# metadata.dc.contributor.advisor[].value
Ortí Celma, Francesc J. (Francesc Josep)

# metadata.dc.description[].value
Treballs 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

# metadata.dc.description.abstract[].value
[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.

# metadata.dc.source[].value
Treballs Finals de Grau (TFG) - Administració i Direcció d’Empreses i Matemàtiques (Doble Grau)