Pair trading in Bovespa with a quantitative approach: cointegration, Ornstein-Uhlenbeck equation and Kelly criterion.

Abstract

Pair trading is an old and well-known technique among traders. In this paper, we discuss an important element not commonly debated in Brazil: the cointegration between pairs, which would guarantee the spread stability. We run the Dickey-Fuller test to check cointegration, and then compare the results with non-cointegrated pairs. We found that the Sharpe ratio of cointegrated pairs is greater than the non-cointegrated. We also use the Ornstein-Uhlenbeck equation in order to calculate the half-life of the pairs. Again, this improves their performance. Last, we use the leverage suggested by Kelly Formula, once again improving the results.