Semiparametric Modelling of the Cross-Section of Expected Returns in the German Stock Market

Abstract

According to the Sharpe-Lintner capital asset pricing model, expected rates of return on individual stocks differ only because of their different levels of non-diversifiable risk (beta). However, Fama/French (1992) show that the two variables size and book-to-market ratio capture the cross-sectional variation of US stock returns better than other combinations of two variables. They report also that in the 1963-1990 period beta has virtually no explanatory power. This paper looks at a comparable data set for Germany for the time period 1968-1990. We analyze this data set in order to identify a “best” nonlinear model for the relationship between rates of return, beta, size and book-to-market. The model and corresponding regression estimates are chosen by “cross-validation” among a very rich class of parametric, semiparametric and nonparametric alternatives. The coefficients in the model are estimated each year. The major result is that the parametric model proposed by Fama/French for US stock returns is almost the best one in Germany. The book-to-market-ratio turns out to be the variable with highest partial correlation with the stock return. In most of the annual regressions the corresponding coefficients have the correct sign and are statistically significant.