Corcuera Valverde, José ManuelOrtí Celma, Francesc J. (Francesc Josep)Bonastre Sanz, Pol2022-06-022022-06-022022-01-24https://hdl.handle.net/2445/186272Treballs Finals del Doble Grau d'Administració i Direcció d'Empreses i de Matemàtiques, Facultat d'Economia i Empresa i Facultat de Matemàtiques i Informàtica, Universitat de Barcelona, Curs: 2021-2022, Tutor: José Manuel Corcuera Valverde i Francesc J. Ortí Celma[en] Investments and mathematics are closely related. In this project will be shown some usefull methods for investors. First of all we expose the Markowitz mean-variance portfolio theory. This let us get eficient portfolios through an optimation problem that is solved by Karush-Kuhn-Tucker conditions (known as KKT conditions), that are an extension of Lagrange multipliers. Mean-variance analysis is the basis of the capital asset pricing model (CAPM), one of the most used methods by investors. CAPM model is based on risk-return trade-off of assets. Alternative asset princing models based on factors are presented, particularly the arbitrage pricing model (APT). Finally a practical example of some concepts of Markowitz model is shown through python language.49 p.application/pdfcatcc-by-nc-nd (c) Pol Bonastre Sanz, 2022http://creativecommons.org/licenses/by-nc-nd/3.0/es/Gestió de carteraValorsInversionsTreballs de fi de grauPortfolio managementSecuritiesInvestmentsBachelor's thesesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess