Pástor and Stambaugh (2012) find that from a forward-looking perspective, stocks are more volatile in the long run than they are in the short run. We demonstrate that when the nonnegative equity premium (NEP) condition is imposed on predictive regressions, stocks are in fact less volatile in the long run, even after taking estimation risk and uncertainties into account. The reason is that the NEP provides an additional parameter identification condition and prior information for future returns. Combined with the mean reversion of stock returns, this condition substantially reduces uncertainty on future returns and leads to lower long-run predictive variance.

中文翻译：

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从长远来看，股票何时波动较小？

Pástor 和 Stambaugh (2012) 发现，从前瞻性的角度来看，股票的长期波动性比短期内更大。我们证明，当对预测回归施加非负股票溢价 (NEP) 条件时，从长远来看，股票实际上波动性较小，即使在考虑了估计风险和不确定性之后也是如此。原因是 NEP 为未来的回报提供了额外的参数识别条件和先验信息。结合股票收益的均值回归，这种情况大大降低了未来收益的不确定性，并导致较低的长期预测方差。