复杂特征空间能帮助发现稀缺定价因子，提升投资组合表现。
The Virtue of Sparsity in Complexity
- 用非线性扩展特征空间，结合基础追踪法寻找稀疏定价因子
- 在复杂度阈值以上，表现优于无正则化基准模型
- 适合关注资产定价中特征工程与模型简化关系的研究者
在现代高维资产定价中，稀疏性与复杂性常被视为对立原则：更丰富的特征空间倾向复杂性，而经济直觉则推崇简约。本文指出这一对立实为误解。我们区分了容量稀疏性（候选特征空间的维度）与因子稀疏性（定价风险的简约结构），认为二者相辅相成：扩大容量有助于发现因子稀疏性。重审Didisheim等（2025）的基准实证设计，并推向更高复杂度场景，发现非线性特征扩展结合基追迹（basis pursuit）所生成的投资组合，在样本外表现超越无正则化基准，且仅在复杂度超过临界阈值后显现优势。证据表明，复杂性的收益并非来自保留更多因子，而是扩大可搜寻空间，从而识别出稀疏的定价结构。资产定价中的复杂性价值，通过因子稀疏性实现。
原文摘要 · Abstract (English)
Sparsity or complexity? In modern high-dimensional asset pricing, these are often viewed as competing principles: richer feature spaces appear to favor complexity, while economic intuition has long favored parsimony. We show that this tension is misplaced. We distinguish capacity sparsity-the dimensionality of the candidate feature space-from factor sparsity-the parsimonious structure of priced risks-and argue that the two are complements: expanding capacity enables the discovery of factor sparsity. Revisiting the benchmark empirical design of Didisheim et al. (2025) and pushing it to higher complexity regimes, we show that nonlinear feature expansions combined with basis pursuit yield portfolios whose out-of-sample performance dominates ridgeless benchmarks beyond a critical complexity threshold. The evidence shows that the gains from complexity arise not from retaining more factors, but from enlarging the space from which a sparse structure of priced risks can be identified. The virtue of complexity in asset pricing operates through factor sparsity.
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