Markowitz Portfolio Optimization Research Articles

Combining the MGHyp distribution with nonlinear shrinkage in modeling financial asset returns

The present paper combines nonlinear shrinkage with the multivariate generalized hyperbolic (MGHyp) distribution, thereby extending a flexible parametric model to high dimensions. An expectation–maximization (EM) algorithm is developed that is fast, stable, and applicable in high dimensions. Theoretical arguments for the monotonicity of the proposed algorithm are provided and it is shown in simulations that it is able to accurately retrieve parameter estimates. Finally, in an extensive Markowitz portfolio optimization analysis, the approach is compared to state-of-the-art benchmark models. The proposed model excels with a strong out-of-sample portfolio performance combined with a comparably low turnover.

The effects of quantum hardware properties on the performances of variational quantum learning algorithms

In-depth theoretical and practical research is nowadays being performed on variational quantum algorithms (VQAs), which have the potential to surpass traditional, classical, algorithms on a variety of problems, in physics, chemistry, biology, and optimization. Because they are hybrid quantum-classical algorithms, it takes a certain set of optimal conditions for their full potential to be exploited. For VQAs, the construction of an appropriate ansatz in particular is crucial, since it lays the ground for efficiently solving the particular problem being addressed. To prevent severe negative effects that hamper quantum computation, the substantial noise, together with the structural limitations, characteristic of currently available devices must be also taken into consideration while building the ansatz. In this work the effect of the quantum hardware structure, namely the topological properties emerging from the couplings between the physical qubits and the basis gates of the device itself, on the performances of VQAs is addressed. Specifically, it is here experimentally shown that a complex connectivity in the ansatz, albeit being beneficial for exploring wider sets of solutions, introduces an overhead of gates during the transpilation on a quantum computer that increases the overall error rate, thus undermining the quality of the training. It is hence necessary, when implementing a variation quantum learning algorithm, to find the right balance between a sufficiently parametrized ansatz and a minimal cost in terms of resources during transpilation. Moreover, the experimental finding allows to construct a heuristic metric function, which aids the decision-making process on the best possible ansatz structure to be deployed on a given quantum hardware, thus fostering a more efficient application of VQAs in realistic situations. The experiments are performed on two widely used variational algorithms, the VQE (variational quantum eigensolver) and the VQC (variational quantum classifier), both tested on two different problems, the first on the Markowitz portfolio optimization using real-world financial data, and the latter on a classification task performed on the Iris dataset.

Exploring the Application of Quadratic Programming Within the Markowitz Economic Model: An Empirical Analysis of the Chinese Real Estate Market

This paper introduces an innovative approach by incorporating quadratic programming (QP) into the Markowitz portfolio optimization framework. The central objective of our study is to explore the integration of QP as a solution scheme for portfolio optimization problems with constraints, particularly in the context of the dynamic and complex Chinese real estate market.By meticulously formulating rigorous mathematical models and implementing systematic procedures, we empirically assess the effectiveness and applicability of QP within the Markowitz portfolio model. Our research contributes to a deeper understanding of portfolio optimization by shedding light on how QP can aid investors in optimizing their portfolios in the intricacies of the Chinese real estate market. We provide valuable advice for investors, enabling them to make more informed and efficient investment decisions, thereby reducing risk and maximizing returns. This study serves as a valuable reference for academics, practitioners, and policymakers seeking to navigate the challenging landscape of the Chinese real estate market.

Dynamic Asset Allocation with Expected Shortfall via Quantum Annealing

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.

Sector Rotation Investment Strategy by Implementing Piotroski F-Score and Markowitz Portfolio Theory for Portfolio Construction: Indonesia Stock Market 2020 to 2022

IHSG or IDX Composite Index crash during 2020 where the index fell 37.5% since beginning of 2020 until mid march to the level points of 3,938, recovered and marking up in 2021 where the index reaching the peak in November to the level points of 6,723, and then consolidating at the year of 2022 where the index move in a ranging movements of up and down within the level points of 6,500 to 7,300. The different cycles of stock market movement are happening because of changes and different economic factors, making investors presented with a different opportunities and risks at the stock market. In order to capitalize these changes at the market, investors need to analyzed their portfolio periodically for evaluation and assessment. These research were conducted to examines what are the best portfolio for each year of 2020, 2021, and 2022 using sector rotation investment strategy by implementing sector comparison analysis and Piotroski F-score for stock screening method, while using Markowitz portfolio optimization theory for portfolio construction.

Investment portfolio tracking using model predictive control

AbstractThe composition of an investment portfolio aiming to increase the financial returns while reducing the exposure to risk is a topic of growing interest in the world. In this direction, we propose a model predictive control (MPC) strategy in order to optimize the investment portfolio selection taking into account the tracking of a reference portfolio with desired return. In addition, an analysis comparing different sizes of the prediction horizon according to VPH‐MPC (Varying Predictive Horizon‐MPC) and FPH‐MPC (Fixed Predictive Horizon‐MPC) algorithms is conducted. Finally, we propose an optimal control problem using the tracking error as a function of loss of CVaR (Conditional Value at Risk) measurement. Numerical experiments are run based on Brazilian Stock Exchange data. The experimental results are compared with the Markowitz portfolio optimization model, a conventional tracking strategy, and benchmarks from the Brazilian financial market. This comparison indicates a good tracking performance obtained by the proposed MPC in the two versions while satisfying the constraints.

Comparison of Stock Selection Methods: An Empirical Research On The Borsa Istanbul

This paper compares the performances of stock selection methods developed by artificial neural network (ANN), second order stochastic dominance (SSD), and Markowitz portfolio optimization by generating annual portfolios whose stocks are selected from several types of indexes traded in the Borsa Istanbul. Daily returns in SSD and Markowitz, and annual ratios in ANN models, are taken as inputs, with the following annual returns as outputs. By the perspective of stock selection literature, this study carries unique value for including comparisons of these methods with the purpose of generating portfolios with higher returns. Thus, two questions emerge: "Are these methods able to overcome losses during financial crises and bear or bull periods, and can they provide positive alpha?" Results indicate that average returns of portfolios generated by ANN are relatively higher than SSD and Markowitz, but all three models provide positive alpha over indexes. However, none of the models could overcome negative returns during economic crises.

On Sensitivity for Portfolio Optimisation Based on a High-dimensional Jump-diffusion Merton Model

The problem of singularity of the variance-covariance matrix and its impact on the sensitivity of Markowitz portfolio optimization has been extensively studied in the literature when the underlying model does not include jump terms. In this paper, we first use a jump-diffusion multivariate Merton model to evaluate sensitivity of portfolio optimization and apply principal component analysis (PCA) for dimensionality reduction as a solution to singularity of the variance-covariance matrix. Finally, we provide a numerical study based on the adjusted daily closing price of $S\&{P}\, 500$ stocks to explore the impact of the dimension of the reduced space and jump terms on the sensitivity of the portfolio optimization. Empirical experiments confirm that for models without jump terms, the sensitivity analysis may not reflect the correct assessment of the impact of dimensionality reduction on the portfolio optimization.

Making a Markowitz portfolio with agricultural commodity futures

This paper constructs a minimum-variance portfolio of six agricultural futures. We make a full sample analysis as well as a pre-COVID and COVID examination. Using Markowitz portfolio optimisation, we find that soybean futures have the highest share (31%) in the full sample portfolio because it has the lowest variance. Both soybean oil and rice futures have the second highest weight in the full sample portfolio, in an amount of 24%, because soybean oil has the second lowest variance, whereas rice has, by far, the lowest average correlation with other agricultural futures. Soybean oil has the highest share of 35% in the pre-COVID period, whereas rice follows with 27%. On the other hand, in the COVID period, soybean has a very high share in an amount of 47% due to the lowest risk, while rice takes second place with 19%. Based on the results, investors should invest the most in soybean oil and rice in tranquil periods, while the choice should be soybean and rice in crisis periods. Rice is the choice in both sub-periods because rice has a very low correlation with other agricultural commodities, which happens due to the price stabilisation of rice that is often conducted by Asian countries.

Explainable artificial intelligence for crypto asset allocation

Many investors have been attracted by Crypto assets in the last few years. However, despite the possibility of gaining high returns, investors bear high risks in crypto markets. To help investors and make the markets more reliable, Robot advisory services are rapidly expanding in the field of crypto asset allocation. Robot advisors not only reduce costs but also improve the quality of the service by involving investors and make the market more transparent. However, the reason behind the given solutions is not clear and users face a black-box model that is complex. The aim of this paper is to improve trustworthiness of robot advisors, to facilitate their adoption. For this purpose, we apply Shapley values to the predictions generated by a machine learning model based on the results of a dynamic Markowitz portfolio optimization model and provide explanations for what is behind the selected portfolio weights.

An Application of Portfolio Mean-Variance and Semi-Variance Optimization Techniques: A Case of Fiji

In this paper, we apply the Markowitz portfolio optimization technique based on mean-variance and semi-variance as measures of risk on stocks listed on the South Pacific Stock Exchange, Fiji. We document key market characteristics and consider monthly returns data from SEP-2019 to FEB-2022 (T = 30) of 17/19 listed companies on the stock exchange to construct various portfolios like 1/N (naïve), maximum return, and market and minimum-variance with and without short-selling constraints. Additionally, we compute each stock’s beta using the market capitalization-weighted stock price index data. We note that well-diversified portfolios (market portfolio and minimum-variance portfolio) with short-selling constraints have relatively higher expected returns with lower risk. Moreover, well-diversified portfolios perform better than the naïve and maximum portfolios in terms of risk. Moreover, we find that both the mean-variance and the semi-variance measures of risk yields a unique market portfolio in terms of expected returns, although the latter has a lower standard deviation and a higher Sharpe ratio. However, for the minimum-variance portfolios and market portfolios without short selling, we find relatively higher returns and risks using the mean-variance than the semi-variance approach. The low beta of individual stock indicates the low sensitivity of its price to the movement of the market index. The study is an initial attempt to provide potential investors with some practical strategies and tools in developing a diversified portfolio. Since not all the portfolios based on mean-variance and the semi-variance analyses are unique, additional methods of investment analysis and portfolio construction are recommended. Subsequently, for investment decisions, our analysis can be complemented with additional measures of risk and an in-depth financial statement/company performance analysis.

Gains from Markowitz Optimization: Evidence from Reoptimization of Mutual Fund Holdings

Prior studies have challenged the practical usefulness of Markowitz portfolio optimization in improving the return–risk trade-off in portfolio management. The authors approach this question from a unique angle by examining whether one can improve the performance of a large sample of actual mutual fund portfolios by reoptimizing the holdings using simple mean–variance optimization methods. The analyses produce compelling evidence of the benefits of Markowitz optimization. Simple portfolio optimization improves mutual fund portfolios’ risk-adjusted performance despite noisy expected return estimates inferred from mutual fund portfolio weights. Several alternative optimization strategies, including the risk-parity portfolio, minimum variance portfolio, mean–variance portfolio, and Sharpe ratio maximization portfolio, all outperform actual mutual fund portfolios in terms of the Sharpe ratio and other risk-adjusted performance measures. Moreover, the results are robust to subsamples partitioned on various dimensions. In contrast to the findings of DeMiguel et al. (2009), the authors find that the 1/N portfolio performs the worst.

Hierarchical Clustering as a Dimension Reduction Technique in the Markowitz Portfolio Optimization Problem

Hierarchical Clustering as a Dimension Reduction Technique in the Markowitz Portfolio Optimization Problem

Developing the Markowitz Portfolio Optimization Model Concerning Investor Non - financial Considerations and Supporting Domestic Products

هدف: امروزه بازار سرمایه به‌ عنوان منبع مهم تامین مالی شرکت‌ها‌ محسوب می‌شود و درصورت طراحی مدل مناسب انتخاب سبد سهام با درنظرگرفتن ترجیحات متفاوت سرمایه‌گذاران می‌توان سرمایه‌های موجود را به سمت این بازار و در نتیجه حمایت از تولیدات داخلی کشور سوق داد. هدف این پژوهش توسعه مدل مارکوویتز به منظور لحاظ کردن ترجیحات غیرمالی سرمایه‌گذاران علاوه ‌بر شاخص‌های مالی می‌باشد. روش: برای سنجش نمره مسئولیت اجتماعی شرکت از مدل اندازه‌گیری با دامنه تعدیل شده و برای سنجش ریسک، مدل ارزش در معرض ریسک شرطی بر روی کارایی متقاطع استفاده شد، سپس با استفاده از روش معیار جامع مدل چندهدفه بهینه‌سازی سبد سهام پیشنهاد شد. یافته‌ها: مدل‌های تک‌هدفه و چندهدفه (معیار جامع) با توآن‌های مختلف در نرم‌افزار گمز اجرا شد. بررسی عملکرد این مدل‌ها با استفاده از شاخص شارپ نشان داد که مدل‌های تک‌هدفه بیشینه‌سازی بازده وکمینه‌سازی ریسک به ترتیب دارای بالاترین عملکرد و مدل تک‌هدفه بیشینه‌سازی مسئولیت‌ اجتماعی دارای پایین‌‌ترین عملکرد است. و مدل پیشنهادی حداقل 5/74 درصد از اهداف سه‌گانه و متناقض را براساس معیار شارپ برآورده نموده است. نتیجه‌گیری: مدل پیشنهادی ضمن بهینه‌سازی همزمان سه تابع هدف و برقراری یک بده - بستان بین این اهداف متناقض، نمره شارپ مناسبی نسبت به سایر مدل‌ها و همچنین سبد بازار بدست آورده و سبد سهام مناسبی را در یک جبهه‌ کارا (پاره‌تو فرانت)، از بین شرکت‌ها‌ی با بیشینه بازده و کمینه ریسک که نمره مسئولیت اجتماعی بالایی داشته‌اند، انتخاب و معرفی نموده است و اگر مدل با توآن‌های بیشتری اجرا شود، شرکت‌ها‌ و سناریوهای بیشتری در اختیار سرمایه‌گذاران قرار می‌دهد.

Analysis the effect of market anomalies and growth options on stock return

در بازارهای مالی اثر هر یک از ناهنجاری‌های سودآوری، درماندگی مالی، بخت‌آزمایی و ریسک غیر سیستماتیک بر بازده سهام به‌تنهایی بررسی شده است. اما ارتباط احتمالی آن‌ها نامشخص است. به‌تازگی این ادعا مطرح‌شده است که فرصت‌های رشد بر تقارن تابع توزیع بازده اثر می‌گذارد و قادر است این ارتباط احتمالی و صرف ریسک ناشی از این ناهنجاری‌ها را توضیح دهد. در این پژوهش با استفاده از خواص آماری حاکم بر گشتاور مرتبه سوم تابع توزیع بازده و با جداسازی چولگی ویژه مورد انتظار ناشی از فرصت‌های رشد این ارتباط بررسی شده است. بدین منظور داده‌های 114 شرکت پذیرفته‌شده در بورس اوراق بهادار تهران با رویکرد حذف سیستماتیک، بین سال‌های 1390 تا 1396 جمع‌آوری شد. فرضیه‌های پژوهش با استفاده از رویکرد سبد بندی و ارزیابی آلفای برخی مدل‌های عاملی آزمون شد. شواهد نشان می‌دهد بین سودآوری، درماندگی مالی، بخت‌آزمایی و ریسک غیر سیستماتیک با بازده آتی رابطه وجود دارد؛ اما مدل‌های مرسوم قیمت‌گذاری دارایی‌های سرمایه‌ای توانایی تبیین صرف ناشی از ناهنجاری‌های مذکور را ندارد. این شواهد به‌صورت غیرمستقیم مؤید وجود معمای سودآوری، بخت‌آزمایی و ریسک غیر سیستماتیک در بازار سرمایه ایران است و نشان می‌دهد سرمایه‌گذاران با گزینش راهبرد سرمایه‌گذاری مبتنی بر این ناهنجاری‌ها می‌توانند بازده متفاوتی داشته باشند.

Portfolio Optimization Using an Alternative Approach. Towards Data Mining Techniques Way

In the light of the current budget constraints, the investors face a challenge when building their stock portfolios that should lead to a minimized risk for an expected level of return. Mathematical tools have become essential for portfolio theory formulation in the last decades. In this article, our main objective is to illustrate the utility of some data mining tools and techniques, with a focus on principal components analysis and cluster analysis. The case study reveals a comparative empirical results analysis of the classical Markowitz portfolio optimization model and a combined data mining techniques model. The results show how useful data mining techniques can be for the finance area, with positive implications for investors’ strategy design and implementation. Our study reveals that stocks selection requires the use of modern techniques that take in account the multidimensional perspective of investment decision. Henceforth, we propose that a debate should be launched concerning the design of stock markets design, which generally focus on simple design oriented to the stocks liquidity. In order to help investors, those indices should combine multiple dimensions of stocks definition, as the return, the risk and the liquidity of a stock are at least of the same importance from an investment decision perspective.

A color fusion model based on Markowitz portfolio optimization for optic disc segmentation in retinal images

Retinal disorders are a severe health threat for older adults because they may lead to vision loss and blindness. Diabetic patients are particularly prone to suffer from Diabetic Retinopathy. Identifying relevant structural components in color fundus images like the optic disc (OD) is crucial to diagnose retinal diseases. Automatic OD detection is complex because of its location in an area where blood vessels converge, and color distribution is uneven. Several image processing techniques have been developed for OD detection so far, but vessel segmentation is sometimes required, increasing computational complexity and time. Moreover, precise OD segmentation methods utilize complex algorithms that need special hardware or extensive labeled datasets. We propose an OD detection approach based on the Modern Portfolio Theory of Markowitz to generate an innovative color fusion model. Specifically, the training phase calculates the optimal weights for each color channel. A fusion of weighted color channels is then applied in the testing phase. This approach acts as a powerful and real-time preprocessing stage. We use four heterogeneous datasets to validate the presented methodology. Three out of four datasets are publicly available (i.e., DRIVE, Messidor, and HRF), and the last corresponds to an in–house dataset acquired from Hospital Universitari Sant Joan de Reus (Spain). Two different segmentation methods are presented and compared with state-of-the-art computer vision techniques to analyze the model performance. An outstanding accuracy and overlap above 0.9 and 80%, respectively, and a minimal execution time of 0.05 s are reached. Therefore, our model could be integrated into daily clinical practice to accelerate the diagnosis of Diabetic Retinopathy due to its simplicity, performance, and speed.

Seleção e alocação eficientes em fundos de investimentos em ações

This article proposes the application of the Markowitz model in equity invest­ment funds when a real yield reduction over financial investments indexed to the Brazilian basic rate decreases. It proposes, also, when observing the increase in the number of new investors in the stock market, that any of them, even beginners, should use the Markowitz portfolio optimization model, that is, allocate resources with a combination of high profitability and lower risk. Simultaneously to real profi­tability reduction over portfolio allocation indexed to basic interest rate, an increase in the number of new investors is observed. A portfolio composition case with equity investment funds’ quotas is analyzed. The proposal of this study can guide resource allocations in securities with less volatility in which the portfolio diversification is a condition for optimization. Besides works and mathematical formulas of the Marko­witz model, we used figures from 106 equity investment funds distributed by XP Investimentos stock broke with daily data between January and December 2019. The equity investment funds have their quotas systematically adjusted by bonuses and market values, which improves the calculation of returns and risks analyzed by the model. With the application of the model, it was possible to select a portfolio with 13 investments funds, which showed a volatility of 4.76% and a return of 15% in the period. Volatility is less than the the ones of the funds that comprise it.

Ispitivanje portfolio optimizacije ulaganjem u berzanske indekse i bitkoin

This paper presents an empirical verification of the effectiveness and usefulness of investment diversification using the main stock exchange indices and Bitcoin. The objective is to determine the effects applying the Markowitz portfolio optimization theory, i.e., the advantages of applying the modern portfolio theory for institutional investors. The research offers an answer to the following question: what are the advantages and disadvantages of using Bitcoin in portfolio optimization? The paper contributes to the representation of the reach and limitations of the modern portfolio theory for institutional investors. The conclusion is that rational behaviour of institutional investors requires consideration of portfolio optimization using the Markowitz model, because it is possible to create portfolios which, on the basis of historical returns, provide desired returns alongside certain risks. The methodology includes the analysis of high frequency data, i.e., daily trading data were used. The results indicate that the use of the Markowitz portfolio selection method, with all its limitations, is desirable, possible and applicable, but that it entails serious flaws in the sense of neglecting transaction costs, foreign exchange differences and the real value in the stock market. The results of the research show that Bitcoin is a good source of diversification in a portfolio that contains traditional financial instruments both for the risk-averse investor as well as for those investors who have a greater appetite for risk. The conclusion is that rational behavior of institutional investors requires consideration of investing in Bitcoin using the Markowitz model. However, given the high degree of volatility, investors should be very careful when making decisions about including Bitcoin in the portfolio.

Decentralized Transactive Energy for Flexible Resources in Distribution Systems

The increasing penetration of proactive agents in electric power distribution systems calls for mechanisms to coordinate their trading activities. The commonly employed centralized and distributed methods for supply-demand coordination are not only limited by hardware requirements but also restrictive for active participation of the market agents. This paper proposes a novel decentralized transactive coordination framework that allows participants to bid and clear transactions via a bilateral interaction process. The framework is based on 1) power consumption flexibility individually reported by demand agents using model-predictive control, 2) bilateral supply-side bidding individually determined by the supply agents using a Markowitz Portfolio Optimization model, and 3) individual simultaneous clearing of transactions by demand agents based on second-price sealed-bid auctions. The suppliers bid in the market to achieve desired returns while minimizing their risks. The demand agents harness their demand flexibility by competitively clearing the supplier bids. Unlike traditional approaches, the proposed framework does not require master nodes to orchestrate transactions and, therefore, facilitates massive participation of market agents. Simulation cases demonstrate that the proposed framework successfully performs the market function for bilateral transactions among thousands of proactive agents.