Portfolio performance under tracking error and benchmark volatility constraints


  • Jan Frederick Hausner Faculty of Commerce, School of Economics, University of Cape Town, Cape Town, South Africa,
  • Gary van Vuuren Centre for Business Mathematics and Informatics, North-West University – Potchefstroom Campus, Potchefstroom, South Africa


Tracking error, Portfolio performance optimisation, Active management


Purpose. Using a portfolio comprising liquid global stocks and bonds, this study aims to limit absolute risk to that of a standardised benchmark and determine whether this has a significant impact on expected return in both high volatility period (HV) and low volatility period (LV).

Design/methodology/approach. Using a traditional benchmark comprising 40% equity and 60% bonds, a constant tracking error (TE) frontier was constructed and implemented. Portfolio performance for different TE constraints and different economic periods (expansion and contraction) was explored.

Findings. Results indicate that during HV, replicating benchmark portfolio risk produces portfolios that outperform both the maximum return (MR) portfolio and the benchmark. MR portfolios outperform those with the same risk as that of the benchmark in LV. The MR portfolio weights assets to obtain the highest return on the TE frontier. During HV, the benchmark replicated risk portfolio obtained a higher absolute risk value than that of the MR portfolio because of an inefficient benchmark. In HV, the benchmark replicated risk portfolio favoured intermediate maturity treasury bills.

Originality/value. There is a dearth of literature exploring the performance of active portfolios subject to TE constraints. This work addresses this gap and demonstrates, for the first time, the relative portfolio performance of several standard portfolio choices on the frontier.

DOI: https://doi.org/10.1108/JEFAS-06-2019-0099


Download data is not yet available.


Bertrand, P. (2005), “A note on portfolio performance attribution: taking risk into account”, Journal of Asset Management, Vol. 5 No. 6, pp. 428-437.

Bertrand, P. (2009), “Risk-adjusted performance attribution: taking risk into account”, Journal of Asset Management, Vol. 10 No. 2, pp. 75-88.

Bertrand, P. (2010), “Another look at portfolio optimization under tracking-error”, Journal of Asset Management, Vol. 66 No. 3, pp. 78-90.

Bertrand, P., Prigent, J.L. and Sobotka, R. (2001), “Optimisation de portefeuille sous contrainte de variance de la tracking-error”, Banque and Marches, Vol. 54 No. 1, pp. 19-28.

Bloomberg (2019), available at: www.bloomberg.com/professional/product/market-data/ (accessed 7 January 2019).

El-Hassan, N. and Kofman, P. (2003), “Tracking error and active portfolio management”, Australian Journal of Management, Vol. 28 No. 2, pp. 183-207.

Grinold, R.C. (1992), “Are benchmark portfolios efficient?”, The Journal of Portfolio Management, Vol. 19 No. 1, pp. 34-40.

Hall, R.E. (2010), “Why does the economy fall to pieces?”, Journal of Economic Perspectives, Vol. 24 No. 4, pp. 3-20.

Jorion, P. (1992), “Portfolio optimization in practice”, Financial Analysts Journal, Vol. 48 No. 1, pp. 68-74.

Jorion, P. (2003), “Portfolio optimization with tracking-error constraints”, Financial Analysts Journal, Vol. 59 No. 5, pp. 70-82.

Maxwell, M., Daly, M., Thomson, D. and van Vuuren, G. (2018), “Optimizing tracking error-constrained portfolios”, Applied Economics, Vol. 50 No. 54, pp. 5846-5858.

Merton, R.C. (1972), “An analytic derivation of the efficient portfolio frontier”, Journal of Financial and Quantitative Analysis, Vol. 7 No. 4, pp. 1851-1872.

MCSI (2012), available at: www.msci.com/documents/10199/eec011d8-459f-4ef6-8edd-a78187985dac

Menchero, J. (2007), “Risk-adjusted performance attribution”, The Journal of Performance Measurement, Vol. 11 No. 2, pp. 22-28.

Plaxco, L. and Arnott, R. (2002), “Rebalancing a global policy benchmark”, The Journal of Portfolio Management, Vol. 28 No. 2, pp. 9-22.

Roll, R. (1992), “A mean/variance analysis of tracking error”, The Journal of Portfolio Management, Vol. 18 No. 4, pp. 13-22.

Stowe, D.L. (2014), “Tracking error volatility optimization”, available at: http://swfa2015.uno.edu/F_Volatility_&_Risk_Exposure/paper_221.pdf

Thomas, B. Rottschafer, D. and Zvingelis, J. (2013), available at: www.envestnet.com/sites/default/files/documents/A%20Tracking%20Error%20Primer%20-%20White%20Paper.pdf




How to Cite

Hausner, J. F., & van Vuuren, G. (2021). Portfolio performance under tracking error and benchmark volatility constraints. Journal of Economics, Finance and Administrative Science, 26(51), 94–111. Retrieved from https://revistas.esan.edu.pe/index.php/jefas/article/view/145