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 difference of EPMs for two independent samples. We also derive the asymptotic distribution for EPM and for the difference 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.

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This research has been partially supported by grants from Beijing Normal University, Erasmus University Rotterdam, Complutense University of Madrid, Asia University, Lingnan University, Research Grants Council (RGC) of Hong Kong (project numbers 12502814 and 12500915), Australian Research Council, National Science Council, Ministry of Science and Technology (MOST), Taiwan, Fundamental Research Funds for the Central Universities, Natural Science Foundation of China (11601227), China Postdoctoral Science Foundation (2016M600951, 2017M610058), and Natural Science Foundation of Jiangsu Province, China (BK20150732).
Econometric Institute Research Papers
Erasmus School of Economics

Niu, C., Guo, X., McAleer, M., & Wong, W.-K. (2017). Theory and Application of an Economic Performance Measure of Risk (No. EI2017-18). Econometric Institute Research Papers. Retrieved from http://hdl.handle.net/1765/100417