Teoria moderna de carteres

Abstract

[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.