Multiplicity in general financial equilibrium with portfolio constraints

This paper explores the role of portfolio constraints in generating multiplicity of equilibrium. We present a simple financial market economy with two goods and two households, households who face constraints on their ability to take unbounded positions in risky stocks. Absent such constraints, equilibrium allocation is unique and is Pareto efficient. With one portfolio constraint in place, the efficient equilibrium is still possible; however, additional inefficient equilibria in which the constraint is binding may emerge. We show further that with portfolio constraints cum incomplete markets, there may be a continuum of equilibria; adding incomplete markets may lead to real indeterminacy.     

Arbitrage and equilibrium in strategic security markets

Summary. In view of the fundamental price taking hypothesis, arbitrage is never compatible with equilibrium in Walrasian markets because the existence of an arbitrage opportunity in a competitive situation always leads to unbounded arbitrage activity. In strategic markets however, the mere effort of individuals to profit alters market clearing prices and thus distorts arbitrage opportunities as well. This observation suggests a different relationship between arbitrage and equilibrium, than in the competitive model. Indeed, we show that in such markets a spread between the cost of a portfolio and its returns is compatible with equilibrium. We provide an example of an equilibrium where a resourceless individual holds a portfolio with zero cost and positive return in every state. We further demonstrate via an asymptotic result, that no arbitrage is intimately related to price taking behaviour.Received: 8 September 2001, Revised: 6 March 2003, JEL Classification Numbers: G12, D4, D5, D52. Correspondence to: Leonidas C. Koutsougeras     

Valuation in infinite-horizon sequential markets with portfolio constraints

Summary. We develop a theory of valuation of assets in sequential markets over an infinite horizon and discuss implications of this theory for equilibrium under various portfolio constraints. We characterize a class of constraints under which sublinear valuation and a modified present value rule hold on the set of non-negative payoff streams in the absence of feasible arbitrage. We provide an example in which valuation is non-linear and the standard present value rule fails in incomplete markets. We show that linearity and countable additivity of valuation hold when markets are complete. We present a transversality constraint under which valuation is linear and countably additive on the set of all payoff streams regardless of whether markets are complete or incomplete. Received: March 9, 2000; revised version: February 13, 2001     

A large CVaR-based portfolio selection model with weight constraints

Although the traditional CVaR-based portfolio methods are successfully used in practice, the size of a portfolio with thousands of assets makes optimizing them difficult, if not impossible to solve. In this article we introduce a large CVaR-based portfolio selection method by imposing weight constraints on the standard CVaR-based portfolio selection model, which effectively avoids extreme positions often emerging in traditional methods. We propose to solve the large CVaR-based portfolio model with weight constraints using penalized quantile regression techniques, which overcomes the difficulties of large scale optimization in traditional methods. We illustrate the method via empirical analysis of optimal portfolios on Shanghai and Shenzhen 300 (HS300) index and Shanghai Stock Exchange Composite (SSEC) index of China. The empirical results show that our method is efficient to solve a large portfolio selection and performs well in dispersing tail risk of a portfolio by only using a small amount of financial assets.     

Financial constraints and unemployment equilibrium

The aim of this paper is to show that a robust determination of unemployment equilibria can be based on the integration of credit rationing into a general equilibrium model. We first review some of the Keynesian macroeconomic models. We show that the problems bequeathed by Keynes’ legacy are only partially solved by the strand of the new Keynesian economics based on market imperfections and endogenous rigidities. In order to overcome these problems we refer to credit rationing. In particular, we build a simple general equilibrium model in which prices are–in principle–perfectly flexible and credit rationing implies unemployment equilibria.     

Fiat money and the value of binding portfolio constraints

We establish necessary and sufficient conditions for the individual optimality of a consumption-portfolio plan in an infinite horizon economy where agents are uniformly impatient and fiat money is the only asset available for intertemporal transfers of wealth. Next, we show that fiat money has a positive equilibrium price if and only if for some agent the zero short sale constraint is binding and has a positive shadow price (now or in the future). As there is always an agent that is long, it follows that marginal rates of intertemporal substitution never coincide across agents. That is, monetary equilibria are never full Pareto efficient. We also give a counter-example illustrating the occurrence of monetary bubbles under incomplete markets in the absence of uniform impatience.     

Asymmetric capacity constraints and equilibrium price dispersion

Price dispersion arises despite perfect information about prices. In equilibrium the higher capacity firm adopts a high-price, high-availability strategy, the lower capacity firm adopts a low-price, low-availability strategy, and consumers are more likely to shop at the high-price firm.     

Labor income,borrowing constraints,and equilibrium asset prices

Summary We develop a duality approach to study an individual's optimal consumption and portfolio policy when the individual has limited opportunities to borrow against future labor income and cannot totally insure the risk of income fluctuations. The individual's intertemporal consumption and portfolio problem is cast in a continuous-time setting under uncertainty. We transform the individual's intertemporal problem into a dual shadow prices problem that solves the shadow prices for the individual's optimal consumption plan or equivalently the individual's intertemporal marginal rates of substitution. We show that the shadow prices process can be expressed as a product of a martingale and a decreasing process (normalized by the bond price). The existence of an optimal solution to the individual's intertemporal consumption and portfolio problem is established via duality. The duality approach also allows us to characterize in a sample way the individual's optimal consumption and portfolio policy in the presence of labor income and borrowing constraints. Equilibrium implications of borrowing constraints on asset prices are also discussed in the paper.This is a revised version of an earlier paper, entitled Consumption and Portfolio Decisions with Labor Income and Borrowing Constraints. We thank George Constandinides, Ayman Hindy, and Chi-fu Huang for helpful comments. We also thank two anonymous referees for their helpful comments and suggestions. Financial support from the Batterymarch Fellowship Program (for Hua He) is gratefully acknowledged.     

Evaluating the impact of inequality constraints and parameter uncertainty on optimal portfolio choice

We present new analytical results for the impact of portfolio weight constraints on an investor’s optimal portfolio when parameter uncertainty is taken into account. While it is well known that parameter uncertainty and imposing weight constraints results in reduced certainty equivalent returns, in the general case, there are no analytical results. In a special case, commonly used in the funds management literature, we derive analytical expression for the certainty equivalent loss that does not depend on the risk aversion parameter. We illustrate our theoretical results using hedge fund data, from the perspective of a fund-of-fund manager. Our contribution is to formalize the framework to investigate this problem, as well as providing tractable analytical solutions that can be implemented using either simulated or asset manager returns.     

Endogenous games and equilibrium adoption of social norms and ethical constraints

We consider a situation in which games are formed endogenously in two senses: (1) there is a pregame in which agents choose to learn a subset of all feasible strategies and can then employ only these strategies in subsequent play, and (2) agents choose their game partners through a costly search process. We show that at any subgame perfect equilibrium, agents will constrain their action sets in the pregame in such a way that a single social norm prevails. Thus, all agents in a society will abide by the same ethical standard, although what standard this will be cannot be predicted. We also show that these are essentially the only SPE outcomes. We suggest that this provides at least a partial explanation for experimental observations that agents apparently choose strategies that do not maximize their payoffs.     

Arbitrage and knowledge

I investigate in depth the contemporary, nation-wide arbitrage phenomenon of copper penny hoarding. While penny hoarding represents a “pure arbitrage” opportunity, it also clearly demonstrates the knowledge problems that face those entrepreneurs who are fully informed about intra-market price differences. This paper contrasts the Neoclassical and Austrian views on the role of information and knowledge in arbitrage, emphasizing the greater depth in understanding to be gained from the knowledge-based Austrian approach, as opposed to the information-based Neoclassical approach.     

International Pricing with Costly Consumer Arbitrage

Consumer arbitrage affects international pricing in several ways. If all consumers face the same arbitrage costs, a monopolist's profit increases with arbitrage costs, and world welfare declines with them (if output does not rise). If arbitrage costs differ across consumers, a monopolist may sell in a second country even if there is no local demand—it can use the second country to discriminate across consumers in the first country. Again, world welfare typically falls with arbitrage costs. When there is also local demand in the second country, world welfare may be increasing in arbitrage costs, even if output falls.     

Operational risk management and regulatory investment constraints on portfolio allocation: evidence from property and casualty insurers

Journal of Regulatory Economics - We examine an insurer’s portfolio allocation choice in the context of a regulatory environment where investment in specific asset classes is constrained. We...     

Arbitrage, martingales and bubbles

Viability of security prices implies linear valuation of payoffs but, if there exist an infinite number of securities or trading dates, does not imply the existence of a risk-neutral probability since countable additivity may fail. An example is given.     

Arbitrage opportunities in frictionless markets with sophisticated investors

An example shows that when preferences change over time and consumers are sophisticated, it is possible that arbitrage opportunities exist in frictionless markets, even in equilibrium. The author would like to thank Han Bleichrodt, P. Jean-Jacques Herings, and Peter P. Wakker for helpful suggestions.     

Real wages,quantity constraints and equilibrium unemployment: Belgium, 1955–1988

This paper examines the determinants of equilibrium wage and unemployment rates in Belgium within the framework of a quantity rationing, right-to-manage model with decentralised wage-setting. Empirical results are obtained by first using the Johansen maximum-likelihood procedure for the analysis of cointegration among the variables of interest. The information from this stage is then used to estimate a three equation econometric model explaining the wage share, the unemployment rate and the capital gap. The slowdown in world trade is depicted as the most important factor explaining the rise in unemployment in Belgium, with dampening effects due to wage control policies imposed in the eighties. Because we obtain only two cointegrating relations, for three endogenous variables, our results are compatible with the hypothesis of path dependency and multiple equilibria.     

Capacity constraints may restore the existence of an equilibrium in the Hotelling model

In this note, we consider the Hotelling model with linear transportation costs. We show that capacity constraints may restore the existence of an equilibrium for locations inside the first and third quartiles.