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Factor models for asset returns based on transformed factors Li, Jialiang


The Famaâ French three factor models are commonly used in the description of asset returns in finance. Statistically speaking, the Famaâ French three factor models imply that the return of an asset can be accounted for directly by the Famaâ French three factors, i.e. market, size and value factor, through a linear function. A natural question is: would some kind of transformed Famaâ French three factors work better 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 Famaâ French three factors are needed for a given data set. Asymptotic properties are established to justify the proposed methods. Extensive simulation studies are conducted to show how the proposed methods perform with finite sample size. Finally, we apply the proposed methods to a real data set, which leads to some interesting findings.

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