The asset pricing literature emphasizes factor models that minimize pricing errors but overlooks unselected candidate factors that could enhance the performance of test assets. This paper proposes a framework for factor model selection and testing by (i) selecting the optimal model that spans the joint efficient frontier of test assets and all candidate factors, and (ii) testing pricing performance on both test assets and unselected candidate factors. Our framework updates a baseline model (e.g., CAPM) sequentially by adding or removing factors based on asset pricing tests. Ensuring model selection consistency, our framework utilizes the asset pricing duality: minimizing cross-sectionally unexplained pricing errors aligns with maximizing the Sharpe ratio of the selected factor model. Empirical evidence shows that workhorse factor models fail asset pricing tests, whereas our proposed 8-factor model is not rejected and exhibits robust out-of-sample performance.

翻译：资产定价文献强调最小化定价误差的因子模型，但忽略了未入选候选因子可能提升检验资产表现的作用。本文提出一个因子模型选择与检验框架，其核心在于：(i)选择能够跨越检验资产与所有候选因子联合有效前沿的最优模型；(ii)同时检验模型在检验资产与未入选候选因子上的定价表现。该框架通过资产定价检验逐步增删因子，实现对基准模型（如CAPM）的迭代更新。为确保模型选择一致性，本框架运用资产定价对偶原理：最小化横截面未解释定价误差等价于最大化所选因子模型的夏普比率。实证证据表明，主流因子模型未能通过资产定价检验，而本文提出的8因子模型未被拒绝且展现出稳健的样本外表现。