Portfolio Frontiers with Restrictions to Tracking Error Volatility and Value at Risk

Asset managers are often given the task of restricting their activity by keeping both the value at risk (VaR) and the tracking error volatility (TEV) under control. However, these constraints can not always be simultaneously satisfied because the VaR is independent of the benchmark portfolio. The management of these restrictions is likely to affect portfolio performances and produces a wide variety of scenarios in the risk-return space. The aim of this paper is to analyse various interactions between portfolio frontiers when restrictions upon TEV and VaR are jointly imposed. Analytical solutions for the intersections are provided and short numerical methods are proposed when solutions are not available. Finally, a new portfolio frontier is introduced.