The goal of this paper is twofold. First, using five of the most
actively traded stocks in the Brazilian financial market, this paper shows
that the normality assumption commonly used in the risk management area to
describe the distributions of returns standardized by volatilities is not
compatible with volatilities estimated by EWMA or GARCH models. In sharp
contrast, when the information contained in high frequency data is used to
construct the realized volatility measures, we attain the normality of the
standardized returns, giving promise of improvements in Value-at-Risk
statistics. We also describe the distributions of volatilities of the
Brazilian stocks, showing that they are nearly lognormal. Second, we
estimate a simple model of the log of realized volatilities that differs
from the ones in other studies. The main difference is that we do not find
evidence of long memory. The estimated model is compared with commonly used
alternatives in out-of-sample forecasting experiment.