Symmetric and Asymmetric Market Betas and Downside Risk
检验了对称的普通市场贝塔与非对称的下行贝塔哪个更适合作为对冲指标，发现普通市场贝塔能更好预测市场崩盘和后续下行贝塔，且高下行贝塔的股票事后并未获得更高平均回报，因此下行贝塔在对冲和风险定价上均无用处。
Abstract Our paper explores whether a symmetric plain or an asymmetric down-beta is a better hedging measure (Roy 1952; Markowitz 1959). Unlike Ang, Chen, and Xing (2006) and Lettau, Maggiori, and Weber (2014), we find that the prevailing plain market beta is the better predictor, even for crashes. It also predicts the subsequent down-beta (i.e., beta measured only on days when the stock market had declined) better than down-beta itself. Stocks with higher down-betas ex ante also do not earn higher average rates of return ex post. Thus, down-betas are useful for neither hedging nor risk-pricing purposes.