Feasible portfolios under tracking error, β, α and utility constraints

Abstract

The investment nous of active managers is judged on their ability to outperform specified benchmarks while complying with strict constraints on, for example, tracking errors, β and Value at Risk. Tracking error constraints give rise to a tracking error frontier – an ellipse in risk/return space which encloses theoretically possible (but not necessarily efficient) portfolios. The β frontier is a parabola in risk/return space and defines the threshold of portfolios subject to a specified β requirement. An α - TE frontier is similarly shaped: portfolios on this frontier have a specified TE for a maximum TE. Utility and associated risk aversion have also been explored for constrained portfolios. This paper contributes by establishing the impossibility of satisfying more than two constraints simultaneously and explores the behavior of these constraints on the maximum risk-adjusted return portfolio (defined arbitrarily here as the optimal portfolio).

Keywords

• alpha
• beta
• optimal portfolios
• tracking error frontier
• utility