Extreme Downside Risk and Expected Stock Returns

Abstract

We propose a measure for extreme downside risk (EDR) to investigate whether bearing such a risk is rewarded by higher expected stock returns. Constructing an EDR proxy with the left tail index in the classical generalized extreme value distribution, we document a significantly positive premium on firm-specific EDR in cross-section of stock returns even after controlling for market, size, value, momentum, and liquidity effects. The EDR premium is more prominent among glamour stocks and when high market returns are expected. High-EDR stocks generally have high idiosyncratic risk, large downside beta, lower coskewness and cokurtosis, and high bankruptcy risk. The EDR premium persists after these characteristics are controlled for. EDR is also closely related to firm-specific Value at Risk (VaR) which substantially impacts EDR’s effect on expected stock returns. EDR supplements VaR in predicting stock returns by exhibiting additional explanatory power.