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.Comment: 38 pages including 7 tables and 3 figure

Volatility fingerprints of large shocks: Endogeneous versus exogeneous

Finance is about how the continuous stream of news gets incorporated into prices. But not all news have the same impact. Can one distinguish the effects of the Sept. 11, 2001 attack or of the coup against Gorbachev on Aug., 19, 1991 from financial crashes such as Oct. 1987 as well as smaller volatility bursts? Using a parsimonious autoregressive process with long-range memory defined on the logarithm of the volatility, we predict strikingly different response functions of the price volatility to great external shocks compared to what we term endogeneous shocks, i.e., which result from the cooperative accumulation of many small shocks. These predictions are remarkably well-confirmed empirically on a hierarchy of volatility shocks. Our theory allows us to classify two classes of events (endogeneous and exogeneous) with specific signatures and characteristic precursors for the endogeneous class. It also explains the origin of endogeneous shocks as the coherent accumulations of tiny bad news, and thus unify all previous explanations of large crashes including Oct. 1987.Comment: Latex document, 12 pages, 2 figure

Preserving preference rankings under non-financial background risk

We investigate the impact of a non-financial background risk ˜" on the preference rankings between two independent financial risks ˜z1 and ˜z2 for an expected-utility maximizer. More precisely, we provide necessary and sufficient conditions for the alternative (x0 + ˜z1, y0 + ˜") to be preferred to (x0 + ˜z2, y0 + ˜") whenever (x0 + ˜z1, y0) is preferred to (x0 + ˜z2, y0). Utility functions that preserve the preference rankings are fully characterized. Their practical relevance is discussed in light of recent results on the constraints for the modeling of the preference for the disaggregation of harms.Multivariate risk, Background risk, Disaggregation of harms, Risk independence