We study conditional linear factor models in the context of asset pricing panels. Our analysis focuses on conditional means and covariances to characterize the cross-sectional and inter-temporal properties of returns and factors as well as their interrelationships. We also review the conditions outlined in Kozak and Nagel (2024) and show how the conditional mean-variance efficient portfolio of an unbalanced panel can be spanned by low-dimensional factor portfolios, even without assuming invertibility of the conditional covariance matrices. Our analysis provides a comprehensive foundation for the specification and estimation of conditional linear factor models.

翻译：我们在资产定价面板数据的背景下研究条件线性因子模型。我们的分析聚焦于条件均值与协方差，以刻画收益与因子的横截面性质、跨期性质及其相互关系。同时，我们回顾了Kozak和Nagel（2024）中概述的条件，并展示了非平衡面板的条件均值-方差有效投资组合如何能够由低维因子投资组合张成，甚至无需假设条件协方差矩阵的可逆性。我们的分析为条件线性因子模型的设定与估计提供了全面的理论基础。