Gerenciamento de riqueza : modelando a dependência não linear

Abstract

The goal of this work is to develop a new optimum portfolio selection method, based on the classic portfolio theory proposed by Markowitz (1952) using the local Gaussian correlation model. Tjostheim e Hufthammer (2013) showed that this tool would be useful for the classical portfolio selection problem. However, since it is a newly developed approach, it has not been implemented yet. This work focuses on the development of a portfolio selection method that incorporates the non-linearity of returns and the empirical observation that the relationship between assets in dynamic in time. In order to evaluate its performance, the new model was applied to simulated data and to stocks that comprise S&P500. The initial simulations indicated a better performance of the new proposed model when compared to the classical model pro- posed by Markowitz (1952). One of the main new features of the new model is the possibility of dealing with non-linearity relations by using the local Gaussian correlation. The performance was evaluated by comparing the mean and standard deviation obtained from the results of the simulations. The portfolio created with the new model presented a higher average and lower standard deviation. Another way to evaluate the performance of the model was by randomly selecting 10 stocks from S&P500 in the data base of Yahoo Finance, during the period of 1985 to 2015, and comparing the performance of the new proposed portfolio selection method against the classical method proposed by Markowitz (1952). The analysis of the results showed that the portfolio selection using the local Gaussian correlation performed better than the traditional method in 63% of the cases when using block bootstrap and in 71% of the cases when using traditional bootstrap. Since the new method presented better Sharpe ratio, it generated a better risk adjusted return more attractive in most of the cases. In summary, the measurement of local Gaussian correlation was able to detect complex and non-linear changes in dependence structures, as well as a promising result that can benefit managers, financial markets and companies, allowing them to perform a more accurate investment analysis. The developed model can be used to build new investment strategies, with the objective of improving the performance in financial market.