Antecedentes y elementos teóricos básicos y conceptuales del modelo de Markowitz

Abstract

Based on the maximum utility model, the contrast tests raised by Markowitz with the diversification model known as the mean-variance technique and the geometric analysis of portfolios with three assets will determine the minimum risk portfolio, the form of the expected value and volatility of the portfolios. The indifference curves are also presented, together with the postulations of the Markowitz model and the process for determining the feasible set and the efficient frontier. It presents the case of the portfolio of two assets to form the efficient frontier, especially when the correlation coefficient between the return on assets is +1, -1, and between these two values . The expressions are given, and it is described how to mathematically build the efficient frontier with and without short sales, for which it is necessary to obtain the performance of the minimum variance portfolio with or without short sales, which is the exogenous variable of the model. Likewise, it illustrates how an investor must define a utility function in terms of the mean and variance in a way that is consistent with the axiom of these measures. Finally, the model of an index to determine returns, covariances and betas of individual securities and portfolios are presented.