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