The effects of beta, size and book-to-market on UK stock returns : risk adjustment, characteristic factors and the cross-section of expected stock returns

Abstract

This research examines the cross-section of expected returns in the UK stock market for the period January 1969-December 2001, with particular reference to the role of risk adjustments and the pricing of characteristic factors. This study has three empirical parts. This first part of the empirical study is concerned with the testing for cross-sectional relationships between expected returns and firm size, book-to-market equity ratio and beta. A methodology similar to that of Fama and French (1992) is employed for this purpose. Most of the research relating the behavior of stock returns to variables such as beta, size and book-to-market equity ratio has been done for the US markets, but there has been limited research relating to the UK markets. In order to further fill the gap, this study provides new evidence by using a more up to date dataset for the UK stock market. In addition, this study further tests the relationship by employing methods not previously employed for the UK market. The cross sectional relationships are tested using robust regressions. Because of seasonal patterns and small-firm effects detected in prior cross-sectional studies, this study also explores cross-section relations for different months of the year and different size cohorts. In the second part, this study analyses models that explain the time series of stock returns using portfolios that mimic the characteristics found to be priced in the first stage cross-section analysis. It was ascertained whether these characteristics proxy for sensitivity to risk factors in returns or whether the characteristics themselves explain the cross section of expected stock returns. This study also discriminates between these two explanations by testing whether it is the time variation in expected risk premiums as measured by the characteristic factors or time variation in the risk loadings as measured by the risk factors arising from characteristic factors. In the third part, it was detennined whether the characteristic factors found to priced in the first and second stage have any explanatory power relative to the loadings on the factors through the different asset pricing risk models. Throughout the study, other issues in both the cross-section and time-series analysis, such as data-snooping biases and residual analysis are also addressed. From all three parts, there is strong evidence that the book-to-market equity ratio is a very important detenninant of the cross-sectional variation in average stock returns while there is hardly any role for beta or size effects in explaining returns. However, the book-to-market effect is only visible for portfolios of small firms and for the month of April. This study further finds some evidence supporting a rational asset-pricing risk model as a possible explanation of book-to-market and size premiums and some evidence supporting book-to-market and size characteristics as a possible explanation. But the analysis of risk-adjusted returns through different factor models suggests that, the priced firm characteristics like book-to-market equity and size are not proxying for loadings on omitted factors that are priced.