A two-Factor Asset Pricing Model and the Fat Tail Distribution of Firm Sizes

TL;DR

This paper introduces a two-factor asset pricing model that incorporates a new systematic risk related to the heavy-tailed distribution of firm sizes, explaining asset pricing anomalies and aligning with empirical data.

Contribution

It proposes a novel two-factor model accounting for diversification risk due to heavy-tailed firm size distribution, extending traditional asset pricing frameworks.

Findings

The model explains asset pricing anomalies using internal consistency and heavy-tailed distributions.

It provides an alternative to the Fama-French three-factor model with similar empirical power.

The size factor is linked to diversification risk, and book-to-market relates to sensitivity to this factor.

Abstract

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.