL model to determine the target portfolio weights. In this model, we formulate a specific objective function based on the environment's reward function, which considers the return, risk, and transaction scale of the portfolio. Our DRL agent is trained by propagating the objective function's gradient to the policy function of our DRL agent. To test our DRL agent, we construct the portfolio based on all the Dow Jones Industrial Average constitute stocks. Empirical results of the experiments conducted on real-world United States stock market data demonstrate that our DRL agent significantly outperforms various comparison portfolio choice strategies and alternative DRL frameworks by at least 42% in terms of accumulated return. In terms of the return per unit of risk, our DRL agent significantly outperforms various comparative portfolio choice strategies and alternative strategies based on other machine learning frameworks. [ABSTRACT FROM AUTHOR]

Researchers usually specify risk aversion coefficients from 1 (lowest) to M (highest) for a portfolio to indicate active or passive approaches. How effective is this practice? Recent studies suggest that the global minimum variance portfolio (GMVP) is statistically equivalent to portfolios with extensive risk aversion coefficients (the GMVP-equivalent). Expressing the risk aversion coefficient as a Taylor series of the target return and efficient set constants, we generalize the previous result to the non-GMVP-equivalents and segment mean-variance portfolios according to a hierarchy of risk aversion coefficients. In this paper, we show that hierarchical risk aversion coefficients are superior to isometric attributes. [ABSTRACT FROM AUTHOR]

Pension funds’ investments are increasingly linked to the changes in climate and environmental protection. The integration of environmental, social and governance (ESG) factors into their investment process is still varying in different countries and regions. The limited number of studies on the application of the ESG investment approach by private pension funds in Bulgaria shows that the country lags behind the trends in Europe. Although pension funds do not perceive environmental investments as riskier or less profitable than conventional ones, many of them remain cautious due to the shorterterm financial performance data of green assets. To achieve adequate retirement savings and a high replacement rate saving “more and for longer” is not enough. As far as the topic of portfolio investment performance is on the agenda, one would reasonably ask what the reflection of environmental investments would be on the widely diversified portfolios of pension funds in the country. The present research is dedicated to а mean-variance (MV) portfolio optimization involving a selection of conventional and green assets under different constraints and “shades of green” by using historical data. The empirical results from the portfolio optimizations performed shed light on the questions raised and complement the motivational spectrum “in favour of” or “against” environmental investment. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The challenge of selecting strategies to adapt to climate change is complicated by the presence of irreducible uncertainties regarding future conditions. Decisions regarding long-term investments in conservation actions contain significant risk of failure due to these inherent uncertainties. To address this challenge, decision makers need an arsenal of sophisticated but practical tools to help guide spatial conservation strategies. Theory asserts that managing risks can be achieved by diversifying an investment portfolio to include assets -- such as stocks and bonds -- that respond inversely to one another under a given set of conditions. We demonstrate an approach for formalizing the diversification of conservation assets (land parcels) and actions (restoration, species reintroductions) by using correlation structure to quantify the degree of risk for any proposed management investment. We illustrate a framework for identifying future habitat refugia by integrating species distribution modeling, scenarios of climate change and sea level rise, and impacts to critical habitat. Using the plains coqui (Eleutherodactylus juanariveroi), an endangered amphibian known from only three small wetland populations on Puerto Rico's coastal plains, we evaluate the distribution of potential refugia under two model parameterizations and four future sea-level rise scenarios. We then apply portfolio theory using two distinct objective functions and eight budget levels to inform investment strategies for mitigating risk and increasing species persistence probability. Models project scenario-specific declines in coastal freshwater wetlands from 2% to nearly 30% and concurrent expansions of transitional marsh and estuarine open water. Conditional on the scenario, island-wide species distribution is predicted to contract by 25% to 90%. Optimal portfolios under the first objective function -- benefit maximization -- emphasizes translocating frogs to existing protected areas rather than investing in the protection of new habitat. Alternatively, optimal strategies using the second objective function -- a risk-benefit tradeoff framework -- include significant investment to protect parcels for the purpose of reintroduction or establishing new populations. These findings suggest that leveraging existing protected areas for species persistence, while less costly, may contain excessive risk and could result in diminished conservation benefits. Although our modeling includes numerous assumptions and simplifications, we believe this framework provides useful inference for exploring resource dynamics and developing robust adaptation strategies using an approach that is generalizable to other conservation problems which are spatial or portfolio in nature and subject to unresolvable uncertainty. [ABSTRACT FROM AUTHOR]

This paper proposes analytic forms of portfolio conditional value at risk (CoVaR) and the mean of the portfolio loss conditional on it being in financial distress (CoCVaR) on the normal tempered stable market model. Since CoCVaR captures the relative risk of the portfolio with respect to a benchmark return, we apply it to relative portfolio optimization. Moreover, we derive analytic forms for the marginal contribution to CoVaR and the marginal contribution to CoCVaR. We discuss the Monte-Carlo simulation method for calculating CoCVaR and the marginal contributions of CoVaR and CoCVaR. We provide an empirical illustration to show relative portfolio optimization with 30 stocks included in the Dow Jones Industrial Average under distressed conditions. Finally, we apply the risk budgeting method to reduce the CoVaR and CoCVaR of the portfolio based on the marginal contributions to CoVaR and CoCVaR. [ABSTRACT FROM AUTHOR]

In mean-variance portfolio optimization, multi-index models often accelerate computation, reduce input requirements, facilitate understanding, and allow easy adjustment to changing conditions more effectively than full covariance matrix estimation in many situations. In this paper, we develop a multi-index model-based portfolio optimization approach that takes into account aspects of the environment, social responsibility and corporate governance (ESG). Investments in assets related to ESG have recently grown, attracting interest from both academic research and investment fund practice. Various literature strands in this area address the theoretical and empirical relation among return, risk and ESG. Our portfolio optimization approach is flexible enough to take these literature strands into account and does not require large-scale covariance matrix estimation. An extension of our approach even allows investors to empirically discriminate among the literature strands. A case study demonstrates the application of our portfolio optimization approach. [ABSTRACT FROM AUTHOR]

This paper considers the expected utility portfolio optimization problem with initial-time and intermediate-time Value-at-Risk constraints on terminal wealth. We derive the closed-form solutions which are optimal among all feasible controls at initial time, i.e., precommitted strategies. Moreover, the precommitted strategies are also optimal at the intermediate time for "bad" market states. A contingent claim on Merton's portfolio is constructed to replicate the optimal portfolio. We find that risk management with intermediate-time risk constraints is prudent in hedging "bad" intermediate market states and performs significantly better than the one terminal-wealth risk constraint solutions under the relative loss ratio measure. [ABSTRACT FROM AUTHOR]

Traditional portfolio construction primarily revolves around a bi-objective approach, focusing on minimizing portfolio variance while maximizing expected returns. However, this approach leaves out other objectives that could interest decision makers. In this work, we incorporate an extra objective, namely the environmental, social, and governance index (ESG), as a secondary objective. This addition empowers investors to customize their portfolios by defining explicit trade-off thresholds between expected returns and risk, considering the ESG index. To achieve this goal, we make use of external archiving techniques and evolutionary algorithms. In particular, we first find approximate solutions to the bi-objective problem; then, we look for efficient solutions for ESG. We tested our approach with data on the Dow Jones, S&P500, and Nasdaq100 from Yahoo Finance. The results show that the proposed methodology can identify portfolios with good returns and risks considering ESG. [ABSTRACT FROM AUTHOR]

Every year agribusinesses develop and market new seed varieties with traits desirable for different planting environments. When agribusinesses experiment the new varieties at different farms, data is generated about the performance of these new seed varieties. However, farmers do not have a decision support tool to process the vast amount of yield performance data to make an informed seed variety selection decision for their farm. An informed decision requires accurate estimation of yield performances of seed varieties on the targeted farmland and balancing trade-offs between the expected yield and the risk associated with the seed varieties selected to grow. This research uses a real data set provided by Syngenta—an agribusiness—to create a decision-support tool. The data set used in this research contains yield information of different soybean varieties experimented at different farms located in the Midwest of the US, as well as information on location, soil, and weather conditions prevailing in those farms. In addition to this data, we also surveyed soybean farmers to understand their preferences and current practices in choosing seed varieties to grow in their farms. We are the first to capture and document farmers' preferences and practices in selecting and growing soybean varieties. The data collected from the survey enabled us to compare the results emerging from the proposed methodology with the status quo practices. Using the Syngenta data and survey responses, this paper proposes an analytics framework that integrates machine learning, clustering, simulation, and portfolio optimization to optimally select soybean varieties to grow at the target farm. We choose a machine learning model, which simulates the yield performance of soybean varieties under different plausible weather scenarios derived from the neighborhood of the target farm. The simulated yields are then used to estimate parameters in a portfolio optimization formulation that selects the optimal portfolio of seed varieties to grow at the target farm. The main methodological contribution of this research is in the development of an approach that integrates machine learning, clustering, simulation, and portfolio optimization to help farmers make an important decision. Specifically, we introduce a novel data-driven simulation-based approach to estimate the parameters needed to solve a portfolio optimization problem. Our analysis indicates that an average farmer will gain as much as $177,369 per year in revenue by utilizing the analytics framework introduced in this research. The methodology developed in this research can be applied to variety selection decisions for other crops and influence farming practice positively. By embracing the machine learning and analytics powered framework introduced in this paper, agribusinesses can position themselves as the innovation leader and create business value by unleashing the potential of the scientific discoveries of agronomy to offer tailored farming decision support to individual farmers. [ABSTRACT FROM AUTHOR]

This study explores the concept of reference dependence in decision-making behavior, particularly in the realm of investment portfolios. Previous research has established that an individual's own circumstances and societal surroundings play a pivotal role in shaping their perception of risk. However, there has been limited exploration into the dynamic nature of reference points in investment decision-making. To address this gap in the literature, the current study is aimed at investigating the performances of relevant dynamic reference points in investment portfolios. In doing so, the personal experience and upward pacesetter reference points are established, and a comparative robust portfolio model incorporating the CVaR measure is utilized. The impacts of different reference behaviors on the proposed portfolio model's performance are also examined. Furthermore, to enhance the portfolio model's out-of-sample performance, a scenario formation method that leverages clustering techniques is proposed. The performances of several clustering methods, including classic hierarchical and spectral clustering, as well as reciprocal-nearest-neighbors supported clustering, are compared. The empirical results indicate that the positive behavior of the personal experience reference point yields a better expected return, while the negative behavior exhibits a lower level of risk. Moreover, the results suggest that the utilization of spectral clustering can significantly improve the out-of-sample performance of the proposed robust portfolio model. [ABSTRACT FROM AUTHOR]

Forecasting stock prices, a task complicated by the inherent volatility of the stock market, poses a significant challenge. The ability to accurately forecast stock prices is crucial, as it provides investors with crucial insights, enabling them to make informed strategic decisions. In this paper, we propose a novel investment strategy that relies on predicting stock prices. Our approach utilizes a hybrid predictive model that combines light gradient-boosting machine (LightGBM) and extreme gradient boosting (XGBoost). This model is designed to generate short to medium-term forecasts for a wide range of stocks. The strategy has shown promising results, surpassing the local market indices used as benchmarks in terms of both risk and return. Our findings demonstrate the strategy's effectiveness in both upward and downward market trends, underscoring its potential as a robust tool for portfolio management in diverse market conditions. [ABSTRACT FROM AUTHOR]

Recent trends in portfolio management emphasize the importance of reducing carbon footprints and aligning investments with sustainable practices. This paper introduces Sensitivity Value-at-Risk (SensitivityVaR), an advanced distortion risk measure that combines Value-at-Risk (VaR) and Expected Shortfall (ES) with the Cornish–Fisher expansion. SensitivityVaR provides a more robust framework for managing risk, particularly under extreme market conditions. By incorporating first- and second-order distorted stochastic dominance criteria, we enhance portfolio decarbonization strategies, aligning financial objectives with environmental targets such as the Paris Agreement's goal of a 7% annual reduction in carbon intensity from 2019 to 2050. Our empirical analysis evaluates the impact of integrating carbon intensity data—including Scope 1, Scope 2, and Scope 3 emissions—on portfolio optimization, focusing on key sectors like technology, energy, and consumer goods. The results demonstrate the effectiveness of SensitivityVaR in managing both risk and environmental impact. The methodology led to significant reductions in carbon intensity across different portfolio configurations, while preserving competitive risk-adjusted returns. By optimizing tail risks and limiting exposure to carbon-intensive assets, this approach produced more balanced and efficient portfolios that aligned with both financial and sustainability goals. These findings offer valuable insights for institutional investors and asset managers aiming to integrate climate considerations into their investment strategies without compromising financial performance. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We propose a novel ranking-based approach combined with long short-term memory (LSTM) networks to generate investor views in the well-known Black – Litterman (BL) model. This approach can effectively distinguish high-quality assets with the potential for future growth. In addition, it discards any information contained in the absolute differences between asset prices to mitigate the negative impact of these estimation errors on the BL model. Our findings suggest that the BL model based on our approach can achieve better out-of-sample performance. [ABSTRACT FROM AUTHOR]

The Financial Services Authority (OJK) has issued Regulation of the Financial Services Authority of the Republic of Indonesia Number 5 Year 2023. Article 11 paragraph 1d explains the limitations of assets allowed in the form of investment, investment in the form of shares listed on the stock exchange for each issuer is a maximum of 10% of the total investment and a maximum of 40% of the total investment. The investment manager of a life insurance company needs to adjust its investment portfolio. In 1991, Konno and Yamazaki proposed an approach to the portfolio selection problem with Mean Absolute Deviation (MAD) model. This model can be solved using linear programming, effectively solving high-dimensional portfolio optimization problems. Another problem in stock portfolio formation is that the ever-changing financial markets demand the development of models to understand and forecast stock price behavior. One method that has been widely used to model stock price movements is the generalized Wiener Process. The generalized Wiener process provides a framework that can accommodate the stochastic nature of stock price changes, thus allowing portfolio managers to be more sensitive to unanticipated market fluctuations. The stock price change model using the Generalized Wiener Process is very good at predicting stock price changes. The results of this stock price prediction can then be used to find the optimal portfolio using the MAD model. The portfolio optimization problem with the MAD model can be solved using linear programming to obtain the optimal stock portfolio for life insurance companies.

This research aims to enhance portfolio selection by integrating machine learning regression algorithms for predicting stock returns with various risk measures. These measures include mean-value-at-risk (VaR) variance (Var), semi-variance mean-absolute-deviation (MAD) and conditional value-at-risk (C-VaR). Addressing gaps in existing literature. Traditional methods lack adaptability to dynamic market conditions. We propose a hybrid approach optimized by genetic algorithms. The study employs multiple machine learning models. These include Random Forest, AdaBoost XGBoost, Support Vector Machine Regression (SVR) K-Nearest Neighbors (KNN) and Artificial Neural Network (ANN). These models are used to forecast stock returns. Utilizing monthly data from the Tehran Stock Exchange, the results indicate that the genetic algorithm prediction model combined with mean-VaR, Var semi-variance and MAD, produces the most efficient portfolios. These portfolios offer superior returns with minimized risk compared to other models. This hybrid strategy provides a robust and efficient method for investors aiming to optimize returns while managing risk effectively. To implement this approach successfully it is crucial to balance investments. This involves both traditional and alternative asset classes, ensuring diversification. It also capitalizes on market opportunities. Regular review and adjustment of fund allocation are essential. Maintain an optimized strategy for maximum returns and minimal risk.

Abstract Financial Portfolio Optimization Problem (FPOP) is a cornerstone in quantitative investing and financial engineering, focusing on optimizing assets allocation to balance risk and expected return, a concept evolving since Harry Markowitz’s 1952 Mean-Variance model. This paper introduces a novel meta-heuristic approach based on the Black Widow Algorithm for Portfolio Optimization (BWAPO) to solve the FPOP. The new method addresses three versions of the portfolio optimization problems: the unconstrained version, the equality cardinality-constrained version, and the inequality cardinality-constrained version. New features are introduced for the BWAPO to adapt better to the problem, including (1) mating attraction and (2) differential evolution mutation strategy. The proposed BWAPO is evaluated against other metaheuristic approaches used in portfolio optimization from literature, and its performance demonstrates its effectiveness through comparative studies on benchmark datasets using multiple performance metrics, particularly in the unconstrained Mean-Variance portfolio optimization version. Additionally, when encountering cardinality constraint, the proposed approach yields competitive results, especially noticeable with smaller datasets. This leads to a focused examination of the outcomes arising from equality versus inequality cardinality constraints, intending to determine which constraint type is more effective in producing portfolios with higher returns. The paper also presents a comprehensive mathematical model that integrates real-world constraints such as transaction costs, transaction lots, and a dollar-denominated budget, in addition to cardinality and bounding constraints. The model assesses both equality/inequality cardinality constraint versions of the problem, revealing that the inequality constraint tends to offer a wider range of feasible solutions with increased return potential.

Abstract Portfolio allocation represents a significant challenge within financial markets, traditionally relying on correlation or covariance matrices to delineate relationships among stocks. However, these methodologies assume time stationarity and only capture linear relationships among stocks. In this study, we propose to substitute the conventional Pearson’s correlation or covariance matrix in portfolio optimization with a similarity matrix derived from the signature. The signature, a concept from path theory, provides a unique representation of time series data, encoding their geometric patterns and inherent properties. Furthermore, we undertake a comparative analysis of network structures derived from the correlation matrix versus those obtained from the signature-based similarity matrix. Through numerical evaluation on the Standard & Poor’s 500, we assess that portfolio allocation utilizing the signature-based similarity matrix yielded superior results in terms of cumulative log-returns and Sharpe ratio compared to the baseline network approach based on Pearson’s correlation. This assessment was conducted across various portfolio optimization strategies. This research contributes to portfolio allocation and financial network representation by proposing the use of signature-based similarity matrices over traditional correlation or covariance matrices.

The metaverse, a virtual universe in which individuals and companies can interact, has become of paramount importance in China in recent years. While the metaverses are still in their infancy, there has been a growing interest and influx of capital into these universes. Shariah-compliant corporations have been gradually attracting significant funds from Islamic countries, given the growing strong engagement and trade. Similarly, metaverse corporations have been gaining significant sizes in the Chinese market and have become cornerstones of the investment landscape. For Islamic investors, questions arise whether these new metaverse corporations provide better returns given the massive hype and media attention they have attracted, and whether a portfolio investment into these corporations deliver the benefits promised. The article provides a comparative analysis between Chinese Islamic metaverse and Shariah-compliant enterprises, where all enterprises have either A or H-shares. The performance analysis over a timespan of 10 years demonstrates that the most optimal portfolios have similar expected returns while general Shariah-compliant enterprises provide significantly lower risks as compared to the metaverse ones. This implies that Shariah-compliant enterprises provide significantly more value for the risk they are attributed and are more sustainable.

This investigation explores Reinforcement Learning (RL) for dynamic portfolio optimization with risk assessment. The challenges include market complexity, uncertain reactions, and regulatory requirements for risk-averse decisions. Our solution leverages Bayesian Neural Network (BNN) to capture uncertainties. We successfully implemented a risk-averse Reinforcement Learning algorithm, achieving 18 percent lower risk. Reinforcement Learning with risk-aversion shows promise for optimizing portfolios for risk-averse investors.

Portfolio optimization plays a crucial role in investment decision-making by balancing risk and return objectives. With the aim of improving portfolio performance, while enhancing risk management, this literature review explores traditional and artificial intelligence-powered approaches for portfolio optimization. From the traditional methods of portfolio optimization, methods such as random matrix theory, shrinkage estimators, correlation asymmetries and partial correlation networks are presented. While, from the artificial intelligence realm, techniques such as machine learning efficient frontiers, performance-based regularization, neural network predictors and deep learning models for direct optimization of portfolio Sharpe ratio are highlighted. Intertwining the traditional methods, with artificial intelligence techniques, this review highlights relevant portfolio optimization research useful for academics and practitioners alike.

Financial Portfolio Optimization Problem (FPOP) is a cornerstone in quantitative investing and financial engineering, focusing on optimizing assets allocation to balance risk and expected return, a concept evolving since Harry Markowitz's 1952 Mean-Variance model. This paper introduces a novel meta-heuristic approach based on the Black Widow Algorithm for Portfolio Optimization (BWAPO) to solve the FPOP. The new method addresses three versions of the portfolio optimization problems: the unconstrained version, the equality cardinality-constrained version, and the inequality cardinality-constrained version. New features are introduced for the BWAPO to adapt better to the problem, including (1) mating attraction and (2) differential evolution mutation strategy. The proposed BWAPO is evaluated against other metaheuristic approaches used in portfolio optimization from literature, and its performance demonstrates its effectiveness through comparative studies on benchmark datasets using multiple performance metrics, particularly in the unconstrained Mean-Variance portfolio optimization version. Additionally, when encountering cardinality constraint, the proposed approach yields competitive results, especially noticeable with smaller datasets. This leads to a focused examination of the outcomes arising from equality versus inequality cardinality constraints, intending to determine which constraint type is more effective in producing portfolios with higher returns. The paper also presents a comprehensive mathematical model that integrates real-world constraints such as transaction costs, transaction lots, and a dollar-denominated budget, in addition to cardinality and bounding constraints. The model assesses both equality/inequality cardinality constraint versions of the problem, revealing that the inequality constraint tends to offer a wider range of feasible solutions with increased return potential. [ABSTRACT FROM AUTHOR]

This survey aims to provide insightful and objective perspectives on the research history of quantitative portfolio management strategies with suggestions for the future of research. The relevant literature can be clustered into four broad themes: portfolio optimization, risk-parity, style integration, and machine learning. Portfolio optimization attempts to find the optimal trade-off of future returns per unit of risk. Risk-parity attempts to match the exposure of various asset classes such that no single asset class dominates portfolio risk. Style integration combines risk factors on a security level such that rebalancing differences cancel out. Finally, machine learning utilizes large arrays of tunable parameters to predict future asset behavior and solve non-convex optimization problems. We conclude that machine learning will likely be the focus of future research. [ABSTRACT FROM AUTHOR]

The Average Oracle, a simple and very fast covariance filtering method, is shown to yield superior Sharpe ratios than the current state-of-the-art (and complex) methods, Dynamic Conditional Covariance coupled to Non-Linear Shrinkage (DCC-NLS). We pit all the known variants of DCC-NLS (quadratic shrinkage, gross-leverage or turnover limitations, and factor-augmented NLS) against the Average Oracle in large-scale randomized experiments. We find generically that while some variants of DCC-NLS sometimes yield the lowest average realized volatility, albeit with a small improvement, their excessive gross leverage and investment concentration, and their 10-time larger turnover contribute to smaller average portfolio returns, which mechanically result in smaller realized Sharpe ratios than the Average Oracle. We also provide simple analytical arguments about the origin of the advantage of the Average Oracle over NLS in a changing world. [ABSTRACT FROM AUTHOR]

Portfolio optimization is an important financial task that has received widespread attention in the field of artificial intelligence. In this paper, a novel deep portfolio optimization (DPO) framework was proposed, combining deep learning and reinforcement learning with modern portfolio theory. DPO not only has the advantages of machine learning methods in investment decision-making, but also retains the essence of modern portfolio theory in portfolio optimization. Additionaly, it was crucial to simultaneously consider the time series and complex asset correlations of financial market information. Therefore, in order to improve DPO performance, features of assets information were extracted and fused. In addition, a novel risk-cost reward function was proposed, which realized optimal portfolio decision-making considering transaction cost and risk factors through reinforcement learning. Our results showed the superiority and generalization of the DPO framework for portfolio optimization tasks. Experiments conducted on two real-world datasets validated that DPO achieved the highest accumulative portfolio value compared to other strategies, demonstrating strong profitability. Its Sharpe ratio and maximum drawdown also performed excellently, indicating good economic benefits and achieving a trade-off between portfolio returns and risk. Additionally, the extraction and fusion of financial information features can significantly improve the applicability and effectiveness of DPO. [ABSTRACT FROM AUTHOR]

A novel method of portfolio selection is provided with further higher moments, filtering with fundamentals in intelligent computing resources. The Evolutional Portfolio Optimization System (EPOS) evaluates unobtrusive relations from a vast amount of accounting and financial data, excluding hoax and noise, to select the optimal portfolio. The fundamental question of Free Will, limited in investment selection, is answered through a new philosophical approach. [ABSTRACT FROM AUTHOR]

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Tsallis entropy is a flexible device to measure indeterminacy of uncertain sets. A formula is obtained to calculate Tsallis entropy of uncertain sets via inversion of membership functions. Also, by considering Tsallis entropy as a risk measure, we optimize portfolio selection problems via mean-entropy models. [ABSTRACT FROM AUTHOR]

Understanding and modeling of agent's risk/reward preferences is a central problem in various applications of risk management including investment science and portfolio theory in particular. One of the approaches is to axiomatically define a set of performance measures and to use a benchmark to identify a particular measure from that set by either inverse optimization or functional dominance. For example, such a benchmark could be the rate of return of an existing attractive financial instrument. This work introduces deviation and drawdown measures that incorporate rates of return of indicated financial instruments (benchmarks). For discrete distributions and discrete sample paths, portfolio problems with such measures are reduced to linear programs and solved based on historical data in cases of a single benchmark and three benchmarks used simultaneously. The optimal portfolios and corresponding benchmarks have similar expected/cumulative rates of return in sample and out of sample, but the former are considerably less volatile. [ABSTRACT FROM AUTHOR]

We derive a Clark-Ocone-Haussmann (COH) type formula under a change of measure for L 1 -canonical additive processes, providing a tool for representing financial derivatives under a risk-neutral probability measure. COH formulas are fundamental in stochastic analysis, providing explicit martingale representations of random variables in terms of their Malliavin derivatives. In mathematical finance, the COH formula under a change of measure is crucial for representing financial derivatives under a risk-neutral probability measure. To prove our main results, we use the Malliavin-Skorohod calculus in L 0 and L 1 for additive processes, as developed by Di Nunno and Vives (2017). An application of our results is solving the local risk minimization (LRM) problem in financial markets driven by pure jump additive processes. LRM, a prominent hedging approach in incomplete markets, seeks strategies that minimize the conditional variance of the hedging error. By applying our COH formula, we obtain explicit expressions for locally risk-minimizing hedging strategies in terms of Malliavin derivatives under the market model underlying the additive process. These formulas provide practical tools for managing risks in financial market price fluctuations with L 1 -additive processes. [ABSTRACT FROM AUTHOR]

Recently, liquidity issues in financial markets and portfolio asset management have attracted much attention among investors and scholars, fuelling a stream of research devoted to exploring the role of liquidity in investment decisions. In this paper, we aim to investigate the effects of introducing liquidity in portfolio optimization problems. For this purpose, first we consider three volume-based liquidity measures proposed in the literature and we build a new one particularly suited to portfolio optimization. Secondly, we formulate an extended version of the Markowitz portfolio selection problem, named mean–variance–liquidity, wherein the goal is to minimize the portfolio variance subject to the usual constraint on the expected portfolio return and an additional constraint on the portfolio liquidity. Thirdly, we consider a sensitivity analysis, with the aim to assess the trade-offs between liquidity and return, on the one hand, and between liquidity and risk, on the other hand. In the second part of the paper, the portfolio optimization framework is applied to a dataset of US ETFs comprising both standard and alternative, often illiquid, investments. The analysis is carried out with all the liquidity measures considered, allowing us to shed light on the relationships among risk, return and liquidity. Finally, we study the effects of the introduction of a Bitcoin ETF, as an asset with an extremely high expected return and risk. [ABSTRACT FROM AUTHOR]

In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by n-dimensional Brownian motions. At first, we derive a Hamilton–Jacobi–Bellman equation including the correlations among the standard Brownian motions. We use an approximation method for the optimization of portfolios. With such approximation, the value function is analyzed using the first-order terms of expansion of the utility function in the powers of time to the horizon. The error of this approximation is controlled using the second-order terms of expansion of the utility function. It is also shown that the one-dimensional version of this analysis corresponds to a known result in the literature. We also generate a close-to-optimal portfolio near the time to horizon using the first-order approximation of the utility function. It is shown that the error is controlled by the square of the time to the horizon. Finally, we provide an approximation scheme to the value function for all times and generate a close-to-optimal portfolio. [ABSTRACT FROM AUTHOR]

In this paper, we consider the issue of solution uniqueness of the mean-deviation portfolio optimization problem and its inverse for asset returns distributed over a finite number of scenarios. Due to the asymmetry of returns, the risk is assessed by a general deviation measure introduced by Rockafellar et al. [(2006b) Optimality conditions in portfolio analysis with general deviation measures, Mathematical Programming 108, 515–540] instead of the standard deviation as in the classical Markowitz optimization problem. We demonstrate that, in general, one cannot expect the uniqueness of Pareto-optimal profit sharing in cooperative investment and the uniqueness of solutions in the mean-deviation Black–Litterman asset allocation model. For a large class of deviation measures, we provide a resolution of the above nonuniqueness issues based on the principle of law-invariance. We provide several examples illustrating the nonuniqueness and the law-invariant solution. [ABSTRACT FROM AUTHOR]

Portfolio optimization has long been a challenging proposition and a widely studied topic in finance and management. It involves selecting and allocating the right assets according to the desired objectives. It has been found that this nonlinear constraint problem cannot be effectively solved using a traditional approach. This paper covers and compares quantum-inspired versions of four popular evolutionary techniques with three benchmark datasets. Genetic algorithm, differential evolution, particle swarm optimization, ant colony optimization, and their quantum-inspired incarnations are implemented, and the results are compared. Experiments have been carried out with more than 10 years of stock price data from NASDAQ, BSE, and Dow Jones. This work proposes several enhancements to allocate funds efficiently, such as improved crossover techniques and dynamic and adaptive selection of parameters. Furthermore, it is observed that the quantum-inspired techniques outperform the classical counterparts. [ABSTRACT FROM AUTHOR]

This research introduces min-max portfolio optimization models that incorporating transaction costs and focus on robust Entropic value-at-risk. This study offers a unified approach to handl the distribution of random parameters that affect the reward and risk aspects. Utilizing the duality theorem, the study transforms the optimization models into manageable forms, thereby accommodating the underlying random variables' discrete box and ellipsoidal distributions. The impact of transaction costs on optimal portfolio selection is examined through numerical examples under a robust return-risk framework. The results underscore the importance of the proposed model in safeguarding capital and reducing exposure to extreme risks, thus outperforming other strategies documented in the literature. This demonstrates the model's effectiveness in balancing maximizing returns and minimizing potential losses, making it a valuable tool for investors that seek to navigate uncertain financial markets. [ABSTRACT FROM AUTHOR]

The metaverse, a virtual universe in which individuals and companies can interact, has become of paramount importance in China in recent years. While the metaverses are still in their infancy, there has been a growing interest and influx of capital into these universes. Shariah-compliant corporations have been gradually attracting significant funds from Islamic countries, given the growing strong engagement and trade. Similarly, metaverse corporations have been gaining significant sizes in the Chinese market and have become cornerstones of the investment landscape. For Islamic investors, questions arise whether these new metaverse corporations provide better returns given the massive hype and media attention they have attracted, and whether a portfolio investment into these corporations deliver the benefits promised. The article provides a comparative analysis between Chinese Islamic metaverse and Shariah-compliant enterprises, where all enterprises have either A or H-shares. The performance analysis over a timespan of 10 years demonstrates that the most optimal portfolios have similar expected returns while general Shariah-compliant enterprises provide significantly lower risks as compared to the metaverse ones. This implies that Shariah-compliant enterprises provide significantly more value for the risk they are attributed and are more sustainable. [ABSTRACT FROM AUTHOR]

Stock selection is a crucial step for investors when constructing a stock portfolio. Selecting stocks becomes challenging when stock data is vast. A portfolio with improper stock weighting is more likely to be suboptimal. This research aims to construct a stock portfolio, where stock selection is based on the results of stock segmentation using prototype-based approach, as well as to optimize the portfolio using the Mean-Variance method. The data used includes the return and the trading volume of active stocks listed on the Indonesia Stock Exchange 2022, collected from Yahoo Finance. The result is a portfolio consisting of 12 stocks, with each stock representing a cluster combination derived from cross-sectional, histogram, and time series data segmentation. The portfolio optimization produces the weight of every stock that corresponds to the Sharpe ratio and risk aversion. Stocks with the highest Sharpe ratio are given the highest weight, while those with positive weight are given the smaller weight as risk aversion level increases. [ABSTRACT FROM AUTHOR]

We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unified viewpoint on the general problem classes and models, and we give concrete examples from diverse application fields such as signal and image processing, portfolio selection, and machine learning. The paper discusses general-purpose modeling techniques and broadly applicable as well as problem-specific exact and heuristic solution approaches. While our perspective is that of mathematical optimization, a main goal of this work is to reach out to and build bridges between the different communities in which cardinality optimization problems are frequently encountered. In particular, we highlight that modern mixed-integer programming, which is often regarded as impractical due to the commonly unsatisfactory behavior of black-box solvers applied to generic problem formulations, can in fact produce provably high-quality or even optimal solutions for cardinality optimization problems, even in large-scale real-world settings. Achieving such performance typically involves drawing on the merits of problem-specific knowledge that may stem from different fields of application and, e.g., can shed light on structural properties of a model or its solutions, or can lead to the development of efficient heuristics. We also provide some illustrative examples. [ABSTRACT FROM AUTHOR]

We propose a portfolio optimization method with a multi-trend objective and an accelerated quasi-Newton method (MTO-AQNM). It leverages a BFGS-based quasi-Newton algorithm and incorporates an ℓ 1 regularization term and the self-funding constraint. The MTO is designed to identify multiple trend reversals. Different trend reversals are asymmetric, and we hoped to extract rich and effective information from them. The AQNM adopts the BFGS method with the Wolfe conditions, which reduces computational complexity and improves convergence speed. We wanted to evaluate the performance of our algorithm through financial markets that were asymmetric in all respects. To this end, we conducted comprehensive experimental approaches on six benchmark data sets of real-world financial markets that were asymmetric in time, frequency, and asset type. Our method demonstrated superior performance over other state-of-the-art competitors across several mainstream evaluation metrics. [ABSTRACT FROM AUTHOR]

This paper proposes three machine learning-based uncertainty set construction methods and a novel uncertainty quantification method for robustness-based optimization. The proposed methods are capable of capturing all possible types of uncertainties in the form of sparse point and/or interval data and efficiently quantify uncertainty in robustness-based optimization. In contrast to traditional approaches that rely on expert opinion or assumptions to construct uncertainty sets, our methods leverage machine learning algorithms to extract uncertainty patterns from historical data and effectively capture epistemic uncertainty in input variables. Another challenge in existing robustness-based optimization under epistemic uncertainty is the high computational cost associated with the iterative method of epistemic analysis. Moreover, these methods struggle with uncertainty sets containing a mixture of point and interval data. To overcome these limitations, we propose a unified probabilistic approach that utilizes maximum likelihood estimation to efficiently quantify uncertainty, regardless of the data form. Using the proposed methods, we introduce new approaches for robustness-based portfolio optimization (RPO) and multidisciplinary design optimization (RO/MDO), namely the worst-case maximum likelihood estimation (WMLE)-based single-loop RPO and WMLE-based RO/MDO approach, respectively. Illustrated through applications to minimum variance portfolios, our methods consistently demonstrate significant improvements over established formulations in terms of both return and risk. Additionally, when applied to a complex multidisciplinary engineering design, the WMLE-based RO/MDO approach showcases a computationally efficient solving technique, yielding more realistic results than the existing methodologies. [ABSTRACT FROM AUTHOR]

This paper will outline the functionality available in the CovRegpy package which was written for actuarial practitioners, wealth managers, fund managers, and portfolio analysts in the language of Python 3.11. The objective is to develop a new class of covariance regression factor models for covariance forecasting, along with a library of portfolio allocation tools that integrate with this new covariance forecasting framework. The novelty is in two stages: the type of covariance regression model and factor extractions used to construct the covariates used in the covariance regression, along with a powerful portfolio allocation framework for dynamic multi-period asset investment management. The major contributions of package CovRegpy can be found on the GitHub repository for this library in the scripts: CovRegpy.py , CovRegpy_DCC.py , CovRegpy_RPP.py , CovRegpy_SSA.py , CovRegpy_SSD.py , and CovRegpy_X11.py. These six scripts contain implementations of software features including multivariate covariance time series models based on the regularized covariance regression (RCR) framework, dynamic conditional correlation (DCC) framework, risk premia parity (RPP) weighting functions, singular spectrum analysis (SSA), singular spectrum decomposition (SSD), and X11 decomposition framework, respectively. These techniques can be used sequentially or independently with other techniques to extract implicit factors to use them as covariates in the RCR framework to forecast covariance and correlation structures and finally apply portfolio weighting strategies based on the portfolio risk measures based on forecasted covariance assumptions. Explicit financial factors can be used in the covariance regression framework, implicit factors can be used in the traditional explicit market factor setting, and RPP techniques with long/short equity weighting strategies can be used in traditional covariance assumption frameworks. We examine, herein, two real-world case studies for actuarial practitioners. The first of these is a modification (demonstrating the regularization of covariance regression) of the original example from Hoff & Niu ((2012). Statistica Sinica , 22(2), 729–753) which modeled the covariance and correlative relationship that exists between forced expiratory volume (FEV) and age and FEV and height. We examine this within the context of making probabilistic predictions about mortality rates in patients with chronic obstructive pulmonary disease. The second case study is a more complete example using this package wherein we present a funded and unfunded UK pension example. The decomposition algorithm isolates high-, mid-, and low-frequency structures from FTSE 100 constituents over 20 years. These are used to forecast the forthcoming quarter's covariance structure to weight the portfolio based on the RPP strategy. These fully funded pensions are compared against the performance of a fully unfunded pension using the FTSE 100 index performance as a proxy. [ABSTRACT FROM AUTHOR]

In this study, we introduce transition density function expansion methods inspired from Yang et al. (J Econom. 2019;209(2):256–288.) to stochastic control issues related to utility maximization, without imposing limitations on the variety of asset price models and utility functions. Utilizing Bellman's dynamic programming principle, we initially recast the conditional expectation via the transition density function pertinent to the diffusion process. Subsequently, we employ the Itô‐Taylor expansion and Delta expansion techniques to the transition density function associated with the multivariate diffusion process, facilitated by a quasi‐Lamperti transformation, aiming to derive explicit recursive expressions for expansion coefficient functions. Our main contributions are that we articulate detailed algorithms, stemming from the backward recursive formulations of the value function and optimal strategies, achieved through discretization methodologies with rigorous proof of expansion convergence in portfolio optimization. Both theoretical and practical demonstrations are presented to validate the convergence of these approximate techniques in addressing stochastic control challenges. To underscore the efficiency and precision of our proposed methods, we apply them to portfolio selection problems within several benchmark models, and highlight the reduced complexity in comparison to the current methodologies. [ABSTRACT FROM AUTHOR]

We study how to best combine the sample mean-variance portfolio with the naive equally weighted portfolio to optimize out-of-sample performance. We show that the seemingly natural convexity constraint—the two combination coefficients must sum to one—is undesirable because it severely constrains the allocation to the risk-free asset relative to the unconstrained portfolio combination. However, we demonstrate that relaxing the convexity constraint inflates estimation errors in combination coefficients, which we alleviate using a shrinkage estimator of the unconstrained combination scheme. Empirically, the constrained combination outperforms the unconstrained one in a range of generally small degrees of risk aversion, but severely deteriorates otherwise. In contrast, the shrinkage unconstrained combination enjoys the best of both strategies and performs consistently well for all levels of risk aversion. [ABSTRACT FROM AUTHOR]