AI 中文总结
本文提出期望损失因子模型（ESFM），捕捉资产下尾损失严重性的共同变化，实证发现其暴露与预期收益正相关，高减低组合年化收益达8.0%-11.7%，且提供均值与分位数因子之外的定价信息。
AI 中文摘要
我们开发了一个期望损失因子模型（ESFM），用于估计和定价大型资产收益面板中下尾损失严重性的共同变化。均值因子模型描述平均收益的共同变化，而分位数因子模型描述尾部阈值的共同变动。ESFM则捕捉这些阈值以下损失平均严重性的共同变化。该模型将观测到的风险暴露与潜在共同因子相结合。我们使用正交化两步程序估计ESFM，在该程序下，第一阶段分位数估计误差对ES系数估计没有一阶影响。我们为ES系数建立了非渐近误差界、有限样本高斯近似以及潜在因子数量的一致选择。应用于大型股票面板时，ESFM揭示了能对市场压力做出剧烈反应且包含均值因子和分位数因子未捕捉信息的共同因子。按ESFM暴露排序的投资组合，平均收益随暴露增加而增加；高减低投资组合的年化收益为8.0%--11.7%，Fama--French五因子alpha为10.3%--15.0%。在分别和联合控制均值和分位数因子暴露后，这些价差仍为正且统计显著。逐尾跨度检验显示，在控制标准交易因子及相应的均值和分位数因子后，ESFM因子仍保持显著的alpha。将ESFM添加到这些基准因子集中，提高了可达到的最大夏普比率。这些发现将共同损失严重性确定为下行风险的一个独特且被定价的维度。
英文摘要
We develop an expected shortfall factor model (ESFM) to estimate and price common variation in the severity of lower-tail losses in large panels of asset returns. Mean factor models describe common variation in average returns, while quantile factor models describe common movements in tail thresholds. ESFM instead captures common variation in the average severity of losses below those thresholds. The model combines observed risk exposures with latent common factors. We estimate ESFM using an orthogonalized two-step procedure under which first-stage quantile estimation error has no first-order effect on the ES coefficient estimates. We establish nonasymptotic error bounds for the ES coefficients, a finite-sample Gaussian approximation, and consistent selection of the number of latent factors. Applied to a large panel of equities, ESFM uncovers common factors that react sharply to market stress and contain information not captured by mean and quantile factors. Average returns increase across portfolios sorted on ESFM exposure; high-minus-low portfolios earn annualized returns of 8.0%--11.7% and Fama--French five-factor alphas of 10.3%--15.0%. These spreads remain positive and statistically significant after conditioning separately and jointly on mean- and quantile-factor exposures. Tail-by-tail spanning tests show that ESFM factors retain significant alphas after controlling for standard traded factors and the corresponding mean and quantile factors. Adding ESFM to these benchmark factor sets increases the maximum attainable Sharpe ratio. These findings identify common loss severity as a distinct and priced dimension of downside risk.
