Motivated by the asset pricing theory with safety-first preference, we introduce and operationalize a conditional extreme risk (CER) measure to describe expected stock performance conditional on a small-probability market downturn (black swan). We document a significant CER premium in the cross-section of expected returns. We also demonstrate that CER explains the premia to downside beta, coskewness, and cokurtosis. CER provides distinct information regarding black swan hedging that cannot be captured by co-crash-based tail dependence measures. As we find that the pricing effect is stronger among black swan hedging stocks, this distinction helps explain the absence of premium to tail dependence.
Feng (Harry) Wu gratefully acknowledges financial support from the General Research Fund (GRF) (No. B-Q42A) of the University Grants Committee of Hong Kong. This paper also benefits from the support from GRF No. B-Q50N, Hong Kong Polytechnic University research funds (1-ZE46 and G-YN81), and Lingnan University research funds. Ghon Rhee is grateful for the 2018 Shidler College of Business Summer Research Grant.
- Asset pricing
- Black swan hedging
- Conditional extreme risk
- Extreme value theory