Abstract: Tail risk is the risk of which a financial asset may lose a large amount of money after an extreme catastrophic event occurs. Since 2018, the number of credit events has increased significantly, and investors have run a greater credit risk than before. Therefore, it is necessary to study the impact of corporate bond tail risk on bond returns, which is helpful for bond market investors to prevent financial risks and enrich investment strategies.
Using the corporate bond data from 2008 to 2019, this paper studies the impact of tail risk on expected corporate bond returns in China. Tail risk in this paper is defined as the absolute value of the 5% value at risk (VaR) in one month for each bond. For example, an average tail risk of 0.74% for the sample implies a 5% probability that the average return on all corporate bonds will lose more than 0.74% (maximum loss) in one month. In each month, we sort the individual corporate bonds into ten groups according to tail risk in the last month. Portfolio analysis suggests that buying high tail risk bond portfolio and selling low tail risk bond portfolio can obtain an average of 0.67% excess return per month. The positive correlation between the expected corporate bond return and tail risk keeps robust after controlling credit rating, maturity, size and liquidity risk. The results of Fama-MacBeth cross-section regression show that tail risk has a significant positive correlation with the expected bond yield. For low credit rating, long time to maturity, small size and illiquid groups, the positive relationship between tail risk and expected returns are more pronounced.
This paper constructs a tail risk pricing factor, which is the value-weighted average of bond returns with the highest 10% tail risk in the past one month minus the value-weighted average of bond returns with the lowest 10% tail risk in the past one month. Based on the bond pricing model of FAMA and FRENCH (1993), this paper adds market factor and tail risk factor into the Fama-French bond two-factor model, and proposes a four-factor pricing model. Factor spanning tests show that the tail risk factor is not redundant, and the tail risk premium cannot be explained by the market risk factor, credit risk factor and term structure factor. The tail risk factor makes a significant marginal contribution to explaining the excess returns of corporate bonds. The explanatory power of the proposed model increases by 15.85% compared with the three-factor model.
In alternative tests, we construct two tail risk proxies, i.e., the absolute value of the 1% and 10% values at risk (VaR) in one month for each bond, respectively. We also examine the independent explanation ability of the pricing factors after excluding the correlations, out of sample forecast, and the impact factor of tail risk. The results show that time trend, industry and returns on assets are significantly related to tail risk, and tail risk can predict the default of corporate bond.
The contribution of this paper is two-folds. First, compared with the existing literature, this paper studies the relationship between tail risk and expected returns of Chinese corporate bonds. This paper finds that the portfolio constructed by lengthening high tail risk bond portfolio and shortening corresponding low tail risk bond portfolio can obtain excess returns. Second, this paper proposes a four-factor pricing model by adding the market factor and the tail risk factor into the Fama-French model. Time series regression shows that the tail risk factor has a significantly marginal contribution to explaining the excess return of corporate bonds, and the proposed model works well in explaining corporate bond returns. Further, we will investigate the impact of tail risk on other credit markets, i.e., bills, enterprise bonds, and interbank bond market etc.

Key words: corporate bond, tail risk, asset pricing, factor model

摘要： 本文选取我国2008年至 2019年的公司债样本,研究尾部风险对公司债收益率的影响。实证结果表明,公司债预期收益率与尾部风险呈显著正相关关系,做多高尾部风险组债券并做空低尾部风险组债券能产生0.67%的月平均收益率。低评级、中长期、小规模与低流动性组合的预期收益与尾部风险之间的正相关关系更加显著。本文在Fama-French债券定价两因子模型的基础上,加入市场风险因子和尾部风险因子,提出我国公司债的四因子定价模型。时间序列回归结果表明,尾部风险因素对解释公司债超额收益率有显著的边际贡献,四因子定价模型对我国公司债收益率有较强的解释能力。

关键词: 公司债券, 尾部风险, 资产定价, 因子模型