The Cross-Section of Risk and Return

In the finance literature, a common practice is to create factor-portfolios by sorting on characteristics (such as book-to-market, profitability or investment) associated with average returns. The goal of this exercise is to create a parsimonious set of factor-portfolios that explain the cross-section of average returns, in the sense that the returns of these factor-portfolios span the mean-variance efficient portfolio. We argue that this is unlikely to be the case, as factor-portfolios constructed in this way fail to incorporate information about the covariance structure of returns. By using a high statistical power methodology to forecast future covariances, we are able to construct a set of portfolios which maintains the expected return, but hedges out much of the unpriced risk. We apply our methodology to hedge out unpriced risk in the Fama and French (2015) five-factors. We find that the squared Sharpe ratio of the optimal combination of the resulting hedged factor-portfolios is 2.29, compared with 1.31 for the unhedged portfolios, and is highly statistically significant