An Empirical Study on the Solvency Prediction of Value at Risk and Risk-Based Capital

風險值與風險基礎資本破產預測能力之實證研究

10.30003/JRM.200611.0004

詹芳書(Linus Fang-Shu Chan)；呂璧如(Pi-Ju Lu)

風險基礎資本 ； 涉險值 ； 動態財務分析 ； 財務監理 ； risk-based capital ； value at risk ； dynamic financial analysis ； solvency regulation

風險管理學報

8卷3期（2006 / 11 / 01）

293 - 308

英文

確保保險公司的財務健全一直是保險監理的焦點。在各種監理方法中，風險基礎資本代表目前在保險業中最先進的方法，而涉險值則是已廣泛被其他金融業的監理機關所採納。本研究的目的，是以美國產險業的實證資料，檢驗這兩種方法在預測產險公司破產的能力上孰優孰劣。我們發現涉險值比較能夠事前偵測出有問題的公司，也比較能正確地區分健全與不健全的公司。風險基礎資本則幾乎沒有預警的能力，必須將風險基礎資本乘以數倍以後才能有一些預警的效果。雖然涉險值比風險基礎資本要好，表現仍差強人意，其型二錯誤率偏高，猜測正確率也偏低。作者們認為這個不盡如意的結果，是因為我們沒有足夠的資料來正確地估計保險公司的損失函數。

Assuring insurance companies' solvencies has always been the focal point of insurance regulation. Among solvency regulation methods, risk based capital (RBC) represents the leading capital adequacy requirement in the insurance industry while value at risk (VaR) has been adopted by more and more regulators in other financial industries. The purpose of this research is to empirically compare the effectiveness of RBC and VaR in the solvency predictions of insurance companies. Using the solvency record of property-casualty insurers in the United States from 1995 to 1998, we examine the Type I and Type II errors of VaR and RBC in classifying insurers. RBC figures are from the annual statements and VaR is estimated from our simulation model that is also based on insurers' financial statements. We find that VaR is better than RBC in spotting unhealthy insurers and correctly classifying insurers. VaR has lower type I error rates and higher hit ratios. On the other hand, RBC has hardly any early warning abilities and very low hit ratios. The capital requirement set up by RBC is too low to detect problematic insurers in advance. Regulators have to raise RBC requirements many times to achieve acceptable early warning abilities. Although VaR is superior to RBC, the performance of VaR obtained from our model is not satisfactory. The type II error rates are high and hit ratios are low. We attribute the unsatisfying outcome to the lack of data in estimating loss functions.

1. A. M. Best Co.(2000).1999 Best's Insurance Reports- Property & Casualty, Oldwick.New Jersey:A.M. Best Co.
2. Ambrose, J. M.,A. M. Carroll(1994).Using Best's Ratings in Life Insurer Insolvency Prediction.Journal of Risk and Insurance,61(2),317-327.
3. Cummins, J. D.,M. F. Grace,R. D. Phillips(1999).Regulatory Solvency Prediction in Property-Liability Insurance: Risk-Based Capital, Audit Ratios, and Cash-Flow Simulation.Journal of Risk and Insurance,66(3),417-458.
4. Cummins, J. D.,S. E. Harrington,R. Klein(1995).Insolvency Experience, Risk-Based Capital, and Prompt Corrective Action in Property-Liability Insurance.Journal of Banking and Finance,19(4),511-527.
5. D''Arcy, S. P.,R. W. Gorvett,T. E. Hettinger,R. J. Walling Ⅲ(1998).Using the Public Access DFA Model: A Case Study, 1998 Call Paper Program, Dynamic Financial Analysis- Applications and Uses, CAS Dynamic Financial Analysis Task Force on Variables.Casualty Actuarial Society.
6. Grace, M. F.,S. E. Harrington,R. Klein(1998).Risk-Based Capital and Solvency Screening in Property-Liability Insurance: Hypotheses and Empirical Tests.Journal of Risk and Insurance,65(3),213-243.
7. Harrington, S. E.,G. R. Niehaus(1999).Risk Management and Insurance.Taipei:Irwin McGraw-Hill.
8. Jorion, P.(2001).Value at Risk: The New Benchmark for Managing Financial Risk.Taipei, Taiwan:McGraw-Hill Companies.
9. Panjer, H. H.,P. P. Boyle,S. H. Cox,D. Dufresne,H. U. Gerber,H. H. Mueller,H. W. Pedersen,S. R. Pliska,M. Sherris,E. S. Shiu,K. S. Tan(1998).Financial Economics: with Applications to Investments, Insurance, and Pensions, Schaumburg.Illinois:The Actuarial Foundation.
10. Pottier, S. W.,D. W. Sommer(2002).The Effectiveness of Public and Private Sector Summary Risk Measures in Predicting Insurer Insolvencies.Journal of Financial Services Research,21(1-2),101-116.
11. Tsai, C. H.,S. Y. Liao(2002).A Simulation Study on the Effectiveness of Alternative Capital Requirements in the Property-Casualty Insurance Industry of Taiwan.Insurance Monograph,18(2),113-130.
12. Walling, R. J. III,T. E. Hettinger,C. C. Emma,S. Ackerman(1999).Customizing the Public Access Model Using Publicly Available Data, in summer 1999 eds, Casualty Actuarial Society Forum.Arlington, Virginia:Casualty Actuarial Society.
13. Webb, B. L.,C. M. Harrison,J. J. Markham(1992).Insurance Operations, Malvern.Pennsylvania:American Institute for Chartered Property Casualty Underwriters.