Portfolio frontiers with restrictions to tracking error volatility and value at risk

Abstract

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 may be impossible to satisfy simultaneously because VaR is independent of the benchmark portfolio. The management of these restrictions is likely to affect portfolio performance 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 risk managers impose joint restrictions upon TEV and VaR. Specifically, we provide analytical solutions for all the intersections and we propose simple numerical methods when such solutions are not available. Finally, we introduce a new portfolio frontier

Benefits and Consequences of Diversification: Evidence from Financialzed Commodity Portfolios

“…Second, it offers new perspective of investigating portfolio VaR and ES in commodity markets. This complements existing literature examining portfolio VaR in foreign exchange market (Chen et al, 2007) and stock and index markets (Lin and Ko, 2009;Goh et al, 2012;Palomba and Riccetti, 2012;Chen and Tu, 2013).…”

Portfolio performance under tracking error and asset weight constraints

“…For a TE = 5%and an inequality restriction that the sum of the domestic weights must be < 80%, the benchmark falls outside the ellipse (in this stylised example), meaning that the benchmark's unique combination of risk and return is not possible for a portfolio subject to these (relatively mild) constraints. The important point is that -even for relatively moderate limits on acceptable asset weights -the range of portfolios that satisfy the relevant constraints becomes severely diminished, and even the benchmark portfolio is rendered unattainable, a result also obtained by Wagner (2003) and Palomba and Riccetti (2012).…”

Index tracking model, downside risk and non-parametric kernel estimation

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