Extreme downside risk and expected stock returns

We propose a measure for extreme downside risk (EDR) to investigate whether bearing such a risk is rewarded by higher expected stock returns. By constructing an EDR proxy with the left tail index in the classical generalized extreme value distribution, we document a significantly positive EDR premium in cross-section of stock returns even after controlling for market, size, value, momentum, and liquidity effects. The EDR premium is more prominent among glamor stocks and when high market returns are expected. High-EDR stocks are generally characterized by high idiosyncratic risk, large downside beta, lower coskewness and cokurtosis, and high bankruptcy risk. The EDR premium persists after these characteristics are controlled for. Although Value at Risk (VaR) plays a significant role in explaining the EDR premium, it cannot completely subsume the EDR effect.

► We propose a measure for extreme downside risk (EDR). ► We construct an EDR proxy with the left tail index in the GEV distribution. ► There is a significantly positive EDR premium in cross-section of stock returns. ► EDR premium persists after traditional risk characteristics are controlled for. ► VaR can significantly explain but cannot completely subsume the EDR effect.