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

We provide simple examples to illustrate how wealth-driven selection works in asset markets. Our examples deliver both good and bad news. The good news is that if individual assets demands are expressed as a fractions of wealth to be invested in each asset, e.g. because traders maximize an expected Constant Relative Risk Aversion utility with unitary coefficient, then market rewards the best informed agent. As a result asset prices eventually reflect this information and the market can be said informationally efficient. However, and this is the bad news, when asset demands are expressed as price dependent fractions, e.g. they are derived from the maximization of expected Constant Relative Risk Aversion utility with non unitary coefficients, anything can happen and the informational content of long-run prices strongly depend on the ecology of traders' preferences and beliefs. Our examples show that the key difference between the two cases lies in the local, i.e. price dependent, versus global nature of wealth-driven selection.