189 research outputs found

### 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

### Testing the Gaussian Copula Hypothesis for Financial Assets Dependences

Using one of the key property of copulas that they remain invariant under an
arbitrary monotonous change of variable, we investigate the null hypothesis
that the dependence between financial assets can be modeled by the Gaussian
copula. We find that most pairs of currencies and pairs of major stocks are
compatible with the Gaussian copula hypothesis, while this hypothesis can be
rejected for the dependence between pairs of commodities (metals).
Notwithstanding the apparent qualification of the Gaussian copula hypothesis
for most of the currencies and the stocks, a non-Gaussian copula, such as the
Student's copula, cannot be rejected if it has sufficiently many ``degrees of
freedom''. As a consequence, it may be very dangerous to embrace blindly the
Gaussian copula hypothesis, especially when the correlation coefficient between
the pair of asset is too high as the tail dependence neglected by the Gaussian
copula can be as large as 0.6, i.e., three out five extreme events which occur
in unison are missed.Comment: Latex document of 43 pages including 14 eps 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

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