双因素资产定价模型与企业规模的厚尾分布
A two-Factor Asset Pricing Model and the Fat Tail Distribution of Firm Sizes
摘要：
在标准的均衡和/或套利定价框架中，任何资产的价值都是唯一指定的，因为人们相信只有系统性风险才需要由市场补偿。在这里，我们表明，即使对于任意的大经济体，当企业资本的分布是足够重尾的情况下，是真实的经济，可能存在一个新的来源，重大的系统性风险，这是完全被忽视了，到现在为止，但必须由市场定价。这种新的风险来源可以很容易地解释几个资产定价异常的唯一基础上的内部一致性的市场模型。对于这一点，我们推导出一个理论上的两个因素模型的资产定价，在经验上有类似的解释能力的法玛-法国三因素模型。除了通常的市场风险之外，我们的模型还考虑了由等权重投资组合代理的多元化风险，这是由于任意大型经济体出现的“内部一致性因素”，这是当公司资本化的分布像真实经济体一样充分重尾时市场投资组合集中的结果。我们的模型合理化Fama和法国的三因素模型在解释股票收益的截面的优越性能：规模因素构成了一个替代代理的多元化因素，而账面市值效应与价值型股票对这个因素的敏感性增加。
英文摘要：
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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