| This thesis studies the realized variance - Beta - GARCH Models. Realized variance is an estimate of the quadratic variation of an asset's return process (from market open to close), which measures the asset's volatility on a particular day. We enhanced the GARCH model with this measure to form the realized variance - GARCH model, which better fits the in-sample data and improves the out-of-sample forecasting. Using the tick data of exchange traded fund (ETF) SPY, which tracks the return of Standard & Poor 500 index, we can further estimate the realized covariance of a stock and the market and realized beta (as ratio of the realized covariance and the realized variance of the market return), which measures the sensitivity of that stock's price to the whole market during the trading hours of that day. Using realized beta, which contains important information for the change of market beta, we developed a time-varying beta model to describe the dynamics of beta. The statistical tests, in-sample fit and out-of-sample forecasting all show that the time-varying beta model outperforms the constant beta model.;This thesis makes the following contributions: First, we show that realized volatility, extracted from tick data, contributes extra information to the volatility dynamics estimation and forecasting. Second, we show the high variability of betas at the daily level. Our approach differs from the short-window least square used in previous studies on time-varying beta, which suffers from a number of econometric problems and does not give daily level dynamics for beta. Third, we demonstrate that volatility and beta forecasting can be significantly improved by including realized variance, realized covariance and realized beta. This approach can be useful for practices in the financial industry. |
