Search Results (50)

Our society is facing serious challenges from global warming and environmental degradation. Scientists have identified carbon dioxide as one of the causes. Our society is embracing carbon offset as a way to field the challenges. The purpose of carbon offset is trying to cancel out the large amounts of carbon dioxide by investing in projects that reduce or remove emissions elsewhere. Examples of carbon offset projects are planting trees, renewable energy projects, and capturing methane from landfills or farms. Not all carbon offset projects are equally effective. In stock markets, investors eagerly pursue carbon offset. Namely, investors favor carbon offset in addition to risk and return when investing. Therefore, investors supervise risk, return, and carbon offset. Investors’ pursuits raise the question of how to model carbon offset for investments. The traditional answer is to adopt carbon offset screening and engineer portfolios by stocks with good carbon offset ratings. However, Nobel Laureate Markowitz emphasizes portfolio selection rather than stock selection. Moreover, carbon offset is composed of multiple components, ranging from business, social, economic, and environmental aspects. This multifaceted nature requires more advanced models than carbon offset screening and portfolio selection. Within this context, we systematically formulate multiple-objective portfolio selection models that include carbon offset. Firstly, we extend portfolio selection and treat carbon offset as a whole. Secondly, we separate carbon offsets into different components and build models to monitor each component. Thirdly, we innovate a model to monitor each component’s expectation and mitigate each component’s risk. Lastly, we optimize the series of models and prove the models’ properties in theorems. Mathematically, this paper makes theoretical contributions to multiple-objective optimization, particularly by proving the consistency of efficient solutions during objective classification and model evolution, describing the structure of properly efficient sets for multiple quadratic objectives, and elucidating the optimization’s sensitivity analyses. Moreover, by coordinating the abstract objective function, our formulation is generalizable. Overall, this paper’s contribution is to model carbon offset investments through multiple-objective portfolio selection. This paper’s methodology is multiple-objective optimization. This paper’s achievements are to provide investors with greater precision and effectiveness than carbon offset screening and portfolio selection through engineering means and to mathematically prove the properties of the model. Full article

Decreases in animal mortality due to wildlife–vehicle collisions have been consistently documented as an environmental effect of human mobility restrictions aimed at containing the spread of the COVID-19 pandemic. In this study, we investigate this phenomenon on the mid-sized Mediterranean island of Lesvos, considering a multi-species group of mammals over a five-year systematic recording of animal casualties. We developed a method to analyze the relationship between actual casualties and risk, drawing inspiration from Markowitz’s theory on multi-asset optimization in economics. Additionally, we treated this phenomenon as a Poisson probabilistic process. Our main finding indicates that the lockdown year diverged markedly in modeled return–risk space, exhibiting a displacement on the order of 10² compared to the multi-year baseline—an outcome that reflects structural changes in risk dynamics, not a literal 100-fold decrease in observed counts. This modeled shift is significantly larger compared to published evidence regarding individual species. The results concerning the vulnerability of specific mammals, analyzed as a Poisson process, underscore the importance of singular events that can overshadow the overall systemic nature of the issue. We conclude that a promising strategy for addressing this problem is for conservationists to integrate animal-friendly measures into general human road safety policies. Full article

The paper examines the application of uncertainty theory to portfolio decision making, specifically focusing on constructing portfolio models based on uncertain preference relations. Firstly, we establish the theoretical foundation by introducing the theory of uncertainty, which includes uncertain measure and normal uncertain distribution. Then, building upon Markowitz portfolio theory, we propose an uncertain preference relation prioritization model with chance constraints and an additive consistency portfolio model to facilitate rational decision making in a complex and uncertain financial environment. Furthermore, empirical analysis validates our model’s feasibility, demonstrating its advantages in maximizing returns and minimizing risks. Full article

This paper proposes a Methodology for Assets Selection in Investment Portfolios (MASIP) focused on creating investment portfolios using heuristic algorithms based on the Markowitz and Sharpe models. MASIP selects and allocates financial assets by applying heuristic methods to accomplish three assignments: (a) Select the stock candidates in an initial portfolio; (b) Forecast the asset values for the short and medium term; and (c) Optimize the investment portfolio by using the Sharpe metric. Once MASIP creates the initial portfolio and forecasts its assets, an optimization process is started in which a set with the best weights determines the participation of each asset. Moreover, a rebalancing process is carried out to enhance the portfolio value. We show that the improvement achieved by MASIP can reach 147% above the SP500 benchmark. We use a dataset of SP500 to compare MASIP with state-of-the-art methods, obtaining superior performance and an outstanding Sharpe Ratio and returns compared to traditional investment approaches. The heuristic algorithms proved effective in asset selection and allocation, and the forecasting process and rebalancing contributed to further improved results. Full article

This study investigates the profitability of portfolios that integrate asymmetric fractality within the Black–Litterman (BL) framework. It predicts 10-day-ahead exchange-traded fund (ETF) prices using recurrent neural networks (RNNs) based on historical price information and technical indicators; these predictions are utilized as BL views. While constructing the BL portfolio, the Hurst exponent obtained from the asymmetric multifractal detrended fluctuation analysis is employed to determine the uncertainty associated with the views. The Hurst exponent describes the long-range persistence in time-series data, which can also be interpreted as the uncertainty in time-series predictions. Additionally, uncertainty is measured using asymmetric fractality to account for the financial time series’ asymmetric characteristics. Then, backtesting is conducted on portfolios comprising 10 countries’ ETFs, rebalanced on a 10-day basis. While benchmarking to a Markowitz portfolio and the MSCI world index, profitability is assessed using the Sharpe ratio, maximum drawdown, and sub-period analysis. The results reveal that the proposed model enhances the overall portfolio return and demonstrates particularly strong performance during negative trends. Moreover, it identifies ongoing investment opportunities, even in recent periods. These findings underscore the potential of fractality in adjusting uncertainty for diverse portfolio optimization applications. Full article

This survey offers a succinct overview of the General Framework of Portfolio Theory (GFPT), consolidating Markowitz portfolio theory, the growth optimal portfolio theory, and the theory of risk measures. Central to this framework is the use of convex analysis and duality, reflecting the concavity of reward functions and the convexity of risk measures due to diversification effects. Furthermore, practical considerations, such as managing multiple risks in bank balance sheets, have expanded the theory to encompass vector risk analysis. The goal of this survey is to provide readers with a concise tour of the GFPT’s key concepts and practical applications without delving into excessive technicalities. Instead, it directs interested readers to the comprehensive monograph of Maier-Paape, Júdice, Platen, and Zhu (2023) for detailed proofs and further exploration. Full article

Portfolio management typically aims to achieve better returns per unit of risk by building efficient portfolios. The Markowitz framework is the classic approach used when decision-makers know the expected returns and covariance matrix of assets. However, the theory does not always apply when the time horizon of investments is short; the realized return and covariance of different assets are usually far from the expected values, and considering additional factors, such as diversification and information ambiguity, can lead to better portfolios. This study proposes models for constructing efficient portfolios using fuzzy parameters like entropy, return, variance, and entropy membership functions in multi-criteria optimization models. Our approach leverages aspects related to multi-criteria optimization and Shannon entropy to deal with diversification, and fuzzy and fuzzy entropy variants provide a better representation of the ambiguity of the information according to the investors’ deadline. We compare 418 optimal portfolios for different objectives (return, variance, and entropy), using data from 2003 to 2023 of indexes from the USA, EU, China, and Japan. We use the Sharpe index as a decision variable, in addition to the multi-criteria decision analysis method TOPSIS. Our models provided high-efficiency portfolios, particularly those considering fuzzy entropy membership functions for return and variance. Full article

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. Full article

This research paper explores the complicated connection between uncertainty and the Markowitz asset allocation framework, specifically investigating how mistakes in estimating parameters significantly impact the performance of strategies during out-of-sample evaluations. Drawing on relevant literature, we highlight the importance of our findings. In contrast to common assumptions, our study systematically compares these approaches with alternative allocation strategies, providing insights into their performance in both anticipated and real-world out-of-sample events. The research demonstrates that incorporating methods to address uncertainty enhances the Markowitz framework, challenging the idea that longer sample periods always lead to better outcomes. Notably, imposing a short-sale constraint proves to be a valuable strategy for improving the effectiveness of the initial portfolio. While revealing the complexities of uncertainty, our study also highlights the surprising resilience of basic asset allocation approaches, such as equally weighted allocation, which exhibit commendable performance. Methodologically, we employ a rigorous out-of-sample evaluation, emphasizing the practical implications of parameter uncertainty on asset allocation outcomes. Investors, portfolio managers, and financial practitioners can use these insights to refine their strategies, considering the dynamic nature of markets and the limitations internal to the traditional models. In conclusion, this paper goes beyond the theoretical scope to provide substantial value in enhancing real-world investment decisions. Full article

The distribution laws of various natural and anthropogenic processes in the world around us are stochastic in nature. The development of mathematics and, in particular, of stochastic modeling allows us to study regularities in such processes. In practice, stochastic modeling finds a huge number of applications in various fields, including finance and economics. In this work, some particular applications of stochastic processes in finance are examined in the conditions of financial crisis, aiming to provide a solid approach for stock price forecasting. More specifically, autoregressive integrated moving average (ARIMA) models and modified ordinary differential equation (ODE) models, previously developed by some of the authors to predict the asset prices of four Bulgarian companies, are validated against a time period during the crisis. Estimated rates of return are calculated from the models for one period ahead. The errors are estimated and the models are compared. The return values predicted with each of the two approaches are used to derive optimal risk portfolios based on the Markowitz model, which is the second major aim of this study. The third aim is to compare the resulting portfolios in terms of distribution (i.e., weights of the stocks), risk, and rate of return. Full article

Business parks account for 30% of China’s total carbon emissions. Exploring emissions reduction approaches for business parks is crucial to achieve a net-zero emissions target, as well as for achieving a representative example for all types of emissions entities. Business parks mainly adopt two types of emissions reduction approaches: energy-saving renovations and purchasing carbon reduction products. However, there are limited studies focusing on the optimal combinations of the two approaches for reaching net-zero emissions and evaluating the cost effectiveness. To find a feasible and quantified way to build net-zero business park, a comprehensive path decision model is proposed. The problem is broken down into two parts: the optimal carbon reduction portfolio and the optimal electricity saving were researched. For the optimal product portfolio, the Markowitz theory is employed to balance the risk of carbon reduction products with the expected cost. In the part of optimal electricity saving, considering a ten-year life cycle, the total cost includes renovation investment, carbon reduction products cost, and cost saving of electricity consumption reduction. Based on the energy consumption, technical, and price data, the combination of energy-saving renovations and carbon reduction products is optimized. The model suggests a business park can save 24% of energy consumption through renovation investment and purchase CCER as 66% of the carbon reduction product portfolio. Taking only purchasing carbon reduction products as a benchmark to assess economic efficiency, implementing an optimized level of energy-saving renovation is found to save 16% of the comprehensive cost for the life cycle required to achieve zero carbon emissions. This model provides a new comprehensive optimization idea that will help future parks make decisions to achieve zero-carbon emission targets. Full article

In this study, we investigated some extensions of the classical portfolio theory and try to evaluate them in a situation of crisis. We studied some additional criteria for portfolio selection, based on market multiples representing the overall situation of companies. Additionally, we investigated semi-variance as an alternative measure of risk. We developed a range of portfolios that were built using different criteria for risk and the fundamental values of companies from the Polish stock market. Then, we compared their returns during the crisis that occurred after the outbreak of the COVID-19 pandemic. The results of empirical research on the major companies traded on the Warsaw Stock Exchange reveal that investors can achieve better investment results by augmenting the standard Markowitz model with an additional criterion connected with the fundamental standing of companies, such as book-to-market or earnings-to-market ratios. The second result is that using nonclassical risk measures such as semi-variance instead of variance provides better results, and this method of measuring risk is especially essential in periods characterized by the collapse of the capital market. Full article

Land use planning involves making an appropriate decision and selecting a use over other alternatives. A step-by-step methodology was developed to evaluate the optimal combination of regional land use technologies and the spatial allocation. For a realistic approach, a case study (specifically Rivadavia department, Salta, Argentina) is considered, which has deforestation problems and the advance of intensive and extractive agriculture. Five management techniques are considered for the area: precision agriculture (T1), advance livestock farming (T2), payment for ecosystem service (T3), traditional agriculture–livestock farming—Criollo (T4), and traditional forest management—Wichi (T5). A land evaluation on a GIS model is carried out to obtain the land suitability for each technique. Analyzing local experts’ opinions using the Markowitz portfolio methodology allows us to obtain an optimal combination of techniques. Finally, a Simplex method analysis linked with the GIS is performed to allocate the five techniques over the territory maximizing land suitability and in compliance with percent surface assignments. The result assigns each GIS polygon to a specific technique, reaching optimal land suitability in 92% of the territory. Natural capital and social attributes had a significant and complex impact on technology choice, but objective and optimized approaches in their allocation were possible and provides valuable information to guide public policies. Full article

The covariance matrix estimation plays an important role in portfolio optimization and risk management. It is well-known that portfolio is essentially a convex quadratic programming problem, which is also a special case of symmetric cone optimization. Accurate covariance matrix estimation will lead to more reasonable asset weight allocation. However, some existing methods do not consider the influence of time-varying factor on the covariance matrix estimations. To remedy this, in this article, we propose an improved dynamic conditional correlation model (DCC) by using nonconvex optimization model under smoothly clipped absolute deviation and hard-threshold penalty functions. We first construct a nonconvex optimization model to obtain the optimal covariance matrix estimation, and then we use this covariance matrix estimation to replace the unconditional covariance matrix in the DCC model. The result shows that the loss of the proposed estimator is smaller than other variants of the DCC model in numerical experiments. Finally, we apply our proposed model to the classic Markowitz portfolio. The results show that the improved dynamic conditional correlation model performs better than the current DCC models. Full article

Recent advances in quantum hardware offer new approaches to solve various optimization problems that can be computationally expensive when classical algorithms are employed. We propose a hybrid quantum-classical algorithm to solve a dynamic asset allocation problem where a target return and a target risk metric (expected shortfall) are specified. We propose an iterative algorithm that treats the target return as a constraint in a Markowitz portfolio optimization model, and dynamically adjusts the target return to satisfy the targeted expected shortfall. The Markowitz optimization is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem. The use of the expected shortfall risk metric enables the modeling of extreme market events. We compare the results from D-Wave’s 2000Q and Advantage quantum annealers using real-world financial data. Both quantum annealers are able to generate portfolios with more than 80% of the return of the classical optimal solutions, while satisfying the expected shortfall. We observe that experiments on assets with higher correlations tend to perform better, which may help to design practical quantum applications in the near term. Full article