Implications of Rationality in Asset Markets

We consider a three period economy where traders trade assets before and after the arrival of a signal (or data). We say that a trader has rationalizable beliefs if i) she is an SEU maximizer and if ii) her likelihood ratio of the data relative to various states of the world is equal to the objective likelihood ratio of the data (a restriction on her beliefs). A candidate equilibrium is an outcome where each trader’s budget constraint is binding, markets clear and prices satisfy no arbitrage. We find that almost all candidate equilibria cannot be rationalized under any belief restriction when the number of traders is sufficiently large. Almost no belief restriction can rationalize a given a candidate equilibrium and those that do are not robust to small changes in their specification. If we impose instead that the likelihood ratio of aggregate data is equated across traders, then a rationalizable belief restriction is always robust, provided that markets are sufficiently incomplete. We take this to mean that if one is to find a robust rationalization of traders’ actions, one needs to allow for some heterogeneity in the way traders interpret the data and some market incompleteness. This paper is a preliminary draft. Dubai School of Government, Convention Tower 7th Floor, Dubai, United Arab Emirates. Email: [email protected]. Department of Economics, Cornell University, Uris Hall, Ithaca, NY, 14853. Email: [email protected] 1