Stochastic equilibria with incomplete financial markets

We demonstrate the existence of equilibria with incomplete financial markets for stochastic economies whose information structure is given by an event tree, restricting attention to purely financial securities, those paying in units of account (e.g., “dollars”). Financial markets may be incomplete: some consumption streams may be impossible to obtain by any trading strategy. Securities may be individually precluded from trade at arbitrary states and dates. Sufficient conditions for the existence of stochastic equilibria are: continuous, convex, strictly monotonic preferences and strictly positive aggregate endowments. These conditions are weakened. A corollary states that any regime of security prices precluding arbitrage can be embedded in an equilibrium.     

OUTPUT CONTINGENT SECURITIES AND EFFICIENT INVESTMENT BY FIRMS

We analyze competitive economies with risky investments. Unlike the classic Arrow–Debreu framing, firms and agents cannot contract upon the exogenous states underlying production risks. They can trade equities and any security written on the endogenous aggregate output. This financial structure is rich enough to promote efficient risk sharing among consumers. However, markets are incomplete from the production perspective, and the absence of prices for each primitive state of nature raises the question about the objective of firms. We show that output‐contingent asset prices convey sufficient information to compute the competitive shareholder value that leads to efficient investment by firms.     

Incomplete financial markets and differential information

We provide a model of an incomplete markets economy where private restrictions on consumption are interpreted as lack of information. We prove existence of an equilibrium where agents are unable to infer any additional information from prices. When assets are nominal, these non-enlightening equilibrium prices result in a reduction of the degree of real indeterminacy.     

No-arbitrage Equilibria with Differential Information: An Existence Proof

On the example of a pure exchange financial economy with two periods incomplete nominal-asset markets and differential information of the adverse selection’s type, Cornet-De Boisdeffre (J Math Econ 38:393-410, 2002) introduced refined concepts of no-arbitrage prices and equilibria, which extended to the asymmetric information setting the classical concepts of the symmetric information literature. We now assess existence issues and extend a standard property of symmetric information models. Namely, we prove that a no-arbitrage equilibrium always exists, as long as financial markets preclude arbitrage, under the same standard conditions, whether agents have symmetric or asymmetric information.     

Inducing liquidity in thin financial markets through combined-value trading mechanisms

Asset pricing theory hypothesizes that investors are only interested in portfolios; individual securities are evaluated only in terms of their contribution to portfolio risk and return. Yet, standard financial market design is that of parallel, unconnected markets, whereby investors cannot submit orders in one market conditional on events in others. When markets are thin, this exposes them to substantial execution risk. Fear of ending up with unbalanced portfolios after trading may even keep investors from submitting orders, further eroding liquidity and the ability of markets to equilibrate. The suggested solution is a portfolio trading mechanism referred to as combined-value trading (CVT). Investors are allowed to submit orders for packages of securities and the system matches trades and computes prices by optimally combining portfolio orders in an open book. We study the performance of the CVT mechanism experimentally and compare it to the performance of parallel, unconnected double auctions in experiments with similar parametrization and either a similar number of subjects or substantially thicker markets. We present evidence that our portfolio trading mechanism facilitates equilibration to the extent that the thicker markets do. Inspection of order submission and trade activity reveals that subjects manage to exploit the direct linkages between markets enabled by the CVT system.     

Nonlinear incentive provision in Walrasian markets: a Cournot convergence approach

The paper studies insurance with moral hazard in a system of contingent-claims markets. Insurance buyers are modelled as Cournot monopolists or oligopolists. The other agents condition their expectations on market prices, as in models of rational-expectations equilibrium with asymmetric information. Thereby they correctly anticipate accident probabilities corresponding to effort incentives induced by insurance buyers’ net trades. When there are many agents to share the insurance buyers’ risks, Cournot equilibrium outcomes are close to being second-best. In contrast, if insurance buyers are price takers, equilibria fail to exist or are bounded away from being second-best.     

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.     

Information, trade and incomplete markets

The no-trade result of Milgrom and Stokey, J Econ Theory 26:17–27 (1982), states that if rational traders begin with an ex-ante Pareto optimal allocation then the arrival of information cannot generate trade. This paper allows traders to trade before and after the arrival of information. If there are enough securities to hedge against all payoff relevant risk, then the preinformation-arrival allocation is Pareto optimal and information arrival has no effect. This no-retrade result is the competitive analog of the no-trade result of (1982). However, information generically generates trade when markets are state-contingent incomplete.We thank seminar participants at Cambridge, Carnegie Mellon,Cornell, Essex, London, Maastricht, USC, and York and participants at the 2003 SITE, the 2003 SAET and the Fall 2002 Cornell–Penn State Macro Conference. We also thank Karl Shell and a referee for this journal for useful comments     

Pricing rules and Arrow–Debreu ambiguous valuation

This paper considers pricing rules of single-period securities markets with finitely many states. Our main result characterizes those pricing rules C that are super-replication prices of a frictionless and arbitrage-free incomplete asset structure with a bond. This characterization relies on the equivalence between the sets of frictionless securities and securities priced by C. The former captures securities without bid-ask spreads, while the second captures the class of securities where, if some of its delivers is replaced by a higher payoff, then the resulting security is characterized by a higher value priced by C. We also analyze the special case of pricing rules associated with securities markets admitting a structure of basic assets paying one in some event and nothing otherwise. In this case, we show that the pricing rule can be characterized in terms of capacities. This Arrow–Debreu ambiguous state price can be viewed as a generalization for incomplete markets of Arrow–Debreu state price valuation. Also, some interesting cases are given by pricing rules determined by an integral w.r.t. a risk-neutral capacity. For instance, incomplete markets of Arrow securities and a bond are revealed by a Choquet integral w.r.t. a special risk-neutral capacity.     

Dynamic information release

This note discusses the desirability of dynamic information releases. It is argued that such releases are socially valuable because theycreate insurance opportunities that do not exist without them. These new insurance opportunities occur because new public information causes prices to change which in turn allows traders to improve the spanning ability of existing securities by dynamic trading. This argument contrasts the static argument pioneered by Hirshleifer (1971) that public information oftendestroys insurance opportunities and is therefore not socially valuable.I thank Robert Litzenberger and Jiang Wang for helpful comments. Financial support from the Royal Swedish Academy of Sciences is gratefully acknowledged. Remaining errors are my own.     

Banking on the FED: QE1-2-3 and the Rebalancing of the Global Economy

Growing income inequality in most countries in the 1990s and 2000s led to a global shortfall between supply and demand. The US economy bridged this shortfall domestically and globally by blowing successive equity market and housing bubbles, but these produced ever more severe financial crises. Rebalancing after the 2008 crisis required trade surplus countries to expand their non-traded sectors, but rebalancing is never immaculate. Instead, the Federal Reserve Bank's three rounds of Large-Scale Asset Purchases, or quantitative easing, shifted investment flows towards some developed and developing economies. As a matter of accounting, capital inflows led to shrinking trade surpluses in those countries. However, their relatively undeveloped securities markets mean that rebalancing largely occurred through rising housing prices, mirroring the same unsustainable phenomenon the USA experienced in the 2000s. In effect, the USA shifted part of its unsustainably large non-traded sector back to trade surplus countries by causing the real-estate part of the non-traded sector in surplus countries to expand. However, this is not a sustainable solution to global trade and financial imbalances in the long run, and risks producing the same kind of crises the USA experienced in 2008.     

Equity home bias,incomplete financial markets,and nominal rigidities

Abstract This paper analyzes optimal portfolio decisions in a monetary open‐economy framework. It is found that market completeness and the specific form of nominal rigidities, namely, nominal price vs. nominal wage rigidities, matter for justifying the observed structure of equity holdings. When markets are complete, sticky prices generate a negative correlation between the non‐diversifiable labour income and the profit of domestic firms with respect to the productivity shocks, which explains why households invest little abroad. In contrast, when markets are incomplete, rigidities in goods prices result in a counterfactual ‘super home bias’, because domestic equities provide a good hedge against not only the labour income risk but also the relative price risk. Wage rigidities, however, have the opposite effect. Therefore, nominal rigidities in both goods prices and wage rates are needed to address the empirical composition of gross equity positions under incomplete markets.     

Trade and Tradability: Exports, Imports, and Factor Markets in the Salter-Swan Model

We extend the Salter-Swan model to include both factor markets and semi-traded goods. In our model, changes in relative factor prices depend on changes in world commodity prices, factor endowments, and the trade balance. In contrast, only changes in world commodity prices can affect factor prices in the neoclassical trade model. The inclusion of semi-traded goods weakens the magnification effect in both the Stolper-Samuelson and Rybczynski theorems. When imports and domestic goods are poor substitutes, a characteristic of some commodities in developing countries, the sign of the Stolper-Samuelson theorem is reversed.     

Daily variation,capital market efficiency and predicting stock returns for the Hong Kong and Tokyo exchanges

Studying capital market efficiency is important because result may infer that there are predictable properties of the time series of prices of traded securities on organized markets. We examine the weak form of the efficient markets hypothesis to indicate its usefulness in terms of the results of this study. Furthermore, this study of individual securities prices of traded securities on the organized markets of Hong Kong and Japan corroborate previous findings of studies of individual stocks and market indexes both in Asian nations, the United States and other stock exchanges in the United Kingdom and Europe. Daily patterns are present in the times series of securities prices. You will note also, that the models identified reflect the returns on individual firms listed on the two of the three largest Asian Stock Exchanges.     

Do sunspots matter under complete ignorance?

In a two-period, sunspot, pure-exchange economy we analyse the case in which agents do not assign subjective probabilistic beliefs to the ‘sunspot activity’. Two generations, each of which is made up of identical agents, populate this economy. Participation in the Arrow securities market is restricted and the generation, which is allowed to trade in assets, can alternatively face uncertainty via two distribution-free decision rules under ‘complete ignorance’ (axiomatized by Milnor [Milnor, J., 1954. Games against nature. In: Thrall, R. Coombs, C., Davis, R. (Eds.), Decision Processes. John Wiley, London, pp. 49–60]): the ‘minimax regret criterion’ [Savage, L.J., 1954. The Foundations of Statistics. Wiley, New York, ch. 9] and the ‘maxmin return criterion’ [Wald, A., 1950. Statistical Decision Functions. Wiley, New York]. When the former is used, then sunspots can matter. In particular, we prove that, if the economy admits two Walrasian equilibria, then a unique sunspot equilibrium always exists. We pin down this equilibrium, determine the prices of the Arrow securities and show that, at these prices, no trade in securities takes place. In the same framework we prove that, with agents using the maxmin return criterion, sunspots do not matter.     

分散保险风险的资本市场创新工具

本文提出并设计出一种全新的金融产品———保险金融券 ,这种保险金融券具有固定收益证券的性质 ,同时又与保险公司的风险挂钩。它能将保险公司的风险有效地分散到资本市场上 ,从而增加保险市场的容量 ,提高保险公司的竞争力。同时又为资本市场的投资者提供了更多的投资品种。本文运用国外最前沿的理论成果 ,结合中国的实际情况 ,对保险金融券进行了定价 ,同时对保险金融券的发行、收益等方面进行了详细的论述。     

Selection in asset markets: the good, the bad, and the unknown

In this paper, we use a series of simple examples to illustrate how wealth-driven selection works in a market for Arrow securities. Our analysis delivers both a good and a bad message. The good message is that, when traders invest constant fractions of their wealth in each asset and have equal consumption rates, markets are informationally efficient: the best informed agent is rewarded and asset prices eventually reflect this information. However, and this is the bad message, when asset demands are not constant fractions of wealth but dependent upon prices, markets might behave sub-optimally. In this case, asymptotic prices depend on preferences and beliefs of the whole ecology of traders and do not, in general, reflect the best available information. We show that the key difference between the two cases lies in the local, i.e. price dependent, versus global nature of wealth-driven selection.     

Elimination of arbitrage states in asymmetric information models

In a financial economy with asymmetric information and incomplete markets, we study how agents, having no model of how equilibrium prices are determined, may still refine their information by eliminating sequentially “arbitrage state(s)”, namely, the state(s) which would grant the agent an arbitrage, if realizable.      

Generic inefficiency of equilibria in the general equilibrium model with incomplete asset markets and infinite time

Summary. We consider a Lucas asset-pricing model with heterogeneous agents, exogenous labor income, and a finite number of exogenous shocks. Although agents are infinitely lived, endowments and dividends are time-invariant functions of the exogenous shock alone and are thus restricted to lie in a finite-dimensional space; genericity analysis can be conducted on sets of zero Lebesgue measure. When financial markets are incomplete, that is, there are fewer financial securities than shocks, we show that generically in individual endowments all competitive equilibria are Pareto inefficient. Received: November 22, 1999; revised version: March 4, 2002 RID="*" ID="*" We are grateful to an anonymous referee for very insightful comments on earlier drafts.     

Optimal asset taxes in financial markets with aggregate uncertainty

This paper studies Pareto-optimal risk-sharing arrangements in a private information economy with aggregate uncertainty and ex ante heterogeneous agents. I show how to implement Pareto optima as equilibria when agents can trade claims to consumption contingent on aggregate shocks in financial markets. The first result is that if aggregate and idiosyncratic shocks are independent, the implementation of optimal allocations does not require any interventions in financial markets. This result can be extended to dynamic settings in the sense that, in this case, only savings need to be distorted, but not trades in financial markets. Second, I characterize optimal trading distortions in financial markets when aggregate and idiosyncratic shocks are not independent. In this case, optimal asset taxes must be higher for those securities that pay out in aggregate states in which consumption is more volatile. For instance, this can provide an efficiency justification for the frequently observed differential tax treatment of different asset classes, such as debt and equity claims.