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Optimal robust and consistent active implementation of a pension fund's benchmark investment strategy

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Abstract

The benchmark investment strategy of a pension fund typically consists of a number of benchmark categories, each of which is assigned a weight in the overall investment budget. In this paper we assume that the benchmark strategy is given, and determine a model for its optimal active implementation. Active implementation involves a number of investment managers each of whom are assigned a specific benchmark category. We present a mean–variance approach to determine, for each investment manager, the optimal budget as well as the fraction of that budget that can be used for deviations from the benchmark. The emphasis is on robustness of the optimal allocation with respect to parameter misestimation, and on consistency in terms of risk-return preferences between active implementation and benchmark investment strategy.

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Notes

  1. The norm ∥A∥ in (14) equals , where λ i (A) denote the eigenvalues of A. Moreover, we use the notation A≥0 to indicate that A is positive semi-definite.

  2. It follows from (19) that robustness implies that the expected return is reduced with a factor θ times the standard deviation of the return, where θ2 satisfies . It can be verified that () features a sharp increase for low values.

  3. Since in (14) β is required to be strictly less than 1, it follows from (16) that the maximum level of robustness with respect to uncertainty in the covariance matrix equals .

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Authors and Affiliations

  1. Department of Econometrics and OR, Tilburg University, Tilburg, 5000, LE, The Netherlands

    Tim van Hest

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  1. Tim van Hest
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  2. Anja De Waegenaere
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Correspondence to Tim van Hest.

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van Hest, T., De Waegenaere, A. Optimal robust and consistent active implementation of a pension fund's benchmark investment strategy. J Asset Manag 8, 176–187 (2007). https://doi.org/10.1057/palgrave.jam.2250072

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  • DOI: https://doi.org/10.1057/palgrave.jam.2250072

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