Portfolio Formation, Measurement Errors, and Beta Shifts: A Random Sampling Approach

This article demonstrates that the portfolio approach could suffer a serious problem when the sorting variables contain not only true values but also measurement errors. The grouped measurement errors will be embedded into the data used to test financial models and further bias the testing results. To correct for this measurement-error problem, I develop a random sampling approach to form portfolios. Results from this new methodology are unbiased and robust. By applying this methodology to investigate beta shifts, I show that the previous results about beta shifts are driven by measurement errors. The actual beta shift pattern is more complicated than that predicted by previous studies. The risk shift hypothesis is unlikely to explain the mean-reversion puzzle for stock returns.