Larry Selden

A General Equilibrium Analysis of Option and Stock Market Interactions

The traditional pricing methodology in finance values derivative securities as redundant assets that have no impact on equilibrium prices and allocations. This paper demonstrates that, when the market is incomplete, primary and derivative asset markets, generically, interact: the valuation of derivative and primary security prices depend on the contractual characteristics of the derivative assets available. In a version of the Mossin mean-variance model, the authors analyze an equilibrium in which a call option (derivative asset) is traded and the equilibrium stock price (primary asset) increases when the options market is opened. Copyright 1991 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Inferior Good and Giffen Behavior for Investing and Borrowing

It is standard in economics to assume that assets are normal goods and demand is downward sloping in price. This view has its theoretical foundation in the classic single period model of Arrow with one risky asset and one risk free asset, where both are assumed to be held long, and preferences exhibit decreasing absolute risk aversion and increasing relative risk aversion. However when short selling is allowed, we show that the risk free asset can not only fail to be a normal good but can in fact be a Giffen good even for widely popular members of the hyperbolic absolute risk aversion (HARA) class of utility functions. Distinct regions in the price-income space are identified in which the risk free asset exhibits normal, inferior and Giffen behavior. An example is provided in which for non-HARA preferences Giffen behavior occurs over multiple ranges of income.

Violation of the Law of Demand

Following the classic work of Mitjuschin, Polterovich and Milleron, necessary and sufficient as well as sufficient conditions have been developed for when the multicommodity Law of Demand holds. We show when the widely cited Mitjuschin and Polterovich sufficient condition also becomes necessary. Using this result, violation regions for the very popular Modified Bergson (or hyperbolic absolute risk aversion) class of utility functions are fully characterized in terms of preference parameters. For a natural extension of the constant elasticity of substitution member of the Modified Bergson family that is neither homothetic nor quasihomothetic, we create the first simple, explicit example of which we are aware that (i) fully characterizes violation regions in both the preference parameter and commodity spaces and (ii) analyzes the range of relative income and price changes within which violations occur.

Approximate aggregation under uncertainty

Abstract For a collection of agents with von Neumann-Morgenstern preferences, a price-independent income distribution, and identical probability beliefs, there exists a von Neumann-Morgenstern approximate aggregator. The risk tolerance of the approximate aggregator is equal to the sum of the individual agent risk tolerances at prices which yield constant, “risk-free”, contingent consumption. The application of the approximate aggregator to standard asset pricing models in finance is discussed briefly.

Changing Tastes and Effective Consistency

In a simple single commodity certainty setting with changing tastes, a consumers consumption plan can be obtained using naive or sophisticated choice. Although in general these solutions diverge, they agree in the special case where the changing tastes are represented by discounted logarithmic utilities. We show more generally that this result does not require preferences to be logarithmic, additively separable, or homothetic. Sufficient conditions are provided for when naive and sophisticated choice agree and the common plan can be rationalized by a non-changing tastes utility. Because the solution generated by this utility is not revised over time, the plan is referred to as being effectively consistent. The optimal consumption plan for a popular form of quasi-hyperbolic discounted utility is shown to be rationalized by a non-changing tastes discounted utility which has a very different pattern of intertemporal discount rates. We also consider the implications of effective consistency for equilibrium interest rates in a standard representative agent term structure model.

On the recoverability of risk and time preferences from consumption and asset demands

Abstract We establish sufficient conditions for the recoverability and uniqueness of utility functions performing generating consumption and asset demands in a two-period setting under uncertainty.

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 sufficient 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 agents risk aversion properties for general utility functions and (ii) necessary and sufficient conditions for the widely used HARA (hyperbolic absolute risk aversion) class.

A note on the recoverability and uniqueness of changing tastes

Abstract This paper demonstrates that it will be impossible, by observing an agents demand behavior, to either refute or confirm the general taste change hypothesis without substantially restricting the class of eligible preferences.

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 of axioms 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.

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.