  In the standard equilibrium and/or arbitrage pricing framework, the value of
any asset is uniquely specified from the belief that only the systematic risks
need to be remunerated by the market. Here, we show that, even for arbitrary
large economies when the distribution of the capitalization of firms is
sufficiently heavy-tailed as is the case of real economies, there may exist a
new source of significant systematic risk, which has been totally neglected up
to now but must be priced by the market. This new source of risk can readily
explain several asset pricing anomalies on the sole basis of the
internal-consistency of the market model. For this, we derive a theoretical
two-factor model for asset pricing which has empirically a similar explanatory
power as the Fama-French three-factor model. In addition to the usual market
risk, our model accounts for a diversification risk, proxied by the
equally-weighted portfolio, and which results from an ``internal consistency
factor'' appearing for arbitrary large economies, as a consequence of the
concentration of the market portfolio when the distribution of the
capitalization of firms is sufficiently heavy-tailed as in real economies. Our
model rationalizes the superior performance of the Fama and French three-factor
model in explaining the cross section of stock returns: the size factor
constitutes an alternative proxy of the diversification factor while the
book-to-market effect is related to the increasing sensitivity of value stocks
to this factor.
