Portfolio Optimization. Application of the Markowitz Model Using Lagrange and Profitability Forecast

Abstract

This paper presents the theoretical and applicative model elaborated by Harry Markowitz on the determination of the structure of the efficient securities portfolio. In this sense, in order to determine the structure of the efficient Markowitz portfolio (PE), a Lagrange function is built and minimized. Also, on the basis of the results obtained from the analysis, the profitability of the portfolio is modeled continuous time and determines the range of values in which it can be found over one year after the analysis period. The data used in our analysis are shares of financial investment companies (SIF), traded on the Bucharest Stock Exchange, and the distribution used in the analysis is lognormal. The structure of the portfolio obtained through the Markowitz model can be compared to the structure of the portfolio obtained through the Sharpe model from a previous article titled ”Portfolio optimization - application of Sharpe model using Lagrange” (Brătian, 2017).

Keywords

• modern portfolio theory
• lagrangian
• stochastic process