Resumen de Essays on expected equity returns and volatility: modeling and prediction
Daniel de Almeida
This thesis is based on modeling and predicting expected equity returns and volatility. In the first step, it focus on multivariate conditional volatility models, where multivariate GARCH (MGARCH) models are the most traditional approach considered in literature. However, the traditional MGARCH models need to be restricted so that their estimation is feasible in large systems and covariance stationarity and positive definiteness of conditional covariance matrices are guaranteed. To overcome this gap, this thesis analyzes the limitations of some very popular restricted parametric MGARCH models often implemented to represent the dynamics observed in real systems of financial returns. These limitations are illustrated using simulated data and a five-dimensional system of exchange rate returns. We show that the restrictions imposed by the BEKK model are very unrealistic generating potentially missleading forecasts of condicional correlations. On the contrary, models based on the DCC specification provide appropriate forecasts. Alternative estimators of the parameters are important to simplify the computations but do not have implications on the estimates of conditional correlations.
In the second step, this thesis focus on predicting the mean of equity risk premium. In particular, we show that existing equity premium forecasts can be improved by combining parsimonious state-dependent regression models, where well-known macroeconomic predictors are interacted with an economic state variable based on technical indicators. The combining forecasts proposed deliver statistically and economically out-of-sample gains vis-a-vis the historical average, traditional univariate regressions and equal-weighted (EW) combination of macroeconomic forecasts. The EW combination is widely reported to be not worse than combining forecasts using estimated weights in equity-premium literature. However, given the relative large set of macroeconomic variables available as candidate predictors, we show that sparse combining method produces promising results for equity risk premium prediction.
