Reconciling Tracking Error Volatility and Value-at-Risk in Active Portfolio Management: A New Frontier

Abstract

This article introduces the Risk Balancing Frontier (RBF), a new portfolio boundary in the absolute risk-total return space: the RBF arises when two risk indicators, the Tracking Error Volatility (TEV) and the Value-at-Risk (VaR), are both constrained not to exceed pre-set maximum values. By focusing on the trade-off between the joint restrictions on the two risk indicators, this frontier is the set of all portfolios characterized by the minimum VaR attainable for each TEV level. First, the RBF is defined analytically and its mathematical properties are discussed: we show its connection with the Constrained Tracking Error Volatility Frontier (Jorion in Financ Anal J, 59(5):70–82, 2003. https://doi.org/10.2469/faj.v59.n5.2565) and the Constrained Value-at-Risk Frontier (Alexander and Baptista in J Econ Dyn Control, 32(3):779–820, 2008. https://doi.org/10.1016/j.jedc.2007.03.005) frontiers. Next, we explore computational issues implied with its construction, and we develop a fast and accurate algorithm to this aim. Finally, we perform an empirical example and consider its relevance in the context of applied finance: we show that the RBF provides a useful tool to investigate and solve potential agency problems.