Portfolio Overlapping Bias in Tests of the Fama and French Three-Factor Model

In the three-factor model of Fama and French (1993), portfolio returns are explained by the factors Small Minus Big (SMB) and High Minus Low (HML) which capture returns related to firm capitalization (size) and the book-to-market ratio (B/M). In the standard approach of the model, both the test portfolios and the factor portfolios SMB and HML are formed on the basis of size and B/M. This gives rise to a potential overlapping bias in the time-series regressions. Based on a resampling method and the split sample approach already proposed by Fama and French (1993), we provide an in-depth analysis of the effect of overlapping for a broad sample of European stocks. We find that the overlapping bias is non-negligible, contrary to what seems to be general opinion. The range of slope coefficients for size- and B/M-portfolios in time-series regressions is more than one third larger than in a setup without portfolio overlap. As a consequence, the estimates of SMB and HML factor premiums in cross-sectional regressions are biased downwards, also by about one third compared to the split sample approach without portfolio overlap