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Determinants of Stock Market Volatility and Risk Premia

Oct 2003
Working Paper
03-001
By  Hehui Jin, Mordecai Kurz, Maurizio Motolese
This paper shows the dynamics of diverse beliefs is the primary propagation mechanism of volatility in asset markets. In a model with a stock and bond market in which agents hold diverse Rational Belief (see Kurz (1994)) our economy replicates well the empirical record of (i) the first two moments of the price/dividend ratio, the risky return on stocks, the riskless interest rate and the equity premium; (ii) the Sharp ratio and the correlation between risky returns and the aggregate consumption growth rate; (iii) the predictability of stock returns and the price/dividend ratio, as reported in the literature, expressed by: (a) Variance Ratio statistic for long lags, (b) autocorrelation of these two variables, (c) mean reversion of the risky returns and the power of the price/dividend ratio to predict the risky return at different horizons. Also, our model predicts and explains the presence of stochastic volatility in equilibrium asset prices and asset returns.

The tool used to model diverse rationalizable beliefs is the market state of belief. This index identifies the distribution of conditional probability functions of agents. We show there are two simple properties of the diversity of beliefs which drive market volatility: (i) rationalizable over confidence, described by amplification of an agent’s probability belief, which generates densities with fat tails, and (ii) rationalizable asymmetry in frequencies of bull or bear states. Diverse price forecasts is essential to our theory. Since at each date agents forecast the market states of belief, in our general equilibrium context this tool is simply a formal method to allow agents to use the equilibrium map but make heterogenous but rationalizable price forecasts.