The equity premium puzzle: analysis in Brazil after the real plan

Available online at http://www.anpad.org.br/bar BAR, Rio de Janeiro, v. 10, n. 2, art. 2, pp. 135-157, Apr./June 2013 The Equity Premium Puzzle: Analysis in Brazil after the Real Plan Fábio Augusto Reis Gomes E-mail address: Fucape Business School Fucape Business School, Av. Fernando Ferrari, 1358, Vitoria, ES, 29075-505, Brazil. Luciana de Andrade Costa E-mail address: Fucape Business School Fucape Business School, Av. Fernando Ferrari, 1358, Vitoria, ES, 29075-505, Brazil. Ruth Carolina Rocha Pupo E-mail address: Université de Lausanne University of Lausanne, Quartier UNIL-Dorigny Bâtiment Internef, CH-1015 Lausanne, Switzerland. Received 10 May 2012; received in revised form 8 August 2012; accepted 15 August 2012; published online 13 November 2012. F. A. R. Gomes, L. de A. Costa, R. C. R. Pupo 136 Abstract Our paper investigates whether there is evidence of an Equity Premium Puzzle (EPP) in Brazil, applying two different methodologies. The EPP was identified by Mehra and Prescott (1985) since the Consumption Capital Asset Pricing Model (CCAPM), when calibrated with reasonable preference parameters, could not explain high historical average risk premiums in the United States. In our first approach, we consider Mehra’s (2003) model and calibrate the coefficient of risk aversion, using 1995:2-2012:1 quarterly data. The Ibovespa index was used as a measure of the market return, whereas the risk-free rate was proxied by the Selic interbank rate and by the savings account rate. In our second approach, we propose a new method to test the puzzle. We jointly estimate, via generalized method of moments, the parameters of interest using a moment condition that has not been previously explored, as far as we are aware of. The two approaches produced a high risk aversion coefficient, however the second approach indicated that we cannot reject the hypothesis of the risk aversion coefficient being statistically equal to zero. A possible explanation for this result might be that in Brazil the equity premium is not statistically different from zero. Therefore there is no evidence of EPP in Brazil for the studied period. Key words: Brazil; equity premium puzzle; risk aversion; GMM. BAR, Rio de Janeiro, v. 10, n. 2, art. 2, pp. 135-157, Apr./June 2013 www.anpad.org.br/bar The Equity Premium Puzzle 137 Introduction The intertemporal choice of households and firms concerning how to allocate their resources is of central interest to economics and finance. This decision depends on investment opportunities available and especially on their returns. Mehra and Prescott (1985) investigated the American riskpremium (the difference between market return and United States (U.S.) treasury bill return) in the 1889-1978 period. It is reasonable to think that there should be a premium, given the risk of equity. However, this study became well known for having identified the Equity Premium Puzzle (EPP) for the American economy. Its result suggests that the Consumption Capital Asset Pricing Model (CCAPM), when calibrated with reasonable preference parameters, cannot explain the high historical average risk premiums in the U.S. In other words, a high risk aversion is needed in order to match the theoretical moment from an Arrow-Debreu asset pricing model and the empirical moment. The purpose of our study is to investigate whether there is evidence of an EPP in Brazil. We take two different approaches in order to check the robustness of our results. We consider the model suggested by Mehra (2003), which uses the CCAPM, with the additional hypothesis that the growth rate of consumption and the gross return on equity are jointly lognormally distributed. This hypothesis allows a more direct investigation of the puzzle, which has not yet been explored in the literature that investigates the EPP in Brazil, as far as we are aware of. The lognormality hypothesis is widely used in finance literature and is especially convenient in our study because it allows us to use two methodologies to obtain the parameter of risk aversion. In the first approach, we obtain the parameter through a calibration exercise, just as Mehra (2003). As far as we are concerned, this is the first application of Mehra’s (2003) model to Brazil and constitutes one of the contributions of our paper. Furthermore, differently from Mehra (2003), we also develop another approach which estimates both the coefficient of risk aversion and the two first moments of the growth rate of consumption by means of Generalized Method of Moments (GMM). We estimate a moment condition obtained from the lognormality hypothesis, which, to the best of our knowledge, has not been explored in this way in the literature. With this estimation procedure, we are able to make statistical inference about the risk aversion parameter and, therefore, to check how robust our results are. Previous studies have examined the EPP in Brazil and did not find evidence of this puzzle, for example Sampaio (2002), Issler and Piqueira (2000), Araújo (2005, 2006), and Samanez and Santos (2007). Using a different methodology, based on the mean-variance frontier, Catalão and Yoshino (2006) also found no puzzle. In contrast, Soriano (2002) found evidence in favor of the EPP, but argues that the magnitude is much smaller than that observed by Mehra and Prescott (1985). In addition, Cysne (2006) also found evidence supporting the puzzle, concluding that the CCAPM is not able to explain the observed risk premium in Brazil. Although these studies refer to different time periods, none of them incorporates data for 2005 onwards. Furthermore, even those using similar samples, reached different conclusions regarding the existence of the puzzle. In this paper we do not intend to explain or justify these discrepancies, since we start from Mehra (2003) and look for a novel methodology, focusing on the post-Real Plan period. Our goal is to be able to check the robustness of our findings by employing two alternative methodologies having Mehra (2003) as a starting point. Our study focuses on the post-Real Plan period, avoiding the great instability that existed previously to its implementation. This choice is supported by studies like Samanez and Santos (2007) that found mixed EPP evidence depending on whether the sample included the pre-Real Plan period or not. Therefore, our study uses data from 1995 until the first quarter of 2012, which constitutes another contribution since previous studies have only investigated the EPP in Brazil until 2005. To examine the existence of the EPP in Brazil, we use the Ibovespa as the risky asset and the Selic interest rate(1) and the savings account rate as risk-free returns so as to obtain different measures of the risk premium. We construct the growth rate of consumption using the household final consumption expenditure. BAR, Rio de Janeiro, v. 10, n. 2, art. 2, pp. 135-157, Apr./June 2013 www.anpad.org.br/bar F. A. R. Gomes, L. de A. Costa, R. (...truncated)