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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).

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Research purpose: Determining the range of possible risk and returns attainable by such constrained portfolios is of interest to active portfolio managers. Weight restrictions reduce the range of achievable returns. This work demonstrates the magnitude of these reductions.Motivation for the study: This research installs and augments an approach that ascertains the effect on a TR (active) constrained portfolio in absolute risk-return space. The effects are displayed in risk-return space, demonstrating the impact on such constraints.Research approach/design and method: A theoretical approach to plot the constant TR frontier was used. Theoretical and quantitative analytical approaches to establish changes in the constant TR frontier on a simulated (but highly stylistic) market portfolios were also employed.Main findings: Considerable reduction is observed in possible investable portfolios, even for limited asset weight restrictions. This effect is amplified if multiple restrictions are imposed simultaneously, driven by both a reduced area in risk-return space enclosed by the constant TR frontier and changes in the frontier long-axis slope.Practical/managerial implications: The change in the long-axis slope sign is also a feature of changing economic conditions, thereby acting as an early warning signal with associated ramifications for asset managers. Contribution/value add:The combined effects on active portfolio performance of TR and asset weight constraints have not been investigated and demonstrated before.