Reconciling TEV and VaR in Active Portfolio Management: A New Frontier

This article investigates the risk-return relationship of managed portfolios when two risk indicators, the Tracking Error Volatility (TEV) and the Value-at-Risk (VaR), are both constrained not to exceed preet maximum values. While in some cases these constraints may not be mutually compatible, it is often possible to find portfolios that satisfy both constraints. In this paper, we analyze the problem of choosing among these. Focusing on the trade-off between the joint restrictions that can be imposed on both risk indicators, we define the Risk Balancing Frontier (RBF), a new portfolio boundary in the traditional absolute risk-total return space, that contains all the portfolios characterized by the minimum VaR attainable for each TEV level. We show that the RBF is the set of all tangency portfolios between two well-known frontiers: the so-called Constrained Tracking Error Volatility Frontier (Jorion, 2003) and the Constrained Value-at-Risk Frontier (Alexander and Baptista, 2008). Thus, the RBF is useful for analyzing the agency problem in delegated portfolio management. The RBF does not have a closed-form definition and must be determined numerically: to this aim, we develop a fast and accurate algorithm.