dorsal/arxiv
View SchemaA two-Factor Asset Pricing Model and the Fat Tail Distribution of Firm Sizes
| Authors | Y. Malevergne, D. Sornette |
|---|---|
| Categories | |
| ArXiv ID | physics/0702027 |
| URL | https://arxiv.org/abs/physics/0702027 |
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.
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"abstract": "In the standard equilibrium and/or arbitrage pricing framework, the value of\nany asset is uniquely specified from the belief that only the systematic risks\nneed to be remunerated by the market. Here, we show that, even for arbitrary\nlarge economies when the distribution of the capitalization of firms is\nsufficiently heavy-tailed as is the case of real economies, there may exist a\nnew source of significant systematic risk, which has been totally neglected up\nto now but must be priced by the market. This new source of risk can readily\nexplain several asset pricing anomalies on the sole basis of the\ninternal-consistency of the market model. For this, we derive a theoretical\ntwo-factor model for asset pricing which has empirically a similar explanatory\npower as the Fama-French three-factor model. In addition to the usual market\nrisk, our model accounts for a diversification risk, proxied by the\nequally-weighted portfolio, and which results from an ``internal consistency\nfactor\u0027\u0027 appearing for arbitrary large economies, as a consequence of the\nconcentration of the market portfolio when the distribution of the\ncapitalization of firms is sufficiently heavy-tailed as in real economies. Our\nmodel rationalizes the superior performance of the Fama and French three-factor\nmodel in explaining the cross section of stock returns: the size factor\nconstitutes an alternative proxy of the diversification factor while the\nbook-to-market effect is related to the increasing sensitivity of value stocks\nto this factor.",
"arxiv_id": "physics/0702027",
"authors": [
"Y. Malevergne",
"D. Sornette"
],
"categories": [
"physics.soc-ph",
"q-fin.PR"
],
"title": "A two-Factor Asset Pricing Model and the Fat Tail Distribution of Firm Sizes",
"url": "https://arxiv.org/abs/physics/0702027"
},
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