We propose a least squares estimator weighted by a combination of lagged realized semivariances related to positive and negative returns (WLS-CRS) and use univariate models alone and in combination to reveal significant return predictability. For an investor with a mean-variance preference who allocates a portfolio based on an equal-weighted combination of WLS-CRS model forecasts, the annual certainty equivalent return is 242.8 basis points higher than that received by an investor whose portfolio is allocated based on historical average forecasts. In forecasting stock returns, WLS-CRS estimates outperform the popular ordinary least squares estimates in both statistical and economic evaluation frameworks. WLS-CRS also outperforms estimators based on least squares weighted by lagged realized volatility. We further demonstrate the dominant role of negative return semivariance in improved forecasting performance. Our main findings hold through several robustness checks, including alternative validation samples, different risk aversion coefficients, and various forecast combinations.

我们提出了一个最小二乘估计量，该估计量由与正回报和负回报相关的滞后已实现半方差 (WLS-CRS) 组合加权，并单独使用单变量模型并结合使用来揭示显着的回报可预测性。对于基于 WLS-CRS 模型预测的等加权组合来分配投资组合的具有平均方差偏好的投资者，其年度确定性等价回报比其投资组合基于历史分配的投资者获得的回报高 242.8 个基点。平均预测。在预测股票收益时，WLS-CRS 估计在统计和经济评估框架中都优于流行的普通最小二乘估计。WLS-CRS 的表现也优于基于滞后已实现波动率加权的最小二乘估计器。我们进一步证明了负回报半方差在提高预测性能中的主导作用。我们的主要发现通过多项稳健性检验得到证实，包括替代验证样本、不同的风险厌恶系数和各种预测组合。