Ambiguity, no Arbitrage, and the Limits to Rational Expectations

Abstract

The traditional finance approach combines the rational expectations hypothesis with the assumption of no arbitrage. However, the numerous anomalies reported in the finance literature reject this approach. The behavioral finance approach takes rational expectations as the maintained hypothesis with as null hypothesis no arbitrage versus the alternative of limits to arbitrage. Anomalies are interpreted as rejecting the null, suggesting that non-rational noise traders affect the outcomes in financial markets, explaining the anomalies. Alternatively, we take no arbitrage as maintained hypothesis and consider as null hypothesis rational expectations versus the alternative of expectations characterized by ambiguity. But also under ambiguity arbitrage opportunities will be exploited, making no arbitrage the relevant maintained hypothesis. Expectations are modeled as output of an econometric model. Ambiguity arises when the econometric model generates multiple probability distributions, for instance, when modeling a complicated, hard to fully understand financial market, possibly with unforeseen contingencies. Anomalies are then a violation of the null of rational expectations, implying that anomalies need not arise due to the presence of non-rational investors, but are just an artefact of imposing the possibly unrealistically strong assumption of rational expectations.

Keywords: Asset pricing, ambiguity, rational expectations, behavioral finance

JEL Classification: G12