Using Stocks or Portfolios in Tests of Factor Models

We examine the asymptotic efficiency of using individual stocks or portfolios as base assets to test asset pricing models using cross-sectional data. The literature has argued that creating portfolios reduces idiosyncratic volatility and allows factor loadings, and consequently risk premia, to be estimated more precisely. We show analytically and demonstrate empirically that the more efficient estimates of betas from creating portfolios do not lead to lower asymptotic variances of factor risk premia estimates. Instead, the standard errors of factor risk premia estimates are determined by the cross-sectional distribution of factor loadings and residual risk. Creating portfolios shrinks the dispersion of betas and leads to higher asymptotic standard errors of risk premia estimates.