Using Random Matrix Theory, we build a covariance matrix between stocks of
the BM&F-Bovespa (Bolsa de Valores, Mercadorias e Futuros de S\~ao Paulo) which
is cleaned of some of the noise due to the complex interactions between the
many stocks and the finiteness of available data, and use a regression model in
order to remove the market effect due to the common movement of all stocks.
These two procedures are then used in order to build portfolios of stocks based
on Markovitz's theory, trying to build better predictions of future risk based
on past data.