Diversification Risk in Asset Pricing with Heavy-Tailed Firm Sizes

Summary

This paper proposes a two-factor asset-pricing model for economies where firm capitalizations have a sufficiently heavy-tailed distribution. Alongside conventional market risk, the model includes diversification risk, proxied by an equally weighted portfolio. The authors argue that concentrated market portfolios create an internal-consistency risk that can affect returns even in large economies.

The framework offers an explanation for some return patterns often addressed by the Fama–French three-factor model. In this account, the size factor can proxy for diversification risk, while the value effect reflects greater sensitivity of value stocks to that risk. The document says the proposed model has empirical explanatory power similar to the three-factor model, but provides no sample details, estimation procedure, or numerical results here. Its claims are theoretical and summarized at a high level, so the excerpt does not establish how robust the explanation is across markets or time periods.

Key ideas

• Heavy-tailed firm capitalization can leave the market portfolio concentrated even in a large economy.
• The model adds diversification risk, proxied by an equally weighted portfolio, to conventional market risk.
• An internal-consistency factor is proposed as the mechanism behind this additional systematic risk.
• The size premium may proxy for diversification risk, while value stocks may be more sensitive to it.
• The excerpt reports explanatory power similar to the Fama–French three-factor model but gives no empirical details.

Tags

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


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









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.

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