We develop an empirical application on a large dataset of European stock returns in order to estimate the risk premia. While traditional factor models often struggle with high levels of pricing errors and noisy proxies in fragmented markets, we show that the Three-Pass Estimation Method (3PEM) serves as both a robust estimator and a diagnostic tool for factor purification. By assuming the Fama–French five-factor model as the baseline model, we first show that the 3PEM yields risk premium estimates for the European market that are more economically plausible and statistically robust than those obtained using the traditional two-pass estimation method (2PEM). Moreover, our results show that the 3PEM is able to detect noise in tradable factors. Furthermore, the 3PEM is used to denoise the observed factors, providing purified versions that better capture the systematic components of risk. We also identify both noisy factors and denoised factor series that improve the estimation of stock-level exposures and expected returns.
Ossola et al. (2026) studied this question.