The Virtue of Sparsity in Complexity

Nima Afsharhajari and Jonathan Yu-Meng Li

Papers from arXiv.org

Abstract: Sparsity or complexity? In modern high-dimensional asset pricing, these are often viewed as competing principles: recent empirical evidence favors richer models, while economic intuition has long favored parsimony. We reconcile this tension by distinguishing capacity sparsity-restrictions on effective model capacity-from factor sparsity-the parsimonious structure of priced risks. Revisiting the benchmark empirical design of Didisheim et al. (2025), we combine nonlinear feature expansions with basis pursuit, using column generation and GPU acceleration to scale estimation to 432 million candidate factors. Reaching this scale reveals a reversal in out-of-sample performance: sparse portfolios trail dense ridgeless benchmarks at lower complexity but achieve a higher Sharpe ratio and lower pricing error at the largest candidate set. Capacity expansion and factor sparsity are therefore complements: enlarging the candidate space allows a parsimonious pricing kernel to outperform its dense counterpart.

Date: 2026-04, Revised 2026-09
New Economics Papers: this item is included in nep-hme
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