Diversification and the optimal construction of basis portfolios

Nontrivial diversification possibilities arise when a factor model describes security returns. This paper catalogs the merits of alternative strategies for constructing basis portfolios to mimic the common factors. We show how to use the χ² statistic for the joint significance of mean basis portfolio returns to rank alternative procedures and the bootstrap to perform inferences on the disparity between χ² statistics across portfolio formation procedure, estimation method, cross-section size, and number of factors. Our main conclusion is that maximum likelihood factor analysis coupled with minimum idiosyncratic risk portfolio formation yields economically and statistically superior basis portfolios compared with those derived from asymptotic principal components.