Optimizing tracking error-constrained portfolios

Abstract

Active portfolios subject to tracking error (TE) constraints are the typical setup for active managers tasked with outperforming a benchmark. The risk and return relationship of such constrained portfolios is described by an ellipse in traditional mean-variance space and the ellipse ' s flat shape suggests an additional constraint which improves the performance of the active portfolio. Although subsequent work isolated and explored different portfolios subject to these constraints, absolute portfolio risk has been consistently ignored. A different restriction - maximization of the traditional Sharpe ratio on the constant TE frontier in absolute risk/return space - is added here to the existing constraint set, and a method to generate this portfolio is explained. The resultant portfolio has a lower volatility and higher return than the benchmark, it satisfies the TE constraint and the ratio of excess absolute return to risk is maximized (i.e. maximum Sharpe ratio in absolute space)