Arbitrage and equilibrium with portfolio constraints

We consider a multiperiod financial exchange economy with nominal assets and restricted participation, where each agent’s portfolio choice is restricted to a closed, convex set containing zero, as in Siconolfi (Non-linear Dynamics in Economics and Social Sciences, 1989). Using an approach that dates back to Cass (CARESS Working Paper, 1984; J Math Econ 42:384–405, 2006) in the unconstrained case, we seek to isolate arbitrage-free asset prices that are also quasi-equilibrium or equilibrium asset prices. In the presence of such portfolio restrictions, we need to confine our attention to aggregate arbitrage-free asset prices, i.e., for which there is no arbitrage in the space of marketed portfolios. Our main result states that such asset prices are quasi-equilibrium prices under standard assumptions and then deduces that they are equilibrium prices under a suitable condition on the accessibility of payoffs by agents, i.e., every payoff that is attainable in the aggregate can be marketed through some agent’s portfolio set. This latter result extends previous work by Martins-da-Rocha and Triki (Working Paper, University of Paris 1, 2005).     

The Stability of Price Dispersion under Seller and Consumer Learning*

In many markets, it is possible to find rival sellers charging different prices for the same good. Earlier research has attempted to explain this phenomenon by demonstrating the existence of dispersed price equilibria when consumers must make use of costly search to discover prices. We ask whether such equilibria can be learned when sellers adjust prices adaptively in response to current market conditions. With consumer behavior fixed, convergence to a dispersed price equilibrium is possible in some cases. However, once consumer learning is introduced, the monopoly outcome first found by Diamond (Journal of Economic Theory3 (1971), 156–68) is the only stable equilibrium.     

Multiple unit auctions with strategic price-quantity decisions

Summary. I study a multiple unit auction where symmetric risk-neutral bidders choose prices and quantities endogenously. In the model, bidders (a) may place non-linear valuations on the auctioned units, and (b) bid for several units at the same price (“lumpy” bids). I characterize quantity-symmetric and strictly monotone-increasing price equilibria for discriminatory and competitive auctions, and show that (i) if quantity strategy profiles are equal across auctions revenue- equivalence holds, (ii) expected revenue is higher if bidders bid for the entire supply rather than for shares of it, and (iii) equilibrium allocations may fail to be Pareto-optimal. Received: April 14, 1995; revised version: September 3, 1997     

Rational expectations,difference of opinions and asset pricing

This article applies the concept of relative overconfidence (the measure of how heavily investors depend on others’ information) to combine the rational expectations equilibrium (REE) and difference of opinions (DO) models. And we discuss the effects of relative overconfidence on asset price efficiency and trading volume. We find that when investors hold assets to maturity, relative overconfidence has no effect on price efficiency and trading volume; however, when investors speculate, relative overconfidence reduces price informativeness and trading volume, because investors will reckon asset prices as more noisy and find it meaningless to speculate on capital gains based on their private information. Our results highlight the role of speculation in differentiating REE and DO models and influencing the effects of overconfidence.     

连续进化金融模型与全局渐进化稳定策略

本文运用达尔文生物进化论思想研究连续交易金融市场选择的动态变化及一般均衡规律。本文发现并证明了:金融资产“赢利”的充要条件是该资产相对股息大于相对股价;投资比例等于股息分发比例的简单混合策略是全局渐近进化稳定策略;在均衡条件下,对应的金融资产价格等于该资产股息占总股息的比例的数学期望;市场变异或金融创新是有效市场形成的动力;全局渐近进化稳定策略业绩可能在某些时候不是最好的,但只要其初始财富大于零,最终将控制市场上的所有财富,而简单混合策略,可能在某个时候业绩优良,然而,在市场存在全局渐近进化稳定策略的条件下,只要其初始财富份额小于1,最终控制的财富趋向于零,从而被市场所淘汰。     

Constrained suboptimality in incomplete markets: a general approach and two applications

Summary. In this paper we re-examine generic constrained suboptimality of equilibrium allocations with incomplete numeraire asset markets. We provide a general framework which is capable of resolving some issues left open by the previous literature, and encompasses many kinds of intervention in partially controlled market economies. In particular, we establish generic constrained suboptimality, as studied by Geanakoplos and Polemarchakis, even without an upper bound on the number of households. Moreover, we consider the case where asset markets are left open, and the planner can make lump-sum transfers in a limited number of goods. We show that such a perfectly anticipated wealth redistribution policy, though consistent with the assumed incomplete financial structure, is typically effective. Received: August 14, 1995; revised version: April 11, 1997     

Feedback effects between credit ratings and financial markets

Credit rating agencies often make sharp adjustments in their pronouncements during times of stress in financial markets. These adjustments typically happen with a delay relative to shocks in market prices. Since prices convey information about what market participants are doing and thinking, it is likely that rating agencies take into account market prices when issuing their pronouncements.In order to understand the relationship between credit ratings and financial prices, we develop a model of debt roll-over in which rating agencies incorporate information publicly available in financial markets. We find that (1) rating agencies respond to market prices, i.e. nonfundamental price volatility can shift financing conditions from a low risk spread and high credit rating equilibrium to an equilibrium with high spread and low rating, and (2) rating agencies can anchor expectations about the equilibrium in financial markets, thus serving as an antidote to nonfundamental price volatility.     

Liquidity and asset prices in rational expectations equilibrium with ambiguous information

The quality of information in financial asset markets is often hard to estimate. Reminiscent of the famous Ellsberg paradox, investors may be unable to form a single probability belief about asset returns conditional on information signals and may act on the basis of ambiguous (or multiple) probability beliefs. This paper analyzes information transmission in asset markets when agents?? information is ambiguous. We consider a market with risk-averse informed investors, risk-neutral competitive arbitrageurs, and noisy supply of the risky asset, first studied by Vives (Rev Financ Stud 8:3?C40, 1995a, J Econ Theory 67:178?C204, 1995b) with unambiguous information. Ambiguous information gives rise to the possibility of illiquid market where arbitrageurs choose not to trade in a rational expectations equilibrium. When market is illiquid, small informational or supply shocks have relatively large effects on asset prices.     

Construction of a state space for interrelated securities with an application to temporary equilibrium theory

Summary We construct an endogenous state space in an exchange economy with possibly infinite horizon. Every period agents trade securities whose payoffs depend on future dividends and asset prices. We reject the perfect foresight assumption on the ground that agents have not only limited knowledge of other individuals' endowments and preferences, but also limited capacity to compute equilibria. We choose instead absence of arbitrage as the principle which allows agents to determine if a system of future prices is possible. We give an alogrithm to compute the set of nonarbitrage prices every period, with both finite and infinite horizon. We then apply this endogenous structure of uncertainty to an infinite horizon temporary equilibrium model.I would like to thank Professor Donald Brown for his constant help and guidance. I have also greatly benefited from helpful discussions with Professors Jacques Drèze, Bernard Dumas, Mordecai Kurz, Carsten Nielsen, Jan Werner, and Ho-Mou Wu.     

Investor sentiment,information and asset pricing model

We present an asset pricing model with investor sentiment and information, which shows that the investor sentiment has a systematic and significant impact on the asset price. The equilibrium price's rational term drives the asset price to the rational, and the sentiment term leads to the asset price deviating from it. In our model, the proportion of sentiment investors and the information quality could amplify the sentiment shock on the asset price. Finally, the information is fully incorporated into prices when sentiment investors learn from prices. The model could offer a partial explanation of some financial anomalies: price bubbles, high volatility, asset prices' momentum effect and reversal effect.     

Coordination and correlation in Markov rational belief equilibria

Summary This paper studies the effect of correlation in the rational beliefs of agents on the volatility of asset prices. We use the technique of generating variables to study stable and non-stationary processes needed to characterize rational beliefs. We then examine how the stochastic interaction among such variables affects the behavior of a wide class of Rational Belief Equilibria (RBE). The paper demonstrates how to construct a consistent price state space and then shows the existence of RBE for any economy for which such price state space is constructed. Next, the results are used to study the volatility of asset prices via numerical simulation of a two agents model. If beliefs of agents are uniformly dispersed and independent, we would expect heterogeneity of beliefs to have a limited impact on the fluctuations of asset prices. On the other hand, our results show that correlation across agents can have a complex and dramatic effect on the volatility of prices and thus can be the dominant factor in the fluctuation of asset prices. The mechanism generating this effect works through the clustering of beliefs in states of different levels of agreement. In states of agreement the conditional forecasts of the agents tend to fluctuatetogether inducing more volatile asset prices. In states of disagreement the conditional forecasts fluctuatein diverse directions tending to cancel each other's effect on market demand and resulting in reduced price volatility.This research was supported, in part, by the Fondazione Eni Enrico Mattei of Milan, Italy, and by the Research Incentive Fund of Stanford University. The authors thank Carsten K. Nielsen and Ho-Mou Wu for valuable discussions on an earlier draft. Carsten K. Nielsen also made an important contribution to the development of Section 3.     

Herding in delegated portfolio management: When is comparative performance information desirable?

We address the issue of investors’ asset allocation decisions when portfolio management is delegated to an agent. Contrary to predictions from traditional financial theory, it is shown that investors may not induce their manager to allocate funds to the asset with the highest return. Instead they may herd in their asset allocation decision and induce trade in a particular asset, because another manager is trading in it and despite the presence of a more profitable alternative. Doing so allows investors to write an efficiency-improving relative-performance contract. On the other hand, herding leads investors to design wage contracts strategically, resulting in more aggressive and thus less profitable trade in equilibrium. We show that herding occurs, when the cost of information is high, information precision is low and when managers are sufficiently risk averse. Moreover, when investors can decide whether or not to disclose information about their manager's performance, they will not do so.     

Pareto improving financial innovation in incomplete markets

Summary. In this paper we develop a differential technique for investigating the welfare effects of financial innovation in incomplete markets. Utilizing this technique, and after parametrizing the standard competitive, pure-exchange economy by both endowments and utility functions, we establish the following (weakly) generic property: Let S be the number of states, I be the number of assets and H be the number of households, and consider a particular financial equilibrium. Then, provided that the degree of market incompleteness is sufficiently larger than the extent of household heterogeneity, S−I≥2H−1 [resp. S−I≥H+1], there is an open set of single assets [resp. pairs of assets] whose introduction can make every household better off (and, symmetrically, an open set of single assets [resp. pairs of assets] whose introduction can make them all worse off ). We also devise a very simple nonparametric procedure for reducing extensive household heterogeneity to manageable size, a procedure which not only makes our restrictions on market incompleteness more palatable, but could also prove to be quite useful in other applications involving smooth analysis. Received: August 14, 1995; revised version: April 14, 1997     

A complete characterization of Pareto optimality for general OLG economies

In the context of general pure exchange OLG economies where agents can have heterogeneous longevities, we provide both sufficient and necessary conditions for Pareto optimality of competitive equilibria. For the case in which all agents live for the same number of periods, we find that these conditions are equivalent. We also find this equivalence when agents can have different lifetimes, but in this case we need to impose particular restrictions on relative equilibrium prices. Moreover, we show that without these conditions on prices the equivalence, and hence a full characterization, is not necessarily obtained.     

Disaggregation of excess demand and comparative statics with incomplete markets and nominal assets

Summary. We prove that locally, Walras' law and homogeneity characterize the structure of market excess demand functions when financial markets are incomplete and assets' returns are nominal. The method of proof is substantially different from all existing arguments as the properties of individual demand are also different. We show that this result has important implications and is part of a more general result that excess demand is an essentially arbitrary function not just of prices, but also of the exogenous parameters of the economy as asset returns, preferences, and endowments. Thus locally the equilibrium manifold, relating equilibrium prices to these parameters has also no structure. Received: September 17, 1996; revised version: November 7, 1997     

Unawareness and bankruptcy: A general equilibrium model

Summary. We present a consistent pure-exchange general equilibrium model where agents may not be able to foresee all possible future contingencies. In this context, even with nominal assets and complete asset markets, an equilibrium may not exist without appropriate assumptions. Specific examples are provided. An existence result is proved under the main assumption that there are sufficiently many states that all the agents foresee. An intrinsic feature of the model is bankruptcy, which agents may involuntarily experience in the unforeseen states. Received: April 23, 1997; revised version: May 19, 1997     

Two-period trading sentiment asset pricing model with information

We present a dynamic asset pricing model with investor sentiment and information, which shows that the investor sentiment plays a systematic and important role in the asset prices and the information is gradually incorporated into prices. The model has an analytical solution to the sentiment equilibrium price. We find that sentiment trading quantity not only increases the market liquidity, but also causes the asset prices' overreaction if the intensity of sentiment demand is more than a constant value. Therefore, the continuing overreactions result in a short-term momentum and a long-term reversal. The model could offer a partial explanation to some financial anomalies such as price bubbles, high volatility, asset prices' overreaction and so on.     

On equilibrium prices in continuous time

State prices are the fundamental building block for dynamic asset pricing models. We provide here a general continuous-time setup that allows to derive non-trivial structural properties for state-prices from economic fundamentals. To this end, we combine general equilibrium theory and théorie générale of stochastic processes to characterize state prices that lead to continuous price systems on the consumption set. We also show that equilibria with such state prices exist.     

Average-cost pricing: Some evidence and implications

We present new survey evidence on pricing behavior for more than 14,000 European firms, and study its macroeconomic implications. Among firms that are price setters, roughly 75% respond that their prices are set as a markup on total costs, a business practice termed “full cost pricing”. Only 25% set prices as markups over variable or marginal costs. Moreover, using industry data for the U.S., we find that the correlation between changes in output prices and changes in variable input prices is significantly lower when fixed costs are likely to be more important.Since our results are similar to the findings in the classic and controversial paper of Hall and Hitch (1939) and subsequent survey evidence, we believe it worth studying the implications of full cost pricing for macroeconomics. We first propose a problem for the firm where full cost pricing can arise as optimizing behavior. We embed this problem, featuring an occasionally binding constraint, into a simple general equilibrium model. We show that when the model is hit by a shock that makes the constraint binding, the response of endogenous variables is amplified significantly more than it would be under the unconstrained regime.