系统性尾部贝塔与市场崩盘风险的对冲:基于崩盘风险的“安全第一准则”投资组合均衡模型

doi:10.15960/j.cnki.issn.1007-6093.2022.04.004

摘要/Abstract

摘要： 近年来随着市场震荡多变，我国A股市场频繁出现千股跌停的现象。如何在市场发生崩盘风险的情形下，预测风险资产的尾部风险，并有效对冲市场崩盘风险等问题引起了广泛的关注。为了回答这些问题，论文在传统“安全第一准则”投资组合模型中引入了市场发生崩盘风险的约束条件，在均衡情形下获得了具有市场崩盘风险的资产定价模型(Crash CAPM: CCAPM)，利用CCAPM中风险负载与传统的市场贝塔，论文构建了一个新的系统性尾部风险度量指标β^∆。利用1995—2018年期间我国A股市场日收益率数据进行实证检验发现，β^∆能够有效地捕捉到市场崩盘与繁荣时期，资产与市场的尾部关联性。特别地，在市场崩盘时期，β^∆与风险资产极端损失风险呈显著的正相关关系，高β^∆组合与低β^∆组合之差构建的投资组合，在市场崩盘时期，能够获得显著为正的尾部超额收益率，这为对冲市场崩盘提供了重要的依据。

关键词: 市场崩盘风险, 系统性尾部贝塔, 崩盘-CAPM, 安全第一准则, 詹森-α

Abstract: Recently, thousands of shares fell on the same trading date frequently happens in China’s A-share market. How to measure and predict the disaster risk when the market crashes are paid to the close attentions. To answer these problems, we establish the “safety-first” portfolio selection model with the market crash risk constraint, and get a crash capital asset pricing model (CCAPM) under the equilibrium condition. Combining the market beta, we construct a new systematic disaster risk measure, systematic tail beta, β^∆, and study its estimation approach. The empirical results using the daily returns of A-share market between 1995 and 2018 show that the β^∆ can effectively capture the tail comovement of the risk asset and the market during the market crash and boom. Especially, β^∆ has a significant positive impact on the tail returns of risk assets during the market crash. The H-L portfolios composed of the difference between High and Low β^∆ portfolios can obtain the significantly and positively average tail returns when the market crash occurs. These empirical results provide the important foundation to effectively hedge the market crash risk.

Key words: market crash risk, systematic tail beta, crash-CAPM, safely first, Jensen's Alpha

中图分类号:

O221.2

凌爱凡, 朱佳磊, 唐乐, 蒋崇辉. 系统性尾部贝塔与市场崩盘风险的对冲:基于崩盘风险的“安全第一准则”投资组合均衡模型[J]. 运筹学学报, 2022, 26(4): 43-63.

LING Aifan, ZHU Jialei, TANG Le, JIANG Chonghui. Systematic tail beta and hedge of the market crash risk: based on a “safety-first” portfolio selection equilibrium model with the crash risk[J]. Operations Research Transactions, 2022, 26(4): 43-63.

参考文献

[1] Arzac E R, Bawa V S. Portfolio choice and equilibrium in capital markets with safety-first investors[J]. Journal of Financial Economics, 1977, 4(3): 277-288.
[2] Ang A, Chen J, Xing Y. Downside risk[J]. The Review of Financial Studies, 2006, 19(4): 1191-1239.
[3] Fama E F, French K R. The cross-section of expected stock returns[J]. The Journal of Finance, 1992, 47(2): 427-465.
[4] Fama E F, French K R. A five-factor asset pricing model[J]. Journal of Financial Economics, 2015, 116(1): 1-22.
[5] Merton R C. A simple model of capital market equilibrium with incomplete information[J]. The Journal of Finance, 1987, 42: 483-511.
[6] Mehra R, Prescott E C. The equity premium: A puzzle[J]. Journal of Monetary Economics, 1985, 15(2): 145-161.
[7] Harvey C R, Siddique A. The cross-section of expected risk exposure[EB/OL]. (2004-10-19)[2021-03-22]. https://faculty.fuqua.duke.edu/charvey/Teaching/CDROMBA4532003/Other_Harvey_Papers/W51_The_cross_section.pdf.
[8] Goyal A, Santa-Clara P. Idiosyncratic risk matters![J]. The Journal of Finance, 2003, 58(3): 975-1007.
[9] Campbell J Y, Hentschel L. No news is good news: An asymmetric model of changing volatility in stock returns[J]. Journal of Financial Economics, 1992, 31(3): 281-318.
[10] Nelson D B. Conditional heteroskedasticity in asset returns: A new approach[J]. Econometrica, 1991: 347-370.
[11] Ang A, Hodrick R J, Xing Y, et al. The cross-section of volatility and expected returns[J]. The Journal of Finance, 2006, 61(1): 259-299.
[12] Bali T G, Cakici N, Yan X, et al. Does idiosyncratic risk really matter?[J]. The Journal of Finance, 2005, 60(2): 905-929.
[13] Bali T G, Cakici N. Idiosyncratic volatility and the cross section of expected returns[J]. Journal of Financial and Quantitative Analysis, 2008: 29-58.
[14] Boyer B, Mitton T, Vorkink K. Expected idiosyncratic skewness[J]. The Review of Financial Studies, 2010, 23(1): 169-202.
[15] Babenko I, Boguth O, Tserlukevich Y. Idiosyncratic cash flows and systematic risk[J]. The Journal of Finance, 2016, 71(1): 425-456.
[16] 左浩苗, 郑鸣, 张翼. 股票特质波动率与横截面收益: 对中国股市“特质波动率之谜”的解释[J]. 世界经济, 2011, 34(05): 117-135.
[17] 郑振龙, 王磊, 王路跖. 特质偏度是否被定价?[J]. 管理科学学报, 2013, 16(05):1-12.
[18] Kahneman D, Tversky A. Prospect theory: An analysis of decision under risk[J]. Econometrica, 1979, 47(2): 363-391.
[19] Rietz T A. The equity risk premium a solution[J]. Journal of Monetary Economics, 1988, 22(1): 117-131.
[20] Bali T G, Cakici N. Value at risk and expected stock returns[J]. Financial Analysts Journal, 2004, 60(2): 57-73.
[21] Kelly B, Jiang H. Tail risk and asset prices[J]. The Review of Financial Studies, 2014, 27(10): 2841-2871.
[22] 陈国进, 许秀, 赵向琴. 罕见灾难风险和股市收益——基于我国个股横截面尾部风险的实证分析[J]. 系统工程理论与实践, 2015, 35(09): 2186-2199.
[23] Ling A, Cao Z. Two-side Cvars and the cross-sectional expected stock returns: Evidences from Chinese stock market[EB/OL]. (2019-10-19)[2021-03-22]. http://dx.doi.org/10.2139/ssrn.3468275.
[24] 陈坚, 张轶凡, 洪集民. 期权隐含尾部风险及其对股票收益率的预测[J]. 管理科学学报, 2019, 22(10):72-81.
[25] Gao G P, Lu X, Song Z. Tail risk concerns everywhere[J]. Management Science, 2019, 65(7): 3111-3130.
[26] Long H, Zhu Y, Chen L, et al. Tail risk and expected stock returns around the world[J]. Pacific-Basin Finance Journal, 2019, 56: 162-178.
[27] Bollerslev T, Todorov V. Tails, fears, and risk premia[J]. The Journal of Finance, 2011, 66(6): 2165-2211.
[28] Bali T G, Cakici N, Whitelaw R F. Hybrid tail risk and expected stock returns: When does the tail wag the dog?[J]. The Review of Asset Pricing Studies, 2014, 4(2): 206-246.
[29] 凌爱凡, 谢林利. 特异性尾部风险、混合尾部风险与资产定价——来自我国A股市场的证据[J]. 管理科学学报, 2019, 22(08): 71-87.
[30] Van Oordt M R C, Zhou C. Systematic tail risk[J]. Journal of Financial and Quantitative Analysis, 2016, 51(2): 685-705.
[31] Van Oordt M R C, Zhou C. Systemic risk and bank business models[J]. Journal of Applied Econometrics, 2019, 34(3): 365-384.
[32] 韦立坚, 张维, 熊熊. 股市流动性踩踏危机的形成机理与应对机制[J]. 管理科学学报, 2017, 20(03):1-23.
[33] 陈海强, 方颖, 王方舟. 融资融券制度对尾部系统风险的非对称影响——基于A股市场极值相关性的研究[J]. 管理科学学报, 2019, 22(05): 99-109.
[34] 李志生, 金凌, 张知宸. 危机时期政府直接干预与尾部系统风险——来自2015年股灾期间“国家队”持股的证据[J]. 经济研究, 2019, 54(04): 67-83.
[35] Barro R J. Rare disasters and asset markets in the twentieth century[J]. The Quarterly Journal of Economics, 2006, 121(3): 823-866.
[36] Gabaix X. Variable rare disasters: An exactly solved framework for ten puzzles in macrofinance[J]. The Quarterly Journal of Economics, 2012, 127(2): 645-700.
[37] Gourio F. Disaster risk and business cycles[J]. American Economic Review, 2012, 102(6): 2734-66.
[38] Wachter J A. Can time-varying risk of rare disasters explain aggregate stock market volatility? [J]. The Journal of Finance, 2013, 68(3): 987-1035.
[39] Hill B M. A simple general approach to inference about the tail of a distribution[J]. Annals of Statistics, 1975: 1163-1174.
[40] De Jonghe O. Back to the basics in banking? A micro-analysis of banking system stability[J]. Journal of Financial Intermediation, 2010, 19(3): 387-417.
[41] Bawa V S, Lindenberg E B. Capital market equilibrium in a mean-lower partial moment framework[J]. Journal of Financial Economics, 1977, 5(2): 189-200.
[42] Dittmar R F. Nonlinear pricing kernels, kurtosis preference, and evidence from the cross section of equity returns[J]. The Journal of Finance, 2002, 57(1): 369-403.
[43] Jensen M C. The performance of mutual funds in the period 1945-1964[J]. The Journal of Finance, 1968, 23(2): 389-416.