Fluctuating Confidence in Stock Markets: Implications for Returns and Volatility

Abstract

The average relative profitability of different firms in the economy jumps erratically. Al? though investors are unable to observe these productivity switches, they continuously update their beliefs regarding high and low productivity firms by observing the total return on each firm, which consists of the average productivity plus noise. The portfolio choices, interest rate, and stock return processes are derived in a Cox-Ingersoll-Ross (1985a) style general equilibrium model. Three stylized facts of stock market returns are addressed: negative skewness, excess kurtosis, and predictive asymmetry (excess returns and future changes in volatility are negatively correlated). To measure the last stylized fact, an EGARCH model is fitted to sample paths simulated from the model. Parameter values that permit faster learning fit the three facts better. I. Introduction This paper has three purposes. First, it presents the special properties of a filter in continuous time that characterizes the dynamics of Bayesian learning about recurrent profitability switches and their relation to fluctuating confidence. Second, the paper shows how fluctuating confidence, which arises due to this up? dating process, is reflected in the statistical properties of interest rate and stock return processes in a Cox-Ingersoll-Ross (1985a and b) (henceforth, CIR) stochas? tic production economy. Portfolio adjustments to hedge the exposure of the risk associated with these fluctuations are discussed. Finally, the paper draws some re? lationships between the speed of learning and the ability of the model to replicate three stylized facts about stock market returns. I argue that the often used Kalman filtering problem is not suitable to model fluctuating confidence and to replicate the three stylized facts.