Desempenho da otimização robusta de carteiras no mercado acionário brasileiro

Abstract

Robust optimization had received increased attention in the recent years due to the possibility of considering the problem of estimation errors in the portfolio selection problems. A topic not well understood, however, is the performance of this contemporary approach in Brazilian market. Suggested by Harry Markowitz, in 1952, the basis of the Modern Theory of Finance converges in one direction: the investment diversification. From the works of Markowitz, others had developed, as the model suggested by William Sharpe, the Capital Asset Pricing Model. In his model, Sharpe argue that the portfolio risk depends not only of the assets covariance, but there is a kind of risk more diffuse than could not be cut out by the investors, it is the systematic risk, measured by the portfolio beta. Should be highlighted the discussions about the Efficiency Market Hypothesis, suggested by Eugene Fama. One consequent question to discussions about the efficiency of markets is the justification for the adoption of active investment strategies, since market portfolios might not be efficient. Some models had been propose trough the time, seeking for optimal portfolios composition. The present study assayed the performance of a robust model of portfolio optimization compared to the traditional mean-variance model and the naïve strategy during the years from 2007 to 2012. Results show that the estimation of returns, risks and covariance of the models had weak performance. The robust models, in comparison to the classic model and the naïve strategy, did not show a better performance, and had high turnover ratio during the periods. In 2007, the portfolios analyzed showed positive returns, however, both the classic portfolios, the classic portfolios with maximum weight restriction and the robust portfolios showed high values of turnover rates, indirectly indicating, high costs of portfolio management. In that year the naïve portfolios showed lower values of turnover ratios, so in this sense, were the better strategy. In 2008, the financial markets showed negative returns, for example, the Ibovespa and either the portfolios proposed. While the Ibovespa computed damages exceeding 40%, the classic portfolios and the classic restricted portfolios showed no lower than -16%. In 2009, the Ibovespa showed strong recovery in comparison to the previous year, ending the year with a gain of more than 70%, so the proposed portfolios also experienced rise in 2009, highlighting the naive portfolios, with returns of 59%. In 2010 the market "walked away", recording a slight increase of 1.044% in the Ibovespa, alternatively, the proposed portfolios presented superior returns, especially robust portfolios (21.48%). The following year, despite the unattractive performance of classics portfolios, restricted portfolios, naïve portfolios and the Ibovespa, the robust portfolios had returns of 22.15%, while the average turnover has been recorded more than 150%, resulting indirectly in high costs of portfolios management throughout the year. In 2012, finally, while the Bovespa almost repeated the performance in 2010, the proposed portfolios returns between 8.02% (naïve portfolios) and 32.52% (restricted portfolios).