Tail estimation and mean–VaR portfolio selection in markets subject to financial instability

Abstract

Risk managers are increasingly required by international Regulatory Institutions to adopt accurate techniques for the measurement and control of portfolios financial risks. The task requires first the identification of the different risk sources affecting the portfolio and the measurement of their impact, then after: the adoption of appropriate portfolio strategies aimed at neutralising these risks. The comprehensive concept of Value-at-Risk (VaR) as a maximum tolerable loss, with a given confidence interval, has become in this regard the industry standard in risk management. In the paper we focus on the implications of different risk measurement techniques and portfolio optimisation strategies in presence of markets subject to periods of severe instability, resulting in significant deviations of financial returns from the Normality assumption typically adopted in mainstream finance. Comparative results on 1 day-VaR(99%) estimation are presented over a range of bond and equity markets with different risk profiles. The reference period of our analysis includes several market shocks and in particular the Argentinean Eurobond crisis of July 2001. The solution of an optimal portfolio problem over the crisis period is discussed within a [mean, variance, VaR99%] portfolio space, emphasising the difficulty of the portfolio's relative return maximisation problem faced by fund managers.