Non-parametric and semi-parametric asset pricing

TL;DR

This paper demonstrates that traditional CAPM models are inadequate for explaining small firm effects and market anomalies, proposing semi-parametric measures that adapt to market conditions and improve asset pricing accuracy.

Contribution

It introduces semi-parametric asset pricing measures that account for market extremities and challenges the linearity assumption of the CAPM.

Findings

CAPM fails to explain small firm effect even with non-parametric forms.

Linearity of CAPM can be statistically rejected.

Semi-parametric measures align with Fama-French three-factor model under certain conditions.

Abstract

We find that the CAPM fails to explain the small firm effect even if its non-parametric form is used which allows time-varying risk and non-linearity in the pricing function. Furthermore, the linearity of the CAPM can be rejected, thus the widely used risk and performance measures, the beta and the alpha, are biased and inconsistent. We deduce semi-parametric measures which are non-constant under extreme market conditions in a single factor setting; on the other hand, they are not significantly different from the linear estimates of the Fama-French three-factor model. If we extend the single factor model with the Fama-French factors, the simple linear model is able to explain the US stock returns correctly.