SummaryBrazil is a country which has experienced increased attention from the rest of the world in the recent years. The BOVESPA (Bolsa de Valores de São Paulo) is the largest stock exchange in Latin America and the economy is in a better state than ever. The economy has experienced a growth rate of about 4 % and the macroeconomic conditions are generally improving. Almost every multinational company has operations in Brazil. Even Norwegian companies such as Statoil and Hydro are now involved in one of the most exiting emerging markets in the world. The stock market has experienced a recent boom and almost ten-doubled its market capitalization between 2002 and 2007. In the same period the participation of international investors rocketed.
However, Brazil does not have a developed economy, both the macroeconomic conditions and the stock market are more volatile than those of more developed countries. This raises concerns about the predictability of Brazil’s stock market for the investors. There have been some studies about the development and predictability of the Brazilian stock market, but these are by no means conclusive.
The CAPM (Capital Asset Pricing Model) is arguably the most important and most frequently tested model within finance. Basically, the CAPM relates the excess return on an asset to the excess return on the market portfolio. An asset has a given level of risk which can be divided into two parts, systematic and unsystematic risk. Systematic risk is the market risk which influences a large number of assets. Unsystematic risk is what can be diminished by diversifying your investments, it is the risk exclusive to the asset. Thus, if you hold a large amount of stocks in your portfolio, the unsystematic risk of the assets will be “netted out”. There is no reward holding unsystematic risk since it can be diversified away, thus priced risk is proportional only to systematic risk. The CAPM introduces the beta term which measures an assets risk in relation to the market portfolios risk. An asset, or a portfolio of assets, can be riskier or less risky than the market portfolio, but in the CAPM world it is always efficient since diversifiable risk has been eliminated. I.e., the reward you get is proportional to the risk you are willing to take.
Unfortunately, empirical tests have shown that the world of asset prices is not that simple. Numerous studies have focused on the power of the CAPM to explain common variation of stock returns and the general conclusion is that it does not work very well. A number of studies have suggested that other firm characteristics than the beta term could provide explanatory power for asset returns. Especially firm size and a firm’s book-to-market (B/M) ratio have been shown to have systematic relationships with stock returns. Perhaps the most important of these studies have been those of Fama and French (1992 and 1993). They introduce the three-factor model which incorporates factors reflecting the influence of firm size and the B/M ratio on stock return variation. Fama and French (1993) sort stock returns on size and on the B/M ratio. The stocks are sorted in two equal portfolios on size and on three portfolios at the 30th and 70th percentiles on the B/M ratio. Six portfolios are independently constructed at the intersection of these. The factors are the SMB (Small minus Big) and HML (High minus Low) factors. The SMB is the average return on the small portfolios minus the average return on the big portfolios and the HML is the average return on the high B/M ratio portfolios less the return on the low B/M ratio portfolios. These factors are designed to capture the additional return investors have historically received investing in stocks with low market capitalization and a high B/M ratio. A positive premium for both small size and a high B/M ratio is found in Fama and French’s paper (1993). It is important, however, to remember that these factors do not build on theory, they are rather arbitrarily constructed ad hoc factors that work, in Fama and French’s words, “surprisingly well” explaining variation of stock returns.
The object of this paper is to attempt to answer if the three-factor model and an international six-factor model yield good explanatory power for the common variation of stock returns for stocks on the BOVESPA between 1995 and 2006. These models can be used in applications where it is needed to calculate expected returns. This includes cost of capital calculations, portfolio performance benchmarks and risk analysis.
The contribution to the existing literature will be twofold. First, the three-factor model will be extended to an international six-factor model incorporating proxies for world factors from the U.S. market. This is done to check for international influence on the Brazilian equity market. The U.S. is chosen because of its assumed relatively large economic integration with Brazil compared to other developed markets. Second, the approach to forming the SMB and HML factors will be different to that of Fama and French (1992). By grouping the stocks dependently, first according to size and then according to the B/M ratio, we will get portfolios with an equal number of securities (give or take one). This approach is chosen because of the relatively few stocks listed on the BOVESPA. By utilizing Fama and French’s methodology, we will at times get very few stocks in some portfolios, thus giving a more uncertain description of the market.
These problems will be addressed by regressing nine excess portfolio returns on the excess market return and the SMB and HML factors using Microsoft Excel’s statistical tools. First we run a number of regressions using Brazilian data only. Then, we extend the model to the international six-factor model where the additional U.S. factors will be utilized. The relative applicability of the different models is discussed comparing the R-squared measure and the average of the absolute values of the intercepts. Moreover, the significance of the slope coefficients for excess market return and the SMB and HML factors will be investigated by studying their p-values.
We find that the domestic three-factor model works better than the CAPM model explaining variation of stock returns. However, the results found here are less convincing than those of the U.S. market. We also find that the portfolio construction applied here gives a better description of the Brazilian stock market since the negative relationship between size and return and the positive relationship between the B/M ratio and return are confirmed.. Moreover, extending the model from the domestic three-factor to the international six-factor model improves somewhat the explanatory power of the model. This effect is almost entirely due to the inclusion of the foreign excess market return. The foreign SMB and HML factors are in general not significant and ad little or no value to the model.