Expected returns and volatility in European stock markets

Abstract

The type of return generating process we test here on three European markets are GARCH and AR GARCH in mean models with innovations that have either normal or student-t densities with time dependant variances. These models are appealing in that they estimate time varying volatility in disturbances of stock returns series and ex -ante relationship between stock returns and volatility. Our results indicate that there is no statistically significant coefficient estimates for the volatility in the mean equation and that variance might not be appropriate as a measure of Other proxies for risk should then be searched for. I. Introduction A considerable number of studies in financial economics, both empirical and theoretical, relate expected returns on common stocks to the notion of These studies mainly measure a stock's risk as the covariance between its return and one or more variables. For instance, the capital asset pricing model of Sharpe (1964) relates returns of stocks to their covariances with the market portfolio's returns; the arbitrage pricing model of Ross (1976) relates stock returns to their covariances with several factors; and the consumption asset pricing model of Breeden (1979) relates stock returns to their covariances with the aggregate consumption. These models have been thoroughly tested, but, in recent years, the increasing evidence of time variation in expected returns an d risk put into question the implications and relevance of these models. Many researchers have in turn re -examined financial valuation models in the conditional form that allow expected returns to vary over time (see Gibbons and Ferson (1985), Keim and Stambaugh (1986), and Campbell (1987)), or both expected returns and variance to be time varying (see French, Schwert, and Stambaugh (1987), Baillie and De Gennaro (1990)). One point emerging from these studies, though not strongly conclusive, is that the use of variance to model risk might not be appropriate. Baillie and De Gennaro, for instance, conclude that their results show almost no evidence of a relationship between mean returns on a portfolio of stocks and the variance or standard deviation of those returns. This implies that simple mean -variance models are inappropriate, and suggests the importance of further research using alternative measures of risk. The notion of variance as a sole proxy for risk has already been questioned in the literature. Am ong others, Kraus and Litzenberger (1976) developed a three moment model in which the investors are averse to variance but prefer positive skewness, and Price, Price, and Nantell (1982) and Bawa and Lindenberg (1977) used lower partial moments in their models. Insofar these studies, which have been exclusively applied to the American markets, have not produced conclusive results. Whether the notion of variance is a good measure of risk in European stock markets is the concern of this paper. The type of return generative processes we test here are GARCH and AR-GARCH in mean models with innovations that have either normal or student -t densities with time dependant variances. These models are appealing in the sense that they estimate time varying volatility in disturbances of stock returns series and ex-ante relationship between stock returns and volatility. The structure of the paper is the following. Sections two and three present the data and the statistical analysis. In the fourth section autoregressive cond itional heteroskedastic processes are discussed. The next section is then devoted to empirical results and their interpretations.