An approach to portfolio selection using an ARX predictor for securities’ risk and return

It is well known that every investment carries a risk associated, and depending on the type of investment, it can be very risky; for instance, securities. However, Markowitz proposed a methodology to minimize the risk of a portfolio through securities diversification. The selection of the securities is a choice of the investor, who counts with several technical analyzes to estimate investment’s returns and risks. This paper presents an autoregressive exogenous (ARX) predictor model to provide the risk and return of some Brazilian securities – negotiated at the Brazilian stock market, BOVESPA – to select the best portfolio, herein understood as the one with minimum expected risk. The ARX predictor succeeded in predicting expected returns and risks of the securities, which resulted in an effective portfolio. Additionally the Markowitz theory was confirmed, showing that diversification reduces the risk of a portfolio.