Why Does Stock Market Volatility Change Over Time? A Time-Varying Variance Decomposition for Stock Returns

Abstract

We extend the variance decomposition model of Campbell (1991) to allow for time-varying stock market volatility. Specifically, we introduce a model in which the covariance matrix of the vector autoregression (VAR) follows a multivariate stochastic volatility (MSV) process. This VAR-MSV model permits the decomposition of unexpected real stock return variance into three time-varying components: variance of news about future dividends, variance of news about future returns, and a covariance term. We develop Bayesian Markov chain Monte Carlo (MCMC) econometric techniques for estimating the VAR-MSV model. These methods are well-suited for estimating models with latent stochastic volatilities, and are not subject to the small-sample biases and unit root problems that plague frequentist estimation of predictive regressions. We report strong evidence that real stock returns are predictable when the dividend-price ratio and a stochastically detrended short-term interest rate are employed as forecasting variables. The time-varying variance of news about future returns is the primary determinant of stock market volatility (both levels and changes). The variance of news about future dividends increased dramatically during the 1973-1974 recession and peaked during the 1980 recession before descending in the 1980s. However, its contribution to stock market volatility was offset by positive correlation between news about future dividends and news about future returns from 1974-1984.

Keywords: Variance decomposition, return predictability, vector autoregression, multivariate stochastic volatility, Markov chain Monte Carlo, Gibbs sampling

JEL Classification: G12, C11, C15, C32