Two-fund separation in dynamic general equilibrium

This paper examines the two-fund separation paradigm in the context of an infinite-horizon general equilibrium model with dynamically complete markets and heterogeneous consumers with time- and state-separable utility functions. With the exception of the dynamic structure, we maintain the assumptions of the classical static models that exhibit two-fund separation with a riskless security. Agents have equi-cautious HARA utility functions. In addition to a security with state-independent payoffs, agents can trade a collection of assets with dividends following a time-homogeneous Markov process. We make no further assumptions about the distribution of asset dividends, returns, or prices. If the riskless security in the economy is a consol then agents' portfolios exhibit two-fund separation. However, if agents can trade only a one-period bond, this result no longer holds. The underlying intuition is that general equilibrium restrictions lead to interest rate fluctuations that destroy the optimality of two-fund separation in economies with a one-period bond and result in different equilibrium portfolios.Portfolio separation, dynamically complete markets, consol, one-period bond, interest rate fluctuation, reinvestment risk

Two-Fund Separation in Dynamic General Equilibrium

The purpose of this paper is to examine the two-fund separation paradigm in the context of an infinite-horizon general equilibrium model with dynamically complete markets and heterogeneous consumers with time and state separable utility functions. With the exception of the dynamic structure, we maintain the assumptions of the classical static models that exhibit two-fund separation with a riskless security. In addition to a se- curity with state-independent payoffs agents can trade a collection of assets with dividends following a time-homogeneous Markov process. We make no further assumptions about the distribution of asset dividends, returns, or prices. Agents have equi-cautious HARA utility functions. If the riskless security in the economy is a consol then agents' portfolios exhibit two-fund separation. But if agents can trade only a one-period bond, this result no longer holds. Examples show this effect to be quantitatively signifcant. The underly- ing intuition is that general equilibrium restrictions lead to interest rate °uctuations that destroy the optimality of two-fund separation in economies with a one-period bond and result in different equilibrium portfolios.

Competitive Equilibria in Semi-Algebraic Economies

This paper examines the equilibrium correspondence in Arrow-Debreu exchange economies with semi-algebraic preferences. We show that a generic semi-algebraic exchange economy gives rise to a square system of polynomial equations with finitely many solutions. The competitive equilibria form a subset of the solution set and can be identified by verifying finitely many polynomial inequalities. We apply methods from computational algebraic geometry to obtain an equivalent polynomial system of equations that essentially reduces the computation of all equilibria to finding all roots of a univariate polynomial. This polynomial can be used to determine an upper bound on the number of equilibria and to approximate all equilibria numerically. We illustrate our results and computational method with several examples. In particular, we show that in economies with two commodities and two agents with CES utility, the number of competitive equilibria is never larger than three and that multiplicity of equilibria is rare in that it only occurs for a very small fraction of individual endowments and preference parameters.computable general equilibrium, semi-algebraic economy, Groebner bases

Controlling price volatility through financial innovation

In this paper, the authors study the possibility of controlling asset price volatility through financial innovation in a three-period finite competitive exchange economy with incomplete financial markets and retrading.incomplete markets; financial innovation; volatility

Monopolistic Security Design in Finance Economies

The purpose of this paper is to analyze endogenous asset innovation by an entrepreneurial exchange owner in a partial equilibrium model of incomplete security markets with financial transaction fees. A monopolistic market maker has the technology to introduce new securities into the economy and charge investors transaction fees if they trade on the exchange. The market maker's objective is to choose the security and transaction fee that maximize profits when opening the exchange. We compute the effects of asset innovation for the case of an option exchange introducing an option on a stock index. In the first set of economies agents with heterogeneous levels of risk aversion trade securities to achieve some risk sharing. In the second set of economies agents have identical risk aversion but heterogeneous beliefs which lead to trading due to the desire for portfolio re-balancing. In both types of models the introduction of the profit-maximizing options leads to a decrease of the prices of established securities. Typically small heterogeneity of beliefs lead to substantial more trading volume in the option than reasonable differences among levels of risk aversion. Our computational approach allows us to examine some previous results in the theoretical literature for heterogeneous-beliefs models about the effects of an option introduction. We show that these results about options leading to a price increase of the underlying stock depend on some very strong assumptions on the parameters and are quantitatively negligible. Typically an opposite result, namely a price decrease of the underlying stock, of much larger quantitative magnitude holds.