Ebook Liquidity and Asset Prices in Rational Expectations Equilibrium with Ambiguous Information
Information in financial markets is plentiful. There are earnings reports, announcements of macroeconomic indices, political news, expert opinions, and many others. Investors use various pieces of information to update their expectations about asset returns. In standard models of asset markets, agents update their prior probabilistic beliefs about asset returns in Bayesian fashion upon observing an information signal drawn from a precisely known distribution. The quality of some information signals in the markets may be difficult to judge. Investors may not have a single probability belief about the information signal.
The situation of insufficient knowledge of probability distribution is, of course, reminiscent of the famous Ellsberg Paradox where agents have to choose between bets based on draws from an urn with a specified mix of balls of different colors and an urn with an unspecified mix. Many agents choose bets with known odds over the bets with the same stakes but unknown odds. A decision criterion which - unlike the standard expected utility - is compatible with this pattern of preferences is the maxmin (or multiple-prior) expected utility. Under the maxmin expected utility, an agent has a set of probability beliefs (priors) instead of a single one, and evaluates an action, such as taking a bet, according to the minimum expected utility over the set of priors. Such behavior is often referred to as ambiguity aversion, for it indicates the dislike of uncertainty with unknown or ambiguous odds. Axiomatic foundations of maxmin expected utility are due to Gilboa and Schmeidler (1987).
The effects of ambiguous uncertainty and ambiguity aversion in financial markets have been studied over the past two decades. Dow and Werlang (1992) showed that an agent facing ambiguous uncertainty about payoff of an asset will choose not to trade the asset for a range of prices. Building on this result, Cao, Wang and Zhang (2005) showed that ambiguity aversion may lead to limited participation in trading in asset market equilibrium. They consider a model of asset markets with heterogeneous ambiguity and study the effects of limited market participation on asset prices. Easley and O’Hara (2009) use a similar model to study the role of regulation in mitigating the effects of nonparticipation induced by ambiguity aversion. Mukerji and Tallon (2003) showed that ambiguity aversion may have adverse effects on risk sharing in asset markets. The recent paper by Epstein and Schneider (2008) studies asset prices in dynamic markets with ambiguous information signals, but without information transmission.
This paper analyzes information transmission in asset markets when the quality of some information signals is unknown and agents treat information of unknown quality as ambiguous. The questions we ask are: how does ambiguity of information affect the process of information transmission in markets, and how does ambiguous information affect asset prices and trading in equilibrium.
Information transmission in financial markets has been extensively studied when information is of precisely known quality. Models of competitive markets with asymmetric information that is partially revealed by asset prices have been developed by Grossman and Stiglitz (1980), Hellwig (1980), Diamond and Verecchia (1981), and Admati (1985). Models of strategic trading under asymmetric information take their origin in the work of Kyle (1985) and Glosten and Milgrom (1985). We consider a market with risk-averse informed investors, risk-neutral uninformed arbitrageurs and random supply of a single risky asset, first studied in Vives (1995a,b) with unambiguous information. Prior to the arrival of information, all investors have ambiguous beliefs about probability distribution of the asset payoff. Ambiguous beliefs are described by a set of probability distributions. Informed agents receive a private information signal about the payoff. The signal reveals the payoff only partially so that the payoff remains uncertain, but it removes the ambiguity of informed investors’ beliefs. They know precisely the conditional distribution of the payoff. Uninformed arbitrageurs do not observe the signal and extract information from prices. Their beliefs about payoff distribution remain ambiguous. Our main focus is on the process of information transmission through prices in the presence of ambiguity.
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