Arbitrage and asset market equilibrium in infinite dimensional economies with risk-averse expected utilities

We consider a model with an infinite numbers of states of nature, von Neumann - Morgenstern utilities and where agents have different prob- ability beliefs. We show that no-arbitrage conditions, defined for finite dimensional asset markets models, are not sufficient to ensure existence of equilibrium in presence of an infinite number of states of nature. How- ever, if the individually rational utility set U is compact, we obtain an equilibrium. We give conditions which imply the compactness of U. We give examples of non-existence of equilibrium when these conditions do not hold

Financial Innovation in Multi-Period Economies

I present an attempt to construct multi-period, finite horizon extensions to the well -known two- period financial innovations literature. I first extend the definition of competitive equilibrium with innovations. It is shown that, with a dominating houseIncomplete markets, financial innovation, multiperiod economies

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

Essays in asset pricing

My dissertation aims at understanding the impact of uncertainty and disagreement on asset prices. It contains three main chapters. Chapter One gives a general introduction into the topic of partial information and heterogeneous beliefs. Chapter Two explains the link between credit spreads and the heterogeneous formation of expectations in an economy where agents with different perception of economic uncertainty disagree about future cash flows of a defaultable firm. The intertemporal risk-sharing of disagreeing investors gives rise to three testable implications: First, larger belief heterogeneity increases credit spreads and their volatility. Second, it implies a higher frequency of capital structure arbitrage violations. Third, it reduces expected equity returns of low levered firms, but the link can be reversed for high levered firms. We use a data-set of firm-level differences in beliefs, credit spreads, and stock returns to empirically test these predictions. The economic and statistical significance of the intertemporal risk-sharing channel of disagreement is substantial and robust to the inclusion of control variables such as Fama and French, liquidity, and implied volatility factors. Chapter Three studies the link between market-wide uncertainty, difference of opinions and co- movement of stock returns. We show that this link plays an important role in explaining the dynamics of equilibrium volatility and correlation risk premia, the differential cross-sectional pricing of index and individual options, and the risk-return profile of several option trading strategies. We use firm-specific data on analyst forecasts and test the model predictions. We obtain the following novel results: (a) The difference of index and individual volatility risk premia is linked to a counter-cyclical common disagreement component about future earnings; (b) This common component helps to explain the differential pricing of index and individual volatility smiles in the cross-section, as well as the time-series of correlation risk premia extracted from option prices; (c) The time series of returns on straddle and dispersion option portfolios reflects a significant time-varying risk premium, which compensates investors for bearing common disagreement risk; (d) Common disagreement is priced in the cross-section of option strategy returns

Essays on asset pricing

I am proposing a simple theory in which an investor distinguishes between positive and negative deviations in the portfolio value for risk estimation. The risk of the portfolio is defined as the average futile return on the portfolio. The investor tries to create such a portfolio that the unconditional average return is as high as possible while conditional (negative) return on the portfolio is as small (in absolute terms) as possible. I am not making any assumptions about the possible distribution of the stock prices and returns. However, assuming the normal (Gaussian) mutual distribution the solution reduces to the standard CAPM solution