Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지
DOI QR코드

DOI QR Code

Diversification, performance and optimal business mix of insurance portfolios

  • Received : 2013.10.03
  • Accepted : 2013.10.28
  • Published : 2013.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

For multi-line insurance companies, allocating the risk capital to each line is a widely-accepted risk management exercise. In this article we consider several applications of the Euler capital allocation. First, we propose visual tools to present the diversification and the line-wise performance for a given loss portfolio so that the risk managers can understand the interactions among the lines. Secondly, on theoretical side, we prove that the Euler allocation is the directional derivative of the marginal or incremental allocation method, an alternative capital allocation rule in the literature. Lastly, we establish the equivalence between the mean-shortfall optimization and the RORAC optimization when the risk adjusted capital is the expected shortfall, and show how to construct the optimal insurance business mix that maximizes the portfolio RORAC. An actual loss sample of an insurance portfolio is used for numerical illustrations.

Keywords

References

  1. Albrecht, P. (2006). Risk based capital allocation. Encyclopedia of Actuarial Sciences, John Wiley & Sons, New York.
  2. Artzner, P., Delbaen, F., Eber, J. M. and Heath, D. (1999). Coherent measure of risk. Mathematical Finance, 9, 203-228. https://doi.org/10.1111/1467-9965.00068
  3. BCBS (2006). International convergence of capital measurement and capital standards: A revised framework comprehensive version, Basel Committee on Banking Supervision, Basel.
  4. Bertsimas, D., Lauprete, G. and Samarov, A. (2004). Shortfall as a risk measure: Properties, optimization and applications. Journal of Economic Dynamics and Control, 28, 1353-1381. https://doi.org/10.1016/S0165-1889(03)00109-X
  5. Buch, A., Doreitner, G. and Wimmer, M. (2011). Risk capital allocation for RORAC optimization. Journal of Banking and Finance, 35, 3001-3009 https://doi.org/10.1016/j.jbankfin.2011.04.001
  6. Chew, D., editor (2001). The new corporate finance: Where theory meets practice, 3rd Ed., McGraw-Hill Companies, New York.
  7. Crouhy, M., Turnbull, S. M. and Wakeman, L. M. (1999). Measuring risk-adjusted performance. Journal of Risk, 2, 5-36. https://doi.org/10.21314/JOR.1999.018
  8. Denault, M. (2001). Coherent risk allocation of risk capital. Journal of Risk, 4, 1-34. https://doi.org/10.1080/136698701455997
  9. Dev, A. (2004). Economic capital: A practitioner guide, Risk Books, London.
  10. Dhaene, J., Tsanakas, A., Valdez, E. and Vandu el, S. (2012). Optimal capital allocation principles. Journal of Risk and Insurance, 79, 1-28. https://doi.org/10.1111/j.1539-6975.2011.01408.x
  11. Garcia Cespedes, J. C., de Juan Herrero, J., Kreinin, A. and Rosen, D. (2006). A simple multi-factor "factor adjustment" for the treatment of credit capital diversification. Journal of Credit Risk , 2, 57-85. https://doi.org/10.21314/JCR.2006.039
  12. Good, P. (2000). Permutation tests: A practical guide to resampling methods for testing hypotheses, Springer Verlag, New York.
  13. Gourieroux, C., Laurent, J. and Scaillet, O. (2000). Sensitivity analysis of values at risk. Journal of Empirical Finance, 7, 225-245. https://doi.org/10.1016/S0927-5398(00)00011-6
  14. Hallerbach, W. (2003). Decomposing portfolio value-at-risk: A general analysis. Journal of Risk , 5, 1-18.
  15. Kalkbrener, M. (2005). An axiomatic approach to capital allocation. Mathematical Finance, 15, 425-437. https://doi.org/10.1111/j.1467-9965.2005.00227.x
  16. Kim, J. H. T. and Hardy, M. R. (2009). A capital allocation based on a solvency exchange option. Insurance:Mathematics and Economics, 44, 357-366. https://doi.org/10.1016/j.insmatheco.2008.11.006
  17. Markowitz, H. (1959). Portfolio selection: Efficient diversification of investment, John Wiley & Sons, New York.
  18. Matten, C. (1996). Managing bank capital, John Wiley & Sons, New York.
  19. McNeil, A. J., Frey, R. and Embrechts, P. (2005). Quantitative risk management, Princeton University Press, New Jersey.
  20. Memmel, C. and Wehn, C. (2006). Supervisor's portfolio: The market price risk of German banks from 2001 to 2004: Analysis and models for risk aggregation. Journal of Banking Regulation, 7, 310-325. https://doi.org/10.1057/palgrave.jbr.2350023
  21. Merton, R. C. and Perold, A. F. (1993). Theory of risk capital in financial firms. Journal of Applied Corporate Finance, 6, 16-32. https://doi.org/10.1111/j.1745-6622.1993.tb00231.x
  22. Myers, S. C. and Read Jr., J. A. (2001). Capital allocation for insurance companies. Journal of Risk and Insurance, 68, 545-580. https://doi.org/10.2307/2691539
  23. Panjer, H. (2002). Measurement of risk, solvency requirements, and allocation of capital within financial conglomerates, IIPR technical report 01-14, University of Waterloo, Waterloo.
  24. Rockafellar, R. and Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk , 2, 21-42. https://doi.org/10.21314/JOR.2000.038
  25. Saita, F. (2007). Value at risk and bank capital management, Academic Press, London.
  26. Sherris, M. (2006). Solvency, capital allocation and fair rate of return in insurance. Journal of Risk and Insurance, 73, 71-96. https://doi.org/10.1111/j.1365-2966.2006.00166.x
  27. Sherris, M. and van der Hoek, J. (2006). Capital allocation in insurance: economic capital and the allocation of the default option value. North American Acutarial Journal, 10, 39-61 https://doi.org/10.1080/10920277.2006.10596247
  28. Shim, J. and Hwang, C (2013). Expected shortfall estimation using kernel machines. Journal of the Korean Data & Information Science Society, 24, 625-636. https://doi.org/10.7465/jkdi.2013.24.3.625
  29. Skoglund, J. and Chen, W. (2009). Risk contributions, information and reverse stress testing. The Journal of Risk Model Validation, 3, 61-77.
  30. Tasche, D. (1999). Risk contributions and performance measurement. Working paper, Zentrum Marhematic (SCA), TU Munchen, Germany.
  31. Tasche, D. (2004). Economic capital: A practitioner's guide. In Allocating Portfolio Economic Capital to Sub-portfolios, edited by A. Dev, Risk Books, London, 275-302.
  32. Tasche, D. (2006). Measuring sectoral diversification in an asymptotic multifactor framework. Journal of Credit Risk, 2, 33-55.
  33. Tasche, D. (2007). Euler allocation: Theory and practice. Arxiv preprint arXiv:0708.2542 .
  34. Zaik, E., Walter, J., Retting, G. and James, C. (2005). RAROC at bank of america: From theory to practice. Journal of Applied Corporate Finance, 9, 83-93.
  35. Zanjani, G. (2002). Pricing and capital allocation in catastrophe insurance. Journal of Financial Economics, 65, 283-305. https://doi.org/10.1016/S0304-405X(02)00141-1