The recent research on asset pricing shows that the higher liquidity that results from the globalization of financial markets has significantly reduced the returns tied to many market anomaly-based strategies. However, in general, that research does not evaluate the effects that the mitigation of market anomalies may imply on the performance of the classic asset pricing models. On this basis, in this paper we study to what extent the lower returns provided by market anomaly-based strategies imply better performance of those models. Hence, the main purpose of our study is to compare the performance over time of some of the most prominent asset pricing models, namely, the CAPM and the Fama and French three- and five-factor models, on the European and US equity markets, using return series that cover more than 30 years. Our results show that, although the CAPM is the model with the worst performance in explaining excess returns in all periods both in Europe and US, the model has increased its explanatory power in the recent years principally due to the attenuation of classic market anomalies, such as the size effect or the value effect. Furthermore, our results show that the CAPM correctly prices the three classic Fama and French factors for the years 2006-2021, which explains the best performance of the model for that time interval. Our results have important implications for investment analysis, as well as for determining the cost of capital.