Portfolio Theory Research Articles

Great Year Bad Sharpe

Returns distributions are heavy tailed across asset classes. In this note, Smerlak examines the implications of this well-known stylized fact for the joint statistics of performance (absolute return) and Sharpe ratio (risk-adjusted return). Using both synthetic and real data, He shows that, all other things being equal, the investments with the best in-sample performance are never associated with the best in-sample Sharpe ratios (and vice versa). This counter-intuitive effect is unrelated to the risk-return tradeoff familiar from portfolio theory: it is, rather, a consequence of asymptotic correlations between the sample mean and sample standard deviation of heavy-tailed variables. In addition to its large sample noise, this non-monotonic association of the Sharpe ratio with performance puts into question its status as the gold standard metric of investment quality.

Comparative Analysis of the Markowitz Model and the Kraljic Matrix Model in Portfolio Optimization and Procurement Management

This research studied two important models of portfolio management: the Markowitz model and the Kraljic Matrix Model. The Markowitz model is the basis of modern portfolio theory and is designed to optimise asset allocation by minimising risk while maximising returns. This paper provides a system to build a balanced portfolio by utilising diversity. On the other hand, the Kraljic Matrix Model classifies products based on supply risk and profit impact and provides a strategic tool for purchasing management. This model categorises products into four categories: noncritical, leverage, strategy, and bottleneck to support informed purchasing decisions. Despite its usefulness, the Kraljic matrix has been criticised for not taking into account the supplier’s perspective and for not providing guidelines for managing the movement of goods within the matrix. This paper studies the application and limitation of the two models, emphasises the need to adapt to the strategy in the portfolio and procurement management, and adjust according to the market dynamics.

ON THE SOLUTION UNIQUENESS IN PORTFOLIO OPTIMIZATION AND RISK ANALYSIS

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.

Digital Technologies in Primary Mathematics Education: Insights from Future Teachers’ Portfolios

The integration of digital technology in education has become an essential competency for primary school teachers, particularly in mathematics education, where innovative tools can enhance learning outcomes and student engagement. This paper investigates the extent and nature of digital technology utilization among future mathematics teachers, focusing on tools like dynamic geometry software (GeoGebra), e-testing platforms (e.g., Kahoot), learning applications (e.g., Learning Apps), and immersive technologies such as augmented and virtual reality. Our research centers on the analysis of final portfolios submitted by graduating students from the Faculty of Education at the University of Ostrava in 2024. These portfolios, which are a culmination of the students’ educational strategies and experiences, offer a unique lens through which to assess the preparedness and innovation potential of future educators. Additionally, we surveyed the views of these students through questionnaires on the use of digital technologies in mathematics teaching. We specifically examined how these candidates plan to integrate digital technologies into their teaching practices and the innovative methods they propose to engage primary school students in mathematics. Through a qualitative study of 24 portfolios and a questionnaire survey of 15 students, we identified prevalent trends and inventive approaches in the use of digital tools. Our analysis highlights not only the variety of digital technologies incorporated into teaching strategies but also the depth of pedagogical integration, reflecting a sophisticated understanding of how to enhance learning environments effectively. The findings underscore the importance of digital literacy in teacher education and suggest that current training programs are effective in equipping future educators with the necessary skills to implement advanced technological tools. This study contributes to the ongoing discussion about digital competence in education, providing evidence of emerging trends and the transformative potential of digital technologies in primary mathematics education.

A comprehensive review of behavioral biases in financial decision-making: from classical finance to behavioral finance perspectives

This paper offers a detailed analysis of the evolution of financial decision-making theories, focusing on the shift from classical finance to behavioral finance. Classical finance theories, including the Efficient Market Hypothesis and Modern Portfolio Theory, assume that investors behave rationally and that the market is efficient. However, these theories have faced criticisms highlighting the importance of considering irrational behaviors in financial markets. Behavioral finance addresses this gap by integrating psychological insights into financial decision-making. This study systematically reviews the literature on behavioral biases that affect individual investors, identifying fundamental biases and their impact on investment decisions. The analysis emphasizes the role of cognitive limitations and psychological tendencies in shaping market dynamics, influencing asset pricing, investment strategies, and market returns. The research also notes a shift in focus from market-level outcomes to the behavior of individual investors, with an increase in publications. The paper concludes that understanding investors’ biases is crucial for developing effective risk management strategies and investment recommendations, ultimately leading to improved market performance. The findings underscore the growing importance of behavioral finance in explaining investor behavior and market anomalies, highlighting areas for future research in this evolving field.

Urban-scale power decarbonization using a modified power purchase agreements framework based on Markowitz mean-variance theory

Urban power decarbonization is essential in the fight against climate change, yet current research often neglects the financial risks faced by investors and the shifting demands of consumers in liberalized electricity markets. This study addresses these gaps by proposing a modified Markowitz Mean-Variance Portfolio (MVP) theory, integrated with the Low Emissions Analysis Platform (LEAP), and a deep learning model. On this basis, an urban energy transition framework centered on Power Purchase Agreements (PPAs) is proposed and developed. The framework is validated considering a case study in Kitakyushu, Japan, highlighting its potential in accelerating power sector decarbonization and achieving net-zero emissions by 2038. Additionally, the internal rate of return (IRR) remains stable between 14.5 % and 19.6 % across seven other cities. While the framework reduces long-term cash flow volatility, its effectiveness hinges on industrial electrification efficiency and regional energy self-sufficiency. The findings indicate that relying solely on renewable energy for low-carbon transitions is unrealistic. Furthermore, green hydrogen could emerge as a viable alternative to fossil fuels, potentially replacing batteries for long-term energy storage. Future research should explore cross-regional energy trade and establish legal frameworks for long-term energy transactions to bolster urban energy transition resilience across diverse geographic and economic contexts.

Portfolio insurance, portfolio theory, market simulation, and risks of portfolio leverage

Portfolio insurance, portfolio theory, market simulation, and risks of portfolio leverage

Comparative Analysis on the Application of Markowitz Model and Index Model in Portfolios

This article presents a comparison between the Markowitz model and the index model, focusing on their applications in portfolio management. The Markowitz model, also known as the mean-variance model, revolutionized portfolio theory by introducing a quantitative method for balancing risk and return. This model constructs optimal portfolios that maximize expected return for a given level of risk or minimize risk for a given expected return, using a covariance matrix to assess relationships between asset returns. In contrast, index models popularized by William Sharpe offer a simplified approach focused on the relationship between individual asset returns and a common benchmark (usually a market portfolio). The article explores the theoretical foundations of the two models, highlighting their mathematical formulations and assumptions. It also discusses the computational methodologies involved in implementing these models and examines the challenges and advances in optimization techniques. It evaluates how these technological innovations have enhanced portfolio optimization, enabling the handling of larger datasets and more complex market dynamics. In addition to comparing these two models, the article delves deeper into the concepts of efficient frontier, inefficient frontier and minimum variance frontier. The efficient frontier is the portfolios that offer the highest expected return for target risk, while the inefficient frontier includes portfolios that do not offer the best return for the level of risk. Minimum variance frontier focuses on portfolios that minimize risk for target expected return, emphasizing the importance of risk management in investment decisions.

Power generation mix in Colombia including wind power: Markowitz portfolio efficient frontier analysis with machine learning

The Colombian power market is hydro-dominated since 67 % of the power produced comes from hydro-power sources. In addition, it has thermal power from natural gas and coal, and in the last years, alternative energy sources such as wind and solar have been introduced, although so far their share is not significant. Due to this condition, the Colombian power market is very volatile and depends on weather conditions. Usually, in rainy seasons prices are low and power is available, while in dry seasons, prices are high and power can be scarce. One of the main advantages of the new energy sources is that they are complementary to hydro-power, in the case of wind regimes, they are higher during dry seasons and lower during rainy seasons. We propose a complementarity analysis in the energy mix using Markowitz Portfolio analysis to determine if the efficient frontier is improved by introducing wind power to the system and the traditional port-folio analysis is improved by introducing Machine Learning (ML) into calculations. Results show that wind power improves the return while minimizing risk. Therefore, wind power would significantly reduce prices in Colombia's power mix while reducing volatility. This work follows the Open Innovation (OI) paradigm, the intersection of Machine Learning, portfolio optimization, and renewable energy presents a promising landscape for research and practical applications. Continued interdisciplinary collaboration and innovation are essential for harnessing the full potential of these technologies for a sustainable energy future.

Turnaround Strategy Of Pt Indofarma Tbk

PT Indofarma Tbk experienced a decline in financial performance from 2016 to 2022 leading to corporate strategy implementation. This study aims to analyze the suitability of the strategy implemented by PT Indofarma to the theory of corporate alternative strategy. This study involved a case study method utilizing annual reports and financial statement data. BCG Matrix was applied as a portfolio analysis tool. PT Indofarma Tbk was identified in the BCG matrix in a low growth and market share quadrant. The strategy implemented by PT Indofarma to recover the company’s performance was identified as a turnaround strategy which aligns with the recommended strategy for a company that experienced low growth and low market share in the BCG matrix. This study concluded that the implementation of the turnaround strategy at PT Indofarma Tbk aligns with the recommendations by researchers for effective turnaround strategy implementation

Applying portfolio theory to benefit endangered amphibians in coastal wetlands threatened by climate change, high uncertainty, and significant investment risk

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.

Identifying optimal funding allocations for public water infrastructure improvements under uncertainty

Diversified and locally managed funding strategies bring substantial benefits to water infrastructure investments across financial, social, institutional, and political spheres. However, these strategies often occupy a secondary role in the public sector's capital allocation process. We outline optimal funding strategies for water infrastructure by zeroing in on communities' specific needs and navigating two types of uncertainty—historical and priority uncertainty—across both long-run (multi-decade) and short-run (recent years) timeframes. Employing Modern Portfolio Theory (MPT), our approach pinpoints optimal funding distribution both across and within categories (namely, individual counties) based on their funding needs. By comparing these distributions with Tennessee's Clean Water State Revolving Fund's historical funding approach, we benchmark how risk and socioeconomic factors influenced past decisions. This analysis yields optimal allocations that inform which counties should be given priority by public funding agencies, moving toward portfolios that adeptly balance risk with funding necessity. Our methodology is executed in two stages, each bearing distinct implications. The initial stage seeks to prioritize groups of counties based on their funding needs, considering both immediate and long-term contexts, in line with what government agencies might aim to achieve. The subsequent stage refines the equilibrium between risk and need at a more detailed level within these groups, facilitating risk diversification that effectively addresses both short- and long-term funding requirements.

Multi-Stage Resource Leveling Problem with Self-operation and Outsourcing Cooperation in Sharing Logistics

Self-operation and outsourcing cooperation have emerged as the prevailing operating mode for logistics companies in the realm of sharing logistics. This mode facilitates the rational and effective coordination of multiple resources for task assignment. However, the competition and cooperation relationship between self-operation and outsourcing remain largely unexplored, leaving logistics companies grappling with the trade-off between cost-effectiveness and risk. To address this gap, we propose a multi-stage resource leveling model that accounts for the fuzzy outsourcing resources, the efficacy of intra-stage resources, and the stability of inter-stage resources. We employ an improved gravitational search algorithm to solve this model efficiently. Inspired by Markowitz's portfolio theory, we propose a resource portfolio strategy under the self-operation and outsourcing cooperation mode based on the mean-variance model to better weigh up the “cost-effectiveness” and “risk” exhibited by logistics resources. The strategy uses expected returns and variance to evaluate the benefits and risks, thereby categorizing allocation schemes according to risk levels. Finally, through experiment analysis, we discuss the optimal scale of self-operation and outsourcing resources for logistics subtasks at different risk levels. This analysis equips logistics companies with the insights needed to make informed decisions aligned with their risk preferences and overall benefits, offering crucial managerial implications for business and strategic decisions.

Modeling dynamic higher-order comoments for portfolio selection based on copula approach

This paper introduces a novel approach to estimating time-varying higher-order comoments from a theoretical standpoint. We present how to estimate the dynamic higher-order comoments of asset returns under the copula framework, which builds on the ARCD and copula-DCC models to capture the time variation in higher-order moments and correlations of asset returns. Additionally, the elements in the coskewness and cokurtosis matrices are calculated by the double, triple, and quadruple integrals associated with the joint density function of asset returns. The empirical application to five international market indexes shows that the portfolio with time-varying higher-order comoments estimated by the copula approach significantly outperforms equally weighted and mean–variance strategies in economic performance. The robustness analysis verifies the validity and robustness of the proposed estimation method. Our research offers fresh insights for portfolio analysis and risk management decision-making in practical scenarios.

Wavelet quantile correlation between DeFi assets and banking stocks

We examine time frequency quantile correlation and portfolio benefits between decentralized finance (DeFi) assets and G7 banking stocks We employ wavelet quantile correlation to examine the correlation between DeFi and bank stocks. Notably, results reveal diversification benefits in the short to medium term and highlight DeFi assets' hedging and safe-haven properties, particularly against Japanese banking stocks. Further, bivariate portfolio analysis provides optimal allocation strategies. Our research offers new guidance for investors, portfolio managers, and regulators regarding the intersection of DeFi and traditional banking stocks.

Adaptive Risk Parity Strategies for Managing Portfolio Risk in Volatile Markets

This paper presents a novel model for Adaptive Risk Parity Portfolio Construction, designed to dynamically adjust portfolio weights based on changing market conditions and economic regimes. Traditional portfolio strategies, such as Modern Portfolio Theory (MPT), often rely on static assumptions that can lead to suboptimal performance in volatile markets. In contrast, the adaptive risk parity approach aims to equalize risk contributions across asset classes while responding to fluctuations in economic indicators, such as GDP growth and inflation rates. By employing techniques such as Markov switching models and machine learning for regime identification, the proposed model allows for real-time adjustments to asset allocations. The back-testing results demonstrate that the adaptive risk parity portfolio outperforms static risk parity and traditional mean-variance optimized portfolios in terms of risk-adjusted returns and drawdown management. This research contributes to the field of portfolio management by providing a framework that enhances resilience and adaptability in investment strategies.

RISKS OF INVESTMENT PORTFOLIO OF BANKS OF KAZAKHSTAN: PROBLEMS AND WAYS TO SOLUTION

The article examines the essence and classification of the definition of «market risk». It is noted that managing market risks in a bank is a complex and multifaceted process that requires constant analysis and monitoring of market conditions, and an important element of the market risk management system is the formation of an effective investment portfolio, which includes various assets with different levels of risk. This will allow you to control and minimize possible losses, and will also help the bank determine the optimal balance between risk and profitability, which will help increase its profits. Using modern data analysis methods, an analysis of the real average investment portfolio of second-tier domestic banks was carried out and an assessment of the generated conditional investment portfolio was given. Based on the study, problems were identified and directions for improving market risk management in the bank were given.

Market segment evaluation based on fuzzy tools

The paper suggests a hybrid model with simplified and extended schemes for evaluating market segments based on strategic diagnostics methods and fuzzy multi-criteria analysis tools. The developed model's novelty and originality consist of forming a system of evaluation criteria based on the GROT criteria of I. Ansoff and the five forces of the M. Porter model (and in the case of an extended calculation scheme – with their decomposition into sets of relevant sub-criteria) and the use of the latest Fuzzy SBWM method (Fuzzy Extension of Simplified Best-Worst Method) to determine their weighting factors. Expert linguistic evaluations on a defined 7-level term set, followed by their transformation into fuzzy numbers with triangular membership functions, are used to evaluate market segments for each identified criteria (sub-criteria). The Fuzzy SAW method determines fuzzy integral estimates of market segments based on these sub-criteria. A practical case of evaluating the confectionery market segments of Ukraine for the simplified calculation scheme is given. The systematic approach makes it possible to determine the attractiveness of market segments for forming strategic recommendations based on the application of portfolio analysis methods, for developing and implementing diversification and logistic strategies.

Analysis of optimal portfolio on finite and small-time horizons for a stochastic volatility model with multiple correlated assets

Analysis of optimal portfolio on finite and small-time horizons for a stochastic volatility model with multiple correlated assets

Variance of deviation from optimal leverage

AbstractWe show that deviations from the firm's target leverage are priced in the cross‐section of stock returns and that the relation between these quantities is nonlinear. The concave nonlinear relation between deviation from the target leverage and next‐period return is strong during economic expansions and vanishes during recessions. Our portfolio analysis provides support for the concave relation between deviation from the target leverage and next‐period returns as well. We develop a factor named variance of deviation from optimal leverage (VDOL) and show that it is an important risk factor that has been omitted in the literature.