Theory of Inverse Demand: Financial Assets

While the comparative statics of asset demand have been studied extensively, surprisingly little work has been done on the behavior of equilibrium asset prices and returns in response to changes in the supplies of securities. This is despite considerable interest in the equity premium and interest rate puzzles. In this paper, we seek to fill this void for the classic case of a representative agent economy with a single risky asset and risk free asset in both one and two period settings. It would seem natural to suppose that in response to an increase in the supply of the risky asset, its price would fall and the gross equity risk premium would increase. We show that in standard settings where preferences are represented by frequently assumed forms of expected utility, one can obtain the opposite result. The necessary and su¢ cient condition for prices (gross equity premium) to increase (decrease) with supply is determined by the sign of the slope of the asset Engel curve. This observation allows us to derive (i) sufficient conditions directly in terms of the representative agent's risk aversion properties for general utility functions and (ii) necessary and su¢ cient conditions for the widely used HARA (hyperbolic absolute risk aversion) class

The identification of attitudes towards ambiguity and risk from asset demand

Individuals behave differently when they know the objective probability of events and when they do not. The smooth ambiguity model accommodates both ambiguity (uncertainty) and risk. For an incomplete, competitive asset market, we develop a revealed preference test for asset demand to be consistent with the maximization of smooth ambiguity preferences; and we show that ambiguity preferences constructed from finite observations converge to underlying ambiguity preferences as observations become dense. Subsequently, we give sufficient conditions for the asset demand generated by smooth ambiguity preferences to identify the ambiguity and risk indices as well as the ambiguity probability measure. We do not require ambiguity beliefs to be observable: in a generalized specification, they may not even be defined. An ambiguity free asset plays an important role for identification

When is a Risky Asset "Urgently Needed"?

The demand for commodities in standard applications typically is increasing in income, whereas the demand for the risk free asset in the classic portfolio problem often decreases with income. The latter is shown to occur if and only if the consumer is uncertainty preferences over assets satisfy the condition that the risk free asset is more readily substituted for the risky asset as the quantity of the risky asset increases. In this case, the risky asset is said to be "urgently needed" following the terminology of Johnson in his classic 1913 certainty analysis [19]. The asset and certainty settings differ in critical ways which result in a much greater likelihood for the urgently needed preference property to be satisfied in the portfolio problem. We provide several sufficient conditions for when the risky asset will be urgently needed and a surprisingly simple, complete characterization for widely popular members of the HARA (hyperbolic absolute risk aversion) class. For more general preferences, two examples are given where it is possible to fully describe the region of asset space in which the risky asset is urgently needed. Finally, using a standard representative agent model we show that the risky asset being urgently needed is equivalent to the equilibrium (relative) price of the risky asset increasing with its own supply

What are asset demand tests of expected utility really testing?

Assuming the classic contingent claim setting, a number of financial asset demand tests of Expected Utility have been developed and implemented in experimental settings. However the domain of preferences of these asset demand tests differ from the mixture space of distributions assumed in the traditional binary lottery laboratory tests of von Neumann-Morgenstern Expected Utility preferences. We derive new sets axioms that are necessary and sufficient for preferences over contingent claims to be representable by an Expected Utility function. We also indicate the additional axioms required to extend the representation to the more general case of preferences over risky prospects

Incomplete market demand tests for Kreps-Porteus-Selden preferences

What does utility maximization subject to a budget constraint imply for intertemporal choice under uncertainty? Assuming consumers face a two period consumption-portfolio problem where asset markets are incomplete, we address this question following both the standard local infinitesimal and finite data approaches. To focus on the separate roles of time and risk preferences, individuals maximize KPS (Kreps-Porteus-Selden) preferences. The consumption-portfolio problem is decomposed into a one period portfolio problem and a two period certainty consumption-saving problem. We derive demand restrictions which are necessary and sufficient, for portfolio choices and certainty intertemporal consumption to have been generated by maximization, respectively, of a one period expected utility representation and a certainty representation of time preferences. Conditions are provided for recovering the building block time and risk preference utilities. For the finite data case, we derive a set of linear inequalities that are necessary and sufficient for observations to be consistent with the maximization of KPS utility