  We reverse-engineer the equilibrium construction process of asset prices in
order to obtain returns which depend on firm characteristics, possibly in a
linear fashion. One key requirement is that agents must have demands that rely
separately on firm characteristics and on the log-price of assets. Market
clearing via exogenous (non-factor driven) supply, combined with linear demands
in characteristics, yields the sought form. The coefficients in the resulting
linear expressions are scaled net aggregate demands for characteristics, as
well as their variations, and both can be jointly estimated via panel
regressions. Conditions underpinning asset pricing anomalies are derived and
underline the theoretical importance of the links between characteristics.
Empirically, when the number of characteristics is small, the value and
momentum anomalies are mostly driven by firm-specific fixed-effects, i.e.,
latent demands, which highlights the shortcomings of low-dimensional models.
