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Theory and Application of an Economic Performance Measure of Risk

Author

Listed:
  • Cuizhen Niu

    (Beijing Normal University, China)

  • Xu Guo

    (Beijing Normal University, China)

  • Michael McAleer

    (National Tsing Hua University, Taiwan; University of Sydney Business School, Australia; Erasmus University Rotterdam, The Netherlands;Complutense University of Madrid, Spain; Yokohama National University, Japan)

  • Wing-Keung Wong

    (Beijing Normal University, China)

Abstract

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.

Suggested Citation

  • Cuizhen Niu & Xu Guo & Michael McAleer & Wing-Keung Wong, 2017. "Theory and Application of an Economic Performance Measure of Risk," Tinbergen Institute Discussion Papers 17-055/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20170055
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    References listed on IDEAS

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    13. Schulze, Klaas, 2014. "Existence and computation of the Aumann–Serrano index of riskiness and its extension," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 219-224.
    14. Homm, Ulrich & Pigorsch, Christian, 2012. "Beyond the Sharpe ratio: An application of the Aumann–Serrano index to performance measurement," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2274-2284.
    15. Zou, G.Y., 2010. "Confidence interval estimation under inverse sampling," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 55-64, January.
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    Cited by:

    1. Nguyen Huu Hau & Tran Trung Tinh & Hoa Anh Tuong & Wing-Keung Wong, 2020. "Review of Matrix Theory with Applications in Education and Decision Sciences," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(1), pages 28-69, March.
    2. Bin Liu & Monica Tan, 2019. "Overconfidence and forecast accuracy," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 38(3), pages 601-618, July.
    3. Kai-Yin Woo & Chulin Mai & Michael McAleer & Wing-Keung Wong, 2020. "Review on Efficiency and Anomalies in Stock Markets," Economies, MDPI, vol. 8(1), pages 1-51, March.
    4. Zhihui Lv & Amanda M. Y. Chu & Michael McAleer & Wing-Keung Wong, 2019. "Modelling Economic Growth, Carbon Emissions, and Fossil Fuel Consumption in China: Cointegration and Multivariate Causality," IJERPH, MDPI, vol. 16(21), pages 1-35, October.
    5. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Management Information, Decision Sciences, and Financial Economics: A Connection," Tinbergen Institute Discussion Papers 18-004/III, Tinbergen Institute.
    6. Xu Guo & Cuizhen Niu & Wing-Keung Wong, 2019. "Farinelli and Tibiletti ratio and stochastic dominance," Risk Management, Palgrave Macmillan, vol. 21(3), pages 201-213, September.
    7. Richard Lu & Chen-Chen Yang & Wing-Keung Wong, 2018. "Time Diversification: Perspectives From The Economic Index Of Riskiness," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 1-15, September.
    8. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," JRFM, MDPI, vol. 11(1), pages 1-29, March.
    9. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, And Big Data: Connections," Advances in Decision Sciences, Asia University, Taiwan, vol. 22(1), pages 36-94, December.
    10. Kim-Hung Pho & Tuan-Kiet Tran & Thi Diem-Chinh Ho & Wing-Keung Wong, 2019. "Optimal Solution Techniques in Decision Sciences A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(1), pages 114-161, March.
    11. Chang, C-L. & McAleer, M.J. & Wong, W.-K., 2018. "Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections," Econometric Institute Research Papers 18-024/III, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Massoud Moslehpour & Shin Hung Pan & Aviral Kumar Tiwari & Wing Keung Wong, 2021. "Editorial in Honour of Professor Michael McAleer," Advances in Decision Sciences, Asia University, Taiwan, vol. 25(4), pages 1-14, December.
    13. Lu, Richard & Horng, Tzyy-Leng & Horng, Min-Sun & Wang, Amy Z.-H., 2023. "A performance evaluation of portfolio insurance under the Black and Scholes framework: An application of the economic index of riskiness," The Quarterly Review of Economics and Finance, Elsevier, vol. 89(C), pages 269-276.
    14. Hodoshima, Jiro & Yamawake, Toshiyuki, 2022. "Temporal aggregation of the Aumann–Serrano and Foster–Hart performance indexes," International Review of Financial Analysis, Elsevier, vol. 83(C).
    15. Jiro Hodoshima & Toshiyuki Yamawake, 2022. "Comparing Dynamic and Static Performance Indexes in the Stock Market: Evidence From Japan," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(2), pages 171-193, June.
    16. Kim-Hung Pho & Thi Diem-Chinh Ho & Tuan-Kiet Tran & Wing-Keung Wong, 2019. "Moment Generating Function, Expectation And Variance Of Ubiquitous Distributions With Applications In Decision Sciences: A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(2), pages 65-150, June.
    17. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 11(1), pages 1-29, March.

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    More about this item

    Keywords

    Economic performance measure; Asymptotic confidence interval; Bootstrap-based confidence interval; Method of variance estimates recovery;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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