Um modelo de seleção de carteiras de ações baseado em otimização convexa online

Abstract

Since the seminal work of Harry Markowitz (1952), which initiated the modern theory of portfolios, the strategies of portfolio allocation were extensively discussed in economic literature. With the development of online optimization techniques, dynamic learning algorithms emerged as an effective approach to develop investment portfolios (COVER, 1991; ARGAWAL et al., 2006). However, there are few attempts aiming to connect the traditional literature of portfolio investment, which evolved based on Markowitz (1952) work, with the recent online methods, developed from Cover (1991). The main objec-tive of this work is to implement online convex optimization techniques to: (i) perform strategies of portfolio allocation; (ii) couple these algorithms with risk factors used in traditional models. Two methods of online algorithms were implemented and adapted, the Online Gradient Descendent (OGD) and the Online Newton Step (ONS). Besides, two new versions for the OGD algorithm are proposed in order to control risk in portfolios. The first one, seeks to limit maximum investment for stocks and, the second, aims to keep control of the /3 of portfolios. Both strategies were compared with the Uniform Constant Re-Balanced Portfolio (UCRP) and the Dow Jones Industrial Index (DJIA). Data from weekly observations of DJIA from March 1987 until February 2009 are used. The OGD algorithm presented the best accumulated return among all strategies. Both algorithms (OGD and ONS) performed better than the UCRP and DJIA index. Furthermore, the risk control mechanism proposed proved to be an useful tool in order to improve results related to the Value at Risk (VaR) and Conditional Value at Risk (CVaR) of the portfolios.