IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v16y2016i5p681-693.html
   My bibliography  Save this article

Performance ratio-based coherent risk measure and its application

Author

Listed:
  • Zhiping Chen
  • Qianhui Hu
  • Ruiyue Lin

Abstract

Utilizing a specific acceptance set, we propose in this paper a general method to construct coherent risk measures called the generalized shortfall risk measure. Besides some existing coherent risk measures, several new types of coherent risk measures can be generated. We investigate the generalized shortfall risk measure’s desirable properties such as consistency with second-order stochastic dominance. By combining the performance evaluation with the risk control, we study in particular the performance ratio-based coherent risk (PRCR) measures, which is a sub-class of generalized shortfall risk measures. The PRCR measures are tractable and have a suitable financial interpretation. Based on the PRCR measure, we establish a portfolio selection model with transaction costs. Empirical results show that the optimal portfolio obtained under the PRCR measure performs much better than the corresponding optimal portfolio obtained under the higher moment coherent risk measure.

Suggested Citation

  • Zhiping Chen & Qianhui Hu & Ruiyue Lin, 2016. "Performance ratio-based coherent risk measure and its application," Quantitative Finance, Taylor & Francis Journals, vol. 16(5), pages 681-693, May.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:5:p:681-693
    DOI: 10.1080/14697688.2015.1075059
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/14697688.2015.1075059
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697688.2015.1075059?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. PAVLO A. Krokhmal, 2007. "Higher moment coherent risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 373-387.
    2. Guastaroba, Gianfranco & Mansini, Renata & Speranza, M. Grazia, 2009. "On the effectiveness of scenario generation techniques in single-period portfolio optimization," European Journal of Operational Research, Elsevier, vol. 192(2), pages 500-511, January.
    3. De Rossi, Giuliano & Harvey, Andrew, 2009. "Quantiles, expectiles and splines," Journal of Econometrics, Elsevier, vol. 152(2), pages 179-185, October.
    4. Chen, Zhiping & Yang, Li, 2011. "Nonlinearly weighted convex risk measure and its application," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1777-1793, July.
    5. Philippe Artzner, 1999. "Application of Coherent Risk Measures to Capital Requirements in Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 11-25.
    6. Bellini, Fabio & Rosazza Gianin, Emanuela, 2008. "On Haezendonck risk measures," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 986-994, June.
    7. Bellini Fabio & Rosazza Gianin Emanuela, 2008. "Optimal portfolios with Haezendonck risk measures," Statistics & Risk Modeling, De Gruyter, vol. 26(2), pages 89-108, March.
    8. Wang, Shaun S. & Young, Virginia R. & Panjer, Harry H., 1997. "Axiomatic characterization of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 173-183, November.
    9. Bellini, Fabio & Klar, Bernhard & Müller, Alfred & Rosazza Gianin, Emanuela, 2014. "Generalized quantiles as risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 41-48.
    10. Farinelli, Simone & Tibiletti, Luisa, 2008. "Sharpe thinking in asset ranking with one-sided measures," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1542-1547, March.
    11. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    12. Goovaerts, Marc J. & Kaas, Rob & Dhaene, Jan & Tang, Qihe, 2004. "Some new classes of consistent risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 505-516, June.
    13. Fischer, T., 2003. "Risk capital allocation by coherent risk measures based on one-sided moments," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 135-146, February.
    14. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    15. Chen, Zhiping & Wang, Yi, 2008. "Two-sided coherent risk measures and their application in realistic portfolio optimization," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2667-2673, December.
    16. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    17. Haezendonck, J. & Goovaerts, M., 1982. "A new premium calculation principle based on Orlicz norms," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 41-53, January.
    18. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    19. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    20. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tomer Shushi, 2018. "Towards a Topological Representation of Risks and Their Measures," Risks, MDPI, vol. 6(4), pages 1-11, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhiping Chen & Qianhui Hu, 2018. "On Coherent Risk Measures Induced by Convex Risk Measures," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 673-698, June.
    2. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007, arXiv.org, revised May 2016.
    3. Marcelo Brutti Righi, 2015. "A composition between risk and deviation measures," Papers 1511.06943, arXiv.org, revised May 2018.
    4. Righi, Marcelo Brutti & Borenstein, Denis, 2018. "A simulation comparison of risk measures for portfolio optimization," Finance Research Letters, Elsevier, vol. 24(C), pages 105-112.
    5. Weiwei Li & Dejian Tian, 2023. "Robust optimized certainty equivalents and quantiles for loss positions with distribution uncertainty," Papers 2304.04396, arXiv.org.
    6. James Ming Chen, 2018. "On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles," Risks, MDPI, vol. 6(2), pages 1-28, June.
    7. Ruodu Wang & Ričardas Zitikis, 2021. "An Axiomatic Foundation for the Expected Shortfall," Management Science, INFORMS, vol. 67(3), pages 1413-1429, March.
    8. Fu, Tianwen & Zhuang, Xinkai & Hui, Yongchang & Liu, Jia, 2017. "Convex risk measures based on generalized lower deviation and their applications," International Review of Financial Analysis, Elsevier, vol. 52(C), pages 27-37.
    9. Chen, Zhiping & Yang, Li, 2011. "Nonlinearly weighted convex risk measure and its application," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1777-1793, July.
    10. Gómez, Fabio & Tang, Qihe & Tong, Zhiwei, 2022. "The gradient allocation principle based on the higher moment risk measure," Journal of Banking & Finance, Elsevier, vol. 143(C).
    11. Marcelo Brutti Righi, 2018. "A theory for combinations of risk measures," Papers 1807.01977, arXiv.org, revised May 2023.
    12. Pesenti, Silvana M. & Millossovich, Pietro & Tsanakas, Andreas, 2019. "Reverse sensitivity testing: What does it take to break the model?," European Journal of Operational Research, Elsevier, vol. 274(2), pages 654-670.
    13. Geissel Sebastian & Sass Jörn & Seifried Frank Thomas, 2018. "Optimal expected utility risk measures," Statistics & Risk Modeling, De Gruyter, vol. 35(1-2), pages 73-87, January.
    14. Marcelo Brutti Righi, 2019. "A composition between risk and deviation measures," Annals of Operations Research, Springer, vol. 282(1), pages 299-313, November.
    15. Chi, Yichun & Liu, Fangda, 2017. "Optimal insurance design in the presence of exclusion clauses," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 185-195.
    16. Bellini Fabio & Rosazza Gianin Emanuela, 2008. "Optimal portfolios with Haezendonck risk measures," Statistics & Risk Modeling, De Gruyter, vol. 26(2), pages 89-108, March.
    17. Bellini, Fabio & Rosazza Gianin, Emanuela, 2012. "Haezendonck–Goovaerts risk measures and Orlicz quantiles," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 107-114.
    18. Krätschmer Volker & Schied Alexander & Zähle Henryk, 2015. "Quasi-Hadamard differentiability of general risk functionals and its application," Statistics & Risk Modeling, De Gruyter, vol. 32(1), pages 25-47, April.
    19. Volker Kratschmer & Alexander Schied & Henryk Zahle, 2014. "Quasi-Hadamard differentiability of general risk functionals and its application," Papers 1401.3167, arXiv.org, revised Feb 2015.
    20. Adam, Alexandre & Houkari, Mohamed & Laurent, Jean-Paul, 2008. "Spectral risk measures and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1870-1882, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:quantf:v:16:y:2016:i:5:p:681-693. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.