Equity-premium puzzle: evidence from Brazilian data

ARTIGOS   Equity-premium puzzle: evidence from Brazilian data*     Rubens Penha Cysne Professor of Economics at the Graduate School of Economics of the Getulio Vargas Foundation (EPGE/FGV) and a Visiting Scholar at the Department of Economics of the University of Chicago     ABSTRACT This paper uses 1992:1-2004:2 quarterly data and two different methods (approximation under lognormality and calibration) to evaluate the existence of an equity-premium puzzle in Brazil. In contrast with some previous works in the Brazilian literature, I conclude that the model used by Mehra and Prescott (1985), either with additive or recursive preferences, is not able to satisfactorily rationalize the equity premium observed in the Brazilian data. The second contribution of the paper is calling the attention to the fact that the utility function calculated under the discrete-state approximation may not exist if the data (as it is the case with Brazilian time series) implies the existence of states in which high negative rates of consumption growth are attained with relatively high probability. This fact is particularly important when the researcher tries to work with high risk-aversion parameters in order to generate high risk premia. Key words: equity premium, puzzle, Brazil, recursive preferences, asset pricing. JEL classification: G12, E40. RESUMO Este trabalho usa dados brasileiros do período 1992:1-2004:2 e dois diferentes métodos (aproximação sob a hipótese de lognormalidade e calibração) para avaliar a existência de um "equity-premium puzzle" no Brasil. Em contraste com alguns trabalhos prévios da literatura nacional, conclui-se que o modelo usado por Mehra and Prescott (1985), seja com preferências aditivas ou recursivas, não é capaz de gerar o prêmio de risco observado na economia brasileira. A segunda contribuição do trabalho é chamar a atenção para o fato de que a função utilidade calculada sob a hipótese de aproximação discreta do espaço de estados pode não existir se os dados (como é o caso no Brasil) implicarem a existência de estados nos quais taxas altamente negativas de crescimento do consumo são alcançadas com probabilidade demasiado elevadas. Este fato é particularmente importante quando se tenta utilizar parâmetros de aversão ao risco altos o suficiente para gerar o prêmio de risco inerente ao caso brasileiro. Palavras-chave: prêmio de risco, precificação de ativos, utilidade recursiva, prêmio de risco no Brasil, "equity-premium puzzle" .     I INTRODUCTION It has been now twenty years since the seminal paper by Mehra and Prescott (1985) raised the question of the "Equity-Premium Puzzle" (henceforth, EPP). This is the name economists give to the fact that basic representative-agent models of asset pricing (e.g., Lucas, 1978; Breeden, 1979; and Mehra and Prescott's, 1985, adaptation of Lucas' (1978) work1) have not been able to satisfactorily rationalize the fact that US real returns on stocks have been, between 1889 and 1978, about six percent per year higher than those on T-Bills. The title Mehra and Prescott used in their (now) famous article generated a curious semantic herd behavior in the profession. What should be just one more case of the universal problem regarding the failure of a certain model to explain a certain data set was named a "puzzle". Following the trend, several other macroeconomically disappointing2 exercises of statistically unsatisfactory analysis,3 pertaining to the domain of what is usually dubbed "calibration", were also given the name "puzzle". Among these is the "risk-free rate puzzle", introduced in the literature by Weil (1989). This puzzle relates to the (low) long-run level of Treasury returns in the United States, when compared to those implied by Mehra and Prescott’s-type models. Consistently with the underlying time frame of their model, Mehra and Prescott used US long-term data. Here, because long-term data is not available for Brazil, I follow Sampaio (2002), Bonomo and Domingues (2002), Alencar (2002) and Issler and Piqueira (2000, 2002) and use short-term data. Relatively to these previous works, this work uses data of a more recent period. The economic reasoning behind the first two puzzles cited above is as follows. Assets paying higher returns should do it, in equilibrium, according to the basic asset-pricing models previously mentioned, based on the fact that they present a higher covariance with the consumption stream of the representative agent. However, the empirical data for the US has shown that, under the values of the risk-aversion and of the time-discount parameters which are considered to be reasonable, stock returns’s covariance with consumption is not sufficiently greater than that of Treasury Bills, in order to explain the observed difference in their yields. This is what is behind the EPP. To explain the high spread between stocks and bonds, one needs values of the risk-aversion parameter that are considered too high. Assuming standard utility functions, in which the risk aversion equals the inverse of the elasticity of substitution, this is to say that agents should highly dislike growth. However, if this were true, the necessary risk-free rates to explain the amount of saving in the US, an economy in which real per-capita consumption growth reaches almost two percent per year, should be much higher than the historical one percent per year observed in the data. This leads to Weil’s "risk-free rate puzzle" to which I have referred above. Such puzzles emerge under the assumptions of complete markets, costless asset trading, and that consumer preferences can be represented by the standard utility function used in macroeconomics. Explanations of the puzzles, therefore, can always be made by leaving aside one or more of these three assumptions. There must be, though, consistent support from the empirical evidence in doing so.4 A considerable amount of academic research has been developed attempting to solve these puzzles. The explanations include simply denying the existence of a puzzle (see, e.g., Cecchetti and Mark, 1990), or arguments based on: i) recursive utility (Epstein and Zin, 1991); ii) habit formation (e.g., Constantinides, 1990; Campbell and Cochrane, 1999); iii) idiosyncratic risk (Heaton and Lucas, 1996; Constantinides and Duffie, 1996); iv) probability of a large drop in consumption (Rietz, 1988); v) borrowing constraints (Davis and Willen, 2000); vi) liquidity premium (Bansal and Coleman, 1996) and; vii) changes in tax rates (McGrattan and Prescott, 2001). In the present work, the only departure from the assumptions outlined in Mehra and Prescott (1985) that I shall consider regards the modification of the utility function to allow for Kreps-Porteus (1978) preferences, in the line of Epstein and Zin (1991). In Brazil, some papers concerning, among other subjects, the possible existence of these two puzzles, have been convenien (...truncated)