Paper: arXiv 2404.08129

Authors: Nicola Borri, Denis Chetverikov, Yukun Liu, Aleh Tsyvinski

Abstract

We propose a new non-linear single-factor asset pricing model $r_{it}=h(f_{t}λ_{i})+ε_{it}$. Despite its parsimony, this model represents exactly any non-linear model with an arbitrary number of factors and loadings – a consequence of the Kolmogorov-Arnold representation theorem. It features only one pricing component $h(f_{t}λ_{I})$, comprising a nonparametric link function of the time-dependent factor and factor loading that we jointly estimate with sieve-based estimators. Using 171 assets across major classes, our model delivers superior cross-sectional performance with a low-dimensional approximation of the link function. Most known finance and macro factors become insignificant controlling for our single-factor.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper introduces a highly innovative non-linear asset pricing model anchored in the Kolmogorov-Arnold representation theorem, bridging deep functional analysis with cross-sectional asset pricing. It validates the framework empirically across 171 multi-asset targets, demonstrating that a single non-parametric factor can subsume traditional linear risk factors.

Research Flowchart

  flowchart TD
    A[Goal: Simplify Asset Pricing with a Non-Linear Single-Factor Model] --> B[Data Input: 171 Multi-Asset Portfolios across Major Asset Classes]
    B --> C[Methodology: Apply Kolmogorov-Arnold Theorem to Express Multi-Factor Models as r_it = h_f_t * λ_i_]
    C --> D[Computation: Jointly Estimate Link Function h and Parameters via Sieve-Based Estimators]
    D --> E[Outcome 1: Superior Cross-Sectional Pricing with Low-Dimensional Approximation]
    D --> F[Outcome 2: Most Known Finance & Macro Factors Become Insignificant]

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