In the first Chapter, we generalize Pitts and Tauchen's (1983) well-known Mixture of Distribution Hypothesis (MDH), which links asset volume and volatility in a way that derives a proxy for divergence of opinion among all individual investors. This new measure has several advantages over the existing proxies such as dispersion in analysts' earnings forecasts and turnover. We then use this measure of divergence of opinion in an empirical asset pricing analysis. In particular, we incorporate the crucial role of divergence of opinion in the determination of cross-sectional asset returns, establishing that when divergence of opinion is high, stock prices tend to be biased upwardly, resulting in lower future returns. These effects are especially pronounced for small, low-book-to-market, and high-momentum stocks, which are more difficult and costly to short sell. Hence the evidence for these stocks support Miller's (1977) view that, given short-sale constraints, observed prices overweight optimistic valuations. The predictions of recent theoretical work, such as Hong and Stein (2003), are valid only for stocks that are easier to short sell. A large literature over several decades reveals both extensive concern with the question of time-varying betas and an emerging consensus that betas are in fact time-varying, leading to the prominence of the conditional CAPM. Set against that background, in the second chapter we assess the dynamics in realized betas, vis-à-vis the dynamics in the underlying realized market variance and individual equity covariances with the market. Working in the recently-popularized framework of realized volatility, we are led to a framework of nonlinear fractional cointegration: although realized variances and covariances are very highly persistent and well approximated as fractionally-integrated, realized betas, which are simple nonlinear functions of those realized variances and covariances, are less persistent and arguably best modeled as stationary I(0) processes. We conclude by drawing implications for asset pricing and portfolio management.