我国养老保险基金投资组合研究
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摘要
目前我国养老保险基金制度正是从现收现付制向部分积累制的转轨时期,中国养老保险基金安全性高但收益微薄,因此对我国养老保险基金进行投资组合研究实现其保值增值的重要性日益凸显。
如果生命周期表中的死亡率数值偏大,会发生个体预期剩余寿命被低估的现象,极易导致养老保险基金储备不足。因此本文首先预测中国人口死亡率,根据全国各年龄别人口死亡状况进行参数估计,对最初形成的空间状态模型进行Kalman滤波变换,然后在其产生的模型基础上进行预测。通过对比分析,显示青年阶段的期望剩余寿命被较严重地低估了。然后,在考虑其交易费用的前提下,利用L-R型模糊数的概念来刻画我国养老保险基金的投资收益水平。由于中国人口老龄化高峰即将来临,特别地,将长寿风险作为风险控制因素之一,同时将政策规定的某些项目投资最低限制设为下限,增加实际操作性。基于模糊环境下建立了长寿风险的投资组合优化模型。并且利用国债指数、基金指数和股票指数的收益来模拟养老保险基金投资国债、基金和股票的情况。
本文不但从静态上得到了模糊环境下考虑长寿风险的投资组合优化模型,同时也从动态上分析了我国养老保险基金的投资组合的VaR。首先,选择GARCH(1,1)模型拟合边缘分布,然后对各类Copula函数进行参数值的估计,通过比较分析,寻找出对已有数据拟合效果最优的tCopula模型。应用该模型计算出国债指数、基金指数和股票指数投资组合的VaR,通过返回检验说明得到的结果比较理想。
The state pension fund of China is currently in the transition between the pay-as-you-go and the partial accumulation system. However, its payoff is still too low even with the consideration of its high safety level, which urges the investment portfolio research on the maintenance and increment of its value.
If the mortality rate is in the high side of the life period table, the expected remaining lifetime of an individual will be underestimated, which may cause the underfunding of the pension fund. Given the importance of the mortality rate of China's population, my thesis starts with the forecast and parameter estimation according to its age and sex conditions. Followed by the estimation of the initial state space model with Kalman filter technique, forecast is conducted in the generated model. By comparison, the expected remaining lifetime at the youth stage is highly underestimated. Hence, the concept of LR-type fuzzy numbers is adopted to characterize the return level of the fund with its transaction cost in consideration. In the same time, the longevity risk is treated as a control factor as the aging peak of China's population approaches. In accordance with minimum investment requirements of policies, the lower limit is set to increase the practical operability. Therefore, a portfolio optimization model of longevity risk is established based in the fuzzy environment. Furthermore, the returns of indices of bonds, funds and stocks are used to simulate the situations of the corresponding investments from the pension insurance fund.
Finally, I can not only obtain an optimal investment portfolio model considering longevity risk in a fuzzy environment, but also analyze the VaR of investment portfolios of China's pension fund. A GARCH(1,1) model is selected to fit a marginal distribution, and parameters of various Copula functions are estimated. After comparative analysis, an optimal fitted tCopula model is found with respect to the available data. The model can be applied to calculate the VaR of investment portfolios of indices of bonds, funds and stocks. The obtained results by regression tests are satisfactory both statically and dynamically.
如果生命周期表中的死亡率数值偏大,会发生个体预期剩余寿命被低估的现象,极易导致养老保险基金储备不足。因此本文首先预测中国人口死亡率,根据全国各年龄别人口死亡状况进行参数估计,对最初形成的空间状态模型进行Kalman滤波变换,然后在其产生的模型基础上进行预测。通过对比分析,显示青年阶段的期望剩余寿命被较严重地低估了。然后,在考虑其交易费用的前提下,利用L-R型模糊数的概念来刻画我国养老保险基金的投资收益水平。由于中国人口老龄化高峰即将来临,特别地,将长寿风险作为风险控制因素之一,同时将政策规定的某些项目投资最低限制设为下限,增加实际操作性。基于模糊环境下建立了长寿风险的投资组合优化模型。并且利用国债指数、基金指数和股票指数的收益来模拟养老保险基金投资国债、基金和股票的情况。
本文不但从静态上得到了模糊环境下考虑长寿风险的投资组合优化模型,同时也从动态上分析了我国养老保险基金的投资组合的VaR。首先,选择GARCH(1,1)模型拟合边缘分布,然后对各类Copula函数进行参数值的估计,通过比较分析,寻找出对已有数据拟合效果最优的tCopula模型。应用该模型计算出国债指数、基金指数和股票指数投资组合的VaR,通过返回检验说明得到的结果比较理想。
The state pension fund of China is currently in the transition between the pay-as-you-go and the partial accumulation system. However, its payoff is still too low even with the consideration of its high safety level, which urges the investment portfolio research on the maintenance and increment of its value.
If the mortality rate is in the high side of the life period table, the expected remaining lifetime of an individual will be underestimated, which may cause the underfunding of the pension fund. Given the importance of the mortality rate of China's population, my thesis starts with the forecast and parameter estimation according to its age and sex conditions. Followed by the estimation of the initial state space model with Kalman filter technique, forecast is conducted in the generated model. By comparison, the expected remaining lifetime at the youth stage is highly underestimated. Hence, the concept of LR-type fuzzy numbers is adopted to characterize the return level of the fund with its transaction cost in consideration. In the same time, the longevity risk is treated as a control factor as the aging peak of China's population approaches. In accordance with minimum investment requirements of policies, the lower limit is set to increase the practical operability. Therefore, a portfolio optimization model of longevity risk is established based in the fuzzy environment. Furthermore, the returns of indices of bonds, funds and stocks are used to simulate the situations of the corresponding investments from the pension insurance fund.
Finally, I can not only obtain an optimal investment portfolio model considering longevity risk in a fuzzy environment, but also analyze the VaR of investment portfolios of China's pension fund. A GARCH(1,1) model is selected to fit a marginal distribution, and parameters of various Copula functions are estimated. After comparative analysis, an optimal fitted tCopula model is found with respect to the available data. The model can be applied to calculate the VaR of investment portfolios of indices of bonds, funds and stocks. The obtained results by regression tests are satisfactory both statically and dynamically.
引文
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[3]Lee, R. D., Carter, L. R.,1992. Modeling and forecasting U. S. mortality. Journal of the American Statistical Association [J].87,659-671.
[4]Renshaw, A. E., Haberman, S.,2003. Lee-Carter mortality forecasting with age-specific enhancement. Insurance:Mathematics and Economics [J].33, 255-272.
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[6]Brouhns, N., Denuit, M., Vermunt, J. K.,2002. A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics [J].31,373-393.
[7]H'ari, N., De Waegenaere, A., Melenberg, B., Nijman, T. E.,2008. Estimating the term structure of mortality. Insurance:Mathematics and Economics[J].42,492-504.
[8]邹公明.寿险精算数学[M].上海：上海财经大学出版社,2006.
[9]Tanaka H, Guo P, Turksen IB. Portfolio selection based on fuzzy probabilities and possibility distributions [J]. Fuzzy Sets and Systems,2000, 111(3):387-397.
[10]Inuiguchi M, Tanino T. Portfolio selection under independent possibilistic information[J]. Fuzzy Sets and Systems,2000,115(1):83-92.
[11]Ramaswamy S. Portfolio Selection Using Fuzzy Decision Theory[M]. Working paper of bank for international settlement,1998.
[12]Ostermark R. A fuzzy control model (FCM) for dynamic portfolio management[J]. Fuzzy Sets and Systems,1996,78:243-254.
[13]王慧,陈华友,王自强.模糊随机环境下带个人偏好的投资组合决策模型[J].运筹与管理,2008,17(2),131-135.
[14]周洪涛,刘康泽.摩擦市场条件下的双目标投资组合模型模糊优化[J].数学的实践与认识,2007,37(7),27-32.
[15]杨湘豫,夏宇.基于Copula方法的开放式基金投资组合的VaR研究[J].系统工程,2008,8(5).
[16]欧阳资生,王非.基于Copula方法的国债市场相依风险度量[J].统计研究,2008,25(7).
[17]于波,陈希镇,华栋.基于蒙特卡罗法的国内股票市场的Copula分析[J].科学技术与工程,2008,8(5).
[18]李石,卢祖帝.Copula函数在风险价值度量中的应用[J].金融管理,2008,20(4).
[19]包卫军,胡杰.基于多维Copula函数的投资组合CVaR分析,2008,23(9).
[20]陈辉,陈建成.我国保险投资组合的模拟和金融风险测量研究,2008,25(11).
[21]关静,郭慧,葛琳.基于阿基米德Copula的投资组合风险分析,2008,41(7).
[22]Dean Fantazzini. The effects of misspecified marginals and copulas on computing the value at risk:A Monte Carlo study[J]. Computational Statistics and Data Analysis 53(2009)2168-2188.
[23]M. Concepcion Ausin, Herdibert F. Lopes. Time-varying joint distribution though copulas [J]. Computational Statistics and Data Analysis,
2009.
[24]张松.养老基金与资本市场互动的理论与实证研究.西南财经大学出版社,2006,1.
[25]李绍光.深化社会保障改革的经济学分析.中国人民大学出版社,2006,203.
[26]李绍光.养老金制度与资本市场.中国发展出版社,1998.
[27]李文浩,王佳妮.国内外养老保险基金运用比较分析及我国养老保险基金的 投资选择.人口与经济,2005,(1).
[28]蒲勇健,刘渝琳.基于委托一代理理论的养老保险基金投资合同设计.经济问题探索,2005,(5).
[29]S. A. Ross. The arbitrage theory of capital asset pricing. Journal of Economic Theory,1976,13:341-360.
[30]王春风.金融市场风险管理.天津大学出版社,2001.
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