Panel data analysis of multi-factor capital asset pricing models

In this article, we propose MFCAPM panel models with fixed effects and test theories associated with risk exposures and anomalies postulated by Fama and French, and we assess their out-of-sample predictive performances. Based on the portfolios formed by French, we construct 10 panel models, each consisting of 10 portfolios grouped by size deciles, and another 10 panels by value deciles. In the presence of cross-section dependence, the MFCAPM panel model is estimated by the feasible generalized least squares (FGLS) method for the sample period 1963(1)-2018(9). The results show that the market, firm-size and value risk exposures are significant and robust across three-, five- and six-factor panel models. Significant time-fixed effects indicate that there are several portfolios resilient to dot.com bubble peak in 2000, while some others resilient to GFC in 2007. We estimate the models for the in-sample period 1963(1)–1999(12) and generate the out-of-sample portfolio returns for the period 2000(1)–2018(9). We find that portfolio returns forecasts generated by the six-factor panel model are superior to other MFCAPM panel models, mostly due to the momentum factor (investor behaviour) explaining large return variations and volatility exposures. The findings have implications for investors, security traders and portfolio risk managers.