A Note on Confidence Momentum and Term Structure of Confidence with Applications to Financial Markets

Abstract

This note is based on a recent confidence index introduced in the context of compensating probability factors for deviations of subjective probability measures from equivalent martingale measures. The index is adjusted for loss gain probability spreads, and it explains momentum in confidence. We use the index to introduce a confidence matrix operator which shows how a subject transforms gain domain into fear of loss. So she is loss averse or risk averse. By contrast, the adjoint confidence matrix operator is an Euclidean motion which rotates and reverses loss domain into hope of gain. Thus, signifying risk seeking over loss domains in hope of gain. Simulation of the model shows that the distribution of prior loss [gain] probabilities is a predictor of confidence momentum and fields of confidence. Moreover, our field theory of confidence mimics a sample of Gallup Monthly Economic Confidence Index, and depicts a term structure of confidence for hope and fear. It plainly shows that the growth rate of Gallup Economic Confidence Index -- which is highly correlated with popular confidence indexes like UBS/Gallup Investor Optimism Index; Michigan Consumer Confidence Index; and Yale Investor Confidence Index -- predict bubbles and crashes.