00Thaler_FM i-xxvi.qxd

provide a concrete framework for describing some of the opposing views
described in the introduction. The first model, which we consider our null
hypothesis, is consistent with the views described by Fama and French
(1993, 1994, 1996) where there exists a “distress” factor with a positive
risk premium. The second model represents an alternative hypothesis in
which the factor structure is stable over time, and expected returns are de-
termined by a firm’s loading on factors with time varying return premia. In
the third model, firm characteristics rather than factor loadings determine
expected returns. Extant empirical evidence is consistent with all three
models, but in sections 3 and 4 we will present empirical evidence that is in-
consistent with all but the characteristic-based model.
In addition to motivating our own research design, the models presented
in this section illustrate some possible pitfalls associated with past studies
that examine whether loadings on factor portfolios explain the returns on
characteristic-based portfolios. First, we argue that empirical studies that
form benchmarks based on principal components or any other form of fac-
tor analysis may falsely reject a linear factor pricing model which in fact
properly prices all assets. These arguments apply to the recent study by Roll
(1994), which shows that factor loadings from a principal components
analysis fail to explain the B/M effect, as well as to earlier tests of the arbi-
trage pricing theory that used factor analysis.^11 In addition, we argue that
research designs that use the returns of characteristic-based portfolios as in-
dependent variables may fail to reject a factor pricing model when the
model is in fact incorrect. Such designs include Fama and French (1993), as
well as Chan, Chen, and Hsieh (1985), Jagannathan and Wang (1996) and
Chan and Chen (1991).

A. Model 1: The Null Hypothesis

Our null hypothesis is that returns are generated by the following factor
structure:

εi,t

(0, σ^2 ei), fj,t

(0, 1)

(1)

where βi,jis the time-invariant loading of firm ion factor jand fj ̃,tis the return
on factor jat time t. In addition, in this equation we separate out θi,t− 1 ,
firm i’s loading on the distress factor, and f ̃D,t, the return on the distress

rEr ̃it,,,,,,,t [ ̃it] i jf ̃ ̃f ̃

j

J

=+ ++− jt it Dt it

=

1 ∑ −

1

βθ ε 1

CHARACTERISTICS AND RETURNS 323

(^11) These would include articles by Lehmann and Modest (1988) and Connor and Korajczyk
(1988) that use size-sorted portfolios as independent variables, but form factors based on indi-
vidual firm returns.