A common practice in the finance literature is to create characteristic portfolios by sorting on characteristics associated with average returns. We show that the resultant portfolios are likely to capture not only the priced risk associated with the characteristic but also unpriced risk. We develop a procedure to remove this unpriced risk using covariance information estimated from past returns. We apply our methodology to the five Fama-French characteristic portfolios. The squared Sharpe ratio of the optimal combination of the resultant characteristic-efficient portfolios is 2.13, compared with 1.17 for the original characteristic portfolios.