Evidence of speculative bubbles on the BOVESPA: an application of the Kalman filter

The existence of bubbles in asset prices is a matter of great importance to governments and investors due to possible serious effects they may have on economies. In the case of shares, the presence of a price bubble can be seen by comparing prices and dividends in the long run. This study aimed to assess the occurrence of price bubbles in the Brazilian stock market, by comparing the IBOVESPA as price index and an index of dividends, built based on the methodology of IBOVESPA. The bubble was considered a unobserved state vector in a state-space model and was estimated using the Kalman filter. The results were compared with the standard present value model and intrinsic bubbles model (Froot e Obstfeld, 1991). Although the model establishes the presence of bubbles, the intrinsic bubbles model (Froot e Obstfeld, 1991) showed similar results with greater accuracy.