Analysis of Multiscale Systemic Risk in Brazil’s

Abstract

This work analyzes whether the relationship between risk and returns predicted by the Capital Asset Pricing Model (CAPM) is valid in the Brazilian stock market. The analysis is based on discrete wavelet decomposition on different time scales. This technique permits us to analyze the relationship between different time horizons, from short-term ones (2 to 4 days) to long-term ones (64 to 128 days). The results indicate that there is a negative or null relationship between systemic risk and returns for Brazil from 2004 to 2007. Because the average excess return of a market portfolio in relation to a risk-free asset during that period was positive, we should expect this relationship to be positive. That is, greater systematic risk should result in greater excess returns, which did not occur. Therefore, during that period, appropriate compensation for systemic risk was not observed in the Brazilian market. When the decompositions are analyzed year by year, the expected risk and return relationship is observed in 2004 and 2005, but is not observed in 2006 and 2007. Moreover, the scales that proved to be most significant to the risk-return ratio (the t statistic of the expected risk premium) and the R2 of the regression of returns and beta were the first three, which corresponded to short-term time horizons. In other words, when treating year-by-year results differently and consequently separating positive and negative premiums, we find that during some years, the risk-return relation predicted by the CAPM was somewhat relevant. However, this pattern did not persist during all years. Therefore, there is not enough strong evidence that asset pricing follows the model. There are other possible risk factors beyond the market portfolio that explain the risk-return ratio in Brazil.