Research Article
BibTex RIS Cite

Risk Measures and Risk Capital Allocation

Year 2012, Volume: 5 Issue: 2, 32 - 42, 01.06.2012

Abstract

The fundamental problem of the portfolio/risk management is the measurementm and the allocation of risk. Various risk measures provide a solution to the former problem. However, in the recent decade’s risk measures have been criticised dramatically and a new concept so called ’coherent risk measures’ have been arisen. In the meantime allocation distributes the diversification benefits among the constituents of the portfolio. We show that risk allocation can provide a better risk management if one pays the necessary attention for the choice of the risk measure and the allocation method.

References

  • P. Artzner, F. Delbaen, J.M. Eber, and D. Heath, 1997, Thinking coherently. RISK, 10:68-71.
  • P. Artzner, F. Delbaen, J.M. Eber, and D. Heath, 1999, Coherent measures of risk, Mathematical Finance, 9-3: 203-228.
  • J-P. Aubin, 1979, Mathematical Methods of Game and Economic Theory, North-Holland Publishing Co., Amsterdam.
  • J-P. Aubin, 1981, Cooperative fuzzy games, Mathematics of Operations and Research, 6-1:1-13.
  • R. J. Aumann and L. S. Shapley, 1974, Values of Non-Atomic Games, Princeton University Press, Princeton.
  • A. Buch and G. Dorfleitner, 2008, Coherent risk measure, coherent capital allocations and the gradient allocation principle, Insurance: Mathematics and Economics, 42:235-242.
  • A. Buch, G. Dorfleitner, and M. Wimmer, 2009, Rethinking risk capital allocation in a rorac framework.
  • J.D. Cummins, 2000, Allocation of capital in the insurance industry, Risk Management & Insurance Review, 3:7-27.
  • F. Delbaen and E.. Ossische, 2000, Technische Hochschule. Coherent risk measures on general probability spaces, ETH Zurich.
  • M. Denault, 2001, Coherent allocation of risk capital, Journal of Risk, 4-1:7-21.
  • J. Dhaene, A. Tsanakas, E. A. Valdez, and S. Vanduffel, 2010, Optimal capital allocation principles, Journal of Risk and Insurance, Forthcoming.
  • K. Dowd and D. Blake, 2006, Discussion paper pi-0603 after var: The theory, estimation and insurance applications of quantile-based risk measures, Technical report, The Pensions Institute.
  • T. Fischer, 2003, Risk capital allocation by coherent risk measures based on one-sided moments. Insurance: Mathematics and Economics, 32-1:135-146.
  • T. Fischer and A. Roehrl, 2003, Risk and performance optimization for portfolios of bonds and stocks, Proceedings of the International AFIR Colloquium
  • K.A. Froot and J.C. Stein, 1998, Risk management, capital budgeting, and capital structure policy for financial institutions: in integrated approach. Journal of Financial Economics, 47:55-82.
  • O. Hesselager and U. Anderson, 2002, Risk sharing and capital allocation, Technical report, Tryg Insurance, Ballerup, Denmark.
  • M. Kalkbrener, 2005, An axiomatic approach to capital allocation. Mathematical Finance, 15-3:425-437.
  • U. Karabey, 2012, Risk Capital Allocation and Risk Quantification in Insurance Companies, PhD thesis, Heriot-Watt University.
  • J. Kim and M. Hardy, 2008, A capital allocation based on a solvency exchange option. Insurance: Mathematics and Economics, 44-3:357-366.
  • R. C. Merton and A. Perold, 1993, Theory of risk capital in financial firms. Journal of Applied Corporate Finance, 6:16-32.
  • S. C. Myers and J. A. Read, 2001, Capital allocation for insurance companies. Journal of Risk and Insurance, 68:545-580.
  • M. B. Neil, 2007, Capital allocation by percentile layer. Enterprise Risk Management Symposium, Society of Actuaries.
  • L. Overbeck, 2000, Allocation of economic capital in loan portfolios. In Measuring Risk in Complex Stochastic Systems, W. Hardle & G. Stahl, Berlin.
  • F. Saita, 1999, Allocation of risk capital in financial institutions. Financial Management, 28:95-111.
  • L. Shapley, 1953, A value for n-person games. In Contribution to the Theory of Games, Princeton University Press Vol. 2.
  • N. M. Stoughton and J. Zechner, 1999, Optimal capital allocation using raroc and eva, Technical report, University of California Irvine und University of Vienna.
  • D. Tasche, 1999, Risk contributions and performance measurement, Technical report, Research paper, Zentrum Mathematik (SCA).
  • D. Tasche, 2002, Expected shortfall and beyond. J. Banking Finance, 26:1519-1533.
  • M. Urban, J. Dittrich, C. Klüppelberg and R. Stölting, 2004, Allocation of risk capital to insurance portfolios, Blatter DGVFM Deutsche Gesellschaft fur versicherungs und finanzmathematike, V. XXVI, 3:389- 406.
  • A. E. Valdez and A. Chernih, 2003, Wang’s capital allocation formula for elliptically contoured distributions. Insurance: Mathematics and Economics, 33:517-532.

Risk Ölçümleri ve Risk Sermayesi Dağıtımı

Year 2012, Volume: 5 Issue: 2, 32 - 42, 01.06.2012

Abstract

Risk Ölçümleri ve Risk Sermayesi Dağıtımı Riskin ölçülmesi ve dağıtılması portföy/risk yönetiminde karsılasılan temel sorunlardır. Birçok risk ölçümü risklerin ölçülmesi için çözümler sunar. Fakat son yıllarda risk ölçümleri önemli ölçüde elestirilmis ve ortaya tutarlı risk ölçümleri olarak adlandırılan yeni bir yaklasım çıkmıstır. Aynı zamanda risk dağıtımı çesitlendirmeden kaynaklanan faydaların portföyü olusturan birimlere dağıtımını yapar. Bu çalısmada risk ölçüm ve risk dağıtım yöntemlerini doğru seçen yöneticilerin daha iyi bir risk yönetimi sağlayabileceğini gösterdik

References

  • P. Artzner, F. Delbaen, J.M. Eber, and D. Heath, 1997, Thinking coherently. RISK, 10:68-71.
  • P. Artzner, F. Delbaen, J.M. Eber, and D. Heath, 1999, Coherent measures of risk, Mathematical Finance, 9-3: 203-228.
  • J-P. Aubin, 1979, Mathematical Methods of Game and Economic Theory, North-Holland Publishing Co., Amsterdam.
  • J-P. Aubin, 1981, Cooperative fuzzy games, Mathematics of Operations and Research, 6-1:1-13.
  • R. J. Aumann and L. S. Shapley, 1974, Values of Non-Atomic Games, Princeton University Press, Princeton.
  • A. Buch and G. Dorfleitner, 2008, Coherent risk measure, coherent capital allocations and the gradient allocation principle, Insurance: Mathematics and Economics, 42:235-242.
  • A. Buch, G. Dorfleitner, and M. Wimmer, 2009, Rethinking risk capital allocation in a rorac framework.
  • J.D. Cummins, 2000, Allocation of capital in the insurance industry, Risk Management & Insurance Review, 3:7-27.
  • F. Delbaen and E.. Ossische, 2000, Technische Hochschule. Coherent risk measures on general probability spaces, ETH Zurich.
  • M. Denault, 2001, Coherent allocation of risk capital, Journal of Risk, 4-1:7-21.
  • J. Dhaene, A. Tsanakas, E. A. Valdez, and S. Vanduffel, 2010, Optimal capital allocation principles, Journal of Risk and Insurance, Forthcoming.
  • K. Dowd and D. Blake, 2006, Discussion paper pi-0603 after var: The theory, estimation and insurance applications of quantile-based risk measures, Technical report, The Pensions Institute.
  • T. Fischer, 2003, Risk capital allocation by coherent risk measures based on one-sided moments. Insurance: Mathematics and Economics, 32-1:135-146.
  • T. Fischer and A. Roehrl, 2003, Risk and performance optimization for portfolios of bonds and stocks, Proceedings of the International AFIR Colloquium
  • K.A. Froot and J.C. Stein, 1998, Risk management, capital budgeting, and capital structure policy for financial institutions: in integrated approach. Journal of Financial Economics, 47:55-82.
  • O. Hesselager and U. Anderson, 2002, Risk sharing and capital allocation, Technical report, Tryg Insurance, Ballerup, Denmark.
  • M. Kalkbrener, 2005, An axiomatic approach to capital allocation. Mathematical Finance, 15-3:425-437.
  • U. Karabey, 2012, Risk Capital Allocation and Risk Quantification in Insurance Companies, PhD thesis, Heriot-Watt University.
  • J. Kim and M. Hardy, 2008, A capital allocation based on a solvency exchange option. Insurance: Mathematics and Economics, 44-3:357-366.
  • R. C. Merton and A. Perold, 1993, Theory of risk capital in financial firms. Journal of Applied Corporate Finance, 6:16-32.
  • S. C. Myers and J. A. Read, 2001, Capital allocation for insurance companies. Journal of Risk and Insurance, 68:545-580.
  • M. B. Neil, 2007, Capital allocation by percentile layer. Enterprise Risk Management Symposium, Society of Actuaries.
  • L. Overbeck, 2000, Allocation of economic capital in loan portfolios. In Measuring Risk in Complex Stochastic Systems, W. Hardle & G. Stahl, Berlin.
  • F. Saita, 1999, Allocation of risk capital in financial institutions. Financial Management, 28:95-111.
  • L. Shapley, 1953, A value for n-person games. In Contribution to the Theory of Games, Princeton University Press Vol. 2.
  • N. M. Stoughton and J. Zechner, 1999, Optimal capital allocation using raroc and eva, Technical report, University of California Irvine und University of Vienna.
  • D. Tasche, 1999, Risk contributions and performance measurement, Technical report, Research paper, Zentrum Mathematik (SCA).
  • D. Tasche, 2002, Expected shortfall and beyond. J. Banking Finance, 26:1519-1533.
  • M. Urban, J. Dittrich, C. Klüppelberg and R. Stölting, 2004, Allocation of risk capital to insurance portfolios, Blatter DGVFM Deutsche Gesellschaft fur versicherungs und finanzmathematike, V. XXVI, 3:389- 406.
  • A. E. Valdez and A. Chernih, 2003, Wang’s capital allocation formula for elliptically contoured distributions. Insurance: Mathematics and Economics, 33:517-532.
There are 30 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Uğur Karabey

Publication Date June 1, 2012
Published in Issue Year 2012 Volume: 5 Issue: 2

Cite

IEEE U. Karabey, “Risk Measures and Risk Capital Allocation”, JSSA, vol. 5, no. 2, pp. 32–42, 2012.