Testing index-based models in U.K. stock returns

We examine whether index-based models similar to Cremers et al. (Crit Financ Rev 2:1–48, 2012) are more effective in explaining cross-sectional U.K. stock returns than the more traditional Fama and French (J Financ Econ 33:3–56, 1993) and Carhart (J Financ 52:57–82, 1997) factor models using the two-pass cross-sectional regression approach. We find that the seven-index model has the highest cross-sectional R2 across all models. However the superior performance of the seven-index model relative to the Fama and French (1993) and Carhart (1997) models is not robust in the multiple model comparison tests of Kan et al. (Rev Financ Stud 22:3449–3490, 2013). For these models and a conditional version of the Fama and French (1993) model, we cannot reject the null hypothesis that these models perform as least as well as the other competing models. In contrast, the four-index model of Cremers et al. (2012) performs poorly relative to the competing models. Our results suggest there is little benefit in using the seven-index model as an alternative to the Carhart (1997) model in practical applications that require the estimation of expected returns.