A Two-Factor Asset Pricing Model and the Fat Tail Distribution of Firm Sizes
38 Pages Posted: 19 Feb 2007
Date Written: January 2007
Abstract
We derive a theoretical two-factor model 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.
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