Forecasting the Quantiles of Daily Equity Returns Using Realized Volatility: Evidence from the Czech Stock Market

Abstract

In this study, we evaluate the quantile forecasts of the daily equity returns on three of the most liquid stocks traded on the Prague Stock Exchange. We follow the recent findings that consider the potential value of intraday information for volatility forecasting and, instead of proxying volatility using daily squared returns, we use both the intraday returns as well as their lower frequency aggregate (realized volatility) to forecast volatility and ultimately the quantiles of the distributions of future returns under different scenarios. We find that a simple autoregressive model for realized volatility together with the assumption of a normal distribution for expected returns results in VaR forecasts that are no worse than those based on other models (HAR, MIDAS) and/or other methods of computing the distribution of future returns. In fact, similar results obtain across the different forecast horizons and at both 2.5% and 5% VaR levels despite superior performance of HAR model in out-of-sample volatility forecasts.Intraday data, heterogeneous autoregressive model, mixed data sampling model, realized volatility, Value-at-Risk