We develop a portfolio trading strategy that aims to achieve optimal performance against arrival prices by minimizing market impact and risk. We first lay the groundwork by formulating a single-security trading strategy and then generalize the framework to the portfolio trading context. Correlations between securities are incorporated via a multi-factor risk model, and the resulting optimization problem is solved numerically by quadratic programming. Comparing the efficient frontier and the early-end VWAP (volume-weighted average price) strategies leads to an intuitive method to determine the risk aversion parameter. We also present an efficient way to identify securities for which block trading opportunities can be pursued without compromising the risk structure of the portfolio.