Leverage effect has become an extensively studied phenomenon which describes the (usually) negative relation between stock returns and their volatility. Although this characteristic of stock re- turns is well acknowledged, most studies of the phenomenon are based on cross-sectional calibration with parametric models. On the statistical side, most previous work are over daily or longer return horizons, and usually do not specify what parameter is being studied! In this talk, we provide non-parametric estimation for a class of stochastic measures of leverage e!ect. The theory covers both the cases with and without microstructure noise, and studies the statistical properties of the estimators when the log price process is a quite general continuous semimartingale. Volatility is allowed to be stochastic, and our asymptotics reflect a high frequency data sampling regime. The consistency and limit distribution of the estimators are derived, and simulation results are presented, which corroborate the asymptotic properties. This estimator also provides the opportunity to study high frequency regression, which leads to the prediction of volatility using not only previous volatility but also the leverage effect. The work also shows a theoretical connection between skewness and leverage effect, which further leads to the prediction of skewness. Furthermore, adopting similar ideas to these, it is easy to extend the study to other important aspects of stock returns, such as volatility of volatility.