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A Note On Confidence Momentum And Term Structure of Confidence with Applications to Financial Markets

G. Cadogan

posted on 14 February 2012

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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 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 loss [gain] probabilities is a predictor of confidence momentum. It supports the trajectories of random fields of confidence which portend a term structure of confidence for hope and fear. Our theory explains why“irrational exuberance” and market confidence predict bubbles and crashes. It plainly shows that the growth rate of popular confidence indexes like UBS/Gallup Investor Optimism Index; Michigan Consumer Confidence Index; and Yale Investor Confidence Index predict bubbles and crashes.


This paper replaces the one entitled "A Note On The Confidence Matrix And Term Structure of Confidence" posted on February 10, 2012. Arguably, it clarified the equation for random field representation; and it added Fig. 3 to show how the confidence matrix operator and its adjoint interacts to form a psuedo general equilibrium. So there is no change in results. Just change in presentation.

The latest version clarifies notation and presents a formal definition of the fields of confidence. It also adds a few references, and use unpublished data from Gallup Economic Confidence Index to show that the field of confidence is well defined. Moreover, it establishes a nexus between Gilboa and Schmeilder (J. Math Econ, 1989); Chateaunerf and Fora (J Math Econ 2009) and Tversky and Wakker (Econometrica 1995) with respect to how a convex set of prior probabilities provides impetus for momentum, and subsequent transformation of probability domain(s).