Theory and Application of an Economic Performance Measure of Risk - Cuizhen Niu; Xu Guo; Michael McAleer; Wing-keung Wong (Tinbergen Institute, 2017)
Homm and Pigorsch (2012a) use the Aumann and Serrano index to develop a new economic performance measure (EPM), which is well known to have advantages over other measures. In this paper, we extend the theory by constructing a one-sample confidence interval of EPM, and construct confidence intervals for the dfference of EPMs for two independent samples. We also derive the asymptotic distribution for EPM and for the dfference of two EPMs when the samples are independent. We conduct simulations to show the proposed theory performs well for one and two independent samples. The simulations show that the proposed approach is robust in the dependent case. The theory developed is used to construct both one-sample and two-sample confidence intervals of EPMs for Singapore and USA stock indices.
Keywords: C12; C15; 330; Economic performance measure; Asymptotic confidence interval; Bootstrap-based confidence interval; Method of variance estimates recovery