Factor Models for Asset Returns Based on Transformed Factors

TL;DR

This paper explores nonparametric transformations of Fama-French three factors to better explain asset returns, proposing a data-driven approach and hypothesis testing, with validation through simulations and real data analysis.

Contribution

It introduces a novel nonparametric method to transform Fama-French factors and tests their necessity, enhancing asset return modeling beyond linear assumptions.

Findings

Transformations improve model fit for asset returns.

Hypothesis tests determine when transformations are needed.

Simulation studies validate the proposed methods.

Abstract

The Fama-French three factor models are commonly used in the description of asset returns in finance. Statistically speaking, the Fama-French three factor models imply that the return of an asset can be accounted for directly by the Fama-French three factors, i.e. market, size and value factor, through a linear function. A natural question is: would some kind of transformed Fama-French three factors work better than the three factors? If so, what kind of transformation should be imposed on each factor in order to make the transformed three factors better account for asset returns? In this paper, we are going to address these questions through nonparametric modelling. We propose a data driven approach to construct the transformation for each factor concerned. A generalised maximum likelihood ratio based hypothesis test is also proposed to test whether transformations on the Fama-French three factors are needed for a given data set. Asymptotic properties are established to justify the proposed methods. Intensive simulation studies are conducted to show how the proposed methods work when sample size is finite. Finally, we apply the proposed methods to a real data set, which leads to some interesting findings.