Noisy Rational Expectations Equilibrium Research Articles

The impact of relative wealth concerns on wealth gap and welfare in a noisy rational expectations economy

We employ a noisy rational expectations equilibrium model to investigate the influence of relative wealth concerns on wealth gap and welfare. Our analysis reveals that the impact is sensitive to the exogeneity or endogeneity of information. When information is exogenous, the average wealth gap between high-precision and low-precision investors is either decreasing or, initially decreases and eventually increases in the degree of relative wealth concerns. Moreover, we identify two or three potential patterns regarding the monotonicity pattern of the welfare of low-precision and high-precision investors. However, when information becomes endogenous, the average wealth gap and welfare decrease.

Comments on “Dynamic noisy rational expectations equilibrium with insider information: Welfare and regulation,” by Jerome Detemple, Marcel Rindisbacher and Scott Robertson

Comments on “Dynamic noisy rational expectations equilibrium with insider information: Welfare and regulation,” by Jerome Detemple, Marcel Rindisbacher and Scott Robertson

Dynamic noisy rational expectations equilibrium with insider information: Welfare and regulation

This paper examines welfare properties of equilibra in the general dynamic model with asymmetric information of Detemple et al. (2020). Explicit formulas for ex-ante and interim welfare are obtained, and equilibria are compared. We show a tax structured as an exchange option based on public information induces the insider to optimally forgo using her private information at all times.

Multi-asset Noisy Rational Expectations Equilibrium with Contingent Claims

Abstract We study a noisy rational expectations equilibrium in a multi-asset economy populated by informed and uninformed investors and noise traders. The assets can include state contingent claims such as Arrow–Debreu securities, assets with only positive payoffs, options or other derivative securities. The probabilities of states depend on an aggregate shock, which is observed only by the informed investor. We derive a three-factor CAPM with asymmetric information, establish conditions under which asset prices reveal information about the shock, and show that information asymmetry amplifies the effects of payoff skewness on asset returns. We also find that volatility derivatives make incomplete markets effectively complete, and their prices quantify market illiquidity and shadow value of information to uninformed investors.

Asset market equilibrium under rational inattention

We propose a noisy rational expectations equilibrium model of asset markets with rationally inattentive investors. We incorporate any finite number of assets with arbitrary correlation. We also do not restrict the signal form and show that investors optimally choose a single signal, which is a noisy linear combination of all risky assets. This generates comovement of asset prices and contagion of shocks, even when asset payoffs are negatively correlated. The model also provides testable predictions of the impact of risk aversion, aggregate risk, and information capacity on the security market line, the portfolio dispersion, and the abnormal return.

Stock-based pay, liquidity, and the role of market making

We study the role of stock market characteristics on managerial compensation. A risk averse manager exerts an unobservable effort that drives future firm value. The value cannot be used in the incentive contract because it realizes in the distant future and compensating the manager cannot be postponed until then. The stock price emerges endogenously because of trading by informed and uninformed traders in a standard competitive noisy rational expectations equilibrium model. We identify new “skin-in-the-game” and “information-overlap” terms in the weights the optimal incentive contract gives to the stock price and to public information. We derive novel comparative statics, e.g., the manager may receive more stock-based pay when traders' information becomes worse. The contract always uses public information except in the special case when uninformed traders are risk-neutral.

Wealth heterogeneity, information acquisition and equity home bias: Evidence from U.S. household surveys of consumer finance

• Equity home bias occurs along both extensive and intensive margins. • Wealthy US households are more likely to participate in the foreign stock market. • As investor wealth increases, portfolio share invested in foreign equities decreases. • Overall international diversification is increasing with wealth. • A noisy rational expectations equilibrium model with wealth heterogeneity, entry costs, and information processing can explain both margins. The well-known equity home bias has two components: an extensive and intensive margin. Using data on direct stock holdings of U.S. households, we find that the decision to participate in foreign stock markets depends on investor wealth, with richer investors more likely to participate (the extensive margin). We document a new finding: as investor wealth increases, the portfolio share invested in foreign equities tends to decrease (the intensive margin). A noisy rational expectations equilibrium model with wealth heterogeneity, entry costs, and endogenously chosen information processing capacity can generate the new negative relationship and help understand the U.S. household equity home bias along both margins.

What Do Interest Rates Reveal About the Stock Market? A Noisy Rational Expectations Model of Stock and Bond Markets

We propose a novel theory and provide supporting empirical evidence that lower long-term interest rates (e.g., because of ``quantitative easing'') harm informational and allocative efficiency. We develop a noisy rational expectations equilibrium model with an endogenous interest rate that investors use to update their beliefs about economic fundamentals. The interest rate reveals information about discount rates, allowing investors to extract more information about cashflows from stock prices. The precision of the interest-rate signal and, hence, stock-price informativeness increase in the interest rate. As a result, informational and allocative efficiency rise with bond and money supplies and with policy transparency.

Stock-Based Pay, Liquidity, and the Role of Market Making

We study the role of stock market characteristics on managerial compensation. A risk averse manager exerts an unobservable effort that drives future firm value. The value cannot be used in the incentive contract because it realizes in the distant future and compensating the manager cannot be postponed until then. Instead, the contract uses the stock price as well as public information about the future value of the firm. The stock price emerges endogenously because of trading by informed and uninformed traders in a standard competitive noisy rational expectations equilibrium model. It is well known that liquidity facilitates trading on private information. We identify a dark side of liquidity for incentive contracting. More liquidity makes the stock price less responsive to trading and hence, less sensitive to the manager's effort. Our model yields novel comparative statics, e.g., the manager may receive more stock-based pay when traders' information becomes worse. The contract always uses public information except in the special case when uninformed traders are risk-neutral.

Wealth Heterogeneity, Information Acquisition and Equity Home Bias

The well-known equity home bias has two components: an extensive and intensive margin. Using data on direct stock holdings of U.S. households, we find that the decision to participate in foreign stock markets depends on investor wealth, with richer investors more likely to participate (the extensive margin). We document a new finding: as investor wealth increases, the portfolio share invested in foreign equities tends to decrease (the intensive margin). A noisy rational expectations equilibrium model with wealth heterogeneity, entry costs, and endogenously chosen information processing capacity can generate the new negative relationship and help understand the U.S. household equity home bias along both margins.

Does Information Intensity Matter for Stock Returns? Evidence from Form 8-K Filings

This paper identifies an important source of variation in U.S. firms’ material information flows: their Form 8-K filing frequency. Exploiting cross-sectional variation in this novel proxy for information intensity, this paper finds that firms with higher information intensity experience lower future returns and lower future volatilities. The marginal return impact is higher at low levels of information intensity and high levels of prior volatility. On average, an information-intensity-based long-short portfolio generates a return spread of 4.3% per year. After adjusting for the Fama–French three factors and the momentum factor, the abnormal return remains 4.4% per year. These novel findings suggest that, because of the dynamic nature of information arrival, the frequency/quantity of information is an important source affecting the information environment and stock returns of public companies. These findings are consistent with the predictions of a broad class of noisy rational expectations equilibrium models and estimation risk models, and they highlight the importance of learning in financial markets with incomplete information. This paper was accepted by Neng Wang, finance.

The Dynamics of Belief Formation and Price Momentum

In classical perfect and complete markets, prices form a Martingale and stock returns (or equivalently, successive price changes) are serially uncorrelated. However, there is considerable evidence in the finance literature showing that stock returns are serially correlated both in the short and the long-term. This empirical phenomenon has been viewed as a violation of semistrong efficiency and has resulted in considerable discussion in the literature. In this paper we demonstrate that within a multi-period noisy rational expectations equilibrium framework, a first order autoregressive (AR-1) liquidity trading process, by itself, suffices to give rise to systematic correlations in price changes, either positive or negative, depending on the specific parameters of the process, even if the (unknown) underlying liquidation value is fixed. That is, unsystematic random fluctuations in observed prices arising from factors such as liquidity trading affect Bayesian belief formation, and thereby trading strategies, in such a way that equilibrium price changes can manifest both momentum and reversals.

Noisy Arrow-Debreu Equilibria

I develop a noisy rational expectations equilibrium model with a continuum of states and a full set of options that render the market complete. I show a major difference in equilibrium behaviour between models with constant absolute risk aversion (CARA) and non-CARA preferences. First, when informed traders have non-CARA preferences, all equilibria are fully revealing, independent of the amount of noise in the supply. Second, when informed traders have CARA preferences, but uninformed traders have non-CARA preferences, the set of equilibria contains a fully revealing equilibrium and a minimally revealing equilibrium. The latter reveals the minimal possible amount of information and is highly inefficient: In this equilibrium, Arrow-Debreu state prices are not sufficient to recover the information contained in the noisy aggregate demand and supply. My results have important implications for price discovery through options.

Earnings management, incentive contracts and private information acquisition

This paper analyzes the optimal design of compensation contracts in the presence of earnings management incentives, and its interplay with investors’ information acquisition decisions. We consider a setting in which compensation contract is based on both accounting earnings and stock price when an agent engages in predictable, pernicious earnings management and stock price is endogenously determined in a Noisy Rational Expectations Equilibrium (NREE) that reflects both the public information from reported earnings and a costly, noisy signal privately acquired by investors. We show that an increase in the precision of the firm’s financial reporting system could reduce the informativeness of stock price and exacerbate the agency problem by inducing lower productive effort and higher earnings management, implying that the firm may not choose a more precise financial reporting system.

Multi-Asset Noisy Rational Expectations Equilibrium with Contingent Claims

We consider a noisy rational expectations equilibrium in a multi-asset economy populated by informed and uninformed investors, and noise traders. We relax the usual assumption of normally distributed asset payos and allow for assets with very general payo distributions, including non-redundant contingent claims, such as options and other derivatives. We provide necessary and sucient conditions under which contingent claims provide information about the source of uncertainty in the economy and, hence, reduce the asymmetry of information. We also apply our results to pricing risky debt and equity and demonstrate that firms cannot manipulate the information contained in debt and equity prices by changing the face value of debt. Our paper provides a new tractable framework for studying asset prices under asymmetric information. When the market is complete, we derive the equilibrium in closed form. When the market is incomplete, we derive it in terms of easily computable inverse functions.

Price Discovery through Options

How does private information get incorporated into option prices? To study this question, I develop a non-linear, noisy rational expectations equilibrium model with asymmetric information and a full menu of call and put options available for trading. The model allows for an arbitrary distribution of the underlying payoff and general trader preferences. All equilibrium prices and portfolios are obtained in closed form. Learning from option prices is characterized explicitly in terms of a novel object, the second derivative of the signal-to-noise ratio, whose sign determines whether particular shapes of option prices are "good news". I show that there is a major difference in equilibrium behaviour for constant absolute risk aversion (CARA) and non-CARA preferences due to feedback effects between wealth, price discovery, and private information: First, if informed traders have non-CARA preferences, strong-form efficiency is always obtained, independent of the amount of noise trading. Second, when informed traders have CARA preferences, the nature of equilibrium changes drastically with wealth effects of uninformed trading: If the latter have non-CARA preferences, weak-form efficiency fails and option prices are not sufficient to recover the information contained in the aggregate demand.

Price Discovery Through Options

How does private information get incorporated into option prices? To study this question, I develop a non-linear, noisy rational expectations equilibrium model with asymmetric information and a full menu of call and put options available for trading. The model allows for an arbitrary distribution of the underlying payoff and general trader preferences. All equilibrium prices and portfolios are obtained in closed form. Learning from option prices is characterized explicitly in terms of a novel object, the second derivative of the signal-to-noise ratio, whose sign determines whether particular shapes of option prices are good news. I show that there is a major difference in equilibrium behaviour for constant absolute risk aversion (CARA) and non-CARA preferences due to feedback effects between wealth, price discovery, and private information: First, if informed traders have non-CARA preferences, strong-form efficiency is always obtained, independent of the amount of noise trading. Second, when informed traders have CARA preferences, the nature of equilibrium changes drastically with wealth effects of uninformed trading: If the latter have non-CARA preferences, weak-form efficiency fails and option prices are not sufficient to recover the information contained in the aggregate demand.

The Speed of Information Revelation and Eventual Price Quality in Markets with Insiders: Comparing Two Theories*

Two theoretical literatures, one using Bayesian Nash equilibrium (BNE), and the other using noisy rational expectations equilibrium (NREE), both provide a foundation for understanding how private information is impounded into asset prices, yet some of their predictions are conflicting. Here, we compare for the first time, the two theories using data from carefully controlled laboratory asset markets. In the dynamics, we find strong evidence for BNE theory, although final prices support predictions of the NREE theory. Finally, we document that price volatility increases when information is being impounded in prices.

Testing Asymmetric-Information Asset Pricing Models

We provide evidence for the importance of information asymmetry in asset pricing by using three natural experiments. Consistent with rational expectations models with multiple assets and multiple signals, we find that prices and uninformed demand fall as asymmetry increases. These falls are larger when more investors are uninformed, turnover is larger and more variable, payoffs are more uncertain, and the lost signal is more precise. Prices fall partly because expected returns become more sensitive to liquidity risk. Our results confirm that information asymmetry is priced and imply that a primary channel that links asymmetry to prices is liquidity. (JEL G12, G14, G17, G24) Theoretical asset pricing models routinely assume that investors have heterogeneous information. The goal of this article is to establish the empirical relevance of this assumption for equilibrium asset prices and investor demands. To do so, we exploit a novel identification strategy that allows us to infer changes in the distribution of information among investors and hence to quantify the effect of information asymmetry on prices and demands. Our results suggest that information asymmetry has a substantial effect on prices and demands and affects assets through a liquidity channel. Asymmetric-information asset pricing models typically rely on a noisy rational expectations equilibrium (REE) in which prices, due to randomness in the risky asset’s supply, only partially reveal the better-informed investors’ information. Random supply might reflect the presence of “noise traders” whose demands are independent of information. Prominent examples of such models include Grossman and Stiglitz (1980), Hellwig (1980), Admati (1985), Wang (1993), and Easley and O’Hara (2004).

Does more information in stock price lead to greater or smaller idiosyncratic return volatility?

We investigate the relation between price informativeness and idiosyncratic return volatility in a multi-asset, multi-period noisy rational expectations equilibrium. We show that the relation between price informativeness and idiosyncratic return volatility is either U-shaped or negative. Using several price informativeness measures, we empirically document a U-shaped relation between price informativeness and idiosyncratic return volatility. Our study therefore reconciles the opposing views in the following two strands of literature: (1) the growing body of research showing that firms with more informative stock prices have greater idiosyncratic return volatility, and (2) the studies arguing that more information in price reduces idiosyncratic return volatility.