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.
[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.