  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.
