Asset Management with TEV and VAR Constraints: The Constrained Efficient Frontiers

The paper aims to clarify the relationship between risk management constraints and portfolio efficiency. 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. On the other hand, the risk management office could impose some restrictions to the asset managers’ activity in order to maintain the overall portfolio risk under control. This situation could lead asset managers to select non efficient portfolios in the total return and absolute risk perspective. We perform an analytical analysis on portfolio allocation when a tracking error volatility (TEV) constraint holds, drawing specific attention to the portfolio efficiency issue. First, we define the TEV Constrained-Efficient Frontier (ECTF), a set of TEV constrained portfolios that are mean-variance efficient. Secondly, we define two further new portfolio frontiers analyzing how the imposition of a maximum variance or maximum VaR restriction can reduce the ECTF. Thirdly, we investigate about the feasibility of such portfolio frontiers and their relationships. We find that variance or value-at-risk constraints can force asset managers to pursue portfolio efficiency.