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Mislearning of Factor Risk Premia under Structural Breaks: A Misspecified Bayesian Learning Framework

Yimeng Qiu

Abstract

While asset-pricing models increasingly recognize that factor risk premia are subject to structural change, existing literature typically assumes that investors correctly account for such instability. This paper studies how investors instead learn under a misspecified model that underestimates structural breaks. We propose a minimal Bayesian framework in which this misspecification generates persistent prediction errors and pricing distortions, and we introduce an empirically tractable measure of mislearning intensity $(Δ_t)$ based on predictive likelihood ratios. The empirical results yield three main findings. First, in benchmark factor systems, elevated mislearning does not forecast a deterministic short-run collapse in performance; instead, it is associated with stronger long-horizon returns and Sharpe ratios, consistent with an equilibrium premium for acute model uncertainty. Second, in a broader anomaly universe, this pricing relation does not generalize uniformly: mislearning is more strongly associated with future drawdowns, downside semivolatility, and other measures of instability, with substantial heterogeneity across anomaly families. Third, the cross-sectional relation between instability and mislearning is inherently conditional: while a monotonic link between break-proneness and average mislearning does not hold in the full cross-section, it re-emerges in low-friction (low-IVOL) environments where break-state severity is more comparable across assets.

Mislearning of Factor Risk Premia under Structural Breaks: A Misspecified Bayesian Learning Framework

Abstract

While asset-pricing models increasingly recognize that factor risk premia are subject to structural change, existing literature typically assumes that investors correctly account for such instability. This paper studies how investors instead learn under a misspecified model that underestimates structural breaks. We propose a minimal Bayesian framework in which this misspecification generates persistent prediction errors and pricing distortions, and we introduce an empirically tractable measure of mislearning intensity based on predictive likelihood ratios. The empirical results yield three main findings. First, in benchmark factor systems, elevated mislearning does not forecast a deterministic short-run collapse in performance; instead, it is associated with stronger long-horizon returns and Sharpe ratios, consistent with an equilibrium premium for acute model uncertainty. Second, in a broader anomaly universe, this pricing relation does not generalize uniformly: mislearning is more strongly associated with future drawdowns, downside semivolatility, and other measures of instability, with substantial heterogeneity across anomaly families. Third, the cross-sectional relation between instability and mislearning is inherently conditional: while a monotonic link between break-proneness and average mislearning does not hold in the full cross-section, it re-emerges in low-friction (low-IVOL) environments where break-state severity is more comparable across assets.
Paper Structure (83 sections, 5 theorems, 80 equations, 9 figures, 22 tables)

This paper contains 83 sections, 5 theorems, 80 equations, 9 figures, 22 tables.

Table of Contents

  1. Introduction
  2. Measuring Mislearning
  3. Testable Predictions
  4. Relation to Literature
  5. Market Structure and the Role of Passive Ownership
  6. Contribution
  7. True Process: Factor Risk Premia with Structural Breaks
  8. Investor Beliefs: Misspecified Bayesian Learning
  9. Maintained misspecification in the subjective state variance.
  10. Mislearning Intensity
  11. Asset Pricing Implications
  12. Empirical Design
  13. Data
  14. Estimating Predictive Densities
  15. Baseline Predictive Tests
  16. ...and 68 more sections

Key Result

Proposition 1

Suppose the true process follows eq:true_state--eq:true_jump, while investors filter using eq:belief_obs--eq:belief_smallvar. If a nonzero break occurs at time $t^\star$, then the posterior mean error $\hat{\lambda}_t-\lambda_t$ remains systematically biased for multiple periods after $t^\star$. The

Figures (9)

  • Figure 1: Monthly factor return series for the six benchmark factors.
  • Figure 2: Family-level coefficients of $\Delta_t$ in 12-month future-Sharpe regressions across anomaly groups.
  • Figure A1: Stable-model filtered state estimates with uncertainty bands.
  • Figure A2: Break-model state probabilities and next-period break probabilities.
  • Figure A3: Mislearning intensity $\Delta_t$ and six-month moving average by factor.
  • ...and 4 more figures

Theorems & Definitions (7)

  • Proposition 1: Slow updating after breaks
  • Proposition 2: Mislearning spikes near structural breaks
  • Proposition 3: Uncertainty Premium and Future Performance
  • Proposition 4: Cross-factor mislearning exposure: decomposition
  • Corollary 4.1: Conditional monotone exposure
  • Remark 1: Cross-sectional implication
  • Remark 2: Passive Ownership as a Secondary Market-Structure Modifier