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This thesis compares traditional methods with machine learning-based approaches, focusing on the predictive optimization methodology by Freitas et al. using Autoregressive Moving Reference Neural Networks (AR-MRNN). The model is reproduced, implemented under real-life market constraints, and applied to weekly return forecasts of IBEX-35 constituents, then benchmarked against the Markowitz mean-variance framework.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/machine-learning-for-financial-portfolio-selection-bachelor-thesis/290886/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/machine-learning-for-financial-portfolio-selection-bachelor-thesis/290886.png","ImageObject",300,407,{"name":92,"@type":93},"Skyler","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the main goal of this thesis?","Question",{"text":113,"@type":114},"To investigate portfolio optimization by comparing traditional approaches with machine learning-based methods, specifically using an AR-MRNN predictive optimization framework.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the thesis benchmark the AR-MRNN approach?",{"text":118,"@type":114},"It reproduces and implements the AR-MRNN model under real-life market constraints, applies it to weekly return forecasts of IBEX-35 constituents, and benchmarks results against the classical Markowitz mean-variance framework.",{"name":120,"@type":111,"acceptedAnswer":121},"What limitations of the Markowitz model does the study highlight?",{"text":122,"@type":114},"The thesis notes that Markowitz relies on idealized assumptions that are rarely met in unstable real-world financial market environments.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},290886,1790467039,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":145,"read_time":146,"preview_page_count":4},2336464648746,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Bachelor’s Degree in Applied Mathematics and Computing  \n2024-2025  \nBachelor Thesis  \n“Machine Learning for Financial Portfolio  \nSelection”  \nFrancesca Romana Val Bagli  \nSupervisor: Francisco Manuel Bernal Martínez  \nLeganés, June 17th 2025  \nThis work is licensed under Creative Commons Attribution – Non Commercial – Non Derivatives  \nABSTRACT  \nPortfolio optimization is the process of strategically allocating assets to maximize returns while minimizing risk. It turns uncertainty into opportunity through smart decisionmaking.  \nThis thesis investigates portfolio optimization through a comparative study of traditional and machine learning-based approaches. In particular, it analyzes the predictive optimization methodology proposed by Freitas et al. using Autoregressive Moving Reference Neural Networks (AR-MRNN), and applies it to weekly return forecasts of the IBEX-35 constituents. The study reproduces the original model, implements it under reallife market constraints, and benchmarks its performance against the classical Markowitz mean-variance framework.  \nWhile the Markowitz model provides analytical tractability and theoretical clarity, its idealized assumptions are rarely present in unstable environments such as financial markets. The AR-MRNN model, by contrast, shows flexibility and improved predictive accuracy. However, being a neural network, it also introduces challenges such as reduced interpretability and sensitivity to hyperparameters.  \nThis work emphasizes that balancing explainability and effectiveness is essential in portfolio theory and future research in the field.  \nKeywords: Portfolio Optimization, Neural Networks, Markowitz, Return, Risk, Normality, Residual, Prediction, Rolling Window.  \nACKNOWLEDGMENTS  \nI would like to thank my supervisor, Francisco Bernal, for introducing me to the fascinating topic of portfolio selection and sparking my passion for finance. Thank you for guiding me.  \nTo my colleagues and mentors at Finaipro, thank you for your trust, encouragement and for making me feel part of something meaningful.  \nTo my parents, thank you for giving me the best possible education and for always supporting me.  \nTo my brother, without you I wouldn’t be who I am. Thank you for always making me laugh.  \nI am also very grateful to all the friends I have made in the last four years. Thank you for being part of the best time of my life. It would not have been the same without you.  \nThank you Pablo for always taking care of me.  \nCONTENTS  \n1. INTRODUCTION .................................... 1  \n1.1. Motivation ...................................... 1  \n1.2. Research Objectives ................................. 4  \n1.3. Structure of this Thesis ............................... 4  \n2. BACKGROUND AND LITERATURE REVIEW .................. 6  \n2.1. Expected Return, Variance, Covariance, and Risk................. 6  \n2.2. Modern Portfolio Theory: Markowitz and the Efficient Frontier......... 7  \n2.2.1. Closed-form solution and the role of short selling .............. 8  \n2.2.2. Assumptions and Limitations of the Markowitz Model............ 10  \n2.2.3. Failure of the Markowitz Model with Real-World Data ........... 10  \n2.3. Extensions and Modifications to Mean-Variance Optimization ......... 10  \n2.3.1. Time Series Forecasting Models: ARIMA and GARCH ........... 11  \n2.3.2. Heuristics for Portfolio Optimization...................... 11  \n2.3.3. Machine Learning Methods for Financial Data ................ 12  \n2.4. Prediction-Based Portfolio Optimization Model (PBPO) ............. 12  \n3. METHODOLOGY ................................... 14  \n3.1. Data Collection and Preparation .......................... 14  \n3.2. Model Implementation................................ 15  \n3.2.1. Overview of the AR-MRNN Predictor ..................... 15  \n3.3. Portfolio Construction and Optimization...................... 17  \n3.3.1. Covariance Matrix Estimation Using Prediction Errors ........... 17  \n3.3.2. Trading Strategy ","cbCaieP9dCD9Slw3","https://ap.wps.com/l/cbCaieP9dCD9Slw3","pdf",3039173,52,"English","# INTRODUCTION\n## Motivation\n## Research Objectives\n## Structure of this Thesis\n# BACKGROUND AND LITERATURE REVIEW\n## Expected Return, Variance, Covariance, and Risk\n## Modern Portfolio Theory: Markowitz and the Efficient Frontier\n## Extensions and Modifications to Mean-Variance Optimization\n## Prediction-Based Portfolio Optimization Model (PBPO)\n# METHODOLOGY\n## Data Collection and Preparation\n## Model Implementation\n## Portfolio Construction and Optimization\n## Benchmarks for Comparison\n## Evaluation and Normality Testing\n## Outputs and Visualization\n# EXPERIMENTS AND RESULTS\n## AR-NN vs AR-MRNN\n## Window-length sensitivity\n## Changing the time period and its consequences\n## Takeaways\n# CONCLUSIONS\n# REGULATORY FRAMEWORK\n## Intellectual Property\n# SOCIO-ECONOMIC ENVIRONMENT\n## Budget\n## Socio-Economic Impact and Sustainable Development Goals Alignment\n# BIBLIOGRAPHY\n# A. FORECAST ACCURACY METRICS","[{\"question\":\"What is the main goal of this thesis?\",\"answer\":\"To investigate portfolio optimization by comparing traditional approaches with machine learning-based methods, specifically using an AR-MRNN predictive optimization framework.\"},{\"question\":\"How does the thesis benchmark the AR-MRNN approach?\",\"answer\":\"It reproduces and implements the AR-MRNN model under real-life market constraints, applies it to weekly return forecasts of IBEX-35 constituents, and benchmarks results against the classical Markowitz mean-variance framework.\"},{\"question\":\"What limitations of the Markowitz model does the study highlight?\",\"answer\":\"The thesis notes that Markowitz relies on idealized assumptions that are rarely met in unstable real-world financial market environments.\"}]","Machine Learning for Financial Portfolio Selection - Bachelor Thesis | PDF",1789642885,131]