We demonstrate the estimation biases that arise when stock returns from 12month prior and 2month prior are included within intermediate and recent past momentum profits. These biases lead to an overestimation of intermediate past momentum but an underestimation of recent past momentum in the US market. There is no significant difference between the predictability of stock performance in the intermediate past and the recent past once we exclude these two months from the construction of momentum strategies in the US and each of the 26 major international markets.

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.