When investors learn with the wrong model, they don't just get wrong answers. They get compensated for being wrong.
Qiu (arXiv:2603.21672) develops a Bayesian framework where investors update beliefs about factor risk premia using a model that ignores structural breaks. The “mislearning intensity” — measured by predictive likelihood ratios — quantifies how badly the model misses. The finding: for benchmark factors, elevated mislearning correlates with stronger long-horizon returns and higher Sharpe ratios. The market pays a premium for acute model uncertainty.
This inverts the usual story about misspecification. The conventional view: wrong models produce wrong predictions that lose money. The equilibrium view: everyone's model is wrong, and the degree of wrongness during regime changes creates a risk that must be priced. When a structural break hits — factor loadings shift, correlations reorganize — misspecified models disagree more, uncertainty spikes, and assets affected by the uncertainty must offer higher expected returns to attract holders.
The mislearning premium is not the same as the volatility premium. Volatility measures price dispersion. Mislearning measures the gap between the model's predictions and the data-generating process during periods when the process has changed but the model hasn't caught up. A calm market with stable parameters produces low volatility and low mislearning. A volatile market with stable parameters produces high volatility but low mislearning. A market that has undergone a structural break produces high mislearning regardless of current volatility.
The result doesn't generalize uniformly. In the anomaly universe — a broader set of factors beyond the standard benchmarks — mislearning links more to future drawdowns and downside semivolatility than to compensating returns. The premium exists for some factors and not others, depending on whether the asset structure supports equilibrium pricing of model uncertainty.
Passive capital doesn't reduce mislearning — it changes how it manifests. With more passive capital, mislearning shifts from Sharpe compensation toward risk realization. The same model uncertainty that once produced higher returns now produces larger losses. Passive investment isn't neutral with respect to model misspecification — it transmutes the form of the premium without eliminating it.