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

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  • Balog, Dóra
  • Bátyi, Tamás László
  • Csóka, Péter
  • Pintér, Miklós

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.

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  • Balog, Dóra & Bátyi, Tamás László & Csóka, Péter & Pintér, Miklós, 2014. "Properties of risk capital allocation methods: Core Compatibility, Equal Treatment Property and Strong Monotonicity," Corvinus Economics Working Papers (CEWP) 2014/13, Corvinus University of Budapest.
    • Handle: RePEc:cvh:coecwp:2014/13
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    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.

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    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)

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