Original Research

Portfolio performance under tracking error and asset weight constraints

Michael H. Daly, Gary van Vuuren
Journal of Economic and Financial Sciences | Vol 13, No 1 | a566 | DOI: https://doi.org/10.4102/jef.v13i1.566 | © 2020 Michael H. Daly, Gary van Vuuren | This work is licensed under CC Attribution 4.0
Submitted: 24 March 2020 | Published: 12 November 2020

About the author(s)

Michael H. Daly, Department of Risk management, Faculty of Commerce, North-West University, Potchefstroom, South Africa
Gary van Vuuren, Centre for Business Mathematics and Informatics, North-West University Potchefstroom, South Africa

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Orientation: Active portfolio managers must simultaneously maximise excess returns (over benchmarks), limit risk and observe constraints on, for example, tracking errors (TRs), betas and asset weights.

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.


active management; tracking error; weight constraints; benchmarks; market portfolios


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