Extremal Expectations: A Paradigm for Fat-Tails

Abstract

The 'rational expectations hypothesis (REH)' assumes that investors' subjective probability measures coincide with their objective probability measures and all new and relevant information is instantaneously absorbed into these objective distribution measure or prices. A related idea is the efficient market hypothesis which states that the prices of securities as observed reflect all publicly available information. The observed randomness of asset returns re-affirms this line of argument. However, the empirical nonnormality (or fat-tails) of the return distributions continues to be an unexplained anomaly. This paper is based on the rational expectations hypothesis but allows the objective probability measures to be modified to form subjective expectations. Investors remain rational but they revise their original expectations prior to trading based on their buy-sell decisions i.e. they attempt to maximize their expected utilities by adopting decision-biased extreme-valued posterior subjective probabilities based on their prior objective probability measures. A hypothesis called the 'extremal expectations hypothesis (EEH)' is proposed using extreme-valued theory concepts to support the empirical findings.