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.     

The dynamics of efficient asset trading with heterogeneous beliefs

This paper analyzes the dynamic properties of portfolios that sustain dynamically complete markets equilibrium when agents have heterogeneous priors. We argue that the conventional wisdom that belief heterogeneity generates continuous trade and significant fluctuations in individual portfolios may be correct but it needs some qualifications. We consider an infinite horizon stochastic endowment economy populated by many Bayesian agents with heterogeneous priors over the stochastic process of the states of nature. Our approach hinges on studying the portfolios that decentralize Pareto optimal allocations. Since these allocations are typically history dependent, we propose a methodology to provide a complete recursive characterization when agents believe that the process of states of nature is i.i.d. but disagree about the probability of the states. We show that even though heterogeneous priors within that class can indeed generate genuine changes in the portfolios of any dynamically complete markets equilibrium, these changes vanish with probability one if the true process consists of i.i.d. draws from a common distribution and the support of some agent's prior belief contains the true distribution. Finally, we provide examples in which asset trading does not vanish because either (i) no agent learns the true conditional probability of the states or (ii) some agent does not know the true process generating the data is i.i.d.     

Competitive equilibrium with unawareness in economies with production

This paper investigates an extension of the GEI-unawareness framework by Modica et al. (Econ. Theory 12 (1998) 259) to economies with entrepreneurial production. Existence of equilibrium is guaranteed given decreasing returns to scale. Firm's value and investment decision in equilibrium are characterized. An example of commodity innovation shows that the effect of different degrees of awareness on investment decisions depend upon the degree of risk aversion. In the case of log preferences unawareness may not matter for commodity innovation, although this depends on other preference features.     

Injecting rational bubbles

This paper proves two theorems about economies with a finite number of infinitely lived agents who trade a complete set of one-period Arrow securities and several infinitely lived securities at each date, subject to short-sales constraints. The first theorem in the paper considers an equilibrium to an economy of this kind. It proves that there exists another economy with perturbed short-sales constraints in which there is an allocation-equivalent equilibrium in which asset prices have a bubble. The second theorem extends to the result to the case in short-sales constraints are endogenously determined in the sense of Alvarez and Jermann [Efficiency, equilibrium, and asset pricing with risk of default, Econometrica 68 (2000) 775-797].     

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.     

How equilibrium prices reveal information in a time series model with disparately informed, competitive traders

Accommodating asymmetric information in a dynamic asset pricing model is technically challenging due to the problems associated with higher-order expectations. That is, rational investors are forced into a situation where they must forecast the forecasts of other agents. In a dynamic setting, this problem telescopes into the infinite future and the dimension of the relevant state space approaches infinity. By using the frequency domain approach of Whiteman [Linear Rational Expectations Models: A User's Guide, University of Minnesota Press, Minneapolis, 1983] and Kasa [Forecasting the forecasts of others in the frequency domain, Rev. Econ. Dynam. 3 (2000) 726-756], this paper demonstrates how information structures previously believed to preserve asymmetric information in equilibrium, converge to a symmetric information, rational expectations equilibrium. The revealing aspect of the price process lies in the invertibility of the observed state space, which makes it possible for agents to infer the economically fundamental shocks and thus eliminating the need to forecast the forecasts of others.     

Aggregation, efficiency and mutual fund separation in incomplete markets

Summary. This paper studies the conditions for aggregation, portfolio separation and effective completeness of competitive allocations in general equilibrium models with incomplete markets where agents have general preference and endowment distributions. We show that these properties are distinct. Demands may aggregate yet may fail to exhibit fund separation and conversely. Fund separation implies effective completeness while aggregation does not. The implications of these properties for the structure of equilibria are discussed, and generalizations of the CAPM, the consumption CAPM and the CAPM with nonmarketed wealth emerge from the analysis. Received: September 12, 1996; revised version: November 7, 1996     

Portfolio choice and pricing in illiquid markets

This paper studies portfolio choice and pricing in markets in which immediate trading may be impossible. It departs from the literature by removing restrictions on asset holdings, and finds that optimal positions depend significantly and naturally on liquidity: When expected future liquidity is high, agents take more extreme positions, given that they do not have to hold those positions for long when they become undesirable. Consequently, larger trades should be observed in markets with more frequent trading. Liquidity need not affect the price significantly, however, because liquidity has offsetting impacts on different agents' demands. This result highlights the importance of unrestricted portfolio choice. The paper draws parallels with the transaction-cost literature and clarifies the relationship between the price level and the realized trading frequency in this literature.     

Representative consumer's risk aversion and efficient risk-sharing rules

We study the representative consumer's risk attitude and efficient risk-sharing rules in a single-period, single-good economy in which consumers have homogeneous probabilistic beliefs but heterogeneous risk attitudes. We prove that if all consumers have convex absolute risk tolerance, so must the representative consumer. We also identify a relationship between the curvature of an individual consumer's individual risk sharing rule and his absolute cautiousness, the first derivative of absolute risk-tolerance. Furthermore, we discuss some consequences of these results and refinements of these results for the class of HARA utility functions.     

South African stock return predictability in the context data mining: The role of financial variables and international stock returns

In this paper, we examine the predictive ability, both in-sample and the out-of-sample, for South African stock returns using a number of financial variables, based on monthly data with an in-sample period covering 1990:01 to 1996:12 and the out-of-sample period of 1997:01 to 2010:04. We use the t-statistic corresponding to the slope coefficient in a predictive regression model for in-sample predictions, while for the out-of-sample, the MSE-F and the ENC-NEW tests statistics with good power properties were utilised. To guard against data mining, a bootstrap procedure was employed for calculating the critical values of both the in-sample and out-of-sample test statistics. Furthermore, we use a procedure that combines in-sample general-to-specific model selection with out-of-sample tests of predictive ability to further analyse the predictive power of each financial variable. Our results show that, for the in-sample test statistic, only the stock returns for our major trading partners have predictive power at certain short and long run horizons. For the out-of-sample tests, the Treasury bill rate and the term spread together with the stock returns for our major trading partners show predictive power both at short and long run horizons. When accounting for data mining, the maximal out-of-sample test statistics become insignificant from 6-months onward suggesting that the evidence of the out-of-sample predictability at longer horizons is due to data mining. The general-to-specific model shows that valuation ratios contain very useful information that explains the behaviour of stock returns, despite their inability to predict stock return at any horizon. The model also highlights the role of multiple variables in predicting stock returns at medium- to long run horizons.     

Modelling conditional heteroskedasticity: Application to the “IBEX-35” stock-return index

This paper compares alternative time-varying volatility models for daily stock-returns using data from Spanish equity index IBEX-35. Specifically, we estimate a parametric family of models of generalized autoregressive heteroskedasticity (which nests the most popular symmetric and asymmetric GARCH models), a semiparametric GARCH model, the generalized quadratic ARCH model, the stochastic volatility model, the Poisson Jump Diffusion model and, finally, a nonparametric model. Those models which use conditional standard deviation (specifically, TGARCH and AGARCH models) produce better fits than all other GARCH models. We also compare the within sample predictive power of all models using a standard efficiency test. Our results show that the asymmetric behaviour of responses is a statistically significant characteristic of these data. Moreover, we observe that specifications with a distribution which allows for fatter tails than a normal distribution do not necessarily outperform specifications with a normal distribution.     

Liquidity shocks and equilibrium liquidity premia

We study an equilibrium in which agents face surprise liquidity shocks and invest in liquid and illiquid riskless assets. The random holding horizon from liquidity shocks makes the return of the illiquid security risky. The equilibrium premium for such risk depends on the constraint that agents face when borrowing against future income; it is insignificant without borrowing constraint, but can be very high with borrowing constraint. Illiquidity, therefore, can have large effects on asset returns when agents face liquidity shocks and borrowing constraints. This result can help us understand why some securities have high liquidity premia, despite low turnover frequency.     

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.     

Renegotiation-proof contracting, disclosure, and incentives for efficient investment

Disclosure by firms would seem to reduce investment inefficiency by reducing informational asymmetry. However, the impact of disclosure is endogenous and depends on incentives within the firm. Given optimal renegotiation-proof contracts, disclosing only accepted contracts does not solve the Myers-Majluf problem. What solves the problem is having either full transparency of all compensation negotiations or, more reasonably, additional forward-looking announcements. The model is robust to renegotiation in equilibrium, the order of moves, and moral hazard. The analysis illuminates disclosure regulation: forward-looking disclosure is beneficial when the manager's contract is optimal and induces truth-telling.     

Fundamentals, information, and international capital flows: A welfare analysis

In the recent discussion surrounding the design of a new international financial architecture, enhancing transparency has widely been proposed as a policy essential for increasing the efficiency of international capital markets. This paper uses a simple two-country (two-agent) general equilibrium model with incomplete markets and production to explore the welfare consequences of an increase in public information about country-specific fundamentals (increase in transparency). An improvement in the quality of information has two effects on the ex ante welfare of individual countries: A direct effect that increases the efficiency of global capital allocation and welfare, and an indirect general equilibrium effect that increases asset price volatility and may decrease welfare. When the degree of risk-aversion is low, at least one country will gain from an increase in information quality. If the degree of risk-aversion is high, then there are robust examples of economies for which an increase in information hurts all countries. The paper also discusses how certain institutional arrangements (international derivative markets, international agency) could ensure that all countries gain from better information by providing insurance against information-induced asset price risk.     

Empirical analysis of jump dynamics, heavy-tails and skewness on value-at-risk estimation

This study provides a comprehensive analysis of the possible influences of jump dynamics, heavy-tails, and skewness with regard to VaR estimates through the assessment of both accuracy and efficiency. To this end, the ARJI model, and its degenerative GARCH model with normal, GED, and skewed normal (SN) distributions were adopted to capture the properties of time-varying volatility, time-varying jump intensity, heavy-tails and skewness, for a range of stock indices across international stock markets during the period of the U.S. subprime mortgage crisis. Empirical results show that, with regard to the evaluation of accuracy, the role of jump dynamics is more substantial than heavy-tails or skewness as it pertains to VaR accuracy at the 90% and 95% levels, while heavy-tails become more important at the 99% level for a long position. However, the influence of the abovementioned properties on VaR estimation does not appear substantial for a short position. In addition, the properties of jump dynamics and skewness appear to be beneficial for the improvement of efficiency.     

Portfolio choice, attention allocation, and price comovement

This paper models the attention allocation of portfolio investors. Investors choose the composition of their information subject to an information flow constraint. Given their expected investment strategy in the next period, which is to hold a diversified portfolio, in equilibrium investors choose to observe one linear combination of asset payoffs as a private signal. When investors use this private signal to update information about two assets, changes in one asset affect both asset prices and may lead to asset price comovement. The model also has implications for the transmission of volatility shocks between two assets.