Three essays on stock market volatility and stock return predictability

The goal of this thesis is to investigate dynamics of the stock market volatility and predictability of stock returns. In Chapter 1, I study the dynamics of the S&P 500 index return and its volatility. The short term Black-Scholes implied volatility, embedded in the options on the S&P 500 index, is shown to be a good proxy of the daily volatility of stock returns. Several existing stochastic volatility models are then tested. Furthermore, I find that there exists a significant positive relationship between the conditional expected return and volatility. Chapter 2 examines the ability of Hie dividend yield in predicting the future stock returns. It is shown that the forecastability depends critically on the assumption of stationarity of the dividend yield series. Although traditional unit root tests lack power against alternatives, the dividend yield is at least close to being nonstationary. Monte Carlo simulations show that the traditional statistical confidence intervals for the predictive regression is too narrow in the presence of local-to-unit root in the dividend yield series. The problem is more pronounced when overlapping samples are used for multi-period regressions. Chapter 3 extends the previous chapter in two dimensions. First, a general framework is developed on predictive regressions when the predictor is nearly integrated. The asymptotic consistent Bonferroni confidence intervals for several predictors such as dividend yield, book/market ratio, default spread, and term spread are estimated. Second, the asymptotic distributions of the multi-period predictive regressions are derived, and the corresponding Bonferroni confidence intervals are constructed for the predictors considered.