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This paper aims to perform an analytical analysis on portfolio allocation when a tracking error volatility (TEV) constraint holds, drawing specific attention to the portfolio efficiency issue. Indeed, it is well known that investors can assign part of their funds to asset managers who are given the task of beating a benchmark portfolio. However, the risk management office often imposes a TEV constraint to the asset managers’ activity to maintain the portfolio risk near to the risk of the benchmark. This situation could lead asset managers to select non efficient portfolios in the total return and absolute risk perspective. However, the risk management office can impose further constraints, such as on maximum variance or maximum value at risk (VaR) to maintain the overall portfolio risk under control.

First the authors define the TEV constrained-efficient frontier (ECTF), a set of TEV constrained portfolios that are mean–variance efficient. Second, they define two new portfolio frontiers analyzing how the imposition of a maximum variance or maximum VaR restriction can reduce the ECTF. Third, they investigate the feasibility of such portfolio frontiers and their relationships.

The authors find that variance or VaR constraint can force asset managers to pursue portfolio efficiency.

This is a practically important issue given that asset managers often receive a constraint on TEV from the risk management office, but the risk management office does not ask them to minimize the TEV as often assumed in the optimizations performed in the literature on this topic.