Abstract

We consider a decomposition of the risk premia of traded factors as the sum of factor means and a parameter vector we denote by phi, which we identify from the cross-section regression of alpha on the vector of factor loadings, betas. If phi is non-zero, then alpha must also be non-zero and one can construct ”phi-portfolios” which exploit the systematic components of non-zero alpha. We show that for known values of betas and when phi is non-zero, there exist phi-portfolios that dominate mean-variance portfolios. The paper then proposes a two-step bias corrected estimator of phi and derives its asymptotic distribution allowing for idiosyncratic pricing errors, weak missing factors, and weak error cross-sectional dependence. Small sample results from extensive Monte Carlo experiments show that the proposed estimator has the correct size with good power properties. The paper then provides an empirical application to a large number of U.S. securities with risk factors selected from a large number of potential risk factors according to their strength and constructs phi-portfolios and compares their Sharpe ratios to mean variance and S&P portfolios.