00Thaler_FM i-xxvi.qxd

The difference between this equation and equation (1) is that there is no
separate distress factor f ̃D. Furthermore, we assume that the remaining β’s
in this model are constant over time, so that the covariance structure does
not change as firms move in and out of distress. Again, the factor structure
describes expected returns:

(3)

Now, however, unlike in Eq. (2), the risk premia on the Jfactors vary
through time. Also, the changes in the premia are negatively correlated
with the past performance of the firms loading on this factor. This means
that when a factor experiences negative realizations, the firms that load on
the factor become distressed (their B/M ratios increase) and their expected
returns increase because the λassociated with this factor increases.
Finally, we again assume that there is an observable variable θi,t(i.e., the
B/M ratio). θobeys a slowly mean-reverting process and the innovations in
θare negatively correlated with past returns (so that distressed firms have
high θ’s). This means that, across firms, θshould be correlated with the fac-
tor loading on the currently distressed factor. Therefore, if a portfolio of the
stocks of high θfirms is assembled, the stocks are likely to be those that
have high loadings on factors with (currently) high λ’s. In other words, the
high θportfolio is successfully timing the factors. This characterization is
similar to that proposed by Jagannathan and Wang (1996), who suggest
that small firms have high average returns because they have high betas on
the market when the expected return on the market is high.^13

C. Model 3: A Characteristic-Based Pricing Model

In contrast to the factor pricing models presented in subsections A and B,
the characteristic-based model presented in this section assumes that high
B/M stocks realize a return premium that is unrelated to the underlying co-
variance structure. This model is thus inconsistent with Merton (1973) or
Ross (1976) in that it permits asymptotic arbitrage.
As in Model 2, covariances are stationary over time and can be described
by a factor structure.^14 Specifically, we again assume that a time-invariant,

Er rtit ft ijjt

j

J

−−

=

11 =+∑

1

[ ̃,,] β,,λ

CHARACTERISTICS AND RETURNS 325

(^13) However, the setting here is slightly different: In the Jagannathan and Wang (1996) set-
ting, the loadings of the individual (small) firms on the market factor change through time,
while in the model presented here, factor loadings are constant but the composition of the
high B/M firms changes over time.
(^14) Although we focus on the relation between B/M ratios and returns in this section, the
analysis also applies to the relation between size and returns.