IDEAS home Printed from https://ideas.repec.org/p/has/discpr/1417.html
   My bibliography  Save this paper

Properties of risk capital allocation methods: Core Compatibility, Equal Treatment Property and Strong Monotonicity

Author

Listed:
  • Dóra Balog

    (Corvinus University of Budapest, Department of Finance)

  • Tamás László Bátyi

    (University of California, Berkeley, Department of Economics)

  • Péter Csóka

    (Momentum Game Theory Research Group, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences and Department of Finance, Corvinus University of Budapest)

  • Miklós Pintér

    (Corvinus University of Budapest, Department of Mathematics and MTA-BCE Lendület Strategic Interactions Research Group)

Abstract

In finance risk capital allocation raises important questions both from theoretical and practical points of view. How to share risk of a portfolio among its subportfolios? How to reserve capital in order to hedge existing risk and how to assign this to different business units? We use an axiomatic approach to examine risk capital allocation, that is we call for fundamental properties of the methods. Our starting point is Csóka and Pintér (2011) who show by generalizing Young (1985)'s axiomatization of the Shapley value that the requirements of Core Compatibility, Equal Treatment Property and Strong Monotonicity are irreconcilable given that risk is quantified by a coherent measure of risk. In this paper we look at these requirements using analytic and simulations tools. We examine allocation methods used in practice and also ones which are theoretically interesting. Our main result is that the problem raised by Csóka and Pintér (2011) is indeed relevant in practical applications, that is it is not only a theoretical problem. We also believe that through the characterizations of the examined methods our paper can serve as a useful guide for practitioners.

Suggested Citation

  • Dóra Balog & Tamás László Bátyi & Péter Csóka & Miklós Pintér, 2014. "Properties of risk capital allocation methods: Core Compatibility, Equal Treatment Property and Strong Monotonicity," CERS-IE WORKING PAPERS 1417, Institute of Economics, Centre for Economic and Regional Studies.
  • Handle: RePEc:has:discpr:1417
    as

    Download full text from publisher

    File URL: http://econ.core.hu/file/download/mtdp/MTDP1417.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Csóka Péter & Pintér Miklós, 2016. "On the Impossibility of Fair Risk Allocation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 16(1), pages 143-158, January.
    2. Tijs, S.H. & Driessen, T.S.H., 1986. "Game theory and cost allocation problems," Other publications TiSEM 376c24c5-c95d-4d29-96b6-4, Tilburg University, School of Economics and Management.
    3. Boonen, Tim J. & De Waegenaere, Anja & Norde, Henk, 2020. "A generalization of the Aumann–Shapley value for risk capital allocation problems," European Journal of Operational Research, Elsevier, vol. 282(1), pages 277-287.
    4. Csoka, Peter & Herings, P. Jean-Jacques & Koczy, Laszlo A., 2007. "Coherent measures of risk from a general equilibrium perspective," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2517-2534, August.
    5. Csóka, Péter & Herings, P. Jean-Jacques & Kóczy, László Á., 2009. "Stable allocations of risk," Games and Economic Behavior, Elsevier, vol. 67(1), pages 266-276, September.
    6. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    7. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Homburg, Carsten & Scherpereel, Peter, 2008. "How should the cost of joint risk capital be allocated for performance measurement?," European Journal of Operational Research, Elsevier, vol. 187(1), pages 208-227, May.
    9. Carlo Acerbi & Giacomo Scandolo, 2008. "Liquidity risk theory and coherent measures of risk," Quantitative Finance, Taylor & Francis Journals, vol. 8(7), pages 681-692.
    10. Michael Kalkbrener, 2005. "An Axiomatic Approach To Capital Allocation," Mathematical Finance, Wiley Blackwell, vol. 15(3), pages 425-437, July.
    11. Kim, Joseph H.T. & Hardy, Mary R., 2009. "A capital allocation based on a solvency exchange option," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 357-366, June.
    12. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    13. Valdez, Emiliano A. & Chernih, Andrew, 2003. "Wang's capital allocation formula for elliptically contoured distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 517-532, December.
    14. 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.
    15. Boonen, T.J. & De Waegenaere, A.M.B. & Norde, H.W., 2012. "A Generalization of the Aumann-Shapley Value for Risk Capital Allocation Problems," Other publications TiSEM 2c502ef8-76f0-47f5-ab45-1, Tilburg University, School of Economics and Management.
    16. Buch, A. & Dorfleitner, G., 2008. "Coherent risk measures, coherent capital allocations and the gradient allocation principle," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 235-242, February.
    17. S. H. Tijs & T. S. H. Driessen, 1986. "Game Theory and Cost Allocation Problems," Management Science, INFORMS, vol. 32(8), pages 1015-1028, August.
    18. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    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. Csóka Péter & Pintér Miklós, 2016. "On the Impossibility of Fair Risk Allocation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 16(1), pages 143-158, January.
    2. Csóka, Péter, 2017. "Fair risk allocation in illiquid markets," Finance Research Letters, Elsevier, vol. 21(C), pages 228-234.

    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. Balog, Dóra & Bátyi, Tamás László & Csóka, Péter & Pintér, Miklós, 2017. "Properties and comparison of risk capital allocation methods," European Journal of Operational Research, Elsevier, vol. 259(2), pages 614-625.
    2. Csóka, Péter & Bátyi, Tamás László & Pintér, Miklós & Balog, Dóra, 2011. "Tőkeallokációs módszerek és tulajdonságaik a gyakorlatban [Methods of capital allocation and their characteristics in practice]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 619-632.
    3. Csóka Péter & Pintér Miklós, 2016. "On the Impossibility of Fair Risk Allocation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 16(1), pages 143-158, January.
    4. Csóka, Péter, 2017. "Fair risk allocation in illiquid markets," Finance Research Letters, Elsevier, vol. 21(C), pages 228-234.
    5. Csóka, Péter & Herings, P. Jean-Jacques, 2014. "Risk allocation under liquidity constraints," Journal of Banking & Finance, Elsevier, vol. 49(C), pages 1-9.
    6. Hougaard, Jens Leth & Smilgins, Aleksandrs, 2016. "Risk capital allocation with autonomous subunits: The Lorenz set," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 151-157.
    7. Boonen, Tim J., 2017. "Risk Redistribution Games With Dual Utilities," ASTIN Bulletin, Cambridge University Press, vol. 47(1), pages 303-329, January.
    8. Dora Balog, 2011. "Capital allocation in financial institutions: the Euler method," CERS-IE WORKING PAPERS 1126, Institute of Economics, Centre for Economic and Regional Studies.
    9. Dóra Balog, 2017. "Capital Allocation in the Insurance Sector," Financial and Economic Review, Magyar Nemzeti Bank (Central Bank of Hungary), vol. 16(3), pages 74-97.
    10. Björn Häckel, 2010. "Risikoadjustierte Wertbeiträge zur ex ante Entscheidungsunterstützung: Ein axiomatischer Ansatz," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 21(1), pages 81-108, June.
    11. Boonen, Tim J. & De Waegenaere, Anja & Norde, Henk, 2020. "A generalization of the Aumann–Shapley value for risk capital allocation problems," European Journal of Operational Research, Elsevier, vol. 282(1), pages 277-287.
    12. Karl Michael Ortmann, 2016. "The link between the Shapley value and the beta factor," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(2), pages 311-325, November.
    13. van Gulick, Gerwald & De Waegenaere, Anja & Norde, Henk, 2012. "Excess based allocation of risk capital," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 26-42.
    14. Kao, Lie-Jane, 2015. "A portfolio-invariant capital allocation scheme penalizing concentration risk," Economic Modelling, Elsevier, vol. 51(C), pages 560-570.
    15. van Gulick, G. & De Waegenaere, A.M.B. & Norde, H.W., 2010. "Excess Based Allocation of Risk Capital," Other publications TiSEM f9231521-fea7-4524-8fea-8, Tilburg University, School of Economics and Management.
    16. Kamil J. Mizgier & Joseph M. Pasia, 2016. "Multiobjective optimization of credit capital allocation in financial institutions," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 24(4), pages 801-817, December.
    17. Jens Leth Hougaard & Aleksandrs Smilgins, 2014. "Risk Capital Allocation: The Lorenz Set," MSAP Working Paper Series 03_2014, University of Copenhagen, Department of Food and Resource Economics.
    18. 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).
    19. Dóra Balog, 2010. "Risk based capital allocation," Proceedings of FIKUSZ '10, in: László Áron Kóczy (ed.),Proceedings of FIKUSZ 2010, pages 17-26, Óbuda University, Keleti Faculty of Business and Management.
    20. Wang, Wei & Xu, Huifu & Ma, Tiejun, 2023. "Optimal scenario-dependent multivariate shortfall risk measure and its application in risk capital allocation," European Journal of Operational Research, Elsevier, vol. 306(1), pages 322-347.

    More about this item

    Keywords

    Coherent Measures of Risk; Risk Capital Allocation; Shapley value; Core; Simulation;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:has:discpr:1417. 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: Nora Horvath (email available below). General contact details of provider: https://edirc.repec.org/data/iehashu.html .

    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.